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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, 2023 | Sep. 30, 2023
--- | --- | ---
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | $ (413,940) | $ (401,150)
Net Carrying Amount - Finite-Lived Intangible | 396,978 |
Intangible Assets, Gross, Total | 874,926 | 853,513
Intangible Assets, Net, Total | 460,986 | 452,363
Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 676,199 | 660,487
Accumulated Amortization of Finite-Lived Intangible | (337,178) | (326,227)
Net Carrying Amount - Finite-Lived Intangible | 339,021 | 334,260
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 | 131,006 | 128,026
Accumulated Amortization of Finite-Lived Intangible | (73,049) | (71,260)
Net Carrying Amount - Finite-Lived Intangible | 57,957 | 56,766
Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 574 | 554
Accumulated Amortization of Finite-Lived Intangible | (574) | (524)
Net Carrying Amount - Finite-Lived Intangible |  | 30
Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | 64,008 | 61,307
Aerospace [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (278,613) | (275,694)
Intangible Assets, Gross, Total | 326,253 | 326,253
Intangible Assets, Net, Total | 47,640 | 50,559
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 | (238,825) | (236,143)
Net Carrying Amount - Finite-Lived Intangible | 42,858 | 45,540
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 | (39,788) | (39,551)
Net Carrying Amount - Finite-Lived Intangible | 4,782 | 5,019
Industrial [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (135,327) | (125,456)
Intangible Assets, Gross, Total | 548,673 | 527,260
Intangible Assets, Net, Total | 413,346 | 401,804
Industrial [Member] | Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 394,516 | 378,804
Accumulated Amortization of Finite-Lived Intangible | (98,353) | (90,084)
Net Carrying Amount - Finite-Lived Intangible | 296,163 | 288,720
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 | 86,436 | 83,456
Accumulated Amortization of Finite-Lived Intangible | (33,261) | (31,709)
Net Carrying Amount - Finite-Lived Intangible | 53,175 | 51,747
Industrial [Member] | Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 574 | 554
Accumulated Amortization of Finite-Lived Intangible | (574) | (524)
Net Carrying Amount - Finite-Lived Intangible |  | 30
Industrial [Member] | Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | $ 64,008 | $ 61,307

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