Segment Reporting (Schedule of Segment Information) (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Net Revenue - United States:
Revenues	$ 3,018.7	$ 2,881.0	$ 2,907.3
Divisional income:
Divisional income	400.2	367.7	316.1
Other operating costs:
Other operating costs	400.2	367.7	316.1
Special charge	47.4	41.5	28.4
Interest expense	(65.6)	(74.0)	(89.6)
Loss on extinguishment of debt	(9.8)	(15.6)	(3.0)
Investment income (expense) and other, net	(22.0)	(6.9)	(14.6)
Income before income taxes	302.8	271.2	208.6
Depreciation, Depletion and Amortization	185.8	178.8	194.8
Extinguishment of Debt, Amount			(3.3)
Non-US [Member]
Net Revenue - United States:
Revenues	920.5	914.2	850.5
Corporate, Non-Segment [Member]
Other operating costs:
Depreciation, Depletion and Amortization	35.4	32.5	28.3
Patient Support Systems [Member]
Other operating costs:
Depreciation, Depletion and Amortization	52.0	43.5	36.2
Front Line Care [Member]
Other operating costs:
Depreciation, Depletion and Amortization	90.0	95.4	101.9
Surgical Solutions [Member]
Other operating costs:
Depreciation, Depletion and Amortization	8.4	7.4	28.4
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Non-allocated operating costs, administrative and other	308.9	264.4	283.0
Operating Segments [Member]
Net Revenue - United States:
Revenues	3,018.7	2,881.0	2,907.3
Operating Segments [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues	2,098.2	1,966.8	2,056.8
Operating Segments [Member] | Non-US [Member]
Net Revenue - United States:
Revenues	920.5	914.2	850.5
Operating Segments [Member] | Patient Support Systems [Member]
Net Revenue - United States:
Revenues	1,568.3	1,539.1	1,490.5
Divisional Income	356.1	332.3	299.9
Operating Segments [Member] | Patient Support Systems [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues	1,162.1	1,133.6	1,135.0
Operating Segments [Member] | Patient Support Systems [Member] | Non-US [Member]
Net Revenue - United States:
Revenues	406.2	405.5	355.5
Operating Segments [Member] | Front Line Care [Member]
Net Revenue - United States:
Revenues	1,117.0	1,025.0	978.1
Divisional Income	348.8	301.8	266.4
Operating Segments [Member] | Front Line Care [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues	785.7	707.4	700.6
Operating Segments [Member] | Front Line Care [Member] | Non-US [Member]
Net Revenue - United States:
Revenues	331.3	317.6	277.5
Operating Segments [Member] | Surgical Solutions [Member]
Net Revenue - United States:
Revenues	333.4	316.9	438.7
Divisional Income	51.6	39.5	61.2
Operating Segments [Member] | Surgical Solutions [Member] | Geographic Distribution, Domestic
Net Revenue - United States:
Revenues	150.4	125.8	221.2
Operating Segments [Member] | Surgical Solutions [Member] | Non-US [Member]
Net Revenue - United States:
Revenues	$ 183.0	$ 191.1	$ 217.5