Gross Carrying Amount and Accumulated Amortization of Other Intangible Assets (Details) - USD ($) $ in Thousands	May 31, 2023	Aug. 31, 2022
Indefinite And Finite Lived Intangible Assets [Line Items]
Accumulated Amortization	$ 138,848	$ 132,708
Gross Carrying Value	177,932	174,215
Net Book Value	39,084	41,507
Tradenames
Indefinite And Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	23,112	22,274
Accumulated Amortization	0	0
Net Book Value	$ 23,112	22,274
Customer relationships
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	14 years
Gross Carrying Value	$ 137,654	135,101
Accumulated Amortization	122,979	117,275
Net Book Value	$ 14,675	17,826
Patents
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	11 years
Gross Carrying Value	$ 13,974	13,708
Accumulated Amortization	13,402	13,104
Net Book Value	$ 572	604
Trademarks and tradenames
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	12 years
Gross Carrying Value	$ 3,192	3,132
Accumulated Amortization	2,467	2,329
Net Book Value	$ 725	$ 803