Revenue Recognition (Details) - USD ($)	3 Months Ended								12 Months Ended
	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2017	Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017	Apr. 01, 2019	Oct. 01, 2018	Sep. 30, 2016
Revenue from External Customer [Line Items]
Revenues	$ 782,800,000	$ 726,800,000	$ 714,200,000	$ 683,500,000	$ 759.2	$ 708.6	$ 710.5	$ 669.7	$ 2,907,300,000	$ 2,848,000,000.0	$ 2,743,700,000
Trade accounts receivable, net of allowances of $20.6 in 2019 and $21.8 in 2018	653,300,000				580,700,000				653,300,000	580,700,000
Product sales and service									2,615,000,000.0	2,469,600,000	2,358,100,000
Rental revenue									292,300,000	378,400,000	385,600,000
Total cost of net revenue									1,330,700,000	1,274,100,000	1,235,800,000
Rental expenses									(151,600,000)	(179,700,000)	(187,300,000)
Income tax expense (benefit)									56,400,000	(55,200,000)	50,700,000
Accounts and Other Receivables, Net, Current					580,700,000					580,700,000			$ 609,800,000
Cumulative Effect on Retained Earnings, Tax									4,800,000
Other current assets	106,700,000				100,200,000				106,700,000	100,200,000			122,000,000.0
Property, Plant and Equipment, Net	296,800,000				328,300,000				296,800,000	328,300,000			322,700,000
Deferred Tax Assets, Net of Valuation Allowance, Noncurrent	33,100,000				35,000,000.0				33,100,000	35,000,000.0			40,600,000
Other assets	91,300,000				75,100,000				91,300,000	75,100,000			78,500,000
Deferred Revenue	107,300,000				40,000,000.0				107,300,000	40,000,000.0
Revenue Deferred due to ASC 606 Initial Adoption									58,400,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Deferred Revenue												$ 10,700,000
Deferred Revenue, Additions									282,100,000
Deferred Revenue, Revenue Recognized									(273,200,000)
Deferred Revenue, Current					40,000,000.0					40,000,000.0			87,500,000
Other current liabilities	95,200,000				67,100,000				95,200,000	67,100,000			67,900,000
Other long-term liabilities	70,500,000				40,400,000				70,500,000	40,400,000			51,300,000
Retained Earnings (Accumulated Deficit)	1,967,400,000				1,876,200,000				1,967,400,000	1,876,200,000			1,871,300,000
Net Income									152,200,000	252,400,000	132,300,000
Capitalized Contract Cost, Gross	10,000,000.0								10,000,000.0
Capitalized Contract Cost, Amortization									14,700,000
Accounting Standards Update 2014-09 [Member]
Revenue from External Customer [Line Items]
Accounts and Other Receivables, Net, Current													29,100,000
Cumulative Effect on Retained Earnings, Net of Tax									(4,900,000)
Other current assets													21,800,000
Property, Plant and Equipment, Net													(5,600,000)
Deferred Tax Assets, Net of Valuation Allowance, Noncurrent													5,600,000
Other assets													3,400,000
Deferred Revenue, Current													47,500,000
Other current liabilities													800,000
Other long-term liabilities													10,900,000
Retained Earnings (Accumulated Deficit)													$ (4,900,000)
Retained Earnings [Member]
Revenue from External Customer [Line Items]
Retained Earnings (Accumulated Deficit)	1,967,400,000				1,876,200,000				1,967,400,000	1,876,200,000	1,676,200,000			$ 1,589,700,000
Retained Earnings [Member] | Accounting Standards Update 2014-09 [Member]
Revenue from External Customer [Line Items]
Cumulative Effect on Retained Earnings, Net of Tax									(4,900,000)
Other Current Assets [Member]
Revenue from External Customer [Line Items]
Equipment and Other Costs	11,900,000								11,900,000
Other Noncurrent Assets [Member]
Revenue from External Customer [Line Items]
Equipment and Other Costs	2,600,000								2,600,000
Other Noncurrent Liabilities [Member]
Revenue from External Customer [Line Items]
Deferred Revenue	125,800,000				$ 47,800,000				125,800,000	47,800,000
reclassification from rental revenue [Member]
Revenue from External Customer [Line Items]
Product sales and service									95,300,000
reclassification from rental expenses [Member]
Revenue from External Customer [Line Items]
Product sales and service									21,100,000
Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									15,200,000
Trade accounts receivable, net of allowances of $20.6 in 2019 and $21.8 in 2018	30,800,000								30,800,000
Product sales and service									112,200,000
Rental revenue									(97,000,000.0)
Total cost of net revenue									26,400,000
Rental expenses									(21,700,000)
Income tax expense (benefit)									2,200,000
Other current assets	13,600,000								13,600,000
Property, Plant and Equipment, Net	(6,100,000)								(6,100,000)
Deferred Tax Assets, Net of Valuation Allowance, Noncurrent	5,600,000								5,600,000
Other assets	2,600,000								2,600,000
Deferred Revenue	31,800,000								31,800,000
Other current liabilities	700,000								700,000
Other long-term liabilities	8,500,000								8,500,000
Retained Earnings (Accumulated Deficit)	3,400,000								3,400,000
Net Income									8,300,000
Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									2,892,100,000
