Section 17 Strength and Durability of Gears - SDP/SI

ELEMENTS OF METRIC GEAR TECHNOLOGY
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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:
σ F = actual stress on dedendum at root
σ F lim = allowable stress
Then Equation (17-4) becomes Equation (17-5)
σ F ≤ σ F lim (17-5)
Equation (17-6) presents the calculation of F t lim :
m n b K L K FX 1
F t lim = σ F lim ––––––– (––––––) ––– (kgf) (17-6)
Y F Y ε Y β K V K O S F
Equation (17-6) can be converted into stress by Equation (17-7):
Y F Y ε Y β K V K
σ O
F = F t –––––– (–––––) S F (kgf/mm 2 ) (17-7)
m n b K L K FX
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 b w and the
narrower one be b s .
And if:
b w – b s ≤ m n , b w and b s can be put directly into Equation (17-6).
b w – b s > m n , the wider one would be changed to b s + m n and the narrower one,
b s , would be unchanged.
17.1.2 Tooth Profile Factor, Y F
The factor Y F is obtainable from Figure 17-1 based on the equivalent number of teeth,
z v , and coefficient of profile shift, x, if the gear has a standard tooth profile with 20° 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, Yε
Load distribution factor is the reciprocal of radial contact ratio.
1
Yε = ––– (17-8)
ε α
Table 17-1 shows the radial contact ratio of a standard spur gear.
Metric
0 10
I
R
T
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
T-151
A