Accumulated Other Comprehensive Loss (Schedule of Reclassifications out of Accumulated Other Comprehensive Loss) (Details) - USD ($)		12 Months Ended
		Sep. 30, 2025		Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
OCI gain (loss) on cash flow hedge, reclassification before tax		$ 3,000,000.0		$ 5,900,000	$ 8,000,000.0
Reclassification to earnings		3,900,000		2,900,000
Gain (Loss) from Litigation Settlement				3,900,000	(6,300,000)
Accumulated other comprehensive loss		(109,800,000)		(154,800,000)
Stockholders' Equity Attributable to Parent		1,553,100,000		1,584,100,000	1,540,500,000	$ 1,467,100,000
OCI before reclassifications	[1]	48,900,000		18,100,000
Foreign Currency Translation Adjustments
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Reclassification to earnings		0		0
Stockholders' Equity Attributable to Parent		(41,300,000)		(68,300,000)	(86,900,000)
OCI before reclassifications	[1]	27,000,000.0		18,600,000
Pension and Post-retirement Activity
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Reclassification to earnings		1,800,000		(1,100,000)
Stockholders' Equity Attributable to Parent		(67,600,000)		(84,800,000)	(86,000,000.0)
OCI before reclassifications	[1]	19,000,000.0		100,000
Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Stockholders' Equity Attributable to Parent		(900,000)		(1,700,000)	2,900,000
Accumulated Gain (Loss), Cash Flow Hedge, Including Noncontrolling Interest
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Reclassification to earnings		2,100,000		4,000,000.0
OCI before reclassifications	[1]	2,900,000		(600,000)
Accumulated other comprehensive loss
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Stockholders' Equity Attributable to Parent		(109,800,000)		(154,800,000)	$ (170,000,000.0)	$ (216,100,000)
intellectual property claim against a third party
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Gain (Loss) from Litigation Settlement				4,900,000
Reclassification out of Accumulated Other Comprehensive Income
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
OCI gain (loss) on cash flow hedge, reclassification, tax		900,000		1,900,000
Amortization of defined benefit pension and postretirement items, tax		600,000		(400,000)
Amortization of defined benefit pension and postretirement items, after tax		1,800,000		(1,100,000)
Reclassification to earnings		3,900,000		2,900,000
Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax		2,100,000		4,000,000.0
Amortization of defined benefit pension and postretirement items, actuarial losses, before tax		2,400,000	[2]	(1,500,000)
Reclassification out of Accumulated Other Comprehensive Income | Nonoperating Income (Expense)
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
OCI gain (loss) on cash flow hedge, reclassification before tax		$ 3,000,000.0		$ 5,900,000

[1] OCI is defined as other comprehensive income.

[2] These AOCI components are included in the computation of net periodic benefit cost. See Note 14 of Notes to Consolidated Financial Statements.