Theoretical And Experimental Research On A Plate Type Two-degree-of-freedom Piezoelectric Motor

Multi-degree-of-freedom (DOF) motor is widely used in electromechanical system which need more than one degree of freedom motion, such as robot joints, panoramic camera systems, optical tracking devices, et al. Compared with the driven form that multi-DOF is achieved by single-degree-of-freedom motors (each of single-degree-of-freedom motors is independently responsible for one dimension of motion, which can be either translation or rotation), multi-DOF motor has superiorities in high integration in structure and high efficiency in the utilization of materials and components which is benefit to simplify the structure, reduce the size and weight of electromechanical system, and thereby improve the accuracy and dynamic performance of electromechanical system.Piezoelectric driving technology has great potential in the field of multi-DOF motor. To apply piezoelectric driving technology in multi-DOF motor has been gradually in-depth researched in recent decades. This dissertation is supported in part by the National Natural Science Foundation of China [grant number 50735002] and the major projects foster fund for university science and technology innovation of Ministry of Education of China [grant number 708028], and focuses on the development of multi-DOF piezoelectric actuators. Based on the fully analysis of the state of the art of multi-DOF piezoelectric actuators, a novel two-degree-of-freedom (two-DOF) piezoelectric motor using only one piezoelectric ceramic is proposed. The notable feature of the developed piezoelectric motor is that multiple piezoelectric elements in the reported motors used to achieve multi-DOF are optimized into a single piezoelectric element. It's compact, easy to manufacture and assembly, and easy to control. The proposed motor can rotate a sphere 2³ times larger than its stator in volume. Therefore, it is available for miniaturization and offers a wide range of engineering applications.In this dissertation, theoretical analysis, finite element simulation, design and processing, prototype testing and other methodologies are used to develop the two-DOF piezoelectric motor using single plate type piezoelectric vibrator. The motion mechanism of the two-DOF piezoelectric motor is revealed, design theory of the plate type two-DOF piezoelectric motor is obtained, and performance and driving ability of the motor are mastered. These research conclusions provide a basis for the practical application of two-DOF piezoelectric motor.1. Motion mechanism of the plate type two-DOF piezoelectric motorBased on the review of the working principles and driven wave signals used in the current developed multi-DOF piezoelectric motors, the elliptical motion formation mechanism of the particles on the surface of the piezoelectric vibrator is analyzed, the characteristics of traveling wave driven and standing wave driven are described and a plate type piezoelectric vibrator for multi-DOF piezoelectric motors is proposed. The working principle of the piezoelectric vibrator used in the B₂₃ and B₃₂ modal, B₄₃ and B₃₄ modal to form two-DOF motion is analyzed. The elliptical motion formation mechanism of the tip of the protrusion is examined, which shows that the motion trajectory of the tip of the protrusion is composed of the vertical displacement given by vibration of the substrate and the horizontal displacement given by the first bending vibration of the protrusion. The horizontal displacement caused by the protrusion lags behind the vertical displacement caused by the substrate. The tip of the protrusion can form an elliptical trajectory. The finite element model of the piezoelectric vibrator is established. By the use of ANSYS software, multi-order vibration modes of the piezoelectric vibrator are obtained in modal analysis, and the elliptical trajectory of the four contact points between the stator and the sphere is demonstrated in transient analysis. The simulation results show that the deformation of protrusions which support the sphere is about 30 percent of that of those which drive the sphere, and the four contact points can form timing reasonable elliptical trajectory which can be used to drive the sphere to form two rotation degrees of freedom. Theoretical analysis and finite element simulation verify the feasibility of the working principle for the motor.2. Vibration analysis of the plate type piezoelectric vibratorThe piezoelectric vibrator is taken as a homogeneous isotropic plate in vibration analysis. According to Rayleigh-Ritz method, the basic formula for calculating the vibration frequency of the piezoelectric vibrator is established by using beam function combination method which is suitable for various boundary conditions. Based on the basic formula, the vibration frequency calculation method is investigated in consideration of the protrusions and the supporting columns. The protrusions are taken as additional quality and the supporting columns are taken as elastic supporting point. The vibration frequency calculation formulas in free vibration state and four-point support condition are established by further derivation. The motion equation of the piezoelectric vibrator under external force and external electric field is derived based on the basic assumptions of small deflection bending and laminated plate theory. The expression for calculating the internal forces (including force