Revenue - Contract Balances (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Revenue from Contract with Customer [Abstract]
Unbilled receivables (contract assets)	$ 37,063		$ 37,063		$ 33,009
Unbilled receivables (contract assets), $ Change			$ 4,054
Unbilled receivables (contract assets), % Change			12.00%
Contract liabilities	(26,290)		$ (26,290)		(39,865)
Contract liabilities, $ Change			$ 13,575
Contract liabilities, % Change			(34.00%)
Net contract liabilities	10,773		$ 10,773		(6,856)
Net contract liabilities, $ Change			17,629
Customer advances	$ 11,682		$ 11,682		$ 12,750
Revenue recognized	30.00%	25.00%	85.00%	75.00%

Contract with Customer, Asset, Percent Change

No definition available.

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Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Customer Advance Liability

+ References

No definition available.

+ Details

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

- Definition

Contract with Customer, Liability, Percent Change

+ References

No definition available.

+ Details

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Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Liability, Revenue Recognized, Percent

+ References

No definition available.

+ Details

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- Definition

Contract with Customer, Net Asset (Liability)

+ References

No definition available.

+ Details

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Period Type:	instant

- Definition

Contract with Customer, Net Asset (Liability), Cumulative Catch-up Adjustment to Revenue, Change in Measure of Progress

+ References

No definition available.

+ Details

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- Definition

Amount of increase (decrease) in revenue recognized for cumulative catch-up adjustment from change in measure of progress which increases (decreases) right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130551-203045

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount, after allowance for credit loss, of right to consideration in exchange for good or service transferred to customer when right is conditioned on something other than passage of time, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=121556615&loc=SL49130531-203044

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-Publisher FASB
-Name Accounting Standards Codification
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-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 8
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130549-203045

+ Details

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Balance Type:	debit
Period Type:	instant

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=121556615&loc=SL49130531-203044

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-Publisher FASB
-Name Accounting Standards Codification
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-Section 50
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-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130549-203045

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121556615&loc=SL49130532-203044

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of increase (decrease) in obligation to transfer good or service to customer for which consideration from customer has been received or is due, from business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121604090&loc=SL49130551-203045

+ Details

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Period Type:	duration

- References

No definition available.

+ Details

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