Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	6 Months Ended
	Mar. 31, 2022 USD ($)
Goodwill
Balance at beginning of period	$ 3,625.9
Acquisition of businesses	11.7
Translation and other	(17.4)
Balance at end of period	3,620.2
Intelligent Devices
Goodwill
Balance at beginning of period	543.1
Acquisition of businesses	0.0
Translation and other	(6.9)
Balance at end of period	536.2
Software & Control
Goodwill
Balance at beginning of period	2,447.5
Acquisition of businesses	0.0
Translation and other	(6.2)
Balance at end of period	2,441.3
Lifecycle Services
Goodwill
Balance at beginning of period	635.3
Acquisition of businesses	11.7
Translation and other	(4.3)
Balance at end of period	$ 642.7