Bending Strength Of Spur And Helical Gears0 pages

Forces acting on the driven gear can be calculated per
Equations (16-25).
(16-25)
If the S term in Equation (16-25) is 90º, it becomes
identical to Equation (16-20). Figure 16-16 presents
the direction of forces in a screw gear mesh when the
shaft angle S = 90º and b1 = b2 = 45º.
SECTION 17 STRENGTH AND DURABILITY OF GEARS
The strength of gears is generally expressed in terms of
bending strength and surface durability. These are
independent criteria which can have differing criticalness,
although usually both are important.
Discussions in this section are based upon equations
published in the literature of the Japanese Gear
Manufacturer Association (JGMA). Reference is made to
the following JGMA specifications:
Specifications of JGMA:
JGMA 401-01
JGMA 402-01
JGMA 403-01
JGMA 404-01
JGMA 405-01
Bending Strength Formula of Spur
Gears and Helical Gears
Surface Durability Formula of Spur
Gears and Helical Gears
Bending Strength Formula of Bevel
Gears
Surface Durability Formula of Bevel
Gears
The Strength Formula of Worm Gears
Generally, bending strength and durability specifications
are applied to spur and helical gears (including double
helical and internal gears) used in industrial machines in
the following range:
Module:
Pitch Diameter:
Tangential Speed:
Rotating Speed:
mdv
n
1.5 to 25 mm
25 to 3200 mm
less than 25m/sec
less than 3600 rpm
Conversion Formulas: Power, Torque and Force
Gear strength and durability relate to the power and forces to be
transmitted. Thus, the equations that relate tangential force at the
pitch circle, Ft(kgf), power, P (kw), and torque, T (kgf.m) are basic to
the calculations. The relations are as follows:
Ft = 102P = 1.95x106P = 2000T (17-1)
V dwn dw
P = Ftv = 10-6 = Ftdwn (17-2)
102 1.95
T = Ftdw = 974P (17-3)
2000 n
where: v : Tangential Speed of Working Pitch
Circle (m/sec)
v : dwn
19100
dw : Working Pitch Diameter (mm)
n : Rotating Speed (rpm)
17.1 Bending Strength Of Spur And Helical Gears
In order to confirm an acceptable safe bending strength, it is
necessary to analyze the applied tangential force at the working pitch
circle, Ft, vs. allowable force, Ftlim This is stated as:
Ft < Ftlim (17-4)
It should be noted that the greatest bending stress is at the root of
the flank or base of the dedendum. Thus, it can be stated:
sF = actual stress on dedendum at root
sFtlim = allowable stress
Then Equation(17-4) becomes Equation(17-5)
sF £ sFlim (17-5)
Equation(17-6) presents the calculation of Ftlim:
(17-6)
Equation (17-6) can be converted into stress by Equation (17-7):
(17-7)
17.1.1 Determination of Factors in the
Bending Strength Equation
If the gears in a pair have different blank widths, let the wider one
be bw and the narrower one be bs.
And if:
bw - bs £ mn bw and bs can be put directly into
Equation (17-6).
bw - bs £ mn the wider one would be changed
to bs + mn and the narrower
one, bs would be unchanged.
17.1.2 Tooth Profile Factor, YF
The factor YF is obtainable from Figure 17-1 based on the
equivalent number of teeth, Zv and coefficient of profile shift, x, if the
gear has a standard tooth profile with 20º pressure angle, per JIS B
1701. The theoretical limit of undercut is shown. Also, for profile
shifted gears the limit of too narrow (sharp) a tooth top land is given.
For internal gears, obtain the factor by considering the equivalent
racks.
17.1.3 Load Distribution Factor, Ye
Load distribution factor is the reciprocal of radial contact ratio.
Ye = 1 (17-8)
ea
Table 17-1 shows the radial contact ratio of a standard spur gear.
400