218
L. Zhao et al.
ρ fp /m n from 0.39 to 0.308 and 0.208. The calculated S Fn , h Fe and ρ F are showed
in Table 17.3. The large reduction root radius ρ F leads to significant increase
in notch parameter q s , and dramatic increases stress correction factor Y s which
is greater than the form factor Y F reduction. So bending stress increases when
pressure angle changes from 20° to 22.5° and 25°.
17.5 Conclusions
From the analysis presented in this study, the following conclusions can be drawn:
(1) The variations of bending stresses from ISO, GATES with correct tip relief and
FEA with pressure angle changing have the same trends. The results in this
study are valid.
(2) For basic rack h fp /m n = 1.4, according to the geometric relationship, the
maximum tool tip radius (ρ fp /m n ) of spur gear with pressure angle equal to
20°, 22.5° and 25° are equal to 0.39, 0.308 and 0.208 respectively. It can greatly
affect the bending stress, so we must consider its influence when we investigate
the effect of pressure angle on bending stress.
(3) Smaller pressure angle such as 14.5° in this study, can result in high contact ratio
spur gears (ε α > 2), at least two teeth sharing the load when gears are in mesh, so
it can get lower bending stress. But we must make sure this is maintained when
considering manufacturing deviations, elastic deflections and misalignment of
shaft and micro modifications, the gears always have transverse contact ratio
greater than 2.0, otherwise, the benefit of lower bending stress will disappear.
(4) For the studied gears with h fp /m n = 1.4, the calculated bending stress reduced
when pressure angle changing from 17.5° to 20° (1 < ε α < 2). And the bending
stress increases when pressure angle changes from 20° to 22.5° and 25° (1 < ε α
< 2).
References
1. ISO 10825:1995, Gears - Wear and damage to gear teeth –Terminology. 1st edn. UK (1995)
2. Panin, S.V., Moiseenko, D.D., Maksimov, P.V., Vlasov, I.V., Byakov, A.V., Maruschak, P.O.,
Berto, F., Schmauder, S., Vinogradov, A.: Influence of energy dissipation at the interphase
boundaries on impact fracture behaviour of a plain carbon steel. Theoret. Appl. Fract. Mech.
97, 478–499 (2018)
3. ISO 53:1998, Cylindrical gears for general and heavy engineering- Standard basic rack tooth
profile. 2nd edn. UK (1998)
4. Gupta, K., Chatterjee, S.: Effect of pressure angle of spur gears on bending and contact stresses:
a comparative study using finite element software. Int. J. Adv. Res. Sci. Eng. 4, 517–526 (2015)
5. Handschuh, R.F., Zakrajsek, A.J.: High-pressure angle gears: comparison to typical gear
designs. J. Mech. Des. 133(11), 114501 (2011)
6. Sankar, S., Kumaresan, M., Nataraj, M.: Effects of pressure angle and tip relief on the life of
speed increasing gearbox: a case study. SpringerPlus 3(1), 746 (2014)
L. Zhao et al.
ρ fp /m n from 0.39 to 0.308 and 0.208. The calculated S Fn , h Fe and ρ F are showed
in Table 17.3. The large reduction root radius ρ F leads to significant increase
in notch parameter q s , and dramatic increases stress correction factor Y s which
is greater than the form factor Y F reduction. So bending stress increases when
pressure angle changes from 20° to 22.5° and 25°.
17.5 Conclusions
From the analysis presented in this study, the following conclusions can be drawn:
(1) The variations of bending stresses from ISO, GATES with correct tip relief and
FEA with pressure angle changing have the same trends. The results in this
study are valid.
(2) For basic rack h fp /m n = 1.4, according to the geometric relationship, the
maximum tool tip radius (ρ fp /m n ) of spur gear with pressure angle equal to
20°, 22.5° and 25° are equal to 0.39, 0.308 and 0.208 respectively. It can greatly
affect the bending stress, so we must consider its influence when we investigate
the effect of pressure angle on bending stress.
(3) Smaller pressure angle such as 14.5° in this study, can result in high contact ratio
spur gears (ε α > 2), at least two teeth sharing the load when gears are in mesh, so
it can get lower bending stress. But we must make sure this is maintained when
considering manufacturing deviations, elastic deflections and misalignment of
shaft and micro modifications, the gears always have transverse contact ratio
greater than 2.0, otherwise, the benefit of lower bending stress will disappear.
(4) For the studied gears with h fp /m n = 1.4, the calculated bending stress reduced
when pressure angle changing from 17.5° to 20° (1 < ε α < 2). And the bending
stress increases when pressure angle changes from 20° to 22.5° and 25° (1 < ε α
< 2).
References
1. ISO 10825:1995, Gears - Wear and damage to gear teeth –Terminology. 1st edn. UK (1995)
2. Panin, S.V., Moiseenko, D.D., Maksimov, P.V., Vlasov, I.V., Byakov, A.V., Maruschak, P.O.,
Berto, F., Schmauder, S., Vinogradov, A.: Influence of energy dissipation at the interphase
boundaries on impact fracture behaviour of a plain carbon steel. Theoret. Appl. Fract. Mech.
97, 478–499 (2018)
3. ISO 53:1998, Cylindrical gears for general and heavy engineering- Standard basic rack tooth
profile. 2nd edn. UK (1998)
4. Gupta, K., Chatterjee, S.: Effect of pressure angle of spur gears on bending and contact stresses:
a comparative study using finite element software. Int. J. Adv. Res. Sci. Eng. 4, 517–526 (2015)
5. Handschuh, R.F., Zakrajsek, A.J.: High-pressure angle gears: comparison to typical gear
designs. J. Mech. Des. 133(11), 114501 (2011)
6. Sankar, S., Kumaresan, M., Nataraj, M.: Effects of pressure angle and tip relief on the life of
speed increasing gearbox: a case study. SpringerPlus 3(1), 746 (2014)