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Intangible Assets, Net (Schedule of Finite-Lived and Indefinite-Lived Intangible Assets by Major Class) (Details) - USD ($) $ in Thousands | Mar. 31, 2023 | Sep. 30, 2022
--- | --- | ---
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | $ (426,133) | $ (399,673)
Net Carrying Amount - Finite-Lived Intangible | 420,638 |
Intangible Assets, Gross, Total | 910,017 | 860,253
Intangible Assets, Net, Total | 483,884 | 460,580
Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 671,806 | 634,600
Accumulated Amortization of Finite-Lived Intangible | (312,497) | (290,377)
Net Carrying Amount - Finite-Lived Intangible | 359,309 | 344,223
Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 12,428 | 12,361
Accumulated Amortization of Finite-Lived Intangible | (12,428) | (12,361)
Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 161,966 | 154,894
Accumulated Amortization of Finite-Lived Intangible | (100,953) | (96,935)
Net Carrying Amount - Finite-Lived Intangible | 61,013 | 57,959
Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 571 | 1,560
Accumulated Amortization of Finite-Lived Intangible | (255) |
Net Carrying Amount - Finite-Lived Intangible | 316 | 1,560
Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | 63,246 | 56,838
Aerospace [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (300,268) | (293,036)
Intangible Assets, Gross, Total | 358,053 | 358,053
Intangible Assets, Net, Total | 57,785 | 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 | (229,858) | (223,565)
Net Carrying Amount - Finite-Lived Intangible | 51,825 | 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 | (70,410) | (69,471)
Net Carrying Amount - Finite-Lived Intangible | 5,960 | 6,899
Industrial [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Accumulated Amortization of Finite-Lived Intangible | (125,865) | (106,637)
Intangible Assets, Gross, Total | 551,964 | 502,200
Intangible Assets, Net, Total | 426,099 | 395,563
Industrial [Member] | Customer Relationships And Contracts [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 390,123 | 352,917
Accumulated Amortization of Finite-Lived Intangible | (82,639) | (66,812)
Net Carrying Amount - Finite-Lived Intangible | 307,484 | 286,105
Industrial [Member] | Intellectual Property [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 12,428 | 12,361
Accumulated Amortization of Finite-Lived Intangible | (12,428) | (12,361)
Industrial [Member] | Process Technology [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 85,596 | 78,524
Accumulated Amortization of Finite-Lived Intangible | (30,543) | (27,464)
Net Carrying Amount - Finite-Lived Intangible | 55,053 | 51,060
Industrial [Member] | Other [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Value - Finite-Lived Intangible | 571 | 1,560
Accumulated Amortization of Finite-Lived Intangible | (255) |
Net Carrying Amount - Finite-Lived Intangible | 316 | 1,560
Industrial [Member] | Trade Name [Member] |  |
Finite-Lived Intangible Assets [Line Items] |  |
Indefinite-Lived Intangible Assets | $ 63,246 | $ 56,838

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