GOODWILL AND OTHER INTANGIBLE ASSETS - Goodwill (Details) $ in Millions	9 Months Ended
	Oct. 01, 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	11.0
Impairments	0.0
Accumulated impairment	0.0
Goodwill, impairment, net of accumulation	0.0
Gross goodwill related to foreign currency translation	(38.6)
Accumulated impairments related to foreign currency translation	18.9
Goodwill related to foreign currency translation	(19.7)
Gross goodwill, end of the period	926.2
Accumulated impairment, balance at the end of the period	(477.6)
Goodwill, balance at the end of the period	448.6
International Tower Lighting, LLC
Changes in the carrying amount of goodwill
Goodwill Resulting from Business Combinations	10.7
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	(18.6)
Accumulated impairments related to foreign currency translation	13.1
Goodwill related to foreign currency translation	(5.5)
Gross goodwill, end of the period	510.4
Accumulated impairment, balance at the end of the period	(321.0)
Goodwill, balance at the end of the period	189.4
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	10.9
Impairments	0.0
Accumulated impairment	0.0
Goodwill, impairment, net of accumulation	0.0
Gross goodwill related to foreign currency translation	(20.0)
Accumulated impairments related to foreign currency translation	5.8
Goodwill related to foreign currency translation	(14.2)
Gross goodwill, end of the period	415.8
Accumulated impairment, balance at the end of the period	(156.6)
Goodwill, balance at the end of the period	$ 259.2