Segment Reporting (Details) - USD ($)	3 Months Ended		6 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2020	Mar. 31, 2019
Segment Reporting Information [Line Items]
Revenues	$ 723,200,000	$ 714,200,000	$ 1,408,200,000	$ 1,397,700,000
Special charges	8,800,000	3,500,000	16,600,000	11,500,000
Operating profit	87,300,000	81,300,000	166,200,000	152,100,000
Interest expense	(19,100,000)	(21,800,000)	(38,500,000)	(43,100,000)
Gain (Loss) on Extinguishment of Debt	0	0	(15,600,000)	0
Investment income (expense) and other, net	(11,400,000)	1,200,000	(12,700,000)	1,300,000
Income Before Income Taxes	56,800,000	60,700,000	99,400,000	110,300,000
Corporate and Other [Member]
Segment Reporting Information [Line Items]
Non-allocated operating costs, administrative and other	70,200,000	69,700,000	128,200,000	123,600,000
Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	723,200,000	714,200,000	1,408,200,000	1,397,700,000
Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	382,100,000	359,600,000	726,300,000	700,600,000
Divisional Income	74,900,000	72,200,000	133,300,000	131,900,000
Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	258,200,000	243,100,000	512,800,000	476,500,000
Divisional Income	77,700,000	67,200,000	151,200,000	128,900,000
Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	82,900,000	111,500,000	169,100,000	220,600,000
Divisional Income	13,700,000	15,100,000	26,500,000	26,400,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	506,500,000	493,000,000.0	988,300,000	961,500,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	289,300,000	267,200,000	555,900,000	515,300,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	179,200,000	170,200,000	357,300,000	336,700,000
Geographic Distribution, Domestic [Member] | Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	38,000,000.0	55,600,000	75,100,000	109,500,000
Non-US [Member] | Operating Segments [Member]
Segment Reporting Information [Line Items]
Revenues	216,700,000	221,200,000	419,900,000	436,200,000
Non-US [Member] | Operating Segments [Member] | Patient Support Systems [Member]
Segment Reporting Information [Line Items]
Revenues	92,800,000	92,400,000	170,400,000	185,300,000
Non-US [Member] | Operating Segments [Member] | Front Line Care [Member]
Segment Reporting Information [Line Items]
Revenues	79,000,000.0	72,900,000	155,500,000	139,800,000
Non-US [Member] | Operating Segments [Member] | Surgical Solutions [Member]
Segment Reporting Information [Line Items]
Revenues	$ 44,900,000	$ 55,900,000	$ 94,000,000.0	$ 111,100,000