17 The Influence of Pressure Angle of Spur Gears …
217
(1) The variations of bending stresses from ISO, GATES with correct tip relief and
FEA with pressure angle changing have the same trends, which can be clearly
seen from Fig. 17.6.
(2) The bending stress is minimum when pressure angle equal to 14.5°.
(3) Bending stress is reduced when pressure angle changing from 17.5° to 20°.
(4) While bending stress is increased when pressure angle changing from 20° to
22.5° and 25°.
There are some reasons to explain the results.
(1) The transverse contact ratio ε α is 2.048 greater than 2.0 when pressure angle
equal to 14.5°, which means there are at least 2 teeth sharing load when gear
meshing as shown in Fig. 17.7. This results in lower bending stresses, without
considering the effects of manufacturing deviations and misalignment.
(2) When pressure angle is increased from 17.5° to 20°, the tooth root chord at the
critical section s Fn is increased, the bending moment arm h Fe is also slightly
higher, while the root radius ρ F is almost same. The detailed s Fn , h Fe and ρ F are
showed in Table 17.3, which will lead to a lower form factor Y F and a slightly
higher stress correction factor Y s , while the decrement of form factor is greater
than the increment of stress correction factor, so bending stress decreases when
pressure angle changes from 17.5° to 20°.
(3) When pressure angle is increased from 20° to 22.5° and 25°, the tooth root chord
at the critical section s Fn and bending moment arm h Fe are also increased, and the
root radius ρ F is largely reduced due to the significant declining of tool tip radius
Fig. 17.7 Number of teeth
sharing load condition when
2 < ε α < 3 for spur gears
Table 17.3 The details of bending stress key factors in the calculation from ISO
α [°]
S Fn /m n
h Fe /m n
ρ fp /m n
ρ F /m n
q s
Y F
Y S
17.5
2.053
1.047
0.39
0.585
1.755
1.503
1.842
20
2.158
1.097
0.39
0.583
1.85
1.421
1.886
22.5
2.273
1.183
0.308
0.528
2.153
1.378
1.994
25
2.405
1.28
0.208
0.463
2.599
1.329
2.138
217
(1) The variations of bending stresses from ISO, GATES with correct tip relief and
FEA with pressure angle changing have the same trends, which can be clearly
seen from Fig. 17.6.
(2) The bending stress is minimum when pressure angle equal to 14.5°.
(3) Bending stress is reduced when pressure angle changing from 17.5° to 20°.
(4) While bending stress is increased when pressure angle changing from 20° to
22.5° and 25°.
There are some reasons to explain the results.
(1) The transverse contact ratio ε α is 2.048 greater than 2.0 when pressure angle
equal to 14.5°, which means there are at least 2 teeth sharing load when gear
meshing as shown in Fig. 17.7. This results in lower bending stresses, without
considering the effects of manufacturing deviations and misalignment.
(2) When pressure angle is increased from 17.5° to 20°, the tooth root chord at the
critical section s Fn is increased, the bending moment arm h Fe is also slightly
higher, while the root radius ρ F is almost same. The detailed s Fn , h Fe and ρ F are
showed in Table 17.3, which will lead to a lower form factor Y F and a slightly
higher stress correction factor Y s , while the decrement of form factor is greater
than the increment of stress correction factor, so bending stress decreases when
pressure angle changes from 17.5° to 20°.
(3) When pressure angle is increased from 20° to 22.5° and 25°, the tooth root chord
at the critical section s Fn and bending moment arm h Fe are also increased, and the
root radius ρ F is largely reduced due to the significant declining of tool tip radius
Fig. 17.7 Number of teeth
sharing load condition when
2 < ε α < 3 for spur gears
Table 17.3 The details of bending stress key factors in the calculation from ISO
α [°]
S Fn /m n
h Fe /m n
ρ fp /m n
ρ F /m n
q s
Y F
Y S
17.5
2.053
1.047
0.39
0.585
1.755
1.503
1.842
20
2.158
1.097
0.39
0.583
1.85
1.421
1.886
22.5
2.273
1.183
0.308
0.528
2.153
1.378
1.994
25
2.405
1.28
0.208
0.463
2.599
1.329
2.138