新型杆式压电电机研究
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摘要
杆式压电电机是一种利用压电陶瓷的逆压电效应来激励定子产生共振进而实现驱动的新原理电机，是压电学、材料学、弹性力学、机械振动学、摩擦学、超精密加工、电力电子和控制理论等多学科交叉发展的结晶。与其他类型压电电机相比，具有结构简单、加工方便等优点，在航空航天、精密器械、微型机器人、医疗设备等领域具有广阔应用前景。传统杆式压电电机存在着输出力矩较小，效率和寿命较低，不适合长时间连续运转，且定转子间的摩擦材料要求较苛刻等不足，为此本文提出一种新型杆式压电电机。该电机利用活齿啮合取代传统杆式压电电机定、转子间的摩擦力来驱动转子旋转，从而减小摩擦和磨损，实现电机低速、大扭矩、高稳定性的目的。
本文首先提出了一种新型杆式压电电机，并阐述了其工作机理。根据Власов半无矩柱壳理论，运用能量法，推导了新型杆式压电电机传动系统中关键零件——柔轮变形能和电机输出力矩的计算公式，得出了柔轮平均变形能和电机的平均输出力矩。讨论了柔轮变形能和电机输出力矩随电机参数的变化规律。研究发现：电机的输出力矩随传动比、柔轮厚度和施加在定子陶瓷片上电压的增大而增大，随柔轮长度的增大而减小。活齿半径对电机的输出力矩没有影响。
在壳体理论的基础上，建立了柔轮在一端固定一端自由边界条件下，自由端在径向受啮合活齿作用的中曲面上各项位移、内力和应力的函数方程，研究了各项位移和各项应力的分布规律，讨论了柔轮自由端处各项位移和固定端处各项应力随相关参数的变化规律。研究发现：为得到较大的柔轮径向位移以增大电机的输出力矩，应适当选择较大的壳体长度、合理的传动比以及施加在陶瓷片上的工作电压。
建立了啮合活齿在中心轮内齿廓不同位置处的力学平衡方程，得出了柔轮、活齿架和中心轮对啮合活齿的作用力表达式。分析了活齿的接触变形、接触应力和啮合刚度随活齿架转角的变化关系。研究了参数变化对活齿所受作用力、应力和接触变形量以及啮合刚度的影响。
借鉴Donnell壳体理论和振动理论，分别建立了新型杆式压电电机传动系统中柔轮的动力学模型及其活齿传动系统动力学模型。对系统进行了振动分析，得出了柔轮和传动系统在啮合活齿个数变化情况下的振动模态。讨论了相关参数变化对系统动态特性的影响。运用有限单元法对新型杆式压电电机定子的模态和谐响应进行了分析。研究了新型杆式压电电机定子的固有频率和定子上端摆动幅度随参数的变化规律。
进行了新型杆式压电电机样机的结构设计、制作和原理性实验。对样机定子一阶弯曲共振频率进行了测试，测量结果和计算值基本一致。
Bar-type piezoelectric motor is a kind of motor which uses the inverse piezoelectriceffect of the piezoelectric ceramic to excite the stator to produce resonance, and thenachieve power transmission. It is the crystallization of the piezoelectric science, materialsscience, elasticity, mechanical vibration, tribology, ultra-precision machining, powerelectronics and control theory, etc. multidisciplinary development. Compared with othertypes of piezoelectric motor, It has the advantages of simple structure, easy to process,and has broad application prospects in the field of aerospace, precision instruments,micro-robots, medical equipment. The traditional rod piezoelectric motor there is lessoutput torque, low efficiency and lifetime, and is not suitable for continuous operation fora long time, and given harsh insufficient friction material requirements between the statorand the rotor. So this paper proposes a new bar-type piezoelectric motor. The motor usemovable teeth meshing replace the friction between the stator and the rotor of thetraditional rod piezoelectric motor to drive the rotor rotating, thereby reducing frictionand wear, achieving the purpose of low speed, high torque, high stability.
