Analysis of static transmission error in harmonic drives based on error mechanism and experimental data phenomenology

JIA Hang; WANG Peng; MA Mingjian; WANG Cheng

doi:10.16578/j.issn.1004.2539.2026.06.003

Abstract：[Objective]Static transmission error is one of the main indexes for evaluating the performance of harmonic drives.Its characteristics can reflect internal machining and assembly defects of the reducer and directly affect the service life.Therefore,revealing its formation mechanism is of great significance.[Methods]Firstly,considering the flexible transmission effect of the flexspline cup,a spatial kinematic model was established to analyze the influence of flexspline working deformation on transmission error.Secondly,error sources were divided into two categories:radial misalignment error and tangential tooth error.Combined with the structural characteristics of the reducer,the frequency characteristics of transmission error under independent and comprehensive actions of error sources were analyzed,and a simplified mathematical model of static transmission error for harmonic drives was proposed.Then,the resampling order analysis method was adopted to process test data and identify model parameters.Finally,the rationality of the simplified model was verified by test data,and two typical machining and assembly quality defects were analyzed.[Results]The results show that the transmission error includes four periodic fluctuation components with different frequencies and one offset constant;the dominant frequency component in typical transmission error curves is 2ωb(ωb is the rotational frequency of the wave generator).When there are abnormal defects in machining or assembly,the amplitude of error components with frequencies of ωb or ωb/N(N is the transmission ratio of the reducer)increases;due to the existence of two error components with close frequencies,the transmission error curve exhibits a beat frequency characteristic;the relative error between model calculation and test results is 8%.