Bending Strength Of Bevel Gears
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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: md 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) 412

Should the bevel gear pair not have any axial shift, then the coefficient C is 1, as per Figure17-7. The tooth profile factor, YF, per Equation (17-31) is simply the YFO This value is from Figure 17-8 or 17-9, depending upon whether it is a straight or spiral bevel gear pair. The graph entry parameter values are per Equation (17-32). YF = YFO (17-31) (17-32) where: ha = Addendum at outer end (mm) hao = Addendum of standard form (mm) m = Radial module (mm) The axial shift factor, K, is computed from the formula: (17-33) 17.3.3.C Load Distribution Factor, Ye Load distribution factor is the...

See Table 17-17 through 17-19 for some calculate examples of radial contact ratio for various bevel gear pairs. 414

17.3.3.D Spiral Angle Factor, Yb The spiral angle factor is a function of the spiral angle. The value is arbitrarily set by the following conditions: (17-36) 17.3.3.E Cutter Diameter Effect Factor, Yc This factor of cutter diameter, Yc, can be obtained from Table 17-20 by the value of tooth flank length, b / cosbm (mm), over cutter diameter. If cutter diameter is not known, assume Yc = 1.00. 17.3.3.F Life Factor, KL We can choose a proper life factor, KL, from Table 17-2 similarly to calculating the bending strength of spur and helical gears. 17.3.3.G Dimension Factor of Root Bending...