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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, 2022 | Sep. 30, 2022
--- | --- | ---
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | $ (415,177) | $ (399,673)
Net Carrying Amount - Finite-Lived Intangible | 423,563 |
Intangible Assets, Gross, Total | 900,821 | 860,253
Intangible Assets, Net, Total | 485,644 | 460,580
Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 665,081 | 634,600
Accumulated Amortization of Finite-Lived Intangible | (303,281) | (290,377)
Net Carrying Amount - Finite-Lived Intangible | 361,800 | 344,223
Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 12,413 | 12,361
Accumulated Amortization of Finite-Lived Intangible | (12,413) | (12,361)
Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 160,680 | 154,894
Accumulated Amortization of Finite-Lived Intangible | (99,372) | (96,935)
Net Carrying Amount - Finite-Lived Intangible | 61,308 | 57,959
Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 566 | 1,560
Accumulated Amortization of Finite-Lived Intangible | (111) |
Net Carrying Amount - Finite-Lived Intangible | 455 | 1,560
Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | 62,081 | 56,838
Aerospace [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (296,654) | (293,036)
Intangible Assets, Gross, Total | 358,053 | 358,053
Intangible Assets, Net, Total | 61,399 | 65,017
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 | (226,714) | (223,565)
Net Carrying Amount - Finite-Lived Intangible | 54,969 | 58,118
Aerospace [Member] | Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 76,370 | 76,370
Accumulated Amortization of Finite-Lived Intangible | (69,940) | (69,471)
Net Carrying Amount - Finite-Lived Intangible | 6,430 | 6,899
Industrial [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (118,523) | (106,637)
Intangible Assets, Gross, Total | 542,768 | 502,200
Intangible Assets, Net, Total | 424,245 | 395,563
Industrial [Member] | Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 383,398 | 352,917
Accumulated Amortization of Finite-Lived Intangible | (76,567) | (66,812)
Net Carrying Amount - Finite-Lived Intangible | 306,831 | 286,105
Industrial [Member] | Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 12,413 | 12,361
Accumulated Amortization of Finite-Lived Intangible | (12,413) | (12,361)
Industrial [Member] | Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 84,310 | 78,524
Accumulated Amortization of Finite-Lived Intangible | (29,432) | (27,464)
Net Carrying Amount - Finite-Lived Intangible | 54,878 | 51,060
Industrial [Member] | Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 566 | 1,560
Accumulated Amortization of Finite-Lived Intangible | (111) |
Net Carrying Amount - Finite-Lived Intangible | 455 | 1,560
Industrial [Member] | Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | $ 62,081 | $ 56,838

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