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17.3 Bending Strength Of Bevel Gears
   This information is valid for bevel gears which are used in power transmission in general industrial machines. The applicable ranges are:
Module:
Pitch Diameter:

 
 
Linear Speed:
Rotating Speed:		 m
d
 
 
 
v
n		 1.5 to 25 mm
less than 1600 mm for straight bevel gears
less than 1000 mm for spiral bevel gears
less than 25 m/sec
less than 3600 rpm

17.3.1 Conversion Formulas
   In calculating strength, tangential force at the pitch circle, Ftm, in kgf; power, P, in kW, and torque, T, in kgf.m, are the design criteria. Their basic relationships are expressed in Equations (17-23) through (17-25).
   Ftm = 102P = 1.95 x 106P = 2000T    (17-23)
             Vm          dmn             dm     
   P = FtmVm = 5.13 X 10-7 Ftmdmn     (17-24)
            102    
   T = Ftmdm = 974P                           (17-25)
         2000        n   
where:
   Vm : Tangential speed at the central pitch circle
   Vm :  dmn
            19100
   dm : Central pitch circle diameter
   dm : d - bsind 
17.3.2 Bending Strength Equations
   The tangential force, Ftm, acting at the central pitch circle should be less than the allowable tangential force, Ftm lim, which is based upon the allowable bending stress sFlim. That is:
        Ftm £  Ftm lim                           (17-26) 
   The bending stress at the root, sF which is derived from Ftm should be less than the allowable bending stress sFlim.
        sF £ sFlim                                 (17-27) 
   The tangential force at the central pitch circle, Ftmlim (kgf), is obtained

 from Equation (17-28).

where: bm : Central spiral angle (degrees)
           m   : Radial module (mm)
           Ra : Cone distance (mm)
   And the bending strength sF (kgf/mm²) at the root of tooth is calculated from Equation (17-29).

17.3.3 Determination of Factors in Bending Strength Equations
   17.3.3.A Tooth Width, b (mm)
   The term b is defined as the tooth width on the pitch cone, analogous to face width of spur or helical gears. For the meshed pair, the narrower one is used for strength calculations.
   17.3.3.B Tooth Profile Factor, YF
   The tooth profile factor is a function of profile shift, in both the radial and axial directions.
Using the equivalent (virtual) spur gear tooth number, the first step is to determine the radial tooth profile factor, YFO, from Figure 17-8 for straight bevel gears and Figure 17-9 for spiral bevel gears. Next, determine the axial shift factor, K, with Equation (17-33) from which the axial shift correction factor, C, can be obtained using Figure 17-7. Finally, calculate YF by Equation (17-30).

     YF = CYFO                                       (17-30)

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