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    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_df39bf75-376b-41fa-9a1c-c9d55cb4cf9a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock_10dd5d7d-7c2e-4c88-af4b-19c0225ed26e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of changes in equity</link:label>
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    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceAttributableToNoncontrollingInterestMember_060eae30-80cb-40a3-9123-0794db065f60_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceAttributableToNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of prior service costs</link:label>
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    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_d8e97453-bb3e-4dba-9fec-fff74b424ce0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends paid</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_e29adec2-47e8-47b0-9657-5dffff49968c_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_b7f1675c-66c6-40df-b456-bf533519f017_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility, maximum borrowing capacity</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent_9326dfc8-bcb7-4902-a529-8159bbb3cb69_negatedLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less current maturities</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt and Lease Obligation, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent"/>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_18da883b-8dfe-49cf-b20c-15f2be04dcf0_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_RestructuringReserve_5a70abd6-0fb2-4842-8f24-dee574b5be1c_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability for business reorganization</link:label>
    <link:label id="lab_us-gaap_RestructuringReserve_ce84f67e-b99c-469f-ad3c-b0979befb36d_periodStartLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserve" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance at beginning of period</link:label>
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    <link:label id="lab_us-gaap_RestructuringReserve_label_en-US" xlink:label="lab_us-gaap_RestructuringReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Reserve</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringReserve" xlink:to="lab_us-gaap_RestructuringReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignExchangeContractMember_8f5c4df3-687e-449a-8768-ff1ca2b11d48_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignExchangeContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign Exchange Contract</link:label>
    <link:label id="lab_us-gaap_ForeignExchangeContractMember_label_en-US" xlink:label="lab_us-gaap_ForeignExchangeContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign Exchange Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignExchangeContractMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ForeignExchangeContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignExchangeContractMember" xlink:to="lab_us-gaap_ForeignExchangeContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress_abcfeb98-7673-4f2f-a7af-2b8e4d1d5daf_terseLabel_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net contract assets, $ Change</link:label>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress_label_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Net Asset (Liability), Cumulative Catch-up Adjustment to Revenue, Change in Measure of Progress</link:label>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress_documentation_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Net Asset (Liability), Cumulative Catch-up Adjustment to Revenue, Change in Measure of Progress</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress" xlink:href="b-20220930.xsd#b_ContractwithCustomerNetAssetLiabilityCumulativeCatchupAdjustmenttoRevenueChangeinMeasureofProgress"/>
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    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_413fbc5e-7617-47cd-bd5b-ea019ff7decd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_4f0fe875-c8e7-4df1-a498-31d69969b42a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable basis spread</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_50d6fa20-ad49-49e4-bbe0-8ed4a85ce023_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for (Proceeds from) Other Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_e3f77cbd-979e-4340-95af-31ad9ddc146d_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_9f39051e-bab0-44ed-8c4c-b4f979c3b3d1_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Indefinite-lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_390e6fc0-6d1a-4654-a13a-78dfa95be798_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ShortTermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtTypeAxis" xlink:to="lab_us-gaap_ShortTermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_8f7aeb9e-ae06-4d5a-9663-a7c28f9e56ed_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stated interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_2fc0c364-2be9-4e31-82c0-9c12705bb4b2_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AdditionalPaidInCapitalCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:to="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_6096aa7a-d15d-4cf6-87cd-4ee0544417dc_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_ca0152ee-fe17-4217-ad19-c73519f7a634_totalLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net periodic benefit cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined Benefit Plan, Net Periodic Benefit Cost (Credit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="lab_us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:type="arc" order="1"/>
    <link:label id="lab_b_AerospaceOriginalEquipmentManufacturingProductsMember_c37efd62-bb88-49ab-bae1-ba74e0cda00a_terseLabel_en-US" xlink:label="lab_b_AerospaceOriginalEquipmentManufacturingProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace Original Equipment Manufacturing Products</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_b_AerospaceOriginalEquipmentManufacturingProductsMember" xlink:href="b-20220930.xsd#b_AerospaceOriginalEquipmentManufacturingProductsMember"/>
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    <link:label id="lab_us-gaap_FairValueNetAssetLiability_2128b7c6-84cc-4fc8-88d0-f83de7a87461_totalLabel_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financial assets and financial liabilities, reported at fair value</link:label>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_label_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetAssetLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FairValueNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetAssetLiability" xlink:to="lab_us-gaap_FairValueNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_b_RestructuringandRelatedActivitiesPercentageReductioninWorkforce_af5e8026-7918-4c68-859b-7537e793e72e_terseLabel_en-US" xlink:label="lab_b_RestructuringandRelatedActivitiesPercentageReductioninWorkforce" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage reduction in workforce</link:label>
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    <link:label id="lab_b_RestructuringandRelatedActivitiesPercentageReductioninWorkforce_documentation_en-US" xlink:label="lab_b_RestructuringandRelatedActivitiesPercentageReductioninWorkforce" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring and Related Activities, Percentage Reduction in Workforce</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_570f0ec0-bf18-49aa-9598-af3d4658e40e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_042bc0f1-9d1b-4456-b088-bb012f1a46ff_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income (loss), net of tax</link:label>
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    <link:label id="lab_us-gaap_AwardTypeAxis_44e63ce8-f545-4039-88b1-8479823f5537_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Award Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_7064be77-af7f-483f-8947-2212af971891_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash provided by operating activities</link:label>
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    <link:label id="lab_us-gaap_RestructuringAndRelatedCostExpectedCost1_b623b70b-fa57-4f7a-b520-da69459c63a5_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedCostExpectedCost1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring and related cost, expected cost</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtNoncurrent_c3835191-9d2f-4e1f-944d-7d25422af2d6_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_972c2398-e6ae-4a2e-bf61-6c35b05f3bcc_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
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    <link:label id="lab_us-gaap_OtherRestructuringCosts_9077b445-5ca3-4a8b-a91b-f1f01691ee95_terseLabel_en-US" xlink:label="lab_us-gaap_OtherRestructuringCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other restructuring costs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherRestructuringCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherRestructuringCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherRestructuringCosts" xlink:to="lab_us-gaap_OtherRestructuringCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_c7e5bcdb-17b3-4162-8544-3e13e8b66e6f_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_ConsolidationItemsDomain"/>
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    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_0a2194a5-9d8a-4b0e-9db6-4e82a3b36b52_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset and Liability</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_56071e79-9b5b-4ee6-9755-3a791e5add6c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche One</link:label>
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    <link:label id="lab_b_ThreePointNineSevenPercentSeniorNotesMember_a66daa4a-3bb1-4726-9ab2-f1b0493d7ae6_terseLabel_en-US" xlink:label="lab_b_ThreePointNineSevenPercentSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">3.97% Senior Notes</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_fc568acc-b6f2-4a4c-9bbe-05539378970e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Changes in Accumulated Other Comprehensive Income (Loss) By Component</link:label>
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    <link:label id="lab_us-gaap_Assets_12133fdb-386a-43cf-a9c2-61a79a3b8c5a_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total assets</link:label>
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    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_4414395b-283a-4b24-94d7-58c1a9fc92c2_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareAbstract_605c22ba-cab1-4518-881b-8a4c123e874c_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Per common share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
