Transmission error compensation method for harmonic reducer based on cross-rod distance selection

XU Xiangyang; LIU Tingkuan; DU Xuesong; WEI Peitang; SONG Hailan; ZHANG Han

doi:10.16578/j.issn.1004.2539.2026.06.002

Abstract：[Objective]To address the problem of transmission accuracy degradation caused by tooth thickness deviations of flexspline and circular spline as well as profile errors of wave generator during the manufacturing of harmonic reducers,the influence mechanism of cross-rod distance(M-value)on transmission error was investigated,and an effective part selection compensation method was proposed.[Methods]Firstly,a two-dimensional finite element model of the harmonic reducer was established using SolidWorks software and HyperMesh software to provide a simulation basis for multi-factor error influence analysis.Secondly,Box-Behnken design(BBD)test was carried out with Design Expert software to quantitatively analyze the sensitivities of the peak-to-peak value of transmission error to the three deviations.Then,an error compensation scheme based on cross-rod distance was formulated combining the machining accuracy of parts and sensitivity analysis results.Finally,experimental verification and spectral analysis were conducted on a comprehensive performance test bench for harmonic reducers to test the effectiveness of the compensation scheme.[Results]The results show that the profile size deviation of the wave generator has the highest sensitivity to the peak-to-peak value of transmission error.The transmission error presents a trend of first decreasing and then increasing with the increase of the three deviations,and there is a significant compensation relation among various factors.Reasonable selection of flexsplines according to the positive and negative deviations of the circular spline M-value can reduce the peak-to-peak value of transmission error to a minimum of 24 arcseconds,and the deviation between the measured value and the theoretical value is no more than 10%.The cross-rod distance selection has the most prominent inhibitory effect on the second-order frequency component of transmission error.The proposed method can provide a reference for high-performance selection and precision control of harmonic reducers.