compute_contact_stress

HelicalGear.compute_contact_stress() → None

It computes the contact_stress generated by the contact with mating gear teeth.

Raises

ValueError

• If a gear mating between two gears has not been set,

• if mating_role is MatingMaster and its slave gear misses module parameter,

• if mating_role is MatingMaster and its slave gear misses elastic_modulus parameter,

• if mating_role is MatingSlave and its master gear misses module parameter,

• if mating_role is MatingSlave and its master gear misses elastic_modulus parameter.

Notes

The contact stress computation is based on the following assumptions:

• perfect elasticity of the materials the two mating gear,

• absence of friction forces in the contact point,

• small size of the contact surface compared to the size of the bodies between which contact occurs.

The contact stress is computed with the following formula:

\[\sigma_c = 0.262922 \, \sqrt{\frac{4 \, F_t \, \cos \beta} {b \, \cos \alpha_t \, \sin \alpha_t} \left( \frac{1}{D_1} + \frac{1}{D_2} \right) \, \frac{E_1 \, E_2}{E_1 + E_2}}\]

where:

• \(F_t\) is the tangential_force applied on the tooth,

• \(\beta\) is the gear helix_angle,

• \(b\) is the gear face_width,

• \(\alpha_t\) is the transverse pressure angle of the gear,

• \(D_1\) is the gear reference_diameter,

• \(D_2\) is the mating gear reference_diameter,

• \(E_1\) is the gear elastic_modulus,

• \(E_2\) is the mating gear elastic_modulus.

The transverse pressure angle of the gear can be computed with the formula:

\[\alpha_t = \tan^{-1} \frac{\tan \alpha}{\cos \beta}\]

where \(\alpha\) is the pressure angle of the gear, always equal to 20 degrees.