Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Goodwill
Beginning balance	$ 3,529.2	$ 3,524.0
Acquisition of businesses	416.6	111.3
Goodwill impairment	0.0	(157.5)	$ 0.0
Translation	47.5	51.4
Ending balance	3,993.3	3,529.2	3,524.0
Gross carrying value of Goodwill	4,150.8
Accumulated impairment losses	(157.5)
Intelligent Devices
Goodwill
Beginning balance	595.8	503.0
Acquisition of businesses	283.1	74.4
Goodwill impairment		0.0
Translation	21.6	18.4
Ending balance	900.5	595.8	503.0
Gross carrying value of Goodwill	900.5
Accumulated impairment losses	0.0
Software & Control
Goodwill
Beginning balance	2,420.1	2,398.7
Acquisition of businesses	0.0	0.0
Goodwill impairment		0.0
Translation	17.0	21.4
Ending balance	2,437.1	2,420.1	2,398.7
Gross carrying value of Goodwill	2,437.1
Accumulated impairment losses	0.0
Lifecycle Services
Goodwill
Beginning balance	513.3	622.3
Acquisition of businesses	133.5	36.9
Goodwill impairment		(157.5)
Translation	8.9	11.6
Ending balance	655.7	$ 513.3	$ 622.3
Gross carrying value of Goodwill	813.2
Accumulated impairment losses	$ (157.5)