Mathematical Model of Dynamic-Kinematic Error of a Harmonic Drive

Reducing the kinematic error when designing a high-precision drive with a harmonic gear train (HGT) is an urgent task. Currently, a large number of studies have been conducted to determine this parameter, but the effect of the wave generator rotation frequency on the kinematic error of the HGT has been considered insufficiently. A mathematical model is proposed for determining the frequency response of the HGT dynamic-kinematic error, taking into account the elastic interaction of its elements and the error of the cam mounting. The results of the calculated determination of the frequency response of a HGT with a cam wave generator are presented. The presence of several resonant frequencies that occur due to periodic changes in the relative position of the HGT elements and the vector of the cam mounting error is defined. It is proved that the two main resonant frequencies are caused by the rotation of the vector of the cam mounting error relative to the large axis of the wave generator and the balls of the flexible bearing.

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