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Revenue Recognition and Contract Balances - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Disaggregation of Revenue [Line Items]      
Cumulative catch-up adjustment to revenue $ 29.9 $ 26.8  
Remaining performance obligation 3,099.3    
Contract asset change $ 41.4    
Contract asset change (percentage) 13.10%    
Contract liability change $ 3.5    
Contract liability change (percentage) 1.70%    
Revenue recognized $ 144.4    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2023-01-02      
Disaggregation of Revenue [Line Items]      
Remaining performance obligation 76.00%    
Remaining performance obligation expected timing of satisfaction 12 months    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2024-01-01      
Disaggregation of Revenue [Line Items]      
Remaining performance obligation 24.00%    
Remaining performance obligation expected timing of satisfaction    
Net sales | Contract type | Fixed-price Contract | Engineered Systems      
Disaggregation of Revenue [Line Items]      
Sales to individual countries outside the United States 49.00% 47.00% 53.00%
Minimum | Net sales | Contract type | Fixed-price Contract | Engineered Systems      
Disaggregation of Revenue [Line Items]      
Sales to individual countries outside the United States 45.00%    
Maximum | Net sales | Contract type | Fixed-price Contract | Engineered Systems      
Disaggregation of Revenue [Line Items]      
Sales to individual countries outside the United States 55.00%