Advanced model for the calculation of meshing forces in spur gear planetary transmissions

Abstract

This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute–involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 + 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies’ flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.