SEGMENT INFORMATION (Details)	3 Months Ended		9 Months Ended
	Sep. 30, 2022 USD ($)	Oct. 02, 2021 USD ($)	Sep. 30, 2022 USD ($) segment	Oct. 02, 2021 USD ($)	Jan. 01, 2022 USD ($)
Segment Reporting Information [Line Items]
Number of operating segments | segment			4
Total Sales	$ 1,325,300,000	$ 892,700,000	$ 3,973,200,000	$ 2,593,700,000
Gross Profit	407,700,000	268,100,000	1,263,100,000	775,600,000
Operating Expenses	233,800,000	144,400,000	724,400,000	432,900,000
Asset Impairments	0	2,800,000	0	5,100,000
Total Operating Expenses	233,800,000	147,200,000	724,400,000	438,000,000.0
Income from Operations	173,900,000	120,900,000	538,700,000	337,600,000
Depreciation and Amortization	74,100,000	30,500,000	230,400,000	92,800,000
Capital Expenditures	22,000,000.0	13,200,000	54,600,000	37,500,000
Assets	10,249,000,000		10,249,000,000		$ 10,367,400,000
Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	289,900,000	268,700,000	885,100,000	775,000,000.0
Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	163,500,000	148,000,000.0	462,900,000	429,600,000
Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	279,200,000	268,400,000	846,600,000	764,800,000
Motion Control Solutions
Segment Reporting Information [Line Items]
Total Sales	592,700,000	207,600,000	1,778,600,000	624,300,000
Intersegment Eliminations
Segment Reporting Information [Line Items]
Total Sales	10,200,000	35,300,000	26,300,000	94,600,000
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	(7,800,000)	(22,500,000)	(18,300,000)	(59,900,000)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	(300,000)	(7,700,000)	(800,000)	(18,700,000)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	(800,000)	(4,400,000)	(3,300,000)	(13,800,000)
Intersegment Eliminations | Motion Control Solutions
Segment Reporting Information [Line Items]
Total Sales	(1,300,000)	(700,000)	(3,900,000)	(2,200,000)
Operating Segments
Segment Reporting Information [Line Items]
Assets	10,249,000,000		10,249,000,000		10,367,400,000
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	297,700,000	291,200,000	903,400,000	834,900,000
Gross Profit	78,200,000	75,800,000	254,600,000	212,100,000
Operating Expenses	38,700,000	40,400,000	120,500,000	118,700,000
Asset Impairments		0		1,800,000
Total Operating Expenses	38,700,000	40,400,000	120,500,000	120,500,000
Income from Operations	39,500,000	35,400,000	134,100,000	91,600,000
Depreciation and Amortization	7,200,000	7,200,000	22,300,000	22,800,000
Capital Expenditures	5,200,000	4,800,000	14,000,000.0	12,600,000
Assets	1,256,800,000		1,256,800,000		1,264,000,000
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	163,800,000	155,700,000	463,700,000	448,300,000
Gross Profit	40,200,000	28,400,000	115,500,000	83,800,000
Operating Expenses	24,500,000	19,500,000	70,700,000	65,700,000
Asset Impairments		0		0
Total Operating Expenses	24,500,000	19,500,000	70,700,000	65,700,000
Income from Operations	15,700,000	8,900,000	44,800,000	18,100,000
Depreciation and Amortization	3,300,000	5,800,000	10,300,000	17,400,000
Capital Expenditures	2,400,000	2,300,000	6,600,000	8,000,000.0
Assets	874,100,000		874,100,000		859,900,000
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	280,000,000.0	272,800,000	849,900,000	778,600,000
Gross Profit	61,200,000	84,700,000	219,000,000.0	235,600,000
Operating Expenses	29,800,000	29,100,000	91,800,000	86,800,000
Asset Impairments		0		500,000
Total Operating Expenses	29,800,000	29,100,000	91,800,000	87,300,000
Income from Operations	31,400,000	55,600,000	127,200,000	148,300,000
Depreciation and Amortization	4,400,000	4,400,000	13,200,000	12,500,000
Capital Expenditures	7,200,000	2,500,000	16,100,000	8,700,000
Assets	1,005,000,000		1,005,000,000		982,700,000
Operating Segments | Motion Control Solutions
Segment Reporting Information [Line Items]
Total Sales	594,000,000.0	208,300,000	1,782,500,000	626,500,000
Gross Profit	228,100,000	79,200,000	674,000,000.0	244,100,000
Operating Expenses	140,800,000	55,400,000	441,400,000	161,700,000
Asset Impairments		2,800,000		2,800,000
Total Operating Expenses	140,800,000	58,200,000	441,400,000	164,500,000
Income from Operations	87,300,000	21,000,000.0	232,600,000	79,600,000
Depreciation and Amortization	59,200,000	13,100,000	184,600,000	40,100,000
Capital Expenditures	7,200,000	$ 3,600,000	17,900,000	$ 8,200,000
Assets	$ 7,113,100,000		$ 7,113,100,000		$ 7,260,800,000