为了提高航天器、机器人等含谐波齿轮传动装置的复杂机械设备的工作精度和运行可靠性，对机械设备中谐波齿轮传动环节的精确建模已成为当前研究的重点。谐波齿轮传动属于柔性传动，其内部存在复杂的非线性动力学行为，而这些动力学行为严重地影响谐波齿轮传动系统在工作中的传动性能。对谐波齿轮传动系统的动力学行为及其建模方法进行了综述：介绍了谐波齿轮传动系统中运动学误差、摩擦和柔性的主要来源、基本性质及其对传动性能的影响规律；总结了描述上述行为常用的动力学模型（运动学误差模型、摩擦模型、非线性刚度模型和滞回刚度模型）的构成、特点及适用范围。指出滞回刚度模型和考虑系统柔性的运动学误差模型是目前谐波齿轮传动系统动力学研究的重点和难点问题，并针对当前谐波齿轮传动系统的动力学建模方面存在的一些不足，提出了该领域需要进一步研究的若干问题。%In order to meet the requirement of higher precision and reliability of complex harmonic drive-based devices,including robot and spacecraft,an accurate modeling for harmonic drive system is the focus of current research.Harmonic drives operate on the principle of elastic deformation of flexspline,and exhibit complex nonlinear dynamic behavior,which seriously degrade the transmission performance.In this paper,studies on the dynamic behavior of harmonic drive system and associated modeling ap-proaches are reviewed.Firstly,the main source and basic properties of kinematic error,friction and compliance and their effects on the transmission performance of harmonic drive system are analyzed.Then,a variety of dynamic models of harmonic drive sys-tem are summarized,including kinematic error model,friction model,nonlinear stiffness model and hysteresis stiffness model. More specifically,forms,characteristics and applicability of these models are discussed in detail.It is shown that the hysteresis stiffness model and the compliance-dependent kinematic error model are two key issues in dynamic modeling of harmonic drive system nowadays.Finally,some topics to be further studied are presented.
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