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    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_f34c12eb-c843-4db1-8bcf-26619ded0842_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember_a92897a1-c755-4300-8342-379790a05f20_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Three</link:label>
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    <link:label id="lab_us-gaap_PerformanceSharesMember_d1929041-6f4e-4979-a499-4ab2e0b15492_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Performance Share Awards</link:label>
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    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_fc219fbb-73b5-40d7-8127-a42ac05fe9ee_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued liabilities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_7fa13f81-8661-4d56-b57d-353dd63cc832_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other comprehensive income (loss) before reclassifications</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
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    <link:label id="lab_b_AerospaceAftermarketProductsandServicesMember_2f5bcf3d-a05a-4684-a7ba-f56b9f055d66_terseLabel_en-US" xlink:label="lab_b_AerospaceAftermarketProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace Aftermarket Products and Services</link:label>
    <link:label id="lab_b_AerospaceAftermarketProductsandServicesMember_label_en-US" xlink:label="lab_b_AerospaceAftermarketProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace Aftermarket Products and Services [Member]</link:label>
    <link:label id="lab_b_AerospaceAftermarketProductsandServicesMember_documentation_en-US" xlink:label="lab_b_AerospaceAftermarketProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace Aftermarket Products and Services [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_AerospaceAftermarketProductsandServicesMember" xlink:href="b-20220930.xsd#b_AerospaceAftermarketProductsandServicesMember"/>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_dbe493ae-09ff-4a26-8224-70ea739bafcc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DerivativeContractTypeDomain"/>
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    <link:label id="lab_us-gaap_BasisOfAccounting_fb44e407-469a-4bb1-b212-203a699d0e9e_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccounting" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccounting_label_en-US" xlink:label="lab_us-gaap_BasisOfAccounting" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis of Accounting [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccounting" xlink:to="lab_us-gaap_BasisOfAccounting" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_c05baab0-92bf-4972-9a95-9a1018b37788_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net sales</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_e3840f58-6c5c-436c-aba9-b05ce145bd06_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net sales</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer, Including Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax"/>
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    <link:label id="lab_dei_EntityRegistrantName_1478909a-e93a-4ac5-bc76-1ccb513fc0d1_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityRegistrantName"/>
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    <link:label id="lab_b_ContractwithCustomerAssetPercentChange_d77fb2c6-8e62-4f7c-86e4-c32e90c0726b_terseLabel_en-US" xlink:label="lab_b_ContractwithCustomerAssetPercentChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unbilled receivables (contract assets), % Change</link:label>
    <link:label id="lab_b_ContractwithCustomerAssetPercentChange_label_en-US" xlink:label="lab_b_ContractwithCustomerAssetPercentChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Percent Change</link:label>
    <link:label id="lab_b_ContractwithCustomerAssetPercentChange_documentation_en-US" xlink:label="lab_b_ContractwithCustomerAssetPercentChange" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset, Percent Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ContractwithCustomerAssetPercentChange" xlink:href="b-20220930.xsd#b_ContractwithCustomerAssetPercentChange"/>
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    <link:label id="lab_country_CN_6668d8ee-66ef-4b02-87ec-d531bf7406d9_terseLabel_en-US" xlink:label="lab_country_CN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">CHINA</link:label>
    <link:label id="lab_country_CN_label_en-US" xlink:label="lab_country_CN" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">CHINA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CN" xlink:href="https://xbrl.sec.gov/country/2022/country-2022.xsd#country_CN"/>
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    <link:label id="lab_us-gaap_RestructuringReserveRollForward_81afe5aa-81cc-4f48-8f47-5bdef6cd3420_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserveRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Reserve [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_RestructuringReserveRollForward_label_en-US" xlink:label="lab_us-gaap_RestructuringReserveRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Reserve [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringReserveRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RestructuringReserveRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringReserveRollForward" xlink:to="lab_us-gaap_RestructuringReserveRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_3c72644c-db1c-4ae0-9f58-b26c18bcfcd4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation</link:label>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill, Foreign Currency Translation Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_GoodwillForeignCurrencyTranslationGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:to="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_b_RabbiTrustAssetFairValueDisclosure_73bcc76d-7964-4c60-952d-dbc127ca5f95_terseLabel_en-US" xlink:label="lab_b_RabbiTrustAssetFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rabbi trust assets</link:label>
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    <link:label id="lab_b_RabbiTrustAssetFairValueDisclosure_documentation_en-US" xlink:label="lab_b_RabbiTrustAssetFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The fair values as of the Balance Sheet date of Rabbi Trust Assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_RabbiTrustAssetFairValueDisclosure" xlink:href="b-20220930.xsd#b_RabbiTrustAssetFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_eb33ce3b-71cb-458e-a9f6-effda3e2183b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign Currency Items</link:label>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Foreign Currency Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_FinanceLeaseLiabilityFairValueDisclosure_8d911c5e-85ca-464a-be61-280e755b4441_terseLabel_en-US" xlink:label="lab_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair value of finance leases</link:label>
    <link:label id="lab_b_FinanceLeaseLiabilityFairValueDisclosure_label_en-US" xlink:label="lab_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finance Lease Liability, Fair Value Disclosure</link:label>
    <link:label id="lab_b_FinanceLeaseLiabilityFairValueDisclosure_documentation_en-US" xlink:label="lab_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finance Lease Liability, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:href="b-20220930.xsd#b_FinanceLeaseLiabilityFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:to="lab_b_FinanceLeaseLiabilityFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue_b486e0dc-de74-4169-9ad9-dbd80388f0d4_terseLabel_en-US" xlink:label="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Grant Date Fair Value</link:label>
    <link:label id="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue_label_en-US" xlink:label="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Grant Date Fair Value</link:label>
    <link:label id="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue_documentation_en-US" xlink:label="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:href="b-20220930.xsd#b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:to="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_d4708854-7d66-49ef-8a4d-32839123e0dd_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_6ea9d92b-3e7b-446d-a2c9-fefe9bdaad42_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Pension and Other Postretirement Benefits</link:label>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:to="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_e1116ba4-24c6-4aeb-a6f2-924a69e13675_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flow hedges</link:label>
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    <link:label id="lab_us-gaap_IntersegmentEliminationMember_2ffa541a-f5b5-48fe-9838-1bc64c8d498c_verboseLabel_en-US" xlink:label="lab_us-gaap_IntersegmentEliminationMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intersegment sales</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_cd96bd0c-27f9-4323-aa9c-6c5a4eeee607_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_9e83fcec-abb4-4033-8356-150d6f98bc79_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fees and expenses for executing admendments</link:label>
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    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_4f0da498-4fb4-40f5-a31c-f5eba7c9dfde_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurements</link:label>
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    <link:label id="lab_b_DebtInstrumentPrepaymentPercentageofPrincipalAmount_e5d6dc43-80af-483f-b506-3c35c3bced36_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentPrepaymentPercentageofPrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percent allowed to be prepaid</link:label>
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    <link:label id="lab_dei_EntityFileNumber_cef04e2c-374b-4ef8-a0c0-e71ba8a3413e_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity File Number</link:label>
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    <link:label id="lab_b_DebtInstrumentCovenantThresholdforPermittedAcquisition_71435c26-34fc-4f1e-9abf-1fe4608f5476_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentCovenantThresholdforPermittedAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt covenant threshold for permitted acquisition</link:label>
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    <link:label id="lab_us-gaap_CorporateNonSegmentMember_286be0ee-7128-40ee-953f-ad5abefaa530_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Corporate, Non-Segment [Member]</link:label>
