A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs

TLDR

Previous models lacked full validation and could not predict both dynamic transmission error and various dynamic factors. This study develops finite‑element and discrete dynamic models for spur gear pairs, validates them experimentally, and seeks to establish a direct link between dynamic transmission error and dynamic factors derived from tooth forces and root stresses. The authors compute DTE and DF from gear mesh loads, tooth loads, and bending stresses across a wide range of speeds, contact ratios, and torques, using the two models and experimental data. Simplified formulas relate predicted DF and DTE, and the study quantifies how nonlinear effects such as tooth separations and jump discontinuities affect DF.

Abstract

In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.