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Revenue (Summary of Amounts Recognized Related to Amortization of Costs to Fulfill Contracts and Contract Liabilities Not Related to Changes in Estimate) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Change In Contract With Customer Asset And Liability [Abstract] |  |  |
Revenue | $ 4,107 | $ 4,455 | $ 1,664
Cost of goods sold | $ 3,077 | $ 3,466 | $ 1,241

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- Definition Amount of amortization expense for asset recognized from cost incurred to obtain or fulfill contract with customer. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 340 -SubTopic 40 -Section 50 -Paragraph 3 -Subparagraph (b) -URI https://asc.fasb.org/extlink&oid=126905575&loc=SL49131252-203054 + Details
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Period Type: | duration

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- References No definition available. + Details
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Namespace Prefix: | us-gaap_
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- Definition Deferred liability revenue amortization + References No definition available. + Details
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Namespace Prefix: | wwd_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration