compute_bending_stress¶

WormWheel.compute_bending_stress() → None

It computes the bending_stress applied on the gear teeth by the mating gear.

Notes

The bending stress computation is based on the following assumptions:

the tooth is stressed by the overall force acting on the tip of the tooth itself,
the most unfavorable situation is considered in the calculation, as if there is only one pair of teeth in contact within the contact segment,
the component of the overall force that determines the bending on the tooth is the only one considered and, for simplicity, is taken as having a value equal to the tangential force on the reference diameter,
the radial component of the overall force that causes a compressive stress on the tooth is neglected.

The bending stress is computed with the following formula:

\[\sigma_b = \frac{F_t}{p_n \, b_{eff} \, Y_{LW}}\]

where:

\(F_t\) is the tangential_force applied on the tooth,
\(p_n\) is the normal pitch,
\(b_{eff}\) is the effective tooth face width,
\(Y_{LW}\) is the gear Lewis factor lewis_factor.

The normal pitch can be computed with:

\[p_n = \frac{\pi d_{wg} \sin \beta}{N}\]

where:

\(d_{wg}\) is the mating worm gear reference_diameter,
\(\beta\) is the mating worm gear helix_angle,
\(N\) is the worm wheel number of teeth n_teeth.

The effective tooth face width \(b_{eff}\) is the minimum between the worm wheel face width face_width and the mating worm gear reference diameter multiplied by 0.67.