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Accounting Policies Goodwill Impairment (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Finite-Lived Intangible Assets [Line Items]      
Other Asset Impairment Charges $ 21.1us-gaap_OtherAssetImpairmentCharges    
Asset Impairments and Other, Net 40.0us-gaap_AssetImpairmentCharges 4.7us-gaap_AssetImpairmentCharges 0us-gaap_AssetImpairmentCharges
Less: Impairment charges 119.5us-gaap_GoodwillImpairmentLoss 76.3us-gaap_GoodwillImpairmentLoss 0us-gaap_GoodwillImpairmentLoss
Power Transmission Solutions [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Other Asset Impairment Charges 15.1us-gaap_OtherAssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
   
Asset Impairments and Other, Net 26.2us-gaap_AssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
0us-gaap_AssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
 
Less: Impairment charges 11.1us-gaap_GoodwillImpairmentLoss
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
12.1us-gaap_GoodwillImpairmentLoss
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
12.1us-gaap_GoodwillImpairmentLoss
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
Impairment Charges 11.1us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
   
Commercial and Industrial Systems [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Other Asset Impairment Charges 0us-gaap_OtherAssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
   
Asset Impairments and Other, Net 0us-gaap_AssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
4.7us-gaap_AssetImpairmentCharges
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
 
Less: Impairment charges 100.7us-gaap_GoodwillImpairmentLoss
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
64.2us-gaap_GoodwillImpairmentLoss
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
 
Impairment Charges   17.0us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
 
Other Intangible Assets [Member]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges 18.9us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_OtherIntangibleAssetsMember
   
Other Intangible Assets [Member] | Power Transmission Solutions [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges 11.1us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_OtherIntangibleAssetsMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
   
Other Intangible Assets [Member] | Commercial and Industrial Systems [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges 0us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_OtherIntangibleAssetsMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
   
Hermetic [Member] [Domain] [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges 13.8us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_HermeticMemberDomainDomain
   
Technology [Member]      
Finite-Lived Intangible Assets [Line Items]      
Less: Impairment charges 1.0us-gaap_GoodwillImpairmentLoss
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_TechnologyMember
   
Impairment Charges 7.8us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_TechnologyMember
16.2us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_TechnologyMember
 
Technology [Member] | Power Transmission Solutions [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges   0us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_TechnologyMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
 
Technology [Member] | Commercial and Industrial Systems [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges   16.2us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= rbc_TechnologyMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain
 
Customer Relationships [Member]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges 10.7us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
0.8us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
 
Customer Relationships [Member] | Power Transmission Solutions [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges   0us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_PowerTransmissionSolutionsDomain
 
Customer Relationships [Member] | Commercial and Industrial Systems [Domain]      
Finite-Lived Intangible Assets [Line Items]      
Impairment Charges   $ 0.8us-gaap_ImpairmentOfIntangibleAssetsFinitelived
/ us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis
= us-gaap_CustomerRelationshipsMember
/ us-gaap_StatementBusinessSegmentsAxis
= rbc_CommercialandIndustrialSystemsDomain