Development of a free-form tooth flank optimization method to improve pitting resistance of spur gears

Abstract

Although steel involute gears are the standard solution for gear transmissions, they tend to suffer from poor pitting resistance. Pitting typically occurs when the gear tooth flanks have high equivalent curvature at the contact point and/or when the equivalent curvature is not constant across the contact path leading to high contact pressures and the development of surface fatigue. In this paper a new optimization method is presented to produce spur gear tooth flanks with improved pitting performance compared to involute ones. The tooth flanks are represented as B-spline curves, the control points of which are the variables for the optimization problem. The constraints were designed to ensure that all the examined profiles satisfy the law of gearing and do not contain any cusps or C1 discontinuities. Deterministic and stochastic algorithms were implemented and both closed and open path of contact gear sets were examined to determine the optimum tooth profile. The optimization results show that the maximum equivalent curvature of the optimum profiles is reduced by 83% compared to the corresponding standard profiles, while the deviation from the mean value is reduced by 98%. Both the standard and the optimized gears where examined comparatively also through finite element analysis. For the case selected the maximum contact pressure developed on the optimized gear set was 77% of the respective maximum contact pressure on the standard gear set whereas the corresponding deviation from the mean value was 5%. At the same time, the bending stresses developed in the optimized gear are slightly lower than those in the standard one.

Improving the wear resistance of 3D printed spur gears through a free-form tooth flank optimization process

“…Building upon the research presented in [15], the objective of the optimization process is to establish a systematic algorithmic procedure capable of generating optimized tooth flanks that adhere to the fundamental principles of gearing (Fig. 1).…”

“…While this approach can be meaningful in certain cases (i.e., to ensure an easy-to-manufacture rack cutter profile), there is a desire among designers to directly control the shape of the tooth flank, which in turn directly affects the desired performance improvements. However, a common challenge arises when applying Buckingham's analytical theory of gearing [24], as it requires solving an implicit equation to calculate the conjugate profiles [15]. Incorporating a numerical convergence algorithm to solve this equation would significantly increase computational cost and potentially undermine the reliability and robustness of the optimization process.…”

“…Bspline curves are employed to model these profiles, and certain modelling challenges are discussed, such as undercutting or cusps in the conjugate profiles. Furthermore, Kalligeros et al [15] presented a comprehensive free-form optimization method aimed at enhancing the pitting resistance of spur gear tooth flanks. The tooth profiles are represented as B-spline curves, and the positions of their control points are optimized to achieve a minimum and uniform distribution of relative curvature along the contact path.…”