Analytical modeling of contact mechanics of helical gear tooth by considering surface roughness effects

Release of metal debris from a pair of gear teeth is a consequence of their contact. Any excessive metal debris can lead to the onset of fatigue and failure. This paper aims to derive a contact mechanics-based model to obtain the energy absorption of helical gear teeth. The proposed model includes the roughness effect of teeth contact surfaces. The mean value of the asperity summit curvature, the standard deviation of the asperity height distribution and the area density of the asperity height distribution are the three statistical parameters that describe the micron-scale surface roughness. An explicit approximation is obtained to relate the contact load and the minimum surface separation and to estimate the energy loss. Then an analytical expression is derived for the plastic energy dissipation per cycle as a function of plasticity index for gear teeth. The proposed function can be applied in the design of gears by engineers and manufacturers. Additionally, a pertinent lumped mass at the area of interaction is assumed to describe the contact frequency and damping ratio using a nonlinear dynamic model.