平板形二自由度压电马达的理论与试验研究
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摘要
多自由度马达作为一种可实现多个自由度运动的驱动部件,在需要做多自由度运动的机电系统中得到了越来越广泛的应用,如机器人关节、全景摄像系统、光电跟踪装置等。与多台单自由度马达组合(每台单自由度马达负责一个转动或移动自由度)形成多自由度驱动的形式相比,多自由度马达的机械集成度高、马达的结构材料和驱动控制系统的元件利用率高,可以简化机电系统的结构,减小系统的体积和重量,从而提高机电系统的精度和动态性能。
压电驱动技术在多自由度驱动领域的运用具有很大的潜力。将压电驱动技术运用于多自由度马达,近年来得到了逐步深入的研究。本文结合国家自然科学基金重点项目等课题,围绕多自由度压电驱动器的研制开展研究工作。在充分分析多自由度压电马达研究现状的基础上,提出了一种采用单片平板形压电振子驱动球形转子,形成二自由度转动的压电马达。这种马达显著的特点是结构紧凑、驱动控制容易、能以较小的定子结构驱动几倍于其体积大小的转子,便于未来结构设计的小型化,具有广阔的工程应用前景。本文通过理论分析、有限元仿真、设计加工、试验测试等方法对平板形单振子二自由度压电马达进行了研究和开发,揭示了马达形成二自由度运动的作用机理,形成了平板形二自由度压电马达的设计理论,掌握了马达的运动性能及驱动能力,为二自由度压电球面马达的实际应用提供了基础依据。
1、平板形二自由度压电马达的作用机理研究
在总结目前研制的多自由度压电马达所采用的驱动方式、驱动波类型的基础上,对压电马达定子表面驱动质点椭圆运动的形成机理进行了分析,阐述了压电马达行波驱动和驻波驱动各自的特点。提出了一种用于多自由度压电马达的平板形压电振子,分析了压电振子在B_(23)与B_(32)模态、B_(43)与B_(34)模态下形成二自由度驱动的工作原理;研究了压电振子凸起端部椭圆运动的形成机理,证明了凸起端部的运动轨迹是由基板弯曲振动引起的垂向位移与凸起一阶弯曲振动引起的水平位移的合成,且水平位移滞后于垂向位移,凸起端部可以形成椭圆运动轨迹。
建立了压电振子的有限元分析模型,利用ANSYS软件对压电振子进了有限元仿真,得出了压电振子各阶模态的振型图;通过ANSYS瞬态分析,获得了马达定子与转子之间的接触点的运动轨迹,分析结果表明各接触点能有效形成时序合理的椭圆运动轨迹,作为支撑足的一组凸起的变形量为作为驱动足的一组凸起的变形量的30%,能够用于驱动球体形成二自由度转动。理论分析与有限元仿真证明了压电振子作用机理的正确性。
2、平板形压电振子的振动解析
将压电振子等效为均质的各向同性矩形板,基于Rayleigh-Ritz法,采用适用于各种边界条件的梁函数组合法,建立了压电振子振动频率计算公式的基本形式;将凸起作为压电振子矩形基板的附加质量,压电振子基板层上表面的支承点作为弹性点支承,探讨了考虑凸起及支承的情况下,压电振子振动频率的计算方法;通过进一步的推导,建立了自由振动状态及四点支承状态下,压电振子振动频率的计算公式。结合小挠度弯曲问题的基本假设,采用层合板理论,推导了压电振子在外力和外加电场作用下的运动方程,建立了压电振子弯曲振动时所产生的内力(包括力F与力矩M)的表达式;根据Ritz法,建立了压电振子的虚功方程,给出了在B_(23)、B_(32)、B_(34)、B_(43)四种振动模态下,压电振子挠度的求解公式。求解了凸起端部的弯曲振动位移,进一步说明了压电振子作用机理的合理性,得到了凸起与球形转子接触点的椭圆运动轨迹方程。平板形压电振子的振动解析为马达的结构设计、马达性能的研究提供了重要的理论基础。
3、平板形二自由度压电马达的设计及分析
以压电振子的长宽比、基板层厚度、凸起的长宽高等结构参数为变量,选取压电振子的挠度及工作频率作为压电振子结构设计的目标,分析了各结构参数对压电振子的挠度及工作频率影响的数值规律。通过有限元仿真分析进一步确定并验证了压电振子结构参数的设计原则。根据数值分析及仿真分析的结果,制作了压电振子,测试了压电振子工作频率和凸起端部位移,试验结果说明了理论分析及仿真分析中主要结论的正确性。
将压电振子用于驱动球体,构建了二自由度球面压电马达,对凸起与球体之间的接触条件、压电振子与球体之间的预紧机构、压电陶瓷的布置与接线形式等构建马达时需注意的问题进行分析与探讨。对二自由度球面压电马达进行了接触静力学分析,通过推导,明确了马达定转子间的力传递关系,建立了马达输出转矩的表达式,获得了马达输出转矩的影响因素。通过对平板形压电马达的设计与实践,基本形成了平板形压电马达的设计理论。
