Goodwill (Schedule of Goodwill by Segment) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
Goodwill [Roll Forward]
Goodwill, net, beginning balance	$ 823.0	$ 911.5
Acquisitions		24.5
Currency translation and other	38.7	(113.0)
Goodwill, net, ending balance	861.7	823.0
Business combinations, tax deductible goodwill		3.2
Americas
Goodwill [Roll Forward]
Goodwill, net, beginning balance	143.2	151.0
Acquisitions		0.0
Currency translation and other	3.4	(7.8)
Goodwill, net, ending balance	146.6	143.2
Asia
Goodwill [Roll Forward]
Goodwill, net, beginning balance	172.7	184.3
Acquisitions		0.0
Currency translation and other	(0.8)	(11.6)
Goodwill, net, ending balance	171.9	172.7
Europe
Goodwill [Roll Forward]
Goodwill, net, beginning balance	457.5	533.5
Acquisitions		17.0
Currency translation and other	36.0	(93.0)
Goodwill, net, ending balance	493.5	457.5
Middle East and India
Goodwill [Roll Forward]
Goodwill, net, beginning balance	15.8	8.0
Acquisitions		7.5
Currency translation and other	0.0	0.3
Goodwill, net, ending balance	15.8	15.8
Corporate and other
Goodwill [Roll Forward]
Goodwill, net, beginning balance	33.8	34.7
Acquisitions		0.0
Currency translation and other	0.1	(0.9)
Goodwill, net, ending balance	$ 33.9	$ 33.8