Segment Reporting (Details) - USD ($)	3 Months Ended		9 Months Ended
	Jun. 30, 2020	Jun. 30, 2019	Jun. 30, 2020	Jun. 30, 2019
Segment Reporting Information [Line Items]
Revenues	$ 767,500,000	$ 726,800,000	$ 2,175,700,000	$ 2,124,500,000
Special charges	9,500,000	6,200,000	26,100,000	17,700,000
Operating profit	135,300,000	69,900,000	301,500,000	222,000,000.0
Interest expense	(17,300,000)	(23,100,000)	(55,800,000)	(66,200,000)
Gain (Loss) on Extinguishment of Debt	0	0	(15,600,000)	0
Investment income (expense) and other, net	2,200,000	(1,100,000)	(10,500,000)	200,000
Income Before Income Taxes	120,200,000	45,700,000	219,600,000	156,000,000.0
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Non-allocated operating costs, administrative and other	70,200,000	94,700,000	198,300,000	218,400,000
Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	767,500,000	726,800,000	2,175,700,000	2,124,500,000
Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	447,800,000	374,500,000	1,174,000,000.0	1,075,100,000
Divisional Income	129,200,000	83,500,000	262,400,000	215,400,000
Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	252,100,000	244,400,000	765,000,000.0	720,900,000
Divisional Income	81,100,000	69,500,000	232,500,000	198,500,000
Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	67,600,000	107,900,000	236,700,000	328,500,000
Divisional Income	4,700,000	17,800,000	31,000,000.0	44,200,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	507,200,000	529,400,000	1,495,600,000	1,490,900,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	316,900,000	290,800,000	872,800,000	806,100,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	167,800,000	178,400,000	525,200,000	515,100,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	22,500,000	60,200,000	97,600,000	169,700,000
Non-US [Member] | Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	260,300,000	197,400,000	680,100,000	633,600,000
Non-US [Member] | Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	130,900,000	83,700,000	301,200,000	269,000,000.0
Non-US [Member] | Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	84,300,000	66,000,000.0	239,800,000	205,800,000
Non-US [Member] | Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	$ 45,100,000	$ 47,700,000	$ 139,100,000	$ 158,800,000