Revenue - Contract Balances (Details) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2020	Dec. 31, 2019
Revenue from Contract with Customer [Abstract]
Unbilled receivables (contract assets)	$ 33,009	$ 22,444
Unbilled receivables (contract assets), $ Change	$ 10,565
Unbilled receivables (contract assets), % Change	47.00%
Contract liabilities	$ (39,865)	(55,076)
Contract liabilities, $ Change	$ 15,211
Contract liabilities, % Change	(28.00%)
Net contract liabilities	$ (6,856)	(32,632)
Net contract liabilities, $ Change	$ 25,776
Net contract liabilities, % Change	(79.00%)
Customer advances	$ 12,750	$ 16,971
Revenue recognized	100.00%	85.00%

Contract with Customer, Customer Advance Liability

No definition available.

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

- Definition

Contract with Customer, Asset (Liability), Percent Change

+ References

No definition available.

+ Details

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Namespace Prefix:	b_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Asset, Percent Change

+ References

No definition available.

+ Details

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Namespace Prefix:	b_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Liability, Percent Change

+ References

No definition available.

+ Details

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Namespace Prefix:	b_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Liability, Revenue Recognized, Percent

+ References

No definition available.

+ Details

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Namespace Prefix:	b_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contract with Customer, Net Asset (Liability)

+ References

No definition available.

+ Details

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Namespace Prefix:	b_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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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Namespace Prefix:	b_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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=118956577&loc=SL49130551-203045

+ Details

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Namespace Prefix:	us-gaap_
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=118944033&loc=SL49130531-203044

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
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-URI http://asc.fasb.org/extlink&oid=118944033&loc=SL49130533-203044

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
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-Section 50
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-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=118956577&loc=SL49130549-203045

+ Details

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Data Type:	xbrli:monetaryItemType
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=118944033&loc=SL49130531-203044

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-Publisher FASB
-Name Accounting Standards Codification
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-URI http://asc.fasb.org/extlink&oid=118956577&loc=SL49130549-203045

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=118944033&loc=SL49130532-203044

+ Details

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Namespace Prefix:	us-gaap_
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=118956577&loc=SL49130551-203045

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- References

No definition available.

+ Details

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