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Accounting Policies (Impairment Schedule) (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 02, 2016
Jan. 03, 2015
Dec. 28, 2013
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets   $ 18.9  
Impairment of Property, Plant and Equipment   21.1  
Less: Gain from Adjustment to the Fair Value of a Contingent Consideration Liability     $ 12.3
Asset Impairments and Other, Net $ 0.0 40.0 4.7
Climate Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets   7.8  
Impairment of Property, Plant and Equipment   6.0  
Less: Gain from Adjustment to the Fair Value of a Contingent Consideration Liability     0.0
Asset Impairments and Other, Net   13.8 0.0
Commercial and Industrial Systems      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets   0.0  
Impairment of Property, Plant and Equipment   0.0  
Less: Gain from Adjustment to the Fair Value of a Contingent Consideration Liability     12.3
Asset Impairments and Other, Net   0.0 4.7
Power Transmission Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets   11.1  
Impairment of Property, Plant and Equipment   15.1  
Less: Gain from Adjustment to the Fair Value of a Contingent Consideration Liability     0.0
Asset Impairments and Other, Net   $ 26.2 0.0
Technology      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     16.2
Technology | Climate Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     0.0
Technology | Commercial and Industrial Systems      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     16.2
Technology | Power Transmission Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     0.0
Customer Relationships      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     0.8
Customer Relationships | Climate Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     0.0
Customer Relationships | Commercial and Industrial Systems      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     0.8
Customer Relationships | Power Transmission Solutions      
Finite-Lived Intangible Assets [Line Items]      
Impairment of Intangible Assets     $ 0.0