4、平板形二自由度压电马达的试验研究
分析了现有的球面多自由度运动的测量方法;在此基础上,提出采用鼠标器测量原理的球面多自由度运动测量方法;给出了两种接触式测量方案和一种非接触式测量方案,设计了各方案的测量电路;讨论了非接触式测量方案通过单次测量获取二自由度运动的测量原理,给出了该方案的测量步骤;搭建了三种测量方案的试验测试系统,对三种测量方案进行了试验研究,结果表明三种测量方案的误差均较小,可用于马达球面运动的测量。利用所搭建的测试系统对基于B_(23)与B_(32)模态、B_(43)与B_(34)模态的两种压电马达样机分别进行了运动能力及驱动性能测试;获得了两种马达的输入频率、输入电压与马达转速之间的关系,马达的瞬态响应特性及机械特性;通过对试验结果的分析,反映出在压电振子的制作过程中,应重点保证凸起间距的加工精度;经测试,马达主要的性能指标为:基于B_(23)与B_(32)模态的压电马达,当驱动电压为90V,驱动频率为43.8kHz时,马达绕压电振子长度方向的转速为37.7r/min,堵转力矩为1.15mNm;基于B_(43)与B_(34)模态的压电马达,当驱动电压为90V,驱动频率为99.5kHz时,马达绕压电振子宽度方向的转速为89.35r/min,堵转力矩为1.34mNm。分析了影响马达工作性能的外界环境和马达内部的因素,为提高马达的性能提供了参考。
5、平板形二自由度压电马达驱动控制电路的研究
设计了一种满足平板形压电马达工作要求的驱动控制电路,该电路能实现稳定的频率、相位、电压输出,且可以根据马达运动的需要,调整驱动信号,跟踪马达的工作频率。讨论了驱动电路与马达的电学匹配问题,通过合理设置放大电路中电感、电容的相互关系,设置占空比为1/3,可有效减少电路中的寄生谐波。讨论了采用PLL锁相环技术实现马达最佳工作频率跟踪的方法。
本文的研究内容涉及压电学、机械学、力学、振动分析、电学、控制学等多学科交叉的知识。论文的研究工作为多自由度压电驱动机构的研究提供了新的思路,为全向驱动轮、机器人的驱动关节、全景摄像系统等方面的应用提供了研究基础,对相近机械结构的研制也具有借鉴参考意义。
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 2~3 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 motor
Based 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 B_(23) and B_(32) modal, B_(43) and B_(34) 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 vibrator
The 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 B_(23), B_(32), B_(34) and B_(43) 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 motor
The 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 motor
Based 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 B_(23) and B_(32) modes, B_(43) and B_(34) 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 B_(23) and B_(32) 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 B_(43) and B_(34) 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 motor
A 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.
