SEGMENT INFORMATION (Details) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 03, 2021 USD ($)	Jun. 27, 2020 USD ($)	Jul. 03, 2021 USD ($) segment	Jun. 27, 2020 USD ($)	Jan. 02, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of operating segments | segment			4
Total Sales	$ 886.9	$ 634.1	$ 1,701.0	$ 1,368.3
Gross Profit	251.5	170.3	496.9	373.6
Operating Expenses	140.2	121.6	288.5	253.5
Gain on Divestitures	0.0	0.0	0.0	(0.1)
Asset Impairments	2.3	2.8	2.3	4.3
Total Operating Expenses	142.5	124.4	290.8	257.7
Income from Operations	109.0	45.9	206.1	115.9
Depreciation and Amortization	30.5	33.3	62.3	65.9
Capital Expenditures	13.6	9.5	24.3	20.4
Assets	4,773.7		4,773.7		$ 4,589.0
Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	269.3	175.9	506.3	375.3
Assets	1,390.5		1,390.5		1,319.6
Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	145.2	120.6	281.6	250.2
Assets	870.2		870.2		837.5
Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	257.3	178.2	496.4	388.3
Assets	966.1		966.1		890.4
Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	215.1	159.4	416.7	354.5
Assets	1,546.9		1,546.9		$ 1,541.5
Intersegment Eliminations
Segment Reporting Information [Line Items]
Total Sales	33.1	30.5	59.3	54.2
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	(19.9)	(16.9)	(37.4)	(28.7)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	(7.3)	(9.1)	(11.0)	(15.8)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	(5.1)	(3.9)	(9.4)	(8.4)
Intersegment Eliminations | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	(0.8)	(0.6)	(1.5)	(1.3)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	289.2	192.8	543.7	404.0
Gross Profit	67.5	42.4	133.0	92.7
Operating Expenses	40.3	34.2	78.3	71.7
Gain on Divestitures				(0.1)
Asset Impairments	1.8	2.0	1.8	2.8
Total Operating Expenses	42.1	36.2	80.1	74.4
Income from Operations	25.4	6.2	52.9	18.3
Depreciation and Amortization	7.8	8.3	15.6	16.6
Capital Expenditures	4.5	2.2	7.8	5.3
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	152.5	129.7	292.6	266.0
Gross Profit	26.2	24.9	53.0	47.9
Operating Expenses	23.1	21.7	46.2	44.6
Gain on Divestitures				0.0
Asset Impairments	0.0	0.0	0.0	0.2
Total Operating Expenses	23.1	21.7	46.2	44.8
Income from Operations	3.1	3.2	6.8	3.1
Depreciation and Amortization	5.7	6.0	11.6	11.9
Capital Expenditures	3.3	2.3	5.7	4.3
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	262.4	182.1	505.8	396.7
Gross Profit	74.0	47.4	148.0	106.8
Operating Expenses	27.0	26.6	57.7	56.0
Gain on Divestitures				0.0
Asset Impairments	0.5	0.8	0.5	1.3
Total Operating Expenses	27.5	27.4	58.2	57.3
Income from Operations	46.5	20.0	89.8	49.5
Depreciation and Amortization	3.6	5.0	8.1	9.7
Capital Expenditures	3.0	2.6	6.2	6.2
Operating Segments | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	215.9	160.0	418.2	355.8
Gross Profit	83.8	55.6	162.9	126.2
Operating Expenses	49.8	39.1	106.3	81.2
Gain on Divestitures				0.0
Asset Impairments	0.0	0.0	0.0	0.0
Total Operating Expenses	49.8	39.1	106.3	81.2
Income from Operations	34.0	16.5	56.6	45.0
Depreciation and Amortization	13.4	14.0	27.0	27.7
Capital Expenditures	$ 2.8	$ 2.4	$ 4.6	$ 4.6