In order to reflect the backlash distributions of harmonic gears more accurately,the tooth root positioning methods of flexspline were improved in the backlash algorithm,and the tooth profile equations under the coordinate transformation was established instead of the tooth thickness equations in the original backlash algorithm.Both of the methods for calculating the backlashs based on circumferential displacement positioning and arc length positioning were proposed.The finite element model of planar tooth rings with involute tooth profile was established,and the backlash distributions under no-load conditions was obtained.Comparing the theoretical backlashs with that from the finite element model,their consistency is excellent.In order to reveal the causes of the backlash deviations,the radial displacement,the circumferential displacements and the normal rotation angles of the flexspline neutral layers in the finite element model were obtained,and the circumferential polar angles were solved to compare with the theoretical algorithm.The circumferential displacements of the flexspline teeth are the major factor of the backlash deviations.%为更真实地反映谐波齿轮的侧隙分布,改进侧隙算法中柔轮齿根的定位方式,建立坐标变换下的齿廓方程以代替原有侧隙算法中的齿厚方程,提出基于周向位移定位和弧长定位的侧隙计算方法,建立含渐开线齿廓的平面齿圈实体有限元模型,获得空载啮合状态下侧隙分布.将理论计算的侧隙值与有限元模型计算的侧隙值比较发现,两者所得结果一致性较高.同时为了揭示侧隙偏差的来源,获取了有限元模型柔轮中性层的径向位移、周向位移和法线转角,并求解了周向位置极角.与理论算法结果比较发现,柔轮齿根周向位移偏差是引起侧隙偏差的主要因素.
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