SEGMENT INFORMATION (Details)	3 Months Ended
	Apr. 03, 2021 USD ($) segment	Mar. 28, 2020 USD ($)	Jan. 02, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of operating segments | segment	4
Total Sales	$ 814,100,000	$ 734,200,000
Gross Profit	245,400,000	203,300,000
Operating Expenses	148,300,000	131,900,000
Gain on Divestitures	0	(100,000)
Asset Impairments	0	1,500,000
Total Operating Expenses	148,300,000	133,300,000
Income from Operations	97,100,000	70,000,000.0
Depreciation and Amortization	31,800,000	32,600,000
Capital Expenditures	10,700,000	10,900,000
Assets	4,627,200,000		$ 4,589,000,000.0
Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	237,000,000.0	199,400,000
Assets	1,324,200,000		1,319,600,000
Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	136,400,000	129,600,000
Assets	847,400,000		837,500,000
Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	239,100,000	210,100,000
Assets	934,600,000		890,400,000
Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	201,600,000	195,100,000
Assets	1,521,000,000.0		$ 1,541,500,000
Intersegment Eliminations
Segment Reporting Information [Line Items]
Total Sales	26,200,000	23,700,000
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	(17,500,000)	(11,800,000)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	(3,700,000)	(6,700,000)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	(4,300,000)	(4,500,000)
Intersegment Eliminations | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	(700,000)	(700,000)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	254,500,000	211,200,000
Gross Profit	65,500,000	50,300,000
Operating Expenses	38,000,000.0	37,500,000
Gain on Divestitures		(100,000)
Asset Impairments		800,000
Total Operating Expenses		38,200,000
Income from Operations	27,500,000	12,100,000
Depreciation and Amortization	7,800,000	8,300,000
Capital Expenditures	3,300,000	3,100,000
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	140,100,000	136,300,000
Gross Profit	26,800,000	23,000,000.0
Operating Expenses	23,100,000	22,900,000
Gain on Divestitures		0
Asset Impairments		200,000
Total Operating Expenses		23,100,000
Income from Operations	3,700,000	(100,000)
Depreciation and Amortization	5,900,000	5,900,000
Capital Expenditures	2,400,000	2,000,000.0
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	243,400,000	214,600,000
Gross Profit	74,000,000.0	59,400,000
Operating Expenses	30,700,000	29,400,000
Gain on Divestitures		0
Asset Impairments		500,000
Total Operating Expenses		29,900,000
Income from Operations	43,300,000	29,500,000
Depreciation and Amortization	4,500,000	4,700,000
Capital Expenditures	3,200,000	3,600,000
Operating Segments | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	202,300,000	195,800,000
Gross Profit	79,100,000	70,600,000
Operating Expenses	56,500,000	42,100,000
Gain on Divestitures		0
Asset Impairments		0
Total Operating Expenses		42,100,000
Income from Operations	22,600,000	28,500,000
Depreciation and Amortization	13,600,000	13,700,000
Capital Expenditures	$ 1,800,000	$ 2,200,000