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    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember_1f16e9b0-227f-419a-b31a-fe58d5882ed6_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Pension and Other Postretirement Benefit Items</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockMember_2da46044-db3e-4db8-8714-215148f0859e_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury Stock</link:label>
    <link:label id="lab_us-gaap_TreasuryStockMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury Stock [Member]</link:label>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_12c0ed5c-0c41-41c3-ae7f-c90342a0ca02_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Indefinite-lived Intangible Assets [Axis]</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_9f9bdbb0-1e62-41ec-8fdd-88b278308b2b_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total stockholders' equity</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders' Equity Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_d694c2d7-c523-4fbf-ac23-7d2eec71fd22_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivatives</link:label>
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    <link:label id="lab_us-gaap_VestingDomain_367093b7-3ea5-4da1-a3e9-913ce3bdaadb_terseLabel_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Vesting [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingDomain" xlink:to="lab_us-gaap_VestingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_b_EffectiveIncomeTaxRateReconciliationTaxHolidayPeriod_11e63cfe-a5b5-4fcc-84b9-79d53c622976_terseLabel_en-US" xlink:label="lab_b_EffectiveIncomeTaxRateReconciliationTaxHolidayPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tax holiday, period</link:label>
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    <link:label id="lab_b_LinesOfCreditAndOverdraftsMember_8b648082-9c8f-49c4-84fb-39ea23c2738e_terseLabel_en-US" xlink:label="lab_b_LinesOfCreditAndOverdraftsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lines of Credit and Overdrafts</link:label>
    <link:label id="lab_b_LinesOfCreditAndOverdraftsMember_label_en-US" xlink:label="lab_b_LinesOfCreditAndOverdraftsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lines of credit and overdrafts [Member]</link:label>
    <link:label id="lab_b_LinesOfCreditAndOverdraftsMember_documentation_en-US" xlink:label="lab_b_LinesOfCreditAndOverdraftsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lines of credit and overdrafts [Member]</link:label>
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    <link:label id="lab_b_OtherMember_fedfa5c6-6bed-4eec-9226-d4e72beef13e_terseLabel_en-US" xlink:label="lab_b_OtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
    <link:label id="lab_b_OtherMember_label_en-US" xlink:label="lab_b_OtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other [Member]</link:label>
    <link:label id="lab_b_OtherMember_documentation_en-US" xlink:label="lab_b_OtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_OtherMember" xlink:href="b-20220930.xsd#b_OtherMember"/>
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    <link:label id="lab_dei_EntityInteractiveDataCurrent_86e3c77b-79bc-40f7-8e0b-6414a3156eab_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Interactive Data Current</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_2002e532-020b-4172-af10-ead1ad2fdd43_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of intangible assets expected in 2025</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_00836413-c25d-45de-9137-a0a1c73ebb2f_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_485cd3db-27c9-4a93-93f3-0dbb97bbab8b_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_9ceb9b2b-e2ff-44a5-aad6-cdc3f1aad7f2_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_46e83a70-b238-4a95-be3f-0ddff4786322_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends declared</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseMember_c67b90a1-c2a9-4a71-9fb5-0da2d36c5720_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseMember_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Nonoperating Income (Expense) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherNonoperatingIncomeExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpenseMember" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_1b135fe4-36b9-430d-bf30-feded4ba8a2a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_edcc7248-9d49-489c-8e39-09b15eaa6b92_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee stock plans</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_3b22a931-9428-496d-bd75-bb9bcf916feb_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_287af239-6018-48a6-978a-cac24c171a16_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock repurchases</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_07c11689-b412-4725-87cf-8196aa0d5126_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesNetCurrent_87f23d42-81ce-4f53-9991-efef03a2ce46_verboseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable, less allowances (2022 - $4,627; 2021 - $5,625)</link:label>
    <link:label id="lab_us-gaap_ReceivablesNetCurrent_label_en-US" xlink:label="lab_us-gaap_ReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Receivables, Net, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ReceivablesNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesNetCurrent" xlink:to="lab_us-gaap_ReceivablesNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_02083af4-7e0e-4cfa-8d9b-bf3f998bc484_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Quarterly Report</link:label>
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    <link:label id="lab_us-gaap_AssetsCurrentAbstract_0752f99c-6305-4b8c-a479-34f90d2c6acc_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets, Current [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_fea98eec-ea99-4c95-89ce-01012de84e0f_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_RangeAxis"/>
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    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain_fa687652-4d05-4483-ac00-424d4f65cb4c_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Domain]</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxHolidayTable_4c0097bc-ebf9-4159-b45b-5f2db037352c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxHolidayTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Holiday [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxHolidayTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxHolidayTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Holiday [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxHolidayTable" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncomeTaxHolidayTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxHolidayTable" xlink:to="lab_us-gaap_IncomeTaxHolidayTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_276edcef-1607-4e8f-b1eb-02d28888fcda_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BaseRateMember_edc036b4-bcb1-4c35-acf3-445aaee4fe95_terseLabel_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Base Rate</link:label>
    <link:label id="lab_us-gaap_BaseRateMember_label_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Base Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BaseRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_BaseRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BaseRateMember" xlink:to="lab_us-gaap_BaseRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_RevenueSharingMember_1489e8f9-f4ed-45c3-ac82-28279e43d957_terseLabel_en-US" xlink:label="lab_b_RevenueSharingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue Sharing Programs (RSPs)</link:label>
    <link:label id="lab_b_RevenueSharingMember_label_en-US" xlink:label="lab_b_RevenueSharingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue Sharing [Member]</link:label>
    <link:label id="lab_b_RevenueSharingMember_documentation_en-US" xlink:label="lab_b_RevenueSharingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue Sharing [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_RevenueSharingMember" xlink:href="b-20220930.xsd#b_RevenueSharingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_RevenueSharingMember" xlink:to="lab_b_RevenueSharingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_EngineeredComponentsProductsMember_6ff5b520-9f8d-42aa-9919-f5c433b01c09_terseLabel_en-US" xlink:label="lab_b_EngineeredComponentsProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Engineered Components Products</link:label>
    <link:label id="lab_b_EngineeredComponentsProductsMember_label_en-US" xlink:label="lab_b_EngineeredComponentsProductsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Engineered Components Products [Member]</link:label>
    <link:label id="lab_b_EngineeredComponentsProductsMember_documentation_en-US" xlink:label="lab_b_EngineeredComponentsProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Engineered Components Products [Member]</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_8fdcf5a3-8824-4036-9c8f-91d76f5e444b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock - par value $0.01 per share Authorized: 150,000,000 shares Issued: at par value (2022 - 64,448,650 shares; 2021 - 64,343,582 shares)</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_e0648eba-9614-463c-b4d5-a772f010baff_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_32551a4e-e030-4228-ab60-8395d60149a4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_4727a0cc-7e57-4ba8-aed2-66e11394a2fd_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Segments</link:label>
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    <link:label id="lab_b_ForceMotionControlProductsMember_323661ee-eee9-4478-acae-0def964d065f_terseLabel_en-US" xlink:label="lab_b_ForceMotionControlProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Force &amp; Motion Control Products</link:label>
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    <link:label id="lab_b_ForceMotionControlProductsMember_documentation_en-US" xlink:label="lab_b_ForceMotionControlProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Force &amp; Motion Control Products [Member]</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_ebb25f4b-bf03-4c41-8ec2-58c17a3116bc_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, cash equivalents and restricted cash at beginning of period</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_d25f4e50-e1d3-47ca-b6af-53b4d8c8700a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation adjustments, net of tax</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_23f33453-ffef-4cff-bdde-b35b523a31e4_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_1f726c64-2a24-4a86-bb27-cd895acd6ff2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
