(From: MODEL ENGINEERS'WORKSHOP magazine, 1996)

 GEARS. involute form                
 TOOTH SIZE                                     
 There are three methods of defining gear tooth size                                     
 Diametral pitch. DP.  The number of teeth per one inch of pitch circle diameter.         
 Module.          MOD. The length, in mm, of the pitch circle diameter per tooth.           
 Circular pitch.  CP.  The distance between adjacent teeth measured along the are at the
                       pitch circle diameter                         
 OTHER DEFINITIONS.                             
 Addendum.        A.   The height of the tooth above the pitch circle diameter.         
 Centre distance. C.   The distance between the axes of two gears in mesh.                 
 Circular tooth thickness. 
                CTT.   The width of a tooth measured along the are at the pitch circle     
 Dedendum.        D.   The depth of the tooth below the pitch circle diameter.               
 Outside diameter.OD.  The outside diameter of the gear.                                   
 Pitch circle dia.PCD. The diameter of the pitch circle.                                  
 Pitch point.     PP.  The point at which the pitch circle diameters of two gears in mesh
                       coincide. Effectively the diameters at which plain discs would create
                       the same ratio if relying on friction alone.                     
 Pitch to back.   PTB. The distance on a rack between the pitch circle diameter line and     
                       the rear face of the rack.                     
 Pressure angle.  PA.  The angle between the tooth profile at the pitch circle diameter     
                       and a radial line passing through the same point. See sketch.                             
 Whole depth.     H.   The total depth of the space between adjacent teeth.                  

FORMULA MODULE System (metric)

 Addendum                  A = MOD                    
 Centre distance                                                         
                                PCD(g) + PCD(p)
                           C = ----------------                            
 Circular pitch                                            
                          CP = m x MOD                
 Circular tooth thickness                                  
                         CTT = ---------                           
                           D =  H - A                  
                         MOD = ------                          
 Number of teeth                                           
                           N = -----                            
 Outside diameter                                          
                          OD = (N + 2) x MOD           
 Pitch circle diameter                                     
                         PCD = N x MOD                 
 Whole depth (finer than 20DP)                             
                           H = 2.4 x MOD               
 Whole depth (20DP and coarser)                            
                           H = 2.25 x MOD              

FORMULA DP System (imperial)

                           A = ----                        
 Centre distance                                         
                               PCD(g) + PCD(p)
                           C = ---------------
 Circular pitch                  PI                      
                          CP = ------                           
 Circular tooth thickness                                
                         CTT = -----                       
                           D = H - A                
 Diametral pitch                                         
                          DP = -----
 Number of teeth                                         
                           N = DP x PCD              
 Outside diameter                                        
                                N + 2             
                          OD = -------                         
 Pitch circle diameter                                   
                         PCD = -----                       
 Whole depth (finer than 20DP)                           
                           H = -----                          
 Whole depth (20DP and coarser}                          
                           H = -----                          

 1. The pressure angle for commercially available gears is invariably 20 degrees.
 Sketch 1 shows, on the left, a 20 degree pressure angle gear, centre 30 degrees, 
 and right 10 degrees.                            
 2. When two gears are meshed correctly their pitch circle diameters coincide at 
 the pitch point (PP). A clearance then results between the top of the tooth on one
 gear, and the bottom of the gap between two adjacent teeth on the other. The amount
 of clearance is the difference between the Addendum and the Dedendum. 
 That is Clearance = D -- A.         
 3. When two gears mesh together the larger is called the gear and the smaller the       
 pinion. That meshed with a rack is also called the pinion.                          
 4. The shape of the space between adjacent teeth varies considerably with the number
 of teeth on the gear. Gears having a few teeth have very rounded teeth whilst gears 
 with a large number of teeth, have almost straight sided teeth. The space between 
 the adjacent teeth, being that cut by the milling cutter, vary considerably. Therefore,
 in theory, a different cutter is required for each number of teeth. In practice, except
 for extremely critical applications, a compromise is adopted and 8 different cutters 
 are required to cut from 12 teeth up to a rack. Table 1 indicates the range of each 
 cutter. Note, metric cutters(MOD) are numbered in reverse.
 5. Gears with small numbers of teeth 11 down to 6 require special consideration. A        
 detailed book on the subject should be read before cutting gears of that size.           

 6. Commercially available gears with 16 or less teeth may have a modified tooth form
 known as an addendum modification, or corrected gears. These mesh correctly with     
 standard gears but at a modified centre distance. Consult supplier for details.        
 7. The tooth shape of the rack is straight sided and with an angle equal to the           
 pressure angle.                                
 8. Sketch 2 shows 24 tooth gears in the metric sizes MOD2, MOD1 and MOD0.5. These      
 are very similar to 12DP, 24DP and 48DP The DP gears would be slightly larger.         
 9. The sketches are approximate representations only. Sketch 2 is nominally
 true to size.                                  
 10. Table 2 compares the DP and MOD ranges. This table does not imply interchangeability
 or mixed usage, though for a few sizes and in a non arduous situation it may be           
 acceptable if gears are to hand.               
 11. A pair of gears, adequately lubricated, meshing smoothly, and at the correct centre
 distance, should have a transmission efficiency in the order of 97%                 

 Table 1                                                 
 Cutter number and ranges                               
  DP number      MOD number          For cutting gears
    1               8                 135T to rack       
    2               7                  557 to 134T       
    3               6                  357 to  54T       
    4               5                  26T to  34T       
    5               4                  21T to  25T       
    6               3                  17T to  20T       
    7               2                  14T to  16T       
    8               1                  12T to  13T       
 Table 2                                                 
  DP and MOD system comparisons                          
  DP           MOD           DP             MOD          
  standard  standard                                     
                             equivalent  equivalent      
              0. 4           63.5                        
              0.5            50.8                        
  48                                        0.53         
              0.6            42.33                       
  40                                        0.63         
              0.7            36.29                       
  32                                        0.79         
              0.8            31.75                       
              1.0            25.4                        
  24                                        1.06         
              1.25           20.32                       
  20                                        1.27         
              1.5            16.93                       
  16                                        1.59         
              2.0            12.7                        
  12                                        2.12         
              3.0            8.47                        
              4.0            6.35                        

Back to previous page