and moment) generated by the piezoelectric vibrator bending vibration is established. According to Ritz method, the virtual work equation of the piezoelectric vibrator is established, and the deflection solving formulas of the piezoelectric vibrator in B₂₃, B₃₂, B₃₄ and B₄₃ vibration modes are given. The deformation of the tip of the protrusion is solved, and the elliptical trajectory equation of the contact point is obtained. Vibration analysis of the plate type piezoelectric vibrator provides a significant theoretical basis for the structural design and performance examination of the piezoelectric motor.3. Design and analysis of the plate type two-DOF piezoelectric motorThe deflection and working frequency of the piezoelectric vibrator which are set as the target variable for the structural optimization are numerical analyzed with the structural parameters such as aspect ratio, substrate thickness and the height, width, thickness of the protrusion set as the variables. Numerical rules between the structural parameters and the deflection and working frequency of the piezoelectric vibrator are obtained. The design principles for the structural parameters of the piezoelectric vibrator are further determined and verified by finite element simulation. A piezoelectric vibrator is fabricated based on the results of numerical analysis and finite element simulation to test the vibration frequency of the piezoelectric vibrator and the tip displacement of the protrusion. The experiment results illustrate the validity of the main conclusions in theoretical analysis and simulation analysis. A two-DOF spherical piezoelectric motor is constructed by using the piezoelectric vibrator. Issues in the specific application of the piezoelectric vibrator and the preload mechanism between the piezoelectric vibrator and sphere are discussed. Contact static analysis is carried out for the two-DOF spherical piezoelectric motor, the force transmission relationship between the stator and rotor are investigated, the output torque expression is established and influence factors of the output torque are obtained.4. Experimental research on the plate type two-DOF piezoelectric motorBased on the review of the measurement methods used in the existing multi-DOF spherical motor, a multi-DOF spherical motion measurement method is proposed. Two contact measurement program and a non-contact measurement program are offered. The measuring principle of the non-contact measurement program for two degrees of freedom motion measurement resolved from a single measurement point is investigated, and the measurement procedure is given. Experimental measurement systems of the three measurement programs are set up, the experiment results show that the measurement error of the three measurement programs is very small, and these measurement programs can be used in the multi-DOF spherical motion measurement of our proposed piezoelectric motor. Kinematic capability and drive performance of the two kinds of prototype based on B₂₃ and B₃₂ modes, B₄₃ and B₃₄ modes, respectively, are test using the constructed measurement system. The relationship between the driven frequency, driven voltage and the rotation speed, the transient response characteristics and mechanical properties of the two kinds of piezoelectric motor are obtained. Analysis of test results demonstrates that the consistency of spacing of the protrusions should be primarily guaranteed in the manufacturing process of the piezoelectric vibrator. The main performance indicators of the piezoelectric motor are: the rotation speed of the motor based on B₂₃ and B₃₂ modes around an axial along the direction of length of the piezoelectric vibrator is 37.7r/min under the drive voltage 90V and excitation frequency 43.8kHz, and its stall torque is 1.15mNm; the rotation speed of the motor based on B₄₃ and B₃₄ modes around an axial along the direction of length of the piezoelectric vibrator is 89.35r/min under the drive voltage 90V and excitation frequency 99.5kHz, and its stall torque is 1.34mNm. The external environment and internal factors impacted on the performance of the piezoelectric motor are also analyzed which provides a reference to further improve the performance of the piezoelectric motor.5. Drive control circuit of the plate type two-DOF piezoelectric motorA drive control circuit which meets the operating requirements of the piezoelectric motor is designed. The circuit can achieve stable voltage, and adjust the drive signal to track the working frequency according to the demands in the operation of the piezoelectric motor. Electrical matching between the drive control circuit and the piezoelectric motor is discussed. And the parasitic harmonics can be effectively reduced by reasonably setting the relationship between inductances and capacitances in the amplification circuit and by setting the duty cycle as 1/3. Method for tracking the optimal working frequency by the use of Phase Locked Loop (PLL) technology is also discussed.This study covers piezoelectrics, mechanology, mechanics, vibration analysis, electricity, cybernetics and other multi-disciplinary knowledges. The research in this dissertation provides new ideas for the research of multi-DOF piezoelectric drive mechanism, a research foundation for the applications in omnidirectional wheels, robot ball joints, panoramic camera system and other electromechanical systems, and a reference for the development of similar mechanical structure.