Accumulated Other Comprehensive Loss, Net (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ 767.5	$ 594.2	$ 505.3
Other comprehensive income	14.8	(4.7)	(1.6)
Amounts reclassified from AOCI, net of tax	0.2	0.1	(0.1)
Other comprehensive gain/(loss)	15.0	(4.6)	(1.7)
Ending balance	904.0	767.5	594.2
Cumulative Effect, Period of Adoption, Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(6.2)	0.0
Ending balance		(6.2)	0.0
Cumulative Effect, Period of Adoption, 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	(36.0)	(31.5)	(30.5)
Other comprehensive income	13.3	(4.5)	(0.8)
Amounts reclassified from AOCI, net of tax	0.0	0.0	(0.2)
Other comprehensive gain/(loss)	13.3	(4.5)	(1.0)
Ending balance	(22.7)	(36.0)	(31.5)
Foreign Currency Translation Adjustment | Cumulative Effect, Period of Adoption, Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		0.0
Ending balance			0.0
Foreign Currency Translation Adjustment | Cumulative Effect, Period of Adoption, 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	(4.1)	(3.3)	(2.6)
Other comprehensive income	1.5	(0.2)	(0.8)
Amounts reclassified from AOCI, net of tax	0.2	0.1	0.1
Other comprehensive gain/(loss)	1.7	(0.1)	(0.7)
Ending balance	(2.4)	(4.1)	(3.3)
Pension Benefits Adjustment | Cumulative Effect, Period of Adoption, Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		(0.7)
Ending balance			(0.7)
Pension Benefits Adjustment | Cumulative Effect, Period of Adoption, Adjusted Balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		(4.0)
Ending balance			(4.0)
Accumulated Other Comprehensive Loss, net
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	(40.1)	(34.8)	(33.1)
Other comprehensive gain/(loss)	15.0	(4.6)	(1.7)
Ending balance	(25.1)	(40.1)	(34.8)
Accumulated Other Comprehensive Loss, net | Cumulative Effect, Period of Adoption, Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance		(0.7)
Ending balance			(0.7)
Accumulated Other Comprehensive Loss, net | Cumulative Effect, Period of Adoption, Adjusted Balance
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning balance	$ (40.1)	(35.5)
Ending balance		$ (40.1)	$ (35.5)