Bending Strength Of Bevel Gears0 pages

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)
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