Study on influence of tooth thickness and pitch deviation on hysteresis error of single-tooth meshing harmonic gears

SHENG Huacheng; CHEN Xiaoxia; XING Jingzhong

doi:10.16578/j.issn.1004.2539.2026.03.004

Abstract：[Objective]Aiming at the unclear correlation between tooth thickness,cumulative pitch deviations and hysteresis error of single-tooth meshing harmonic gears,the distribution law and key influencing factors of hysteresis error were revealed,providing a reference for the optimization of harmonic gear transmission accuracy.[Methods]Firstly,discrete point data of the tooth profiles of the circular spline and flexspline were obtained by an image measuring instrument,and cumulative pitch deviation and tooth thickness deviation were extracted to provide accurate basic data for modeling.Secondly,a geometric model of hysteresis error for single-tooth meshing was constructed based on the deviation data,and transmission error expressions for forward and reverse rotations were derived to establish the correlation mechanism between deviations and hysteresis error.Then,hysteresis errors under single-wave and double-wave transmissions were calculated through left and right meshing angle errors to compare the transmission characteristics of different wave numbers.Finally,combined with the balancing effect of meshing zones,the smoothing effect of multi-wave transmission on output end error was analyzed to clarify the advantages of multi-wave transmission.[Results]The results show that the hysteresis error of harmonic gears is negatively correlated with the tooth thickness deviation of the fixed gear and positively correlated with the tooth space width deviation.Compared with single-wave transmission,the amplitude of hysteresis error of double-wave transmission is reduced by 32.2%,the amplitudes of left and right meshing angle errors are reduced by 23.1%and 34.3%respectively,the envelope diagram of the curve has higher consistency,and the transmission stability is significantly improved.