Accumulated Other Comprehensive Loss, Net (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ 904.0	$ 767.5	$ 594.2
Other comprehensive income (loss)	(65.5)	14.8	(4.7)
Amounts reclassified from AOCI, net of tax	0.0	0.2	0.1
Other comprehensive (loss)/income	(65.5)	15.0	(4.6)
Ending balance	1,070.1	904.0	$ 767.5	$ 594.2
Accounting Standards Update [Extensible Enumeration]			Accounting Standards Update 2016-13 [Member]	Accounting Standards Update 2018-02 [Member]	Accounting Standards Update 2018-02 [Member]
Cumulative transition adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		(6.2)	$ 0.0
Ending balance			(6.2)	$ 0.0
Adjusted balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		761.3	594.2
Ending balance			761.3	594.2
Foreign Currency Translation Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(22.7)	(36.0)	(31.5)
Other comprehensive income (loss)	(11.7)	13.3	(4.5)
Amounts reclassified from AOCI, net of tax		0.0	0.0
Other comprehensive (loss)/income	(11.7)	13.3	(4.5)
Ending balance	(34.4)	(22.7)	(36.0)	(31.5)
Foreign Currency Translation Adjustment | Cumulative transition adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			0.0
Ending balance				0.0
Foreign Currency Translation Adjustment | Adjusted balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			(31.5)
Ending balance				(31.5)
Pension Benefits Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(2.4)	(4.1)	(3.3)
Other comprehensive income (loss)	(0.3)	1.5	(0.2)
Amounts reclassified from AOCI, net of tax		0.2	0.1
Other comprehensive (loss)/income	(0.3)	1.7	(0.1)
Ending balance	(2.7)	(2.4)	(4.1)	(3.3)
Pension Benefits Adjustment | Cumulative transition adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			(0.7)
Ending balance				(0.7)
Pension Benefits Adjustment | Adjusted balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			(4.0)
Ending balance				(4.0)
Cash Flow Hedge
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	0.0	0.0	0.0
Other comprehensive income (loss)	(53.5)	0.0	0.0
Amounts reclassified from AOCI, net of tax		0.0	0.0
Other comprehensive (loss)/income	(53.5)	0.0	0.0
Ending balance	(53.5)	0.0	0.0	0.0
Cash Flow Hedge | Cumulative transition adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			0.0
Ending balance				0.0
Cash Flow Hedge | Adjusted balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			0.0
Ending balance				0.0
Accumulated Other Comprehensive Loss, net
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(25.1)	(40.1)	(34.8)
Other comprehensive (loss)/income	(65.5)	15.0	(4.6)
Ending balance	$ (90.6)	(25.1)	(40.1)	(34.8)
Accumulated Other Comprehensive Loss, net | Cumulative transition adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance			(0.7)
Ending balance				(0.7)
Accumulated Other Comprehensive Loss, net | Adjusted balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		$ (40.1)	(35.5)
Ending balance			$ (40.1)	$ (35.5)