Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis (TCA) and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.%摆线针轮减速器由于其结构紧凑、传动比大和高刚性等优点,被广泛应用于工业领域.齿轮的啮合刚度是高准确性齿轮动力学模型的关键参数.然而,现在没有计算摆线针轮齿轮副啮合刚度的分析模型.这是由于其齿轮副背隙确定的困难性以及啮合过程中多齿接触变形的复杂性.本文考虑齿廓修形与偏心距误差的影响,提出了计算摆线针轮齿轮副啮合刚度的新方法.基于轮齿接触分析与非线性赫兹接触理论,分别确定了摆线针轮齿轮副的时变啮合参数与载荷分布,并用于单齿对的接触刚度以及多齿对的扭转刚度的准确计算.通过详细的参数分析,揭示了齿廓修形、应用转矩和偏心距对扭转啮合刚度、承载传动误差、赫兹接触应力和载荷分布因子的影响.该模型可用于对摆线针轮减速器的回差与动态特性的进一步研究,有助于优化其传动精度、振动与噪声等级.
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