Goodwill (Schedule of Goodwill by Segment) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Goodwill [Roll Forward]
Goodwill, net, beginning balance	$ 911.5	$ 891.5
Acquisitions	24.5	21.0
Currency translation and other	(113.0)	(1.0)
Goodwill, net, ending balance	823.0	911.5
Business combinations, tax deductible goodwill	3.2
Americas
Goodwill [Roll Forward]
Goodwill, net, beginning balance	151.0	152.6
Acquisitions	0.0	0.0
Currency translation and other	(7.8)	(1.6)
Goodwill, net, ending balance	143.2	151.0
Asia
Goodwill [Roll Forward]
Goodwill, net, beginning balance	184.3	180.4
Acquisitions	0.0	0.0
Currency translation and other	(11.6)	3.9
Goodwill, net, ending balance	172.7	184.3
Europe
Goodwill [Roll Forward]
Goodwill, net, beginning balance	533.5	516.3
Acquisitions	17.0	21.0
Currency translation and other	(93.0)	(3.8)
Goodwill, net, ending balance	457.5	533.5
Middle East and India
Goodwill [Roll Forward]
Goodwill, net, beginning balance	8.0	7.8
Acquisitions	7.5	0.0
Currency translation and other	0.3	0.2
Goodwill, net, ending balance	15.8	8.0
Corporate and other
Goodwill [Roll Forward]
Goodwill, net, beginning balance	34.7	34.4
Acquisitions	0.0	0.0
Currency translation and other	(0.9)	0.3
Goodwill, net, ending balance	$ 33.8	$ 34.7