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Intangible Assets, Net (Schedule of Finite-Lived and Indefinite-Lived Intangible Assets by Major Class) (Details) - USD ($) $ in Thousands | Dec. 31, 2024 | Sep. 30, 2024
--- | --- | ---
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | $ (422,478) | $ (440,603)
Net Carrying Amount - Finite-Lived Intangible | 344,092 |
Intangible Assets, Gross, Total | 826,895 | 881,022
Intangible Assets, Net, Total | 404,417 | 440,419
Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 639,144 | 680,713
Accumulated Amortization of Finite-Lived Intangible | (345,766) | (360,543)
Net Carrying Amount - Finite-Lived Intangible | 293,378 | 320,170
Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 3,139 | 3,139
Accumulated Amortization of Finite-Lived Intangible | (3,139) | (3,139)
Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 123,730 | 131,827
Accumulated Amortization of Finite-Lived Intangible | (73,016) | (76,329)
Net Carrying Amount - Finite-Lived Intangible | 50,714 | 55,498
Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 557 | 592
Accumulated Amortization of Finite-Lived Intangible | (557) | (592)
Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | 60,325 | 64,751
Aerospace [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (287,894) | (286,498)
Intangible Assets, Gross, Total | 326,253 | 326,253
Intangible Assets, Net, Total | 38,359 | 39,755
Aerospace [Member] | Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 281,683 | 281,683
Accumulated Amortization of Finite-Lived Intangible | (247,391) | (246,152)
Net Carrying Amount - Finite-Lived Intangible | 34,292 | 35,531
Aerospace [Member] | Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 44,570 | 44,570
Accumulated Amortization of Finite-Lived Intangible | (40,503) | (40,346)
Net Carrying Amount - Finite-Lived Intangible | 4,067 | 4,224
Industrial [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (134,584) | (154,105)
Intangible Assets, Gross, Total | 500,642 | 554,769
Intangible Assets, Net, Total | 366,058 | 400,664
Industrial [Member] | Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 357,461 | 399,030
Accumulated Amortization of Finite-Lived Intangible | (98,375) | (114,391)
Net Carrying Amount - Finite-Lived Intangible | 259,086 | 284,639
Industrial [Member] | Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 3,139 | 3,139
Accumulated Amortization of Finite-Lived Intangible | (3,139) | (3,139)
Industrial [Member] | Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 79,160 | 87,257
Accumulated Amortization of Finite-Lived Intangible | (32,513) | (35,983)
Net Carrying Amount - Finite-Lived Intangible | 46,647 | 51,274
Industrial [Member] | Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 557 | 592
Accumulated Amortization of Finite-Lived Intangible | (557) | (592)
Industrial [Member] | Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | $ 60,325 | $ 64,751

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