Debt (Debt Schedule) (Details) - USD ($) $ in Thousands	Sep. 30, 2020	Dec. 31, 2019
Debt Instrument [Line Items]
Carrying amount of debt	$ 14,490	$ 7,724
Carrying amount of finance leases	5,842	6,266
Fair value of finance leases	5,998	6,515
Carrying amount of debt and finance leases	717,723	834,775
Fair value of debt and finance leases	733,487	856,616
Less current maturities	(16,310)	(9,758)
Long-term debt	701,413	825,017
Revolving Credit Agreement [Member]
Debt Instrument [Line Items]
Carrying amount of debt	597,102	720,379
Fair value of debt	602,054	737,816
Senior Notes [Member] \| 3.97% Senior Notes [Member]
Debt Instrument [Line Items]
Carrying amount of debt	100,000	100,000
Fair value of debt	110,656	104,151
Lines of Credit and Overdrafts [Member]
Debt Instrument [Line Items]
Carrying amount of debt	14,490	7,724
Fair value of debt	14,490	7,724
Foreign Bank Borrowings [Member]
Debt Instrument [Line Items]
Carrying amount of debt	289	406
Fair value of debt	$ 289	$ 410

Debt and Lease Obligation, Fair Value Disclosure

No definition available.

Name:	b_DebtandLeaseObligationFairValueDisclosure
Namespace Prefix:	b_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Finance Lease Liability, Fair Value Disclosure

+ References

No definition available.

+ Details

Name:	b_FinanceLeaseLiabilityFairValueDisclosure
Namespace Prefix:	b_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Long-term Debt and Lease Obligation, Excluding Current Maturities

+ References

No definition available.

+ Details

Name:	b_LongtermDebtandLeaseObligationExcludingCurrentMaturities
Namespace Prefix:	b_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(1)
-URI http://asc.fasb.org/extlink&oid=109500613&loc=SL6031897-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(16))
-URI http://asc.fasb.org/extlink&oid=119400593&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

+ Details

Name:	us-gaap_DebtInstrumentCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value portion of debt instrument payable, including, but not limited to, notes payable and loans payable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=118260190&loc=d3e13433-108611

+ Details

Name:	us-gaap_DebtInstrumentFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Present value of lessee's discounted obligation for lease payments from finance lease, classified as noncurrent.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=77888419&loc=SL77918627-209977

+ Details

Name:	us-gaap_FinanceLeaseLiabilityNoncurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of long-term debt and lease obligation, classified as current.

+ References

+ Details

Name:	us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of long-term debt and lease obligation, including portion classified as current.

+ References

No definition available.

+ Details

Name:	us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Reflects the total carrying amount as of the balance sheet date of debt having initial terms less than one year or the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-URI http://asc.fasb.org/extlink&oid=119400593&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

+ Details

Name:	us-gaap_ShortTermBorrowings
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=b_RevolvingCreditAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=b_ThreePointNineSevenPercentSeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=b_LinesOfCreditAndOverdraftsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=b_ForeignBankBorrowingsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: