Goodwill and Intangible Assets (Schedule of Amortizable Intangible Assets) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2023	Mar. 31, 2022	Mar. 31, 2023	Mar. 31, 2022	Sep. 30, 2022
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	$ 686.3		$ 686.3		$ 684.3
Amortizable intangible assets, accumulated amortization	290.8		290.8		274.7
Amortizable intangible assets, net	395.5		395.5		409.5
Amortization of intangibles	7.7	$ 7.9	15.4	$ 14.0
Amortizable intangible assets, amortization expense, remainder of 2023	15.4		15.4
Amortizable intangible assets, amortization expense, fiscal 2024	30.7		30.7
Amortizable intangible assets, amortization expense, fiscal 2025	30.7		30.7
Amortizable intangible assets, amortization expense, fiscal 2026	30.5		30.5
Amortizable intangible assets, amortization expense, fiscal 2027	30.4		30.4
Amortizable intangible assets, amortization expense, fiscal 2028	30.3		30.3
Amortizable intangible assets, amortization expense, after fiscal 2028	227.5		227.5
Indefinite-lived Intangible Assets [Line Items]
Indefinite-lived intangible assets	594.6		594.6		587.1
Trade names and brands
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	339.7		339.7		339.4
Amortizable intangible assets, accumulated amortization	80.4		80.4		72.2
Amortizable intangible assets, net	259.3		259.3		267.2
Technology and patents
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	78.5		78.5		77.8
Amortizable intangible assets, accumulated amortization	76.0		76.0		75.0
Amortizable intangible assets, net	2.5		2.5		2.8
Customer related and other
Finite-Lived Intangible Assets [Line Items]
Amortizable intangible assets, gross carrying amount	268.1		268.1		267.1
Amortizable intangible assets, accumulated amortization	134.4		134.4		127.5
Amortizable intangible assets, net	$ 133.7		$ 133.7		$ 139.6