Trade accounts receivable, net of allowances of $20.6 in 2019 and $21.8 in 2018	622,500,000								622,500,000
Product sales and service									2,502,800,000
Rental revenue									389,300,000
Total cost of net revenue									1,304,300,000
Rental expenses									(173,300,000)
Income tax expense (benefit)									54,200,000
Other current assets	93,100,000								93,100,000
Property, Plant and Equipment, Net	302,900,000								302,900,000
Deferred Tax Assets, Net of Valuation Allowance, Noncurrent	27,500,000								27,500,000
Other assets	88,700,000								88,700,000
Deferred Revenue	75,500,000								75,500,000
Other current liabilities	94,500,000								94,500,000
Other long-term liabilities	62,000,000.0								62,000,000.0
Retained Earnings (Accumulated Deficit)	$ 1,964,000,000.0								1,964,000,000.0
Net Income									143,900,000
Patient Support Systems [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									13,500,000
Patient Support Systems [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									1,477,000,000.0
Front Line Care [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									1,700,000
Front Line Care [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									976,400,000
Surgical Solutions [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									0
Surgical Solutions [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									438,700,000
Operating Segments [Member]
Revenue from External Customer [Line Items]
Revenues									2,907,300,000	2,848,000,000.0	2,743,700,000
Operating Segments [Member] | Patient Support Systems [Member]
Revenue from External Customer [Line Items]
Revenues									1,490,500,000	1,429,500,000	1,423,900,000
Operating Segments [Member] | Front Line Care [Member]
Revenue from External Customer [Line Items]
Revenues									978,100,000	960,200,000	885,300,000
Operating Segments [Member] | Surgical Solutions [Member]
Revenue from External Customer [Line Items]
Revenues									438,700,000	458,300,000	434,500,000
UNITED STATES
Revenue from External Customer [Line Items]
Revenues									2,056,800,000	1,956,400,000	1,887,600,000
UNITED STATES | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									14,800,000
UNITED STATES | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									2,042,000,000.0
UNITED STATES | Patient Support Systems [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									13,100,000
UNITED STATES | Patient Support Systems [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									1,121,900,000
UNITED STATES | Front Line Care [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									1,700,000
UNITED STATES | Front Line Care [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									698,900,000
UNITED STATES | Surgical Solutions [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									0
UNITED STATES | Surgical Solutions [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									221,200,000
UNITED STATES | Operating Segments [Member] | Patient Support Systems [Member]
Revenue from External Customer [Line Items]
Revenues									1,135,000,000.0
UNITED STATES | Operating Segments [Member] | Front Line Care [Member]
Revenue from External Customer [Line Items]
Revenues									700,600,000
UNITED STATES | Operating Segments [Member] | Surgical Solutions [Member]
Revenue from External Customer [Line Items]
Revenues									221,200,000
Non-US [Member]
Revenue from External Customer [Line Items]
Revenues									850,500,000	$ 891,600,000	$ 856,100,000
Non-US [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									400,000
Non-US [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									850,100,000
Non-US [Member] | Patient Support Systems [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									400,000
Non-US [Member] | Patient Support Systems [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									355,100,000
Non-US [Member] | Front Line Care [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									0
Non-US [Member] | Front Line Care [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									277,500,000
Non-US [Member] | Surgical Solutions [Member] | Difference between Revenue Guidance in Effect before and after Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									0
Non-US [Member] | Surgical Solutions [Member] | Calculated under Revenue Guidance in Effect before Topic 606 [Member]
Revenue from External Customer [Line Items]
Revenues									217,500,000
Non-US [Member] | Operating Segments [Member] | Patient Support Systems [Member]
Revenue from External Customer [Line Items]
Revenues									355,500,000
Non-US [Member] | Operating Segments [Member] | Front Line Care [Member]
Revenue from External Customer [Line Items]
Revenues									277,500,000
Non-US [Member] | Operating Segments [Member] | Surgical Solutions [Member]
Revenue from External Customer [Line Items]
Revenues									$ 217,500,000
Voalte [Member]
Revenue from External Customer [Line Items]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Deferred Revenue												$ 10,700,000