SEGMENT INFORMATION (Details) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 02, 2021 USD ($)	Sep. 26, 2020 USD ($)	Oct. 02, 2021 USD ($) segment	Sep. 26, 2020 USD ($)	Jan. 02, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of operating segments | segment			4
Total Sales	$ 892.7	$ 758.2	$ 2,593.7	$ 2,126.5
Gross Profit	254.6	221.6	751.5	595.2
Operating Expenses	144.4	131.6	432.9	385.1
Gain on Divestitures	0.0	0.0	0.0	(0.1)
Asset Impairments	2.8	0.0	5.1	4.3
Total Operating Expenses	147.2	131.6	438.0	389.3
Income from Operations	107.4	90.0	313.5	205.9
Depreciation and Amortization	30.5	32.9	92.8	98.8
Capital Expenditures	13.2	9.3	37.5	29.7
Assets	4,485.0		4,485.0		$ 4,589.0
Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	268.7	218.5	775.0	593.8
Assets	1,217.1		1,217.1		1,319.6
Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	148.0	138.8	429.6	389.0
Assets	846.2		846.2		837.5
Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	268.4	234.0	764.8	622.3
Assets	924.6		924.6		890.4
Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	207.6	166.9	624.3	521.4
Assets	1,497.1		1,497.1		$ 1,541.5
Intersegment Eliminations
Segment Reporting Information [Line Items]
Total Sales	35.3	27.1	94.6	81.3
Intersegment Eliminations | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	(22.5)	(14.5)	(59.9)	(43.2)
Intersegment Eliminations | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	(7.7)	(7.4)	(18.7)	(23.2)
Intersegment Eliminations | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	(4.4)	(4.6)	(13.8)	(13.0)
Intersegment Eliminations | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	(0.7)	(0.6)	(2.2)	(1.9)
Operating Segments | Commercial Systems
Segment Reporting Information [Line Items]
Total Sales	291.2	233.0	834.9	637.0
Gross Profit	70.8	60.7	203.8	153.4
Operating Expenses	40.4	36.1	118.7	107.8
Gain on Divestitures				(0.1)
Asset Impairments	0.0		1.8	2.8
Total Operating Expenses	40.4		120.5	110.5
Income from Operations	30.4	24.6	83.3	42.9
Depreciation and Amortization	7.2	7.9	22.8	24.5
Capital Expenditures	4.8	3.2	12.6	8.5
Operating Segments | Industrial Systems
Segment Reporting Information [Line Items]
Total Sales	155.7	146.2	448.3	412.2
Gross Profit	25.9	31.9	78.9	79.8
Operating Expenses	19.5	24.6	65.7	69.2
Gain on Divestitures				0.0
Asset Impairments	0.0		0.0	0.2
Total Operating Expenses	19.5		65.7	69.4
Income from Operations	6.4	7.3	13.2	10.4
Depreciation and Amortization	5.8	6.0	17.4	17.9
Capital Expenditures	2.3	1.7	8.0	6.0
Operating Segments | Climate Solutions
Segment Reporting Information [Line Items]
Total Sales	272.8	238.6	778.6	635.3
Gross Profit	81.2	69.1	229.2	175.9
Operating Expenses	29.1	29.9	86.8	85.9
Gain on Divestitures				0.0
Asset Impairments	0.0		0.5	1.3
Total Operating Expenses	29.1		87.3	87.2
Income from Operations	52.1	39.2	141.9	88.7
Depreciation and Amortization	4.4	5.0	12.5	14.7
Capital Expenditures	2.5	1.8	8.7	8.0
Operating Segments | Power Transmission Solutions
Segment Reporting Information [Line Items]
Total Sales	208.3	167.5	626.5	523.3
Gross Profit	76.7	59.9	239.6	186.1
Operating Expenses	55.4	41.0	161.7	122.2
Gain on Divestitures				0.0
Asset Impairments	2.8		2.8	0.0
Total Operating Expenses	58.2		164.5	122.2
Income from Operations	18.5	18.9	75.1	63.9
Depreciation and Amortization	13.1	14.0	40.1	41.7
Capital Expenditures	$ 3.6	$ 2.6	$ 8.2	$ 7.2