GOODWILL AND OTHER INTANGIBLE ASSETS - Goodwill (Details) $ in Millions	6 Months Ended
	Jun. 27, 2020 USD ($)
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	$ 936.2
Accumulated impairment, balance at the beginning of the period	(486.9)
Goodwill, balance at the beginning of the period	449.3
Goodwill resulting from business combinations	(1.3)
Impairments	0.0
Gross goodwill related to foreign currency translation	(0.6)
Accumulated impairments related to foreign currency translation	1.0
Goodwill related to foreign currency translation	0.4
Gross goodwill, end of the period	936.9
Accumulated impairment, balance at the end of the period	(485.9)
Goodwill, balance at the end of the period	451.0
HVAC reportable segment
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	277.1
Accumulated impairment, balance at the beginning of the period	(144.6)
Goodwill, balance at the beginning of the period	132.5
Goodwill resulting from business combinations	(1.3)
Impairments	0.0
Gross goodwill related to foreign currency translation	(0.1)
Accumulated impairments related to foreign currency translation	0.3
Goodwill related to foreign currency translation	0.2
Gross goodwill, end of the period	278.3
Accumulated impairment, balance at the end of the period	(144.3)
Goodwill, balance at the end of the period	134.0
Detection and Measurement reportable segment
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	304.1
Accumulated impairment, balance at the beginning of the period	(133.6)
Goodwill, balance at the beginning of the period	170.5
Goodwill resulting from business combinations	0.0
Impairments	0.0
Gross goodwill related to foreign currency translation	(1.2)
Accumulated impairments related to foreign currency translation	1.4
Goodwill related to foreign currency translation	0.2
Gross goodwill, end of the period	302.9
Accumulated impairment, balance at the end of the period	(132.2)
Goodwill, balance at the end of the period	170.7
Engineered Solutions reportable segment
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	334.2
Accumulated impairment, balance at the beginning of the period	(187.9)
Goodwill, balance at the beginning of the period	146.3
Goodwill resulting from business combinations	0.0
Impairments	0.0
Gross goodwill related to foreign currency translation	0.7
Accumulated impairments related to foreign currency translation	(0.7)
Goodwill related to foreign currency translation	0.0
Gross goodwill, end of the period	334.9
Accumulated impairment, balance at the end of the period	(188.6)
Goodwill, balance at the end of the period	146.3
All Other
Changes in the carrying amount of goodwill
Gross goodwill, beginning of the period	20.8
Accumulated impairment, balance at the beginning of the period	(20.8)
Goodwill, balance at the beginning of the period	0.0
Goodwill resulting from business combinations	0.0
Impairments	0.0
Gross goodwill related to foreign currency translation	0.0
Accumulated impairments related to foreign currency translation	0.0
Goodwill related to foreign currency translation	0.0
Gross goodwill, end of the period	20.8
Accumulated impairment, balance at the end of the period	(20.8)
Goodwill, balance at the end of the period	0.0
Patterson-Kelley, LLC
Changes in the carrying amount of goodwill
Goodwill resulting from business combinations	(1.4)
Goodwill decrease	0.5
SGS Refrigeration Inc.
Changes in the carrying amount of goodwill
Goodwill resulting from business combinations	$ (0.4)