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Summary of Significant Accounting Policies - Additional Information (Details)
 12 Months Ended
Sep. 30, 2021
USD ($)
Step
Sep. 30, 2020
USD ($)
Sep. 30, 2019
USD ($)
Accounting Policies [Abstract]      
Research and development costs charged to expense $ 103,100,000 $ 103,900,000 $ 99,000,000.0
Advertising cost 17,700,000 16,000,000.0 24,900,000
Amortization of Debt Issuance Costs $ 1,600,000 3,600,000 $ 1,600,000
Write off of Deferred Debt Issuance Cost   $ 1,800,000  
Number of steps to evaluate uncertain income tax positions (in steps) | Step 2    
Minimum percentage likelihood of tax benefit being realized (as a percent) 50.00%    
Maximum percentage likelihood of tax benefit being realized (as a percent) 50.00%    
Amount of tax benefit realized for tax positions currently estimated to have a less than likelihood percentage of being sustained $ 0    
Maximum remaining maturity period at time of purchase of liquid investments classified as cash equivalents (in months) 3 months    
Inventory valued using LIFO method (as a percent) 85.00% 83.00%