Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	3 Months Ended
	Dec. 31, 2022 USD ($)
Goodwill
Balance at beginning of period	$ 3,524.0
Acquisition of business	64.5
Translation	52.1
Balance at end of period	3,640.6
Intelligent Devices
Goodwill
Balance at beginning of period	503.0
Acquisition of business	64.5
Translation	19.1
Balance at end of period	586.6
Software & Control
Goodwill
Balance at beginning of period	2,398.7
Acquisition of business	0.0
Translation	22.4
Balance at end of period	2,421.1
Lifecycle Services
Goodwill
Balance at beginning of period	622.3
Acquisition of business	0.0
Translation	10.6
Balance at end of period	$ 632.9