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    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems_3ee624e0-3db1-4b49-82a2-6233ea094f47_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction [Line Items]</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt_bb7c1827-2453-447d-89f0-c2fba3656141_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from the issuance of long-term debt</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToCurtailments_811d6677-d5c5-4726-9f1d-f8c6210e8f96_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToCurtailments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Curtailment loss</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToCurtailments" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToCurtailments"/>
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    <link:label id="lab_b_RestructuringAndRelatedCostNumberOfManufacturingSites_f3fc8dee-2d5f-4940-a35c-b9268a6341a7_terseLabel_en-US" xlink:label="lab_b_RestructuringAndRelatedCostNumberOfManufacturingSites" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of manufacturing sites</link:label>
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    <link:label id="lab_dei_AmendmentFlag_b852dd0f-99d9-478b-991c-2ed02c5c50ea_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amendment Flag</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_c46a4deb-078c-48c0-b4d1-103711925fe5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Range of life</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_2880d8e7-68d1-45ae-8d0f-8e0fd766a56f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash used by investing activities</link:label>
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    <link:label id="lab_b_FiniteLivedIntangibleAssetsBeforeForeignCurrencyTranslationAdjustment_4dd3bd20-2b26-4096-bbff-45956d68c3b7_terseLabel_en-US" xlink:label="lab_b_FiniteLivedIntangibleAssetsBeforeForeignCurrencyTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gross Amount</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_4b526e5d-530b-471b-938b-c56c06f65e06_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total other comprehensive loss, net of tax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_bce8a5c8-29a4-4dc2-b6dc-f07f55b37953_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_d011873d-1d93-4b24-b041-bbe1f4deb7fc_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of exchange rate changes on cash flows</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Continuing Operations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_ccef2a17-bf11-4d69-9623-e8c540599f6a_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CurrencyAxis_6d3a8d61-159d-45c3-ab0e-aa37cf0526d4_terseLabel_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Currency [Axis]</link:label>
    <link:label id="lab_srt_CurrencyAxis_label_en-US" xlink:label="lab_srt_CurrencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Currency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CurrencyAxis" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_CurrencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CurrencyAxis" xlink:to="lab_srt_CurrencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_604319a2-7944-4b55-ae7a-6afa5e590c17_negatedLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments on long-term debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_b_CustomerListsAndRelationshipsMember_fad81042-335c-4da6-8acc-5a21ab0e4c8b_terseLabel_en-US" xlink:label="lab_b_CustomerListsAndRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_b_CustomerListsAndRelationshipsMember_label_en-US" xlink:label="lab_b_CustomerListsAndRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer Lists and Relationships [Member]</link:label>
    <link:label id="lab_b_CustomerListsAndRelationshipsMember_documentation_en-US" xlink:label="lab_b_CustomerListsAndRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer Lists and Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_CustomerListsAndRelationshipsMember" xlink:href="b-20220930.xsd#b_CustomerListsAndRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_CustomerListsAndRelationshipsMember" xlink:to="lab_b_CustomerListsAndRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements_42a5c808-3e3f-4a7d-9ae5-3e1a93192883_terseLabel_en-US" xlink:label="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of banks transacted with for interest rate swap agreements (in banks)</link:label>
    <link:label id="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements_label_en-US" xlink:label="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Banks Transacted With for Interest Rate Swap Agreements</link:label>
    <link:label id="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements_documentation_en-US" xlink:label="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Banks Transacted With for Interest Rate Swap Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:href="b-20220930.xsd#b_NumberOfBanksTransactedWithForInterestRateSwapAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:to="lab_b_NumberOfBanksTransactedWithForInterestRateSwapAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_092862a8-6282-42bf-bafb-1265e0d2c985_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA_85153eff-b5f3-44da-bbd0-53f66b988e05_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt covenant material acquisition, debt to EBITDA</link:label>
    <link:label id="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA_label_en-US" xlink:label="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Covenant, Material Acquisition, Total Consolidated Debt to Consolidated EBITDA</link:label>
    <link:label id="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA_documentation_en-US" xlink:label="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Covenant, Material Acquisition, Total Consolidated Debt to Consolidated EBITDA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:href="b-20220930.xsd#b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:to="lab_b_DebtInstrumentCovenantMaterialAcquisitionTotalConsolidatedDebttoConsolidatedEBITDA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValue_17502a51-f6bb-4f87-8fa0-2383e2d67e6f_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury stock, at cost (2022 - 13,881,687 shares; 2021 - 13,658,483 shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury Stock, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_TreasuryStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValue" xlink:to="lab_us-gaap_TreasuryStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_d60207d7-c849-4fdf-b926-be217d4de12a_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of Individual [Domain]</link:label>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_label_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of Individual [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax_56a01745-d9d5-4996-bdc0-e1996eb3a2c9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined benefit pension and other postretirement benefits, net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Comprehensive (Income) Loss, Defined Benefit Plan, after Reclassification Adjustment, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_00a02dae-bb51-492b-a03c-19794100bba4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Non-cash goodwill impairment charge</link:label>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_label_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:to="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_de30cf30-1262-4537-8207-02563b422df5_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Allowance for doubtful accounts</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_88fff53d-c3f0-4576-855d-107f3d03fc4f_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other expense (income), net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_b79f582f-e402-40dc-94c3-d14ffef9dd2c_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance Sheet Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_b2694bf3-0a6e-4a69-928e-7c448a63d067_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CommonStockSharesAuthorized"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsNotDesignatedAsHedgingInstrumentsGainLossNet_1903327d-4d3e-4b11-bf3d-ce247d003bfe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsNotDesignatedAsHedgingInstrumentsGainLossNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amount of gain (loss) recognized in income on derivative</link:label>
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    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_f8762c21-0a8b-4860-b7a4-85fe744050a8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
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    <link:label id="lab_srt_MaximumMember_fb08895b-b4a3-4ed7-8388-b7c3aa87c7b6_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_621f4e4e-4f75-4b08-b1b2-31dbadf4f319_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated other non-owner changes to equity</link:label>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_bd7f0bd2-2afb-4b5f-9fd6-121e4adc40ba_periodEndLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance at end of period</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_b_MaturityOfBankAcceptances_5718da2c-33ab-4279-a4a9-60fe6001ed72_terseLabel_en-US" xlink:label="lab_b_MaturityOfBankAcceptances" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maturity of bank acceptances</link:label>
    <link:label id="lab_b_MaturityOfBankAcceptances_label_en-US" xlink:label="lab_b_MaturityOfBankAcceptances" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maturity of Bank Acceptances</link:label>
    <link:label id="lab_b_MaturityOfBankAcceptances_documentation_en-US" xlink:label="lab_b_MaturityOfBankAcceptances" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maturity of Bank Acceptances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_MaturityOfBankAcceptances" xlink:href="b-20220930.xsd#b_MaturityOfBankAcceptances"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_MaturityOfBankAcceptances" xlink:to="lab_b_MaturityOfBankAcceptances" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination_9dc34086-cf25-46f8-b90a-d9090a30ee8f_negatedLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract liabilities, $ Change</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Liability, Increase (Decrease) for Contract Acquired in Business Combination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination"/>
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    <link:label id="lab_b_ContractwithCustomerCustomerAdvanceLiability_2d19c735-8ba8-43ad-ad99-dbb5876bfdda_terseLabel_en-US" xlink:label="lab_b_ContractwithCustomerCustomerAdvanceLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer advances</link:label>
