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

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.The authors would like to acknowledge Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology

The torsional stiffness of involute spur planetary gears

This paper presents the results of torsional stiffness analysis of involute spur planetary gears in mesh using finite element methods. A planetary gear model with 3 planet gears and its subsystem models have been developed to study the relationship between the overall torsional stiffness and the subsystem torsional stiffness. The subsystem models include one isolated sun-planet-ring pair, one isolated sun-planet external pair and one isolated planet-ring internal pair. A strategy utilising a small preload step via a weak spring was first applied to eliminate the gap between the teeth and then different torque levels were applied to calculate the transmission error due to the resulting elastic deformations. This calculation was repeated at multiple positions covering two tooth mesh cycles in the overall and subsystem models. The theoretical gear contact position was determined using an ANSYS APDL program and the gear rolling range was digitized into equidistant rolling angles. The sun-planet torsional stiffness variation has been shown to dominate the combined torsional stiffness and, based on the subsystem torsional stiffness, an analytical method for predicting the overall torsional stiffness is presented