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When mating gear teeth are designed to produce a constant angular velocity ratio during meshing they are said to have 'conjugate action'. To provide this an 'involute' type profile is almost universally used for tooth forms.
There are two modes that are important causes of gear failures. Bending stresses (leading to tooth breakage) which are a maximum at the tooth root and compressive stresses (leading to pitting) that are a maximum on the tooth face. Because tooth loading is cyclic, both of these mechanisms are of a fatigue nature. The design of gears needs to counter both of these potential failure modes. An important part of providing the resistance to the high contact stresses is to use gears of appropriate hardness. The lower the levels of impurities in a material, the better it is normally able to resist fatigue.
Link to page showing some gear nomenclature.
Loads on Teeth
The tangential force on the teeth can be found from:
Wt = 60H/(3.14159.d.n) where:
Wt = transmitted load, N
H = power, W
d = gear diameter, m
n = speed, rev/min.
Bending Stresses - The Lewis Formula
Although this was published in 1893, it is still very widely used for assessing bending stresses when designing gears. The method involves moving the tangential force and applying it to the tooth tip and assuming the load is uniformly distributed accross the tooth width with the tooth acting as a simple cantilever of constant rectangular cross section, the beam depth being put equal to the thickness of the tooth root (t) and the beam width being put equal to the tooth, or gear, width (bw).