(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: |
m d v n |
1.5 to
25 mm 25 to 3200 mm less than 25m/sec less than 3600 rpm |
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.