A novel bar-type piezoelectric motor is firstly proposed. The working mechanism ofthe motor is described. According to Власов semi-cylindrical shell theory withoutmoments, using the energy method, The calculation formula of the flexible ringdeformation energy which is the key part in the new bar-shaped piezoelectric motor drivesystem and the motor output torque are derived. The average deformation energy of theflexible ring and the average output torque of the motor are also given. And thedeformation energy of the flexible ring and the motor output torque with parameters arediscussed. Results show: The output torque of the motor increases along with the driveratio, the thickness of the flexible ring and the voltage applied to the ceramic plates in themotor stator increase, decreases with increasing the length of the flexible ring. Movabletooth radius has no effect on the output torque of the motor.
At one fixed end and the other free end boundary condition, the function equationsof the radial displacement, internal forces and stress of the flexible ring are established bythe action of the free end of the meshing movable tooth on the basis of the shell theory.The distribution of the displacements and stresses are researched, the changes of thevarious displacements of the free end of the flexible ring and all kinds of stresses at thefixed end along with the relevant parameters are discussed. Results show: In order toobtain larger the flexible ring radial displacement for increasing the output torque of themotor, longer length of the flexible ring, and reasonable transmission ratio and largerexciting voltage applied to ceramic plate.
The mechanical equations of meshing teeth in different position of the fixed rigidgear internal profile were established. The forces expressions from the flexible ring, therotor and the rigid gear were obtained. Changes of the movable tooth contact deformation,contact stress and the meshing stiffness with rotating angle of the rotor are analyzed. Theinfluences of suffered force, stress and contact deformation by movable tooth as well asmeshing stiffness with relative parameters changing are studied. Results show: Comparedwith other contacts, contact force, contact stress and meshing stiffness between themovable teeth and the rigid gear are the largest. Meshing movable teeth are in the middleposition of the rigid gear working profile, each amount of change is small, the outputtorque is more stable.
Learn from Donnell shell theory and theory of vibration, the dynamics models offlexible ring and movable teeth transmission for a novel bar-shaped piezoelectric motordrive system are proposed. Vibration analysis is done. With the meshing movable teethnumbers changing, vibration modes between the flexible ring and movable teeth drivesystem are given. Mean while, it is analyzed which the system's dynamic characteristicsare influenced by the relevant parameter's variation. The modal and the harmonyresponse analyses of the stator of the bar-type piezoelectric motor are done by using thefinite element method. Variation of the natural frequencies of the new bar-shapedpiezoelectric motor stator and the swing amplitude of the stator along with parameters areresearched.
The structure design and experimental prototype of the new bar-shaped piezoelectricmotor are given. The principle experiment of the motor is done. Finally, measure the firstbending resonance frequency of the prototype stator. The measurement results and thecalculated values are consistent.
本文首先提出了一种新型杆式压电电机，并阐述了其工作机理。根据Власов半无矩柱壳理论，运用能量法，推导了新型杆式压电电机传动系统中关键零件——柔轮变形能和电机输出力矩的计算公式，得出了柔轮平均变形能和电机的平均输出力矩。讨论了柔轮变形能和电机输出力矩随电机参数的变化规律。研究发现：电机的输出力矩随传动比、柔轮厚度和施加在定子陶瓷片上电压的增大而增大，随柔轮长度的增大而减小。活齿半径对电机的输出力矩没有影响。
在壳体理论的基础上，建立了柔轮在一端固定一端自由边界条件下，自由端在径向受啮合活齿作用的中曲面上各项位移、内力和应力的函数方程，研究了各项位移和各项应力的分布规律，讨论了柔轮自由端处各项位移和固定端处各项应力随相关参数的变化规律。研究发现：为得到较大的柔轮径向位移以增大电机的输出力矩，应适当选择较大的壳体长度、合理的传动比以及施加在陶瓷片上的工作电压。
建立了啮合活齿在中心轮内齿廓不同位置处的力学平衡方程，得出了柔轮、活齿架和中心轮对啮合活齿的作用力表达式。分析了活齿的接触变形、接触应力和啮合刚度随活齿架转角的变化关系。研究了参数变化对活齿所受作用力、应力和接触变形量以及啮合刚度的影响。
借鉴Donnell壳体理论和振动理论，分别建立了新型杆式压电电机传动系统中柔轮的动力学模型及其活齿传动系统动力学模型。对系统进行了振动分析，得出了柔轮和传动系统在啮合活齿个数变化情况下的振动模态。讨论了相关参数变化对系统动态特性的影响。运用有限单元法对新型杆式压电电机定子的模态和谐响应进行了分析。研究了新型杆式压电电机定子的固有频率和定子上端摆动幅度随参数的变化规律。
进行了新型杆式压电电机样机的结构设计、制作和原理性实验。对样机定子一阶弯曲共振频率进行了测试，测量结果和计算值基本一致。