    <link:label id="lab_b_ContractwithCustomerCustomerAdvanceLiability_label_en-US" xlink:label="lab_b_ContractwithCustomerCustomerAdvanceLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Customer Advance Liability</link:label>
    <link:label id="lab_b_ContractwithCustomerCustomerAdvanceLiability_documentation_en-US" xlink:label="lab_b_ContractwithCustomerCustomerAdvanceLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Customer Advance Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ContractwithCustomerCustomerAdvanceLiability" xlink:href="b-20220930.xsd#b_ContractwithCustomerCustomerAdvanceLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_ContractwithCustomerCustomerAdvanceLiability" xlink:to="lab_b_ContractwithCustomerCustomerAdvanceLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockCompensationPlanMember_384efd36-5f0c-48de-9423-f95eb9d1c8b0_terseLabel_en-US" xlink:label="lab_us-gaap_StockCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Awards</link:label>
    <link:label id="lab_us-gaap_StockCompensationPlanMember_label_en-US" xlink:label="lab_us-gaap_StockCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockCompensationPlanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StockCompensationPlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockCompensationPlanMember" xlink:to="lab_us-gaap_StockCompensationPlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_4f6e3c3a-55cd-4231-8669-174f8119e515_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_3ba29ee1-b7f2-485f-932b-e53d02f3aab0_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and cash equivalents at end of period</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_f849527a-a919-464f-a52f-d22185ce8415_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current assets</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_133deca7-44af-4509-b6e3-203dd0f58009_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivatives designated as hedging instruments</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanCostOfProvidingSpecialOrContractualTerminationBenefitRecognizedDuringPeriod_bbb5dfc8-f40a-491e-bbe8-040037e32dda_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanCostOfProvidingSpecialOrContractualTerminationBenefitRecognizedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Special termination benefits</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanCostOfProvidingSpecialOrContractualTerminationBenefitRecognizedDuringPeriod_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanCostOfProvidingSpecialOrContractualTerminationBenefitRecognizedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined Benefit Plan, Cost of Providing Special and Contractual Termination Benefits</link:label>
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    <link:label id="lab_b_OtherGeographicMarketMember_6b8cf908-debf-4cb3-8b48-f8251b425364_terseLabel_en-US" xlink:label="lab_b_OtherGeographicMarketMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Rest of World</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_b_OtherGeographicMarketMember" xlink:href="b-20220930.xsd#b_OtherGeographicMarketMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_OtherGeographicMarketMember" xlink:to="lab_b_OtherGeographicMarketMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_DebtandLeaseObligationFairValueDisclosure_432103bf-8910-4266-8532-0fb50c44aa4a_terseLabel_en-US" xlink:label="lab_b_DebtandLeaseObligationFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair value of debt and finance leases</link:label>
    <link:label id="lab_b_DebtandLeaseObligationFairValueDisclosure_label_en-US" xlink:label="lab_b_DebtandLeaseObligationFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt and Lease Obligation, Fair Value Disclosure</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_b_DebtandLeaseObligationFairValueDisclosure" xlink:href="b-20220930.xsd#b_DebtandLeaseObligationFairValueDisclosure"/>
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    <link:label id="lab_dei_EntitySmallBusiness_c88d78ab-62a1-4042-a6cb-ee3bfc3a22b1_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_fa99e01e-26bf-4540-af89-df57908ce68c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Basis [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTaxParent_ea148dec-63f1-4d77-907f-de4e131ac4c1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTaxParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unrealized loss on hedging activities, net of tax</link:label>
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    <link:label id="lab_us-gaap_SharesOutstanding_2efacafa-e057-4173-ad5e-4b024074d4d2_periodStartLabel_en-US" xlink:label="lab_us-gaap_SharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance at beginning of period (in shares)</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_a8e531fb-7712-4837-869a-bfa2e939c9c4_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders Equity</link:label>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_9dcbdebc-fd5c-4606-aae9-ec27ff0d9300_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dividends declared (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock_4f073afd-b0fa-4a03-a43f-4c8d9702fadf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNetBenefitCostsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Net Benefit Costs</link:label>
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    <link:label id="lab_b_RepaymentPeriod_71761fa4-d42c-4e4a-8187-c8ac0b613718_terseLabel_en-US" xlink:label="lab_b_RepaymentPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayment period</link:label>
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    <link:label id="lab_b_RepaymentPeriod_documentation_en-US" xlink:label="lab_b_RepaymentPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Repayment period</link:label>
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    <link:label id="lab_us-gaap_RestrictedCash_a1dbc907-afdb-4225-b1dc-9a34ef036c70_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Cash</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_781925c9-9d0a-4bd0-946b-f8f6874868b2_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Remaining performance obligation, expected timing</link:label>
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    <link:label id="lab_us-gaap_ShortTermBorrowings_e07cd889-07bf-460d-86ca-d91c5c4a2d9d_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Notes and overdrafts payable</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowings_a86a1a0e-5c6e-460f-8130-a2114cbe3b4e_verboseLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Carrying amount of debt</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowings_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-Term Debt</link:label>
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    <link:label id="lab_dei_Security12bTitle_dc9530fe-8bc7-46ca-8ee6-7268be083c72_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of 12(b) Security</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_Security12bTitle"/>
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    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable_4f0b529d-1d34-4f2b-a984-df0ba813e964_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Defined Benefit Plans Disclosures [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:to="lab_us-gaap_ScheduleOfDefinedBenefitPlansDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsFairValueDisclosure_109e68c2-5e19-4e57-ba56-154e33e1a680_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset fair value</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsFairValueDisclosure" xlink:to="lab_us-gaap_OtherAssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardCompundAnnualGrowthRate_e7c7221d-e2a0-4af3-8687-e28fbf1aa98c_terseLabel_en-US" xlink:label="lab_b_ShareBasedCompensationArrangementByShareBasedPaymentAwardCompundAnnualGrowthRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share Based Compensation Arrangement By Share Based Payment Award, Compund Annual Growth Rate</link:label>
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    <link:label id="lab_b_LineOfCreditFacilityAccordionFeatureIncreaseLimit_f3163053-9dab-49b3-953a-0fcb5b446cca_terseLabel_en-US" xlink:label="lab_b_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility, accordion feature</link:label>
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    <link:label id="lab_b_LineOfCreditFacilityAccordionFeatureIncreaseLimit_documentation_en-US" xlink:label="lab_b_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Accordion Feature, Increase Limit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_LineOfCreditFacilityAccordionFeatureIncreaseLimit" xlink:href="b-20220930.xsd#b_LineOfCreditFacilityAccordionFeatureIncreaseLimit"/>
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    <link:label id="lab_us-gaap_CostsAndExpenses_50d046d7-f24a-40db-93dc-e4dbd14fed72_totalLabel_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total operating costs and expenses</link:label>
    <link:label id="lab_us-gaap_CostsAndExpenses_label_en-US" xlink:label="lab_us-gaap_CostsAndExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Costs and Expenses</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostsAndExpenses" xlink:to="lab_us-gaap_CostsAndExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_721f8a38-bba4-4709-9980-1c3eaf3277c7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_b2c6c884-44d4-41d0-8e2e-6ff4d17eaf32_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee stock plans (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_ClassOfStockLineItems_2a6d1916-d4b7-41d6-8e46-6c4665588d4c_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ClassOfStockLineItems"/>
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    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_92caf99e-3149-4512-85fa-d06ba5a47a7e_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Information on Business Segments</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalOther_7cc2fef9-5133-44d8-9690-ab9d5827752b_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Residual interest in subsidiary</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalOther_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to Additional Paid in Capital, Other</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_4f85edab-e862-46d9-bd5c-b5e6e31c68a2_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of intangible assets expected in 2024</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_0d1c129c-0817-445b-8625-0a3e0229916f_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_7562992a-138d-4c3f-b8b8-963b9f79265c_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Estimate of Fair Value, Fair Value Disclosure</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_b24d584f-f448-403b-ab1c-4bae39641cac_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangements by Share-based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiability_c6332e3d-4671-48b9-808e-f849c511b813_totalLabel_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net contract assets</link:label>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiability_label_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Net Asset (Liability)</link:label>
