Goodwill and Intangible Assets (Schedule of Changes To Goodwill) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2021	Dec. 28, 2019	Dec. 29, 2018
Goodwill [Roll Forward]
Goodwill, beginning balance	$ 1,501.3	$ 1,509.2
Divestiture		(2.8)
Impairment Charge	(10.5)	0.0	$ (9.5)
Translation and Other	27.4	(5.1)
Goodwill, ending balance	1,518.2	1,501.3	1,509.2
Cumulative Goodwill Impairment Charges	295.7
Commercial Systems
Goodwill [Roll Forward]
Goodwill, beginning balance	426.6	427.4
Divestiture		0.0
Impairment Charge	0.0
Translation and Other	6.7	(0.8)
Goodwill, ending balance	433.3	426.6	427.4
Cumulative Goodwill Impairment Charges	183.2
Industrial Systems
Goodwill [Roll Forward]
Goodwill, beginning balance	170.8	171.5
Divestiture		0.0
Impairment Charge	(10.5)
Translation and Other	3.4	(0.7)
Goodwill, ending balance	163.7	170.8	171.5
Cumulative Goodwill Impairment Charges	72.1
Climate Solutions
Goodwill [Roll Forward]
Goodwill, beginning balance	331.2	330.6
Divestiture		0.0
Impairment Charge	0.0
Translation and Other	(0.4)	0.6
Goodwill, ending balance	330.8	331.2	330.6
Cumulative Goodwill Impairment Charges	17.2
Power Transmission Solutions
Goodwill [Roll Forward]
Goodwill, beginning balance	572.7	579.7
Divestiture		(2.8)
Impairment Charge	0.0
Translation and Other	17.7	(4.2)
Goodwill, ending balance	590.4	$ 572.7	$ 579.7
Cumulative Goodwill Impairment Charges	$ 23.2