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Segment Reporting - Schedule of Segment Report (Details)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 01, 2022
segment
Jan. 31, 2023
USD ($)
Jan. 31, 2022
USD ($)
Jan. 31, 2023
USD ($)
Jan. 31, 2022
USD ($)
Segment Reporting Information          
Number of reportable segments | segment 3        
Net sales   $ 828.3 $ 802.5 $ 1,675.6 $ 1,563.4
Earnings (loss) before income taxes   113.3 94.5 229.8 198.5
Operating Segments          
Segment Reporting Information          
Net sales   828.3 802.5 1,675.6 1,563.4
Corporate and unallocated          
Segment Reporting Information          
Earnings (loss) before income taxes   (17.9) (8.0) (30.1) (14.6)
Mobile Solutions | Operating Segments          
Segment Reporting Information          
Net sales   522.5 513.5 1,077.4 1,000.8
Earnings (loss) before income taxes   78.6 58.6 158.9 124.2
Mobile Solutions | Operating Segments | Off-Road          
Segment Reporting Information          
Net sales   106.2 91.9 209.8 182.3
Mobile Solutions | Operating Segments | On-Road          
Segment Reporting Information          
Net sales   34.5 33.1 70.5 64.6
Mobile Solutions | Operating Segments | Aftermarket          
Segment Reporting Information          
Net sales   381.8 388.5 797.1 753.9
Industrial Solutions | Operating Segments          
Segment Reporting Information          
Net sales   246.4 218.5 476.0 419.3
Earnings (loss) before income taxes   46.3 27.2 83.9 51.8
Industrial Solutions | Operating Segments | Industrial Filtration Solutions          
Segment Reporting Information          
Net sales   211.8 191.4 407.8 364.7
Industrial Solutions | Operating Segments | Aerospace and Defense          
Segment Reporting Information          
Net sales   34.6 27.1 68.2 54.6
Life Sciences | Operating Segments          
Segment Reporting Information          
Net sales   59.4 70.5 122.2 143.3
Earnings (loss) before income taxes   $ 6.3 $ 16.7 $ 17.1 $ 37.1