Segment Information (Schedule of Financial Information Attributable To The Reporting Segments) (Details) - USD ($)	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting Information [Line Items]
Net Sales	$ 5,217,900,000	$ 3,810,300,000	$ 2,907,000,000
Gross Profit*	1,669,700,000	1,111,600,000	806,600,000
Operating Expenses	978,400,000	714,700,000	512,900,000
Goodwill Impairment	0	33,000,000.0	10,500,000
Asset Impairments	900,000	5,600,000	5,300,000
Gain on Sale of Business	0	0	(100,000)
Income (Loss) from Operations*	690,400,000	358,300,000	278,000,000.0
Depreciation and Amortization	307,400,000	170,600,000	131,400,000
Capital Expenditures	83,800,000	54,500,000	47,500,000
Commercial Systems
Segment Reporting Information [Line Items]
Net Sales	1,145,400,000	1,032,100,000	820,200,000
Goodwill Impairment		0
Industrial Systems
Segment Reporting Information [Line Items]
Net Sales	616,000,000.0	576,300,000	528,800,000
Goodwill Impairment		33,000,000.0
Climate Solutions
Segment Reporting Information [Line Items]
Net Sales	1,081,800,000	1,030,600,000	846,800,000
Goodwill Impairment		0
Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales	2,374,700,000	1,171,300,000	711,200,000
Goodwill Impairment		0
Intersegment Eliminations
Segment Reporting Information [Line Items]
Net Sales	33,600,000	138,500,000	111,500,000
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales	(23,000,000.0)	(88,700,000)	(62,500,000)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales	(1,000,000.0)	(26,600,000)	(27,700,000)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales	(4,300,000)	(19,100,000)	(18,800,000)
Intersegment Eliminations | Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales	(5,300,000)	(4,100,000)	(2,500,000)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Net Sales	1,168,400,000	1,120,800,000	882,700,000
Gross Profit*	328,200,000	274,200,000	212,800,000
Operating Expenses	162,500,000	161,100,000	144,900,000
Goodwill Impairment		0	0
Asset Impairments	0	1,800,000	2,800,000
Gain on Sale of Business			(100,000)
Income (Loss) from Operations*	165,700,000	111,300,000	65,200,000
Depreciation and Amortization	29,300,000	29,900,000	32,600,000
Capital Expenditures	20,700,000	17,800,000	15,300,000
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Net Sales	617,000,000.0	602,900,000	556,500,000
Gross Profit*	152,700,000	107,600,000	94,600,000
Operating Expenses	97,700,000	88,000,000.0	91,600,000
Goodwill Impairment		33,000,000.0	10,500,000
Asset Impairments	0	0	200,000
Gain on Sale of Business			0
Income (Loss) from Operations*	55,000,000.0	(13,400,000)	(7,700,000)
Depreciation and Amortization	13,800,000	23,200,000	23,900,000
Capital Expenditures	10,400,000	9,500,000	8,100,000
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Net Sales	1,086,100,000	1,049,700,000	865,600,000
Gross Profit*	282,900,000	312,300,000	246,900,000
Operating Expenses	121,700,000	115,500,000	115,500,000
Goodwill Impairment		0	0
Asset Impairments	0	500,000	1,300,000
Gain on Sale of Business			0
Income (Loss) from Operations*	161,200,000	196,300,000	130,100,000
Depreciation and Amortization	17,600,000	16,500,000	19,600,000
Capital Expenditures	21,200,000	11,700,000	12,100,000
Operating Segments | Motion Control Solutions
Segment Reporting Information [Line Items]
Net Sales	2,380,000,000	1,175,400,000	713,700,000
Gross Profit*	905,900,000	417,500,000	252,300,000
Operating Expenses	596,500,000	350,100,000	160,900,000
Goodwill Impairment		0	0
Asset Impairments	900,000	3,300,000	1,000,000.0
Gain on Sale of Business			0
Income (Loss) from Operations*	308,500,000	64,100,000	90,400,000
Depreciation and Amortization	246,700,000	101,000,000.0	55,300,000
Capital Expenditures	$ 31,500,000	$ 15,500,000	$ 12,000,000.0