Gross Carrying Amount and Accumulated Amortization of Other Intangible Assets (Details) - USD ($) $ in Thousands	6 Months Ended
	Feb. 28, 2023	Aug. 31, 2022
Indefinite And Finite Lived Intangible Assets [Line Items]
Accumulated Amortization	$ 136,685	$ 132,708
Gross Carrying Value	176,401	174,215
Net Book Value	39,716	41,507
Tradenames
Indefinite And Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	22,708	22,274
Accumulated Amortization	0	0
Net Book Value	$ 22,708	22,274
Customer relationships
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	14 years
Gross Carrying Value	$ 136,693	135,101
Accumulated Amortization	121,013	117,275
Net Book Value	$ 15,680	17,826
Patents
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	11 years
Gross Carrying Value	$ 13,838	13,708
Accumulated Amortization	13,262	13,104
Net Book Value	$ 576	604
Trademarks and tradenames
Indefinite And Finite Lived Intangible Assets [Line Items]
Weighted Average Amortization Period (Years)	12 years
Gross Carrying Value	$ 3,162	3,132
Accumulated Amortization	2,410	2,329
Net Book Value	$ 752	$ 803