Goodwill and Intangible Assets (Schedule of Accumulated Amortization) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Finite-lived Intangible Assets [Roll Forward]
Accumulated Amortization, Beginning balance	$ 501.7
Amortization	77.4	$ 47.3	$ 50.3
Translation Adjustments	(6.2)
Accumulated Amortization, Ending balance	572.9	501.7
Intangible Assets, Net of Amortization	2,429.2	530.3
Customer Relationships
Finite-lived Intangible Assets [Roll Forward]
Accumulated Amortization, Beginning balance	349.4
Amortization	60.7
Translation Adjustments	(5.1)
Accumulated Amortization, Ending balance	405.0	349.4
Technology
Finite-lived Intangible Assets [Roll Forward]
Accumulated Amortization, Beginning balance	108.0
Amortization	6.5
Translation Adjustments	(0.4)
Accumulated Amortization, Ending balance	114.1	108.0
Trademarks
Finite-lived Intangible Assets [Roll Forward]
Accumulated Amortization, Beginning balance	27.7
Amortization	10.2
Translation Adjustments	(0.7)
Accumulated Amortization, Ending balance	37.2	27.7
Patent and Engineering Drawings
Finite-lived Intangible Assets [Roll Forward]
Accumulated Amortization, Beginning balance	16.6
Amortization	0.0
Translation Adjustments	0.0
Accumulated Amortization, Ending balance	$ 16.6	$ 16.6