    <link:label id="lab_b_ContractwithCustomerNetAssetLiability_documentation_en-US" xlink:label="lab_b_ContractwithCustomerNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ContractwithCustomerNetAssetLiability" xlink:href="b-20220930.xsd#b_ContractwithCustomerNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_ContractwithCustomerNetAssetLiability" xlink:to="lab_b_ContractwithCustomerNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_1acdf3e0-6273-4589-b070-9c887402360a_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryNet_11ab3c1b-fde6-496c-b11a-7855014731b0_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_4ca503ff-9052-458d-ab2a-c11b8290040b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCharges_31521549-734a-445e-9162-1ec9b911c02a_verboseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Charge for business reorganization</link:label>
    <link:label id="lab_us-gaap_RestructuringCharges_407224fa-bd4a-4a11-b171-60e53ab83d24_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee severance and other termination benefits</link:label>
    <link:label id="lab_us-gaap_RestructuringCharges_label_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RestructuringCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCharges" xlink:to="lab_us-gaap_RestructuringCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_4f5dc320-6fa7-4aef-a296-d1cf1da30fd3_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_029864a7-45e1-4fc5-8d57-806a513591ad_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Filer Category</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityFilerCategory"/>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_35ee01bf-72c3-4966-8aac-d52997371f83_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from the issuance of common stock</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_35e1f8a2-f5e9-4120-8eb4-2eb2657901d1_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basic (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_b_IncreaseDecreaseInPrepaidExpensesAndOtherCurrentAssets" xlink:href="b-20220930.xsd#b_IncreaseDecreaseInPrepaidExpensesAndOtherCurrentAssets"/>
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    <link:label id="lab_b_DebtInstrumentCovenantTotalConsolidatedDebttoConsolidatedEBITDA_255e62b8-a234-4c47-b05b-1ef51d83a212_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentCovenantTotalConsolidatedDebttoConsolidatedEBITDA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt covenant ratio of total debt to EBITDA</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_11c58502-8588-40a9-b376-04ca6e53de49_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and contingencies (Note 15)</link:label>
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    <link:label id="lab_dei_SecurityExchangeName_06b4f46e-0173-49dc-9305-9ae24fccd8c4_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_9e2276a9-70c2-47d9-8559-406f3d969ba3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Debt</link:label>
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    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_fb878681-bc9b-4e52-a8c2-acc5ab2015b3_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ShortTermDebtTypeDomain"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanServiceCost_2f59173f-e0bb-44d4-86b8-f766dc161094_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Service cost</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanServiceCost" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DefinedBenefitPlanServiceCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanServiceCost" xlink:to="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:type="arc" order="1"/>
    <link:label id="lab_b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent_d6f73bd7-e52f-4cab-8f77-95e664596d67_terseLabel_en-US" xlink:label="lab_b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue transferred percent</link:label>
    <link:label id="lab_b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent_label_en-US" xlink:label="lab_b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer, Including Assessed Tax, Percent</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent" xlink:href="b-20220930.xsd#b_RevenuefromContractwithCustomerIncludingAssessedTaxPercent"/>
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    <link:label id="lab_b_AutomationProductsMember_415c97fb-e962-4396-bd1c-236a1cc5936e_terseLabel_en-US" xlink:label="lab_b_AutomationProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Automation Products</link:label>
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    <link:label id="lab_b_AutomationProductsMember_documentation_en-US" xlink:label="lab_b_AutomationProductsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Automation Products [Member]</link:label>
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    <link:label id="lab_dei_CoverAbstract_914bd983-41a2-4d74-b835-73972fff2a9b_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cover [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_26d0d200-fc08-4dfb-b8be-ef7bacffac18_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_70cf817f-68e4-490e-b71f-079c6c32a395_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_b26572e7-718e-4896-8c1a-46467d9cf0c5_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income before income taxes</link:label>
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    <link:label id="lab_b_LongtermDebtandLeaseObligationExcludingCurrentMaturities_406644f2-592a-457d-8a83-6fb8155c96a9_terseLabel_en-US" xlink:label="lab_b_LongtermDebtandLeaseObligationExcludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term debt</link:label>
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    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_05273d2e-6aab-4062-82be-f9ad74b23b48_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill impairment charge</link:label>
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    <link:label id="lab_us-gaap_TimingOfTransferOfGoodOrServiceDomain_555a323a-7bb1-4e18-888d-0f4265f70739_terseLabel_en-US" xlink:label="lab_us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Timing of Transfer of Good or Service [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TimingOfTransferOfGoodOrServiceDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_TimingOfTransferOfGoodOrServiceDomain"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
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    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_d2ca55b8-cf9f-4ede-b29b-03313b2ceb25_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Changes in Accumulated Other Comprehensive Income by Component [Roll Forward]</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_a425a0d9-c6b5-47ba-9c3e-7bdb7a46992b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
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    <link:label id="lab_dei_CurrentFiscalYearEndDate_9865d9d8-371c-4095-80cc-1e7b728314d8_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
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    <link:label id="lab_b_DebtInstrumentCovenantConsolidatedSeniorDebtToConsolidatedEBITDAAtPeriodEnd_6856ddc7-a5d2-454d-bad0-377f246c9ac3_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentCovenantConsolidatedSeniorDebtToConsolidatedEBITDAAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Senior debt to consolidated EBITDA at period end</link:label>
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    <link:label id="lab_us-gaap_VestingAxis_8d8168fe-2bc7-4ea9-be8a-f83133f10bc8_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Vesting [Axis]</link:label>
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    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_556514fb-2a61-48ab-bac9-85dab7b224d3_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other intangible assets, net</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_e641f2c8-e5c7-4ea0-a9b8-c0716bb35806_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Diluted (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_61f96317-efd1-4c3e-a28a-0143ceeffd25_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Two</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_9fa72c5f-48eb-4b72-8fd0-cf819eff2dc7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from disposition of property, plant and equipment</link:label>
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    <link:label id="lab_us-gaap_TrademarksAndTradeNamesMember_85fa1c80-75bf-443b-a4d5-b16854070d51_terseLabel_en-US" xlink:label="lab_us-gaap_TrademarksAndTradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trademarks/trade names</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesCurrent_df8dfb76-26eb-4785-ab53-094f0412b8ea_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current liabilities</link:label>
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    <link:label id="lab_b_MoldingSolutionsProductsMember_66dd1110-8b10-4bf9-b955-ea35fe3c04ab_terseLabel_en-US" xlink:label="lab_b_MoldingSolutionsProductsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Molding Solutions Products</link:label>
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    <link:label id="lab_us-gaap_AccruedIncomeTaxesNoncurrent_b5018c96-21f3-4ad3-aedd-f050f351f782_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term tax liability</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_6af98ecf-9e34-41c1-b8be-fe058b4a09cd_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_label_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RestructuringCostAndReserveLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:to="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember_351d740d-f534-41a7-a7c4-f54f1853858d_terseLabel_en-US" xlink:label="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fifth Amendment Maturity February 2022 and 3.97% Senior Notes</link:label>
    <link:label id="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember_label_en-US" xlink:label="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fifth Amendment Maturity February 2022 and Three Point Seven Percent Senior Notes [Member]</link:label>
