Business Segment Information - Sales and Operating Results (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Sales and operating results of reportable segments
Sales	$ 2,126.0	$ 2,275.4	$ 4,178.1	$ 4,256.4
Purchase accounting depreciation and amortization	(37.1)	(26.6)	(72.7)	(52.6)
Corporate and other	(28.2)	(29.2)	(68.2)	(56.5)
Non-operating pension and postretirement benefit credit (cost)	4.9	(105.4)	9.8	(93.0)
Change in fair value of investments	2.8	63.0	5.9	203.6
Interest expense, net	(36.2)	(34.5)	(64.5)	(67.3)
Income before income taxes	310.4	351.4	570.0	819.3
Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	404.2	484.1	759.7	885.1
Intelligent Devices
Sales and operating results of reportable segments
Sales	973.5	1,023.2	1,900.8	1,959.4
Intelligent Devices | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	161.0	206.9	311.2	416.3
Software & Control
Sales and operating results of reportable segments
Sales	570.0	741.1	1,173.6	1,314.4
Software & Control | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	146.3	249.3	297.3	416.6
Lifecycle Services
Sales and operating results of reportable segments
Sales	582.5	511.1	1,103.7	982.6
Lifecycle Services | Operating Segments
Sales and operating results of reportable segments
Segment operating earnings	$ 96.9	$ 27.9	$ 151.2	$ 52.2