Piezoelectric actuators are widely used in precision equipment because of their rapid response, high motion accuracy, and immunity to electromagnetic interference. However, the multi-scale characteristics of contact at the transmission interface between the stator and mover, along with stick-slip motion produce complex nonlinear behaviors in the mover system, resulting in difficulties in solving the dynamic response of the mover. To address this, a multi-asperity line contact mechanics model considering the substrate deformation and roughness is deduced based on the statistical approach to reflect the contact effect between the transmission interface more accurately. Moreover, the contact model is further extended, overcoming the asperity contact limit, to apply to slight and very heavy loads by introducing the Hertz solution. Furthermore, the stick-slip motion considering the tangential stiffness of the interface is solved through the iteration process to determine the stick and slip region. Newmark-β method is used to obtain the dynamic response of the mover when the normal and tangential contact stresses are calculated. Besides, a classical traveling wave piezoelectric actuator is selected for experimental verification of the proposed model. Numerical and experimental results show that the proposed model can effectively calculate the normal contact stress distribution and capture the evolution of stick-slip motion. The predicted torque-velocity curves have good agreement with the experimental values and the accuracy is higher than previous models. In addition, the proposed model can well predict the transient start-up characteristics of the mover. This research provides a theoretical reference for the modelling and dynamic response prediction of piezoelectric actuators, especially for small-size actuators.

中文翻译：

---

一种新型基于多凹凸度的动态 （MABD） 压电致动器模型：理论、数值框架和实验验证


压电致动器因其响应速度快、运动精度高和抗电磁干扰性而被广泛用于精密设备。然而，定子和动子之间传动界面接触的多尺度特性以及粘滑运动在动子系统中产生了复杂的非线性行为，导致难以求解动子的动态响应。针对这一问题，基于统计方法推导了考虑基体变形和粗糙度的多凹凸线接触力学模型，以更准确地反映传输界面之间的接触效应。此外，通过引入 Hertz 解决方案，进一步扩展了接触模型，克服了粗糙接触限制，适用于轻微和非常重的负载。此外，通过迭代过程求解考虑界面切向刚度的粘滑运动，以确定粘滑区域。Newmark-β 方法用于获得计算法向和切向接触应力时动子的动态响应。此外，选择经典行波压电致动器对所提出的模型进行实验验证。数值和实验结果表明，所提模型能够有效地计算法向接触应力分布，捕捉粘滑运动的演变。预测的扭矩-速度曲线与试验值吻合较好，精度高于以往模型。此外，所提模型能够较好地预测动子的瞬态启动特性。 本研究为压电致动器的建模和动态响应预测提供了理论参考，尤其是对于小尺寸致动器。