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Shareholders' Equity (Narrative) (Details) - USD ($)
12 Months Ended
Dec. 31, 2022
Jan. 01, 2022
Jan. 02, 2021
Oct. 26, 2021
Dec. 29, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Stock repurchase program, authorized amount       $ 500,000,000  
Stock acquired and retired (in shares) 1,698,227 156,184 315,072    
Treasury stock acquired (in dollars per share) $ 140.89 $ 165.05 $ 79.38    
Stock repurchased $ 239,200,000 $ 25,800,000 $ 25,000,000    
Share-based compensation expense 22,500,000 24,900,000 9,200,000    
Income tax benefit recognized for share-based compensation 5,400,000 6,000,000 2,200,000    
Fair value of shares and options vested 25,600,000 $ 26,100,000 $ 7,700,000    
Unrecognized compensation cost related to share-based compensation $ 27,400,000        
Share-based compensation expected to recognize over a weighted average period, years 1 year 9 months 18 days        
SARs          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Expiration period   10 years      
SARs | Tranche one          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Award vesting period     5 years    
SARs | Tranche two          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Award vesting period   3 years      
Options and SAR's          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based compensation expected to recognize over a weighted average period, years 1 year 8 months 12 days        
Stock based compensation $ 6,100,000 $ 5,600,000 $ 2,800,000    
Compensation costs not yet recognized $ 6,900,000        
Restricted Stock          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based compensation expected to recognize over a weighted average period, years 4 months 24 days        
Award vesting period 1 year        
Stock based compensation $ 1,400,000 $ 1,200,000 $ 1,200,000    
Compensation costs not yet recognized $ 500,000        
Weighted average grant date fair value (in dollars per share) $ 131.27 $ 144.73 $ 70.05    
Restricted Stock Units (RSUs)          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based compensation expected to recognize over a weighted average period, years 1 year 10 months 24 days        
Stock based compensation $ 10,300,000 $ 9,700,000 $ 3,800,000    
Compensation costs not yet recognized $ 13,300,000        
Weighted average grant date fair value (in dollars per share) $ 147.70 $ 143.44 $ 86.70    
Restricted Stock Units (RSUs) | Tranche one          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share based compensation granted percentage 33.00%        
Restricted Stock Units (RSUs) | Tranche two          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share based compensation granted percentage 33.00%        
Restricted Stock Units (RSUs) | Tranche three          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share based compensation granted percentage 33.00%        
Performance Share Units          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Share-based compensation expected to recognize over a weighted average period, years 1 year 9 months 18 days        
Award vesting period 3 years        
Expiration period 3 years        
Stock based compensation $ 4,700,000 $ 8,400,000 $ 1,400,000    
Compensation costs not yet recognized $ 6,700,000        
Weighted average grant date fair value (in dollars per share) $ 151.27 $ 120.19 $ 117.63    
Potential payout as a percentage of target 100.00%        
Performance Share Units | Rexnord Transactions          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Stock based compensation   $ 4,300,000      
Performance Share Units | Minimum          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Potential payout as a percentage of target 0.00%        
Performance Share Units | Maximum          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Potential payout as a percentage of target 200.00%        
2019 Plan          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Remaining number of shares authorized to be repurchased (in shares) 195,000,000.0        
2018 Plan | Common Stock          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Authorized shares of common stock (in shares)         2,100,000
Share available for future grant or payment under the various plans (in shares) 2,300,000        
2013 Equity Incentive Plan | Common Stock          
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]          
Authorized shares of common stock (in shares)         1,500,000