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Derivative Financial Instruments (Narrative) (Details) (USD $)
In Millions, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Derivative [Line Items]    
Derivative Instruments, Gain (Loss) Reclassification from Accumulated OCI to Income, Estimated Net Amount to be Transferred $ (2.2)us-gaap_DerivativeInstrumentsGainLossReclassificationFromAccumulatedOCIToIncomeEstimatedNetAmountToBeTransferred $ (0.7)us-gaap_DerivativeInstrumentsGainLossReclassificationFromAccumulatedOCIToIncomeEstimatedNetAmountToBeTransferred
Unrealized Gain (Loss) on Cash Flow Hedging Instruments (31.0)us-gaap_UnrealizedGainLossOnCashFlowHedgingInstruments  
Notional amount of receive-variable/pay-fixed interest rate swaps 100.0invest_DerivativeNotionalAmount 250.0invest_DerivativeNotionalAmount
Prepaid Expenses and Other Current Assets [Member] | Foreign Exchange Contract [Member]    
Derivative [Line Items]    
Current derivative assets, gross 1.6rbc_CurrentDerivativeAssetsGross
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
8.4rbc_CurrentDerivativeAssetsGross
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Derivative Asset, Fair Value, Amount Offset Against Collateral (1.3)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
(0.6)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Current Derivatives, Fair Value, Net 0.3rbc_CurrentDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
7.8rbc_CurrentDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Prepaid Expenses and Other Current Assets [Member] | Derivative Commodity Contracts [Member]    
Derivative [Line Items]    
Current derivative assets, gross 2.3rbc_CurrentDerivativeAssetsGross
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
4.7rbc_CurrentDerivativeAssetsGross
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Derivative Asset, Fair Value, Amount Offset Against Collateral (2.3)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
(2.4)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Current Derivatives, Fair Value, Net 0rbc_CurrentDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
2.3rbc_CurrentDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Other Noncurrent Assets [Member] | Foreign Exchange Contract [Member]    
Derivative [Line Items]    
Derivative Assets, Noncurrent   0.5us-gaap_DerivativeAssetsNoncurrent
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherNoncurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Derivative Asset, Fair Value, Amount Offset Against Collateral   (0.2)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherNoncurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Long-term derivative assets, gross   0.7rbc_LongTermDerivativeAssetsGross
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherNoncurrentAssetsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Hedging Obligations Current [Member] | Foreign Exchange Contract [Member]    
Derivative [Line Items]    
Current derivative liabilities, gross 17.5rbc_CurrentDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
3.1rbc_CurrentDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Derivative Liability, Fair Value, Amount Offset Against Collateral (1.3)us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
(0.6)us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Derivative, Net Liability Position, Aggregate Fair Value 16.2us-gaap_DerivativeNetLiabilityPositionAggregateFairValue
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
2.5us-gaap_DerivativeNetLiabilityPositionAggregateFairValue
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Hedging Obligations Current [Member] | Derivative Commodity Contracts [Member]    
Derivative [Line Items]    
Current derivative liabilities, gross 12.2rbc_CurrentDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
2.5rbc_CurrentDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Derivative Liability, Fair Value, Amount Offset Against Collateral (2.3)us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
(2.4)us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Derivative, Net Liability Position, Aggregate Fair Value 9.9us-gaap_DerivativeNetLiabilityPositionAggregateFairValue
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
0.1us-gaap_DerivativeNetLiabilityPositionAggregateFairValue
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsCurrentMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
Hedging Obligations [Member]    
Derivative [Line Items]    
Long-term Derivatives Fair Value, Net   0.5rbc_LongTermDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
Hedging Obligations [Member] | Foreign Exchange Contract [Member]    
Derivative [Line Items]    
Derivative Asset, Fair Value, Amount Offset Against Collateral   (0.2)us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
Derivative Liability, Fair Value, Amount Offset Against Collateral 0us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
 
Long-term Derivatives Fair Value, Net 0.1rbc_LongTermDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
 
Long-term derivative liabilities, gross 10.5rbc_LongTermDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_ForeignExchangeContractMember
 
Hedging Obligations [Member] | Derivative Commodity Contracts [Member]    
Derivative [Line Items]    
Derivative Liability, Fair Value, Amount Offset Against Collateral 0us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
 
Long-term Derivatives Fair Value, Net 10.5rbc_LongTermDerivativesFairValueNet
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
 
Long-term derivative liabilities, gross $ 0.1rbc_LongTermDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember
$ 0.7rbc_LongTermDerivativeLiabilitiesGross
/ us-gaap_BalanceSheetLocationAxis
= rbc_HedgingObligationsMember
/ us-gaap_DerivativeInstrumentRiskAxis
= us-gaap_CommodityContractMember