Analysis of Energy Efficiency in Spur Gear Transmissions: Cycloidal Versus Involute Profiles

The involute profile is used almost exclusively in the manufacturing of spur gears. Nevertheless, in machinery design, the evaluation of environmental factors, such as energy efficiency, has become increasingly important when choosing between feasible solutions. As a result, the study of alternative profiles is gaining interest. The key novelty of this study is the comparative analysis of involute and cycloidal gear profiles with respect to frictional power losses in the tooth contact, as well as their impact on energy efficiency in spur gear transmissions. The coefficient of friction is approximated using two widely applied analytical lubrication models: the elastohydrodynamic and mixed elastohydrodynamic, both of which provide enough accurate values with a reasonable amount of computation burden in comparison with numerical methods. An additional contribution of this study is a sensitivity assessment of the energy efficiency of the cycloidal profile with regard to the auxiliary centrode diameters. This allows for an understanding of the geometrical constraints of this profile, specifically the maximum pressure angle—which is related to the radial loads applied to the shaft—and the tooth height—which is related to the bending moment at the tooth root—and hence, setting the appropriate ones to be equivalent to the involute profile. For the comparative analysis, equivalent profiles are selected based on similar tooth bending moments and radial loads supported by the shaft. After determining the centrode diameters of the cycloidal profile, the efficiency of both gear profiles and their sensitivity to gear size and gear ratio are compared. This study concludes that, for both profiles and friction analytical models, efficiency improves with increasing gear sizes and gear ratios, eventually converging to a constant value. Furthermore, both cycloidal and involute profiles exhibit comparable performance in terms of energy efficiency across both lubrication analytical models.