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.

Frictional power losses on spur gears with tip reliefs. The friction coefficient role

“…As something worth of mention, this LCM takes into account the torque level and profile modification effects on the friction coefficient and load sharing. This LCM has been previously developed by the authors [13,16,44], extended to the modelling of planetary gears [20,21] and currently used to calculate the efficiency of spur gear transmissions [9,10]. This LCM allows for including profile modifications, which affect directly the dynamic behaviour and efficiency of the system, as well as opens the possibility of studying manufacturing and assembly errors [14,15] effects on power losses.…”

Gear transmission rattle: Assessment of meshing forces under hydrodynamic lubrication

“…Nevertheless, they are not only used for this specific application but in aeronautic [3], energy [19,22], agricultural sectors [16], among others. In gearboxes, there is a gear/stage, which is called active, that transmit the power from the input to the output shaft.…”

Effects of Tooth Breakage Size and Rotational Speed on the Vibration Response of a Planetary Gearbox

“…where k(X) is the healthy gear pair mesh stiffness defined in Equation (3). Taking this model into Equation (10), the nonlinear mesh stiffness model for a gear pair with one tooth broken is obtained as Equation (14),…”

“…Iglesias et al developed a hybrid method of the analytical solution and the finite element model for the contact force calculation [3], and they studied the effect of manufacturing errors such as eccentricity and planet pin positioning errors on the load sharing behavior of a three-planet planetary transmission [4]. Sun et al built a lumped-parameter model of a two-stage helical planetary gear transmission system and studied the dynamic sensitivity of the load-sharing coefficient to errors [5].…”