    <link:label id="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember_documentation_en-US" xlink:label="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fifth Amendment Maturity February 2022 and Three Point Nine Seven Percent Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:href="b-20220930.xsd#b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:to="lab_b_FifthAmendmentMaturityFebruary2022AndThreePointSevenPercentSeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_MinimumRangeOfTargetAwardOfStockPlan_7d99852b-5557-4f01-961c-0252f9f1424c_terseLabel_en-US" xlink:label="lab_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Minimum range of target award of stock plan</link:label>
    <link:label id="lab_b_MinimumRangeOfTargetAwardOfStockPlan_label_en-US" xlink:label="lab_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Minimum Range of Target Award of Stock Plan</link:label>
    <link:label id="lab_b_MinimumRangeOfTargetAwardOfStockPlan_documentation_en-US" xlink:label="lab_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Minimum Range of Target Award for performance share awards under the long-term Relative Measure Program</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:href="b-20220930.xsd#b_MinimumRangeOfTargetAwardOfStockPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:to="lab_b_MinimumRangeOfTargetAwardOfStockPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_2285bbdc-f471-40e3-82b0-1dbb3d729d23_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Remaining performance obligations</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RevenueRemainingPerformanceObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_8e86873f-0694-4f76-9a60-924be7661391_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Expiration Period</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_c1d073f9-2b8d-4462-a27f-d2f2ef6bf786_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LineOfCreditFacilityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_b_WeightedAverageCommonSharesOutstandingAbstract_b61f7463-1b02-4d86-a391-014aed28441f_terseLabel_en-US" xlink:label="lab_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted average common shares outstanding:</link:label>
    <link:label id="lab_b_WeightedAverageCommonSharesOutstandingAbstract_label_en-US" xlink:label="lab_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Common Shares Outstanding [Abstract]</link:label>
    <link:label id="lab_b_WeightedAverageCommonSharesOutstandingAbstract_documentation_en-US" xlink:label="lab_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Common Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:href="b-20220930.xsd#b_WeightedAverageCommonSharesOutstandingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:to="lab_b_WeightedAverageCommonSharesOutstandingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AmericasMember_c97f983b-0c70-47b6-a4aa-d155579f0a73_terseLabel_en-US" xlink:label="lab_srt_AmericasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Americas</link:label>
    <link:label id="lab_srt_AmericasMember_label_en-US" xlink:label="lab_srt_AmericasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Americas [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AmericasMember" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_AmericasMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AmericasMember" xlink:to="lab_srt_AmericasMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_e0e733c8-778f-4b6e-b1a9-e5a48b6a074f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_d1a39ffc-d81c-4558-9b01-a5226c2d7a30_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other (Note 9)</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_82273a93-9f9d-4b3c-8242-deeb5b915837_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash payments from settlement</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from (Payments for) Other Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_e9bd159b-8592-45b0-ac8e-f15df62cfbd4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_763c3223-61b8-4a2d-9f60-b3f2bb1ae767_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EuropeMember_05928a57-16af-4eee-80be-bd867f0d28ac_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Europe</link:label>
    <link:label id="lab_srt_EuropeMember_label_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Europe [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EuropeMember" xlink:href="https://xbrl.fasb.org/srt/2022/elts/srt-2022.xsd#srt_EuropeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EuropeMember" xlink:to="lab_srt_EuropeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets_241b2e8a-9955-4ed7-88ea-30cec7f70bb9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected return on plan assets</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined Benefit Plan, Expected Return (Loss) on Plan Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:to="lab_us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_fd01684e-b960-4f39-89cd-66c4ea847ad8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_242e9eca-e772-4d03-b799-2d6b8de7df5e_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Remaining borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_b_IndustrialMember_e5bae212-a292-4024-a4e5-b959c3c5e866_terseLabel_en-US" xlink:label="lab_b_IndustrialMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Industrial</link:label>
    <link:label id="lab_b_IndustrialMember_label_en-US" xlink:label="lab_b_IndustrialMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Industrial [Member]</link:label>
    <link:label id="lab_b_IndustrialMember_documentation_en-US" xlink:label="lab_b_IndustrialMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Industrial [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_IndustrialMember" xlink:href="b-20220930.xsd#b_IndustrialMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_IndustrialMember" xlink:to="lab_b_IndustrialMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_45231837-edae-4cb0-881a-606844ec352f_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_a5251135-c40b-4028-b940-10778577dd0b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_e98fe0eb-26b6-47d1-874d-d7820703ce73_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeNamesMember_488edf6e-7e30-4d4e-879f-1d6c88fe0ec6_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trade names</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_a1dfcfd6-5d70-49e2-ab9c-91cefaa4f486_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RetirementPlanTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTypeAxis" xlink:to="lab_us-gaap_RetirementPlanTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_71c4d5a9-bc0a-45b4-adbb-d6473eefe65d_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InventoryDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureTextBlock" xlink:to="lab_us-gaap_InventoryDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_ccffd838-5b5d-45e2-add3-0f36364f6c02_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_36878d74-1916-4c7a-834c-9d3a522dddd8_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InventoryDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureAbstract" xlink:to="lab_us-gaap_InventoryDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_68950afe-2604-4915-ab98-797338d3cc12_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2022/dei-2022.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_b_AerospaceMember_c537c906-53df-4152-b9ac-31920bc27cd1_terseLabel_en-US" xlink:label="lab_b_AerospaceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace</link:label>
    <link:label id="lab_b_AerospaceMember_label_en-US" xlink:label="lab_b_AerospaceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace [Member]</link:label>
    <link:label id="lab_b_AerospaceMember_documentation_en-US" xlink:label="lab_b_AerospaceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Aerospace [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_AerospaceMember" xlink:href="b-20220930.xsd#b_AerospaceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_AerospaceMember" xlink:to="lab_b_AerospaceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_2a799cf1-1051-4105-8803-620540deb1c4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Noncurrent Assets</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Noncurrent Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncurrentAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherNoncurrentAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncurrentAssetsMember" xlink:to="lab_us-gaap_OtherNoncurrentAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity_3a161658-3109-46f6-a9d6-fbf36f2da33c_terseLabel_en-US" xlink:label="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility with accordian feature, maximum borrowing capacity</link:label>
    <link:label id="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity_label_en-US" xlink:label="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility With Accordian Feature, Maximum Borrowing Capacity</link:label>
    <link:label id="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity_documentation_en-US" xlink:label="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit facility with accordian feature, maximum borrowing capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:href="b-20220930.xsd#b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:to="lab_b_LineofCreditFacilityWithAccordianFeatureMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_6495e7c8-d301-4dd8-95c3-db53cf88947f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fixed interest rate</link:label>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DerivativeFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFixedInterestRate" xlink:to="lab_us-gaap_DerivativeFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_b_BankAcceptancesFairValueDisclosure_2f8b27ed-978a-4e1c-a5b0-b841ad96e2bd_terseLabel_en-US" xlink:label="lab_b_BankAcceptancesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bank acceptances</link:label>
    <link:label id="lab_b_BankAcceptancesFairValueDisclosure_label_en-US" xlink:label="lab_b_BankAcceptancesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bank Acceptances, Fair Value Disclosure</link:label>
    <link:label id="lab_b_BankAcceptancesFairValueDisclosure_documentation_en-US" xlink:label="lab_b_BankAcceptancesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Bank Acceptances, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_BankAcceptancesFairValueDisclosure" xlink:href="b-20220930.xsd#b_BankAcceptancesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_BankAcceptancesFairValueDisclosure" xlink:to="lab_b_BankAcceptancesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment_8f377151-0a15-4326-bb8e-ebdc90204f14_negatedTerseLabel_en-US" xlink:label="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation</link:label>
