This Recommended Practice is intended for service only.  Use SAE Standard, Involute Splines, Serrations, and Inspection-SAE J498 for new applications.

Straight Shafts

N = Number of serrations
B = Included angle of the space in the hole, and the tooth on the shaft.

The pitch diameter (PD) and the hole are basic.

The pitch line is midway between the inner and outer sharp points. 

The minimum hole with maximum shaft as measured across wires in Table1, produce basic (no clearance) fit.

The wire diameter in Table 1 is the diameter that will bear on the pitch line. 

Tolerance for diameter across wires= .001 on tooth thickness of hole and shaft sizes from 1/3 to 1 ¾ in., and -.0015 on sizes from 2 to 3 in., inclusive. 

Tooth thickness on the shaft may be varied from the tolerance given, to secure desired fit. 

We= Constant to be added to measurement across wires for shaft, subtracted for hole, for each .001-in. increase in wire diameter used over wire size in Table1. 

When serrations are hobbed, the sides of teeth are involute.  This departure from flat sides is slight and is ignored.

Formulas

1. Diameter over sharp points
   (OD) = 1.0476479 PD for 36 serrations.
            = 1.0349592 PD for 48 serrations.
    
2. Diameter under sharp points
   (RD) = .9523521 PD for 36 serrations.
            = .9650408 PD for 48 serrations.
    
3. Diameter of wire that will bear on pitch line of hole
   (Wh) = .05309792 PD for 36 serrations
            = .04133332 PD for 48 serrations
   Diameter of wire that will bear on pitch line of shaft
   (Ws) = .06565005 PD for 36 serrations
            =.0485955 PD for 48 serrations
    
4. Measurement across wires for hole
           = .9119441 PD for 36 serrations
           = .9309375 PD for 48 serrations
   Measurement across wires for shaft
           = 1.1113285 PD for 36 serrations
           = 1.0823601 PD for 48 serrations
    
5. Tolerance constant for measurement across wires per .0001-in. tooth
   thickness for hole =  .001       sin 45
                                            sin (45-180/N)
   for shaft  =  .001     sin (45-180N)
                                         sin 45
    
6. Wire diameter constant for use of other diameter wire than that which bears on pitch line. (We)
   thickness for hole   =.001+       .001        for hole
                                            sin (45-180/N)
   for shaft   = .001+  .001     for shaft        
                                 cos 45