Goodwill and Intangible Assets (Schedule of Changes To Goodwill) (Details) - USD ($)	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Goodwill [Roll Forward]
Goodwill, beginning balance	$ 4,039,200,000	$ 1,518,200,000
Impairment Charge	0	(33,000,000.0)	$ (10,500,000)
Acquisitions	27,200,000	2,576,800,000
Translation and Other	(47,600,000)	(22,800,000)
Goodwill, ending balance	4,018,800,000	4,039,200,000	1,518,200,000
Cumulative Goodwill Impairment Charges	328,700,000
Commercial Systems
Goodwill [Roll Forward]
Goodwill, beginning balance	428,900,000	433,300,000
Impairment Charge		0
Acquisitions	0	0
Translation and Other	(6,400,000)	(4,400,000)
Goodwill, ending balance	422,500,000	428,900,000	433,300,000
Cumulative Goodwill Impairment Charges	183,200,000
Industrial Systems
Goodwill [Roll Forward]
Goodwill, beginning balance	128,800,000	163,700,000
Impairment Charge		(33,000,000.0)
Acquisitions	0	0
Translation and Other	(2,000,000.0)	(1,900,000)
Goodwill, ending balance	126,800,000	128,800,000	163,700,000
Cumulative Goodwill Impairment Charges	105,100,000
Climate Solutions
Goodwill [Roll Forward]
Goodwill, beginning balance	330,500,000	330,800,000
Impairment Charge		0
Acquisitions	0	0
Translation and Other	(700,000)	(300,000)
Goodwill, ending balance	329,800,000	330,500,000	330,800,000
Cumulative Goodwill Impairment Charges	17,200,000
Motion Control Solutions
Goodwill [Roll Forward]
Goodwill, beginning balance	3,151,000,000	590,400,000
Impairment Charge		0
Acquisitions	27,200,000	2,576,800,000
Translation and Other	(38,500,000)	(16,200,000)
Goodwill, ending balance	3,139,700,000	$ 3,151,000,000	$ 590,400,000
Cumulative Goodwill Impairment Charges	$ 23,200,000