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Highlights • A general purpose method to model the complete dynamic response of the linear ultrasonic motors is presented. • The whole-machine model is solved at a low computational cost so that can be run on an average computer. • A linear ultrasonic motor with V-shaped stator is systematically investigated as an example. • An optimization method of electrical input parameters are designed by using this model. Graphical abstract Abstract A general purpose dynamic modeling method of linear ultrasonic motors (LUMs) is presented in this paper. The proposed model considers all the LUMs elements, including the stator, the mover and the contact between stator and mover. For the stator, a model in modal space was derived based on finite element method. The mover was analytically modeled with considering the complex contact between the stator and mover. The stator-mover intermittent contact problem was mathematically described by the normal and tangential contact model. Interpenetration-dependent penalty and continuous functions approximating to Coulomb friction were used to tangential contact and normal contact, respectively. A hybrid overall dynamic model was built by assembling all these models and solved at a low computational cost. The model enables us to understand the dynamic behavior of LUMs, including the vibration of stator, the contact process, the output performance of the mover and the interactive coupling between each element. The effectiveness of the developed model was validated in a LUM with V-shaped stator by comparing with available measurement results. Furthermore, this model was combined with the particle swarm algorithm to find the optimal electrical input parameters. It is believed that the proposed modeling method is useful for the performance evaluation and input parameters' optimization of LUMs. [ABSTRACT FROM AUTHOR]

Piezoelectric ultrasonic motor is an electromechanical coupling system, which is driven by the interface friction between the stator and the rotor/slider. A novel friction model is developed to study the stick–slip motion in a linear piezoelectric ultrasonic motor using longitudinal and bending modes. In this model, the influence of the ultrasonic oscillation on the dynamic friction coefficient is taken into account, which is described by a friction law related to the vibration amplitude at the interface. In addition, the friction contact model involves intermittent separation non-linearity induced by the variable normal force, which can result in complex stick–slip–separation motion at the contact interface. Analytical transition criteria between stick and slip are established by using the switch model. Based on the developed model, numerical simulations are performed to analyze the force transmission between the stator and the slider involving stick–slip motion. A transformed phase plane is proposed to study various states of the contact interface (stick, slip and separation), on which slip–separation, stick–slip, stick–slip–separation, and pure stick motions are intuitively characterized. The influence of some input parameters on the stick–slip motion is analyzed. Furthermore, the low-voltage dead-zone behavior is clarified by stick motion. [ABSTRACT FROM AUTHOR]

A vibro-impact system is proposed to investigate the normal motion and impact of the driving foot of the linear ultrasonic motors based on longitudinal and bending modes. Using coefficient of restitution (CoR) method a dynamical model is developed to simulate the normal impacts between the stator and mover taking into account the preload and vibration of barycenter of the stator. Furthermore, the sticking motions that can occur are simulated when the stator impacts the mover via a Lagrange multiplier. It is shown that the sticking motions occurring in the system are affected by some factors like CoR, preload and stiffness of the preload spring in clamping parts. Results indicate that a friction material with a higher hardness, modest preload and stiffness of the preload spring can weaken sticking motion in the system. [ABSTRACT FROM AUTHOR]