GOODWILL AND OTHER INTANGIBLE ASSETS - Goodwill (Details) $ in Millions	6 Months Ended
	Jul. 02, 2022 USD ($)
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	$ 953.8
Accumulated impairment, balance at the beginning of the period	(496.5)
Goodwill, balance at the beginning of the period	457.3
Goodwill Resulting from Business Combinations	12.3
Impairments	0.0
Accumulated impairment	0.0
Goodwill, impairment, net of accumulation	0.0
Gross goodwill related to foreign currency translation	(19.6)
Accumulated impairments related to foreign currency translation	9.7
Goodwill related to foreign currency translation	(9.9)
Gross goodwill, end of the period	946.5
Accumulated impairment, balance at the end of the period	(486.8)
Goodwill, balance at the end of the period	459.7
International Tower Lighting, LLC
Changes in the carrying amount of goodwill
Goodwill Resulting from Business Combinations	12.0
Sealite Acquisition
Changes in the carrying amount of goodwill
Increase in goodwill	0.2
Cincinnati Fan
Changes in the carrying amount of goodwill
Increase in goodwill	0.1
HVAC reportable segment
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	528.9
Accumulated impairment, balance at the beginning of the period	(334.1)
Goodwill, balance at the beginning of the period	194.8
Goodwill Resulting from Business Combinations	0.1
Impairments	0.0
Accumulated impairment	0.0
Goodwill, impairment, net of accumulation	0.0
Gross goodwill related to foreign currency translation	(9.7)
Accumulated impairments related to foreign currency translation	6.8
Goodwill related to foreign currency translation	(2.9)
Gross goodwill, end of the period	519.3
Accumulated impairment, balance at the end of the period	(327.3)
Goodwill, balance at the end of the period	192.0
Detection and Measurement reportable segment
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	424.9
Accumulated impairment, balance at the beginning of the period	(162.4)
Goodwill, balance at the beginning of the period	262.5
Goodwill Resulting from Business Combinations	12.2
Impairments	0.0
Accumulated impairment	0.0
Goodwill, impairment, net of accumulation	0.0
Gross goodwill related to foreign currency translation	(9.9)
Accumulated impairments related to foreign currency translation	2.9
Goodwill related to foreign currency translation	(7.0)
Gross goodwill, end of the period	427.2
Accumulated impairment, balance at the end of the period	(159.5)
Goodwill, balance at the end of the period	$ 267.7