Accounting Policies (Narrative) (Details)	3 Months Ended								12 Months Ended
	Jan. 01, 2022 USD ($)	Oct. 02, 2021 USD ($)	Jul. 03, 2021 USD ($)	Apr. 03, 2021 USD ($)	Jan. 02, 2021 USD ($)	Sep. 26, 2020 USD ($)	Jun. 27, 2020 USD ($)	Mar. 28, 2020 USD ($)	Jan. 01, 2022 USD ($) segment	Jan. 02, 2021 USD ($)	Dec. 28, 2019 USD ($)	Dec. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)	Dec. 29, 2018 USD ($)
Property, Plant and Equipment [Line Items]
Number of operating segments (in segment) | segment									4
Payment terms									due upon delivery to 120 days after delivery
Amortization period	12 months								12 months
Research development and engineering costs									$ 74,500,000	$ 67,000,000.0	$ 64,600,000
Goodwill Impairment	$ 33,000,000.0								33,000,000.0	10,500,000	0
Impairment of long-lived assets									5,600,000	5,300,000
Goodwill	4,039,200,000				$ 1,518,200,000				4,039,200,000	1,518,200,000	1,501,300,000
Net Sales	1,216,600,000	$ 892,700,000	$ 886,900,000	$ 814,100,000	780,500,000	$ 758,200,000	$ 634,100,000	$ 734,200,000	3,810,300,000	2,907,000,000	3,238,000,000
Allowance for doubtful accounts receivable	18,700,000				18,300,000				18,700,000	18,300,000
Decrease to retained earnings	(6,350,100,000)				(2,577,000,000)				(6,350,100,000)	(2,577,000,000)	(2,380,400,000)			$ (2,338,500,000)
Right-of-use asset	112,400,000				73,400,000				112,400,000	73,400,000
Lease liabilities	116,700,000								116,700,000
Accounting Standards Update 2016-02
Property, Plant and Equipment [Line Items]
Right-of-use asset													$ 93,000,000
Lease liabilities													$ 93,000,000
Global Industrial Motors
Property, Plant and Equipment [Line Items]
Goodwill	80,100,000								80,100,000
Adjustment
Property, Plant and Equipment [Line Items]
Allowance for doubtful accounts receivable												$ 3,400,000
Decrease to retained earnings											2,700,000
Disposal Group, Disposed of by Sale, Not Discontinued Operations
Property, Plant and Equipment [Line Items]
Impairment of long-lived assets										5,300,000
Customer Relationships | Hermetic Climate | Disposal Group, Disposed of by Sale, Not Discontinued Operations
Property, Plant and Equipment [Line Items]
Asset Impairments									0	0
Retained Earnings
Property, Plant and Equipment [Line Items]
Decrease to retained earnings	$ (1,854,500,000)				$ (2,010,700,000)				$ (1,854,500,000)	$ (2,010,700,000)	(1,886,700,000)			$ (1,777,900,000)
Retained Earnings | Adjustment
Property, Plant and Equipment [Line Items]
Decrease to retained earnings											$ 2,700,000	$ 2,700,000