    <link:label id="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment_label_en-US" xlink:label="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite Lived Intangible Assets Foreign Currency Translation Adjustment</link:label>
    <link:label id="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment_documentation_en-US" xlink:label="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cumulative foreign currency translation adjustment for all finite lived intangible assets as of balance sheet date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:href="b-20220930.xsd#b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:to="lab_b_FiniteLivedIntangibleAssetsForeignCurrencyTranslationAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_9a514d90-95a0-4f32-8d46-3e556c059fa7_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_b_DebtInstrumentVariableRateBasis_fe4a749f-f459-416e-b293-8547c8eb8a35_terseLabel_en-US" xlink:label="lab_b_DebtInstrumentVariableRateBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis for variable basis spread</link:label>
    <link:label id="lab_b_DebtInstrumentVariableRateBasis_label_en-US" xlink:label="lab_b_DebtInstrumentVariableRateBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Variable Rate Basis</link:label>
    <link:label id="lab_b_DebtInstrumentVariableRateBasis_documentation_en-US" xlink:label="lab_b_DebtInstrumentVariableRateBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Variable Rate Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_DebtInstrumentVariableRateBasis" xlink:href="b-20220930.xsd#b_DebtInstrumentVariableRateBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_DebtInstrumentVariableRateBasis" xlink:to="lab_b_DebtInstrumentVariableRateBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_79b46d48-f4f0-4161-9c99-6ab5c59dadf7_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount_b3272996-5522-4efd-b7a3-a9b40cc31ebd_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitment fee amount</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock_1eb1143c-cd49-4a53-a5c8-7a24393e6512_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Change of Liability for Business Reorganization</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_14f5ac39-d6d2-489f-81a0-d026efa76294_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted average number of diluted shares outstanding adjustment (in shares)</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_774abda6-8929-4172-9552-1207e269179c_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of intangible assets expected in 2027</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive"/>
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    <link:label id="lab_dei_EntityCentralIndexKey_f37aea2a-d33d-43fe-ae47-6339cb83356e_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract_2bdbf3a9-050c-41ae-bfe8-1997c06c2d4d_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Intangible Assets, Future Amortization Expense</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_0798df2b-778a-4049-898a-ff900fb73d2b_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
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    <link:label id="lab_b_SixthAmendmentMaturityFebruary2022AndThreePointNineSevenPercentSeniorNotesMember_7e61043e-331f-42ca-a25c-84b64ab0271c_terseLabel_en-US" xlink:label="lab_b_SixthAmendmentMaturityFebruary2022AndThreePointNineSevenPercentSeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sixth Amendment Maturity February 2022 and 3.97% Percent Senior Notes</link:label>
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    <link:label id="lab_b_ComponentRepairProgramMember_1b51106c-fd00-4b05-9dd0-0d0dc05171f8_terseLabel_en-US" xlink:label="lab_b_ComponentRepairProgramMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Component Repair Programs (CRPs)</link:label>
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    <link:label id="lab_b_ComponentRepairProgramMember_documentation_en-US" xlink:label="lab_b_ComponentRepairProgramMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Component Repair Program [Member]</link:label>
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    <link:label id="lab_dei_CityAreaCode_fd8c118f-23ee-4064-9baf-38940f3f02c7_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_us-gaap_AssetsAbstract_a37d8dc0-e0db-4bdf-bd27-14fa8fd7aacc_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_d3d8edb1-8655-417c-a36a-37038b6d59c8_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
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    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_567ede1d-1a3b-461c-b455-68303f92ac0b_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_1f1cd100-cfdf-44d3-a259-b30ab31dc547_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_CompensationAndRetirementDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:to="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_currency_EUR_402bd98b-0fa7-4bd4-b1b7-0decf117426a_terseLabel_en-US" xlink:label="lab_currency_EUR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Euro Member Countries, Euro</link:label>
    <link:label id="lab_currency_EUR_label_en-US" xlink:label="lab_currency_EUR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Euro Member Countries, Euro</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_currency_EUR" xlink:href="https://xbrl.sec.gov/currency/2022/currency-2022.xsd#currency_EUR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_currency_EUR" xlink:to="lab_currency_EUR" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_331631aa-78de-49af-87fc-9f21814afecc_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Remaining performance obligations, percentage</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue, Remaining Performance Obligation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_RevenueRemainingPerformanceObligationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_7c0eb673-518a-4325-b5ea-eba373d8693c_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensation_d634b9b2-1a4b-440e-b0f8-73b4712ac93e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable_65c4a28a-b8bc-4f9d-9e5f-e6d3f4676fb6_terseLabel_en-US" xlink:label="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Goodwill and Intangible Assets [Table]</link:label>
    <link:label id="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable_label_en-US" xlink:label="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Goodwill and Intangible Assets [Table]</link:label>
    <link:label id="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable_documentation_en-US" xlink:label="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Goodwill and Intangible Assets [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:href="b-20220930.xsd#b_ScheduleOfGoodwillAndIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:to="lab_b_ScheduleOfGoodwillAndIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_d8afdab0-0a92-407c-93c5-ab263c81f656_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_b_ContractWithCustomerAssetLiabilityPercentChange_a5359b18-a943-4fb2-a30b-571bd7e8f80d_terseLabel_en-US" xlink:label="lab_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net contract assets, % change</link:label>
    <link:label id="lab_b_ContractWithCustomerAssetLiabilityPercentChange_label_en-US" xlink:label="lab_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset (Liability), Percent Change</link:label>
    <link:label id="lab_b_ContractWithCustomerAssetLiabilityPercentChange_documentation_en-US" xlink:label="lab_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contract with Customer, Asset (Liability), Percent Change</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:href="b-20220930.xsd#b_ContractWithCustomerAssetLiabilityPercentChange"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:to="lab_b_ContractWithCustomerAssetLiabilityPercentChange" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_d331e0a9-f705-4b58-a6e1-83922264eda0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateContractMember_1ac74a1b-ee7c-465b-845f-c1582c01647a_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Contract</link:label>
    <link:label id="lab_us-gaap_InterestRateContractMember_label_en-US" xlink:label="lab_us-gaap_InterestRateContractMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest Rate Contract [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateContractMember" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_InterestRateContractMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateContractMember" xlink:to="lab_us-gaap_InterestRateContractMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_90e6a90c-a1c4-46c8-99a4-e980e5c6fb0d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Capital expenditures</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTermOfContract_15cea43a-f214-4a7b-bb1f-9217ac0f8f49_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Term of contract</link:label>
    <link:label id="lab_us-gaap_DerivativeTermOfContract_label_en-US" xlink:label="lab_us-gaap_DerivativeTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DerivativeTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTermOfContract" xlink:to="lab_us-gaap_DerivativeTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_573da60e-a43f-40b4-bb71-1d78d6903aa6_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_92fdd83f-8975-4f3a-ab5a-b9f5157972ba_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amortization of intangible assets expected in 2023</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_2a1c984a-458b-44f5-aae2-5e4fc0f8aab6_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative amount of hedge</link:label>
    <link:label id="lab_us-gaap_DerivativeAmountOfHedgedItem_label_en-US" xlink:label="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Amount of Hedged Item</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_DerivativeAmountOfHedgedItem"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAmountOfHedgedItem" xlink:to="lab_us-gaap_DerivativeAmountOfHedgedItem" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_a46cf3cd-588b-4cb3-b017-46798c8d0183_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign currency translation adjustment, tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Translation Adjustment, Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:href="https://xbrl.fasb.org/us-gaap/2022/elts/us-gaap-2022.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTranslationAdjustmentTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_280a5455-e8ed-4e91-ab7a-0e01c6d88d2c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of credit, interest rate at period end</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility, Interest Rate at Period End</link:label>
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