Tooth-root-stress evaluation for plastic gears considering effect of contact ratio under load

Abstract

In a plastic gear pair, the low rigidity of plastics can lead to a higher actual contact ratio due to tooth deflection under load compared to the geometrical one. This phenomenon contributes to a decrease in tooth root stress. The effect of transmitted torque on the actual contact ratio under load is more noticeable in internal gear pairs than in external ones. Therefore, no regard for the contact ratio under load results in evaluating higher tooth root stresses in internal gear pairs. In other words, assessing the bending strength of plastic material through running tests of external gear pairs leads to underestimating the load capacity of internal gear pairs. Consistent tooth-root-stress evaluations in external and internal gear pairs require considering the actual contact ratio under load. The present study proposed a mechanical model applicable to spur gears, which enables considering the effect of the actual contact ratio under load in tooth-root-stress evaluations for plastic gears. This model extends the geometrical contact length by the Hertzian-contact semi-width at the tooth tip and defines the contact ratio under load as the extended contact length divided by the base pitch. Furthermore, the proposed model is also acceptable to helical gears through virtual spur gears with virtual overlap; i.e., an imaginary overlap in the virtual spur gear pair. Introducing a new factor, a contact ratio factor; i.e., the quotient of the geometrical and the actual contact ratios, reduced the evaluated tooth root stresses of plastic internal gear pairs and improved the consistency of the evaluations in external and internal gear pairs.