Accounting Policies (Narrative) (Details) $ in Millions	3 Months Ended			9 Months Ended	12 Months Ended
	Jan. 02, 2016 USD ($)	Apr. 04, 2015 USD ($) VEF / $	Jan. 03, 2015 USD ($) VEF / $	Sep. 27, 2014 USD ($)	Jan. 02, 2016 USD ($)	Jan. 03, 2015 USD ($) unit VEF / $	Dec. 28, 2013 USD ($)
Property, Plant and Equipment [Line Items]
Loss on Venezuela Currency Devaluation					$ (1.5)	$ (10.4)	$ (3.6)
Research and development costs					30.1	32.9	28.3
Commitments for purchases of property, plant, and equipment					9.7
Goodwill Impairment	$ 79.9		$ 118.5	$ 1.0	79.9	119.5	76.3
Impairment of Intangible Assets						18.9
Gain from Adjustment to the Fair Value of a Contingent Consideration Liability							12.3
Deferred income tax benefit reclassified					(10.4)	(26.4)	(5.5)
Reduction of total assets	(4,591.7)		(3,357.2)		(4,591.7)	(3,357.2)	(3,611.3)
Accounting Standards Update 2015-17 [Member]
Property, Plant and Equipment [Line Items]
Deferred income tax benefit reclassified						67.0
Accounting Standards Update 2015-03 [Member]
Property, Plant and Equipment [Line Items]
Reduction of total assets			$ 1.3			1.3
Technology
Property, Plant and Equipment [Line Items]
Goodwill Impairment						1.0
Impairment of Intangible Assets							16.2
Customer Relationships
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets							$ 0.8
Commercial and Industrial Systems
Property, Plant and Equipment [Line Items]
Goodwill Impairment					79.9	100.7
Number of reporting units							0.0
Impairment of Intangible Assets						$ 0.0
Gain from Adjustment to the Fair Value of a Contingent Consideration Liability							$ 12.3
Commercial and Industrial Systems | Technology
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets							16.2
Commercial and Industrial Systems | Customer Relationships
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets							0.8
Climate Solutions and Power Transmission Solutions [Member]
Property, Plant and Equipment [Line Items]
Number of reporting units | unit						2
Goodwill Impairment [Member]
Property, Plant and Equipment [Line Items]
Goodwill Impairment					79.9	$ 119.5	76.3
Asset Impairments and Other, Net [Member] | Hydraulic Fracturing Equipment [Member]
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets						26.2
Asset Impairments and Other, Net [Member] | Hermetic Climate Applications [Member]
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets						$ 13.8
Asset Impairments and Other, Net [Member] | Technology
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets							16.2
Asset Impairments and Other, Net [Member] | Customer Relationships
Property, Plant and Equipment [Line Items]
Impairment of Intangible Assets							$ 0.8
VENEZUELA
Property, Plant and Equipment [Line Items]
Loss on Venezuelan Asset Write Down					$ 12.8
SIMADI [Member] | VENEZUELA
Property, Plant and Equipment [Line Items]
Loss on Venezuela Currency Devaluation		$ 1.5
SIMADI [Member] | VENEZUELA | Venezuelan bolívar fuerte
Property, Plant and Equipment [Line Items]
Exchange rate translation | VEF / $		193
SICAD2 [Member] | VENEZUELA
Property, Plant and Equipment [Line Items]
Loss on Venezuela Currency Devaluation	$ 10.4
SICAD2 [Member] | VENEZUELA | Venezuelan bolívar fuerte
Property, Plant and Equipment [Line Items]
Exchange rate translation | VEF / $			51.0			51.0