Dynamic Interactions Between Sliding Friction and Tip Relief in Spur Gears

Abstract

The chief objective of this article is to examine dynamic interactions between sliding friction and profile modifications in a spur gear pair. First, a new computational method is proposed that incorporates the sliding friction and realistic time-varying stiffness into a multi-degree-of-freedom system model. Second, competing friction formulations, such as the Coulomb dry friction model and empirical expressions based on elasto-hydrodynamic and/or boundary lubrication regime principles, are briefly evaluated and validated by comparing friction force predictions with measurements. Third, effect of the profile modification on the dynamic transmission error is analytically examined under the influence of sliding friction. An out-of-phase relationship between the normal load and friction force is found to be critical as it could amplify motions or forces in the off-line-of-action direction. Typical tip relief schemes are examined including the perfect involute profile (baseline), short tip relief (at light load), intermediate tip relief (at medium load) and long tip relief (at peak load). Case studies are evaluated over a range of operating loads; interactions between sliding friction and profile modifications are observed. Finally, principles that could minimize dynamic transmission errors in the presence of sliding friction are introduced.