In a piezoelectric ultrasonic motor (USM) or resonance drive type piezoelectric motor (RPM), movement is generated between a vibrator (stator) and a slider (rotor). Since the microscopic vibrations on a stator are transferred to a slider through friction interaction, the movement of a slider has a nonlinear characteristic due to the nature of the friction force. This nonlinear behavior causes large position errors due to the occurrence of discontinuous stick-slip movements and unpleasant audible noise, especially at a low velocity drive. This friction induced acoustic sound is magnified at low velocities as the natural frequency of the mechanical system of a piezoelectric motor with mass and the holding and prestress spring forces are dependent on the closed loop motion controller. This study addresses the abovementioned issues. First, a mechanical model, which considers the nature of movements in a resonance drive type piezoelectric motor, was established. The model could suitably define the friction induced forced vibration and noise source. Second, a new driving method for resonance drive type piezoelectric motors was proposed, in which the piezoelectric vibrator was excited using two driving sources at two different frequencies. The difference between the two excitation frequencies was synchronized to the servo sampling frequency of the digital control unit. Finally, the performance of the proposed driving method was compared with those of the conventional driving methods. It was noted that in addition to the realization of silent and smooth low velocity movements, the positioning error for the linear movements between the desired and actual positions decreased to less than 10 nm for velocities ranging from 1 mm/s to 0.001 mm/s.
Ultrasonic motors employ resonance to amplify the vibrations of piezoelectric actuator, offering precise positioning and relatively long travel distances and making them ideal for robotic, optical, metrology and medical applications. As operating in resonance and force transfer through friction lead to nonlinear characteristics like creep and hysteresis, it is difficult to apply model-based control, so data-driven control offers a good alternative. Data-driven techniques are used here for iterative feedback tuning of a proportional integral derivative (PID) controller parameters and comparing between different motor driving techniques, single source and dual source dual frequency (DSDF). The controller and stage system used are both produced by the company Physik Instrumente GmbH, where a PID controller is tuned with the help of four search methods: grid search, Luus–Jaakola method, genetic algorithm, and a new hybrid method developed that combines elements of grid search and Luus–Jaakola method. The latter method was found to be quick to converge and produced consistent result, similar to the Luus–Jaakola method. Genetic Algorithm was much slower and produced sub optimal results. The grid search has also proven the DSDF driving method to be robust, less parameter dependent, and produces far less integral position error than the single source driving method.
The main goal of this paper consists in the modeling of rate-dependent behavior of piezoelectric materials within a three-dimensional finite element setting. We propose a rate-dependent polarization framework which is applied to cyclic electrical loading at various frequencies. The reduction in free energy of a grain is used as a criterion for the onset of the domain switching process. Nucleation in new grains and propagation of the domain walls during domain switching is modeled by a linear kinetics theory. Averaging over all individual grains renders the macroscopic response of the bulk material. Intergranular effects, which are essential for realistic simulations, are phenomenologically captured via a probabilistic approach. The presented numerical examples, as based on the proposed three-dimensional finite element framework, are related to the simulation of PIC-151 ceramics. In particular, averaged electric displacement versus electric field curves are plotted and compared with experimental data reported in the literature.
In this contribution a micromechanically motivated model for rate-dependent switching effects in piezoelectric materials is developed. The proposed framework is embedded into a three-dimensional finite element setting whereby each element is assumed to represent an individual grain. Related dipole (polarization) directions are thereby initially randomly oriented at the element level to realistically capture the originally un-poled state of grains in the bulk ceramics. The onset of domain switching processes is based on a representative energy criterion and combined with a linear kinetics theory accounting for time-dependent propagation of domain walls during switching processes. In addition, grain boundary effects are incorporated by making use of a macromechanically motivated probabilistic approach. Standard volume-averaging techniques with respect to the response on individual grains in the bulk ceramics are later on applied to obtain representative hysteresis and butterfly curves under macroscopically uniaxial loading conditions at different loading frequencies. It turns out that the simulations based on the developed finite element formulation nicely match experimental data reported in the literature.
In this paper, a three-dimensional micromechanical model is presented for simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The model is based on linear constitutive, nonlinear domain switching, and linear kinetics theories. The simulation starts with a virgin bulk material of randomly oriented grains. Then the material is electrically loaded with an alternating voltage of various frequencies, which are in the order of 0.01 Hz to 1 Hz. An energy equation in combination with a probability function is used to determine the onset of the domain switching inside the grains. Such a probability function leads to a better phenomenological model for the domain switching even for electrical loadings, which are in a range far below the coercive fields. The propagation of the domain wall during the domain switching process in grains is modeled by means of linear kinetics relations after domain nucleation. The response of the bulk ceramic is predicted by averaging the response of individual grains using Euler angles for the transformation from local coordinates of the grains to global coordinate. Electric displacement hysteresis loops for different frequencies and amplitudes of the alternating electric fields are simulated. A simple micromechanical model without the probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature.
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