Bar-type piezoelectric motor is a kind of motor which uses the inverse piezoelectriceffect of the piezoelectric ceramic to excite the stator to produce resonance, and thenachieve power transmission. It is the crystallization of the piezoelectric science, materialsscience, elasticity, mechanical vibration, tribology, ultra-precision machining, powerelectronics and control theory, etc. multidisciplinary development. Compared with othertypes of piezoelectric motor, It has the advantages of simple structure, easy to process,and has broad application prospects in the field of aerospace, precision instruments,micro-robots, medical equipment. The traditional rod piezoelectric motor there is lessoutput torque, low efficiency and lifetime, and is not suitable for continuous operation fora long time, and given harsh insufficient friction material requirements between the statorand the rotor. So this paper proposes a new bar-type piezoelectric motor. The motor usemovable teeth meshing replace the friction between the stator and the rotor of thetraditional rod piezoelectric motor to drive the rotor rotating, thereby reducing frictionand wear, achieving the purpose of low speed, high torque, high stability.
A novel bar-type piezoelectric motor is firstly proposed. The working mechanism ofthe motor is described. According to Власов semi-cylindrical shell theory withoutmoments, using the energy method, The calculation formula of the flexible ringdeformation energy which is the key part in the new bar-shaped piezoelectric motor drivesystem and the motor output torque are derived. The average deformation energy of theflexible ring and the average output torque of the motor are also given. And thedeformation energy of the flexible ring and the motor output torque with parameters arediscussed. Results show: The output torque of the motor increases along with the driveratio, the thickness of the flexible ring and the voltage applied to the ceramic plates in themotor stator increase, decreases with increasing the length of the flexible ring. Movabletooth radius has no effect on the output torque of the motor.
At one fixed end and the other free end boundary condition, the function equationsof the radial displacement, internal forces and stress of the flexible ring are established bythe action of the free end of the meshing movable tooth on the basis of the shell theory.The distribution of the displacements and stresses are researched, the changes of thevarious displacements of the free end of the flexible ring and all kinds of stresses at thefixed end along with the relevant parameters are discussed. Results show: In order toobtain larger the flexible ring radial displacement for increasing the output torque of themotor, longer length of the flexible ring, and reasonable transmission ratio and largerexciting voltage applied to ceramic plate.
The mechanical equations of meshing teeth in different position of the fixed rigidgear internal profile were established. The forces expressions from the flexible ring, therotor and the rigid gear were obtained. Changes of the movable tooth contact deformation,contact stress and the meshing stiffness with rotating angle of the rotor are analyzed. Theinfluences of suffered force, stress and contact deformation by movable tooth as well asmeshing stiffness with relative parameters changing are studied. Results show: Comparedwith other contacts, contact force, contact stress and meshing stiffness between themovable teeth and the rigid gear are the largest. Meshing movable teeth are in the middleposition of the rigid gear working profile, each amount of change is small, the outputtorque is more stable.
Learn from Donnell shell theory and theory of vibration, the dynamics models offlexible ring and movable teeth transmission for a novel bar-shaped piezoelectric motordrive system are proposed. Vibration analysis is done. With the meshing movable teethnumbers changing, vibration modes between the flexible ring and movable teeth drivesystem are given. Mean while, it is analyzed which the system's dynamic characteristicsare influenced by the relevant parameter's variation. The modal and the harmonyresponse analyses of the stator of the bar-type piezoelectric motor are done by using thefinite element method. Variation of the natural frequencies of the new bar-shapedpiezoelectric motor stator and the swing amplitude of the stator along with parameters areresearched.
The structure design and experimental prototype of the new bar-shaped piezoelectricmotor are given. The principle experiment of the motor is done. Finally, measure the firstbending resonance frequency of the prototype stator. The measurement results and thecalculated values are consistent.
引文
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