Income Taxes (Details 4)	12 Months Ended
Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Income Tax Disclosure [Abstract]
U.S. federal statutory income tax rate	21.00%	21.00%	35.00%
State taxes (net of federal benefit)	0.10%	0.00%	0.10%
Transition Tax	0.00%	(0.30%)	45.00%
U.S. Corporate Tax Rate change	0.00%	(0.40%)	2.10%
Indefinite Reinvestment Assertion	0.00%	(0.60%)	3.50%
Foreign losses without tax benefit	2.00%	1.50%	1.50%
Foreign operations taxed at different rates	2.00%	1.30%	(11.50%)
GILTI	0.60%	1.20%	0.00%
Tax Holidays	(1.30%)	(1.70%)	(0.80%)
Stock awards excess tax benefit	(0.90%)	(0.80%)	(1.20%)
Swiss Legal Entity Reduction	0.00%	0.00%	(3.40%)
Reduction of Valuation Allowances	(0.30%)	(2.50%)	0.00%
Audit Settlements	0.30%	0.00%	(2.70%)
Other	(0.10%)	1.20%	2.00%
Consolidated effective income tax rate	23.40%	19.90%	69.60%

Effective Income Tax Rate Reconciliation, Foreign Losses Without Tax Benefit

No definition available.

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

- Definition

Effective Income Tax Rate Reconciliation, GILTI

+ References

No definition available.

+ Details

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

- Definition

Effective Income Tax Rate Reconciliation, Indefinite Reinvestment Assertion, Percent

+ References

No definition available.

+ Details

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

- Definition

Effective Income Tax Rate Reconciliation, Transition Tax, Percent

+ References

No definition available.

+ Details

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

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08.(h)(2))
-URI http://asc.fasb.org/extlink&oid=26873400&loc=d3e23780-122690

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to changes in the valuation allowance for deferred tax assets.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to disposition of a business not qualifying as a discontinued operation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationDispositionOfBusiness
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to statutory income tax expense (benefit) outside of the country of domicile.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operation, attributable to nondeductible expense for share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB TOPIC 6.I)
-URI http://asc.fasb.org/extlink&oid=116825942&loc=d3e330036-122817

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 13
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32698-109319

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=84230637&loc=d3e32687-109319

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to income exempt from income tax because of a tax holiday.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationTaxHolidays
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to income tax settlements. Including, but not limited to, domestic tax settlement, foreign tax settlement, state and local tax settlement, and other tax settlements.

+ References

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateReconciliationTaxSettlements
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

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