压电驱动技术在多自由度驱动领域的运用具有很大的潜力。将压电驱动技术运用于多自由度马达,近年来得到了逐步深入的研究。本文结合国家自然科学基金重点项目等课题,围绕多自由度压电驱动器的研制开展研究工作。在充分分析多自由度压电马达研究现状的基础上,提出了一种采用单片平板形压电振子驱动球形转子,形成二自由度转动的压电马达。这种马达显著的特点是结构紧凑、驱动控制容易、能以较小的定子结构驱动几倍于其体积大小的转子,便于未来结构设计的小型化,具有广阔的工程应用前景。本文通过理论分析、有限元仿真、设计加工、试验测试等方法对平板形单振子二自由度压电马达进行了研究和开发,揭示了马达形成二自由度运动的作用机理,形成了平板形二自由度压电马达的设计理论,掌握了马达的运动性能及驱动能力,为二自由度压电球面马达的实际应用提供了基础依据。
1、平板形二自由度压电马达的作用机理研究
在总结目前研制的多自由度压电马达所采用的驱动方式、驱动波类型的基础上,对压电马达定子表面驱动质点椭圆运动的形成机理进行了分析,阐述了压电马达行波驱动和驻波驱动各自的特点。提出了一种用于多自由度压电马达的平板形压电振子,分析了压电振子在B_(23)与B_(32)模态、B_(43)与B_(34)模态下形成二自由度驱动的工作原理;研究了压电振子凸起端部椭圆运动的形成机理,证明了凸起端部的运动轨迹是由基板弯曲振动引起的垂向位移与凸起一阶弯曲振动引起的水平位移的合成,且水平位移滞后于垂向位移,凸起端部可以形成椭圆运动轨迹。
建立了压电振子的有限元分析模型,利用ANSYS软件对压电振子进了有限元仿真,得出了压电振子各阶模态的振型图;通过ANSYS瞬态分析,获得了马达定子与转子之间的接触点的运动轨迹,分析结果表明各接触点能有效形成时序合理的椭圆运动轨迹,作为支撑足的一组凸起的变形量为作为驱动足的一组凸起的变形量的30%,能够用于驱动球体形成二自由度转动。理论分析与有限元仿真证明了压电振子作用机理的正确性。
2、平板形压电振子的振动解析
将压电振子等效为均质的各向同性矩形板,基于Rayleigh-Ritz法,采用适用于各种边界条件的梁函数组合法,建立了压电振子振动频率计算公式的基本形式;将凸起作为压电振子矩形基板的附加质量,压电振子基板层上表面的支承点作为弹性点支承,探讨了考虑凸起及支承的情况下,压电振子振动频率的计算方法;通过进一步的推导,建立了自由振动状态及四点支承状态下,压电振子振动频率的计算公式。结合小挠度弯曲问题的基本假设,采用层合板理论,推导了压电振子在外力和外加电场作用下的运动方程,建立了压电振子弯曲振动时所产生的内力(包括力F与力矩M)的表达式;根据Ritz法,建立了压电振子的虚功方程,给出了在B_(23)、B_(32)、B_(34)、B_(43)四种振动模态下,压电振子挠度的求解公式。求解了凸起端部的弯曲振动位移,进一步说明了压电振子作用机理的合理性,得到了凸起与球形转子接触点的椭圆运动轨迹方程。平板形压电振子的振动解析为马达的结构设计、马达性能的研究提供了重要的理论基础。
3、平板形二自由度压电马达的设计及分析
以压电振子的长宽比、基板层厚度、凸起的长宽高等结构参数为变量,选取压电振子的挠度及工作频率作为压电振子结构设计的目标,分析了各结构参数对压电振子的挠度及工作频率影响的数值规律。通过有限元仿真分析进一步确定并验证了压电振子结构参数的设计原则。根据数值分析及仿真分析的结果,制作了压电振子,测试了压电振子工作频率和凸起端部位移,试验结果说明了理论分析及仿真分析中主要结论的正确性。
将压电振子用于驱动球体,构建了二自由度球面压电马达,对凸起与球体之间的接触条件、压电振子与球体之间的预紧机构、压电陶瓷的布置与接线形式等构建马达时需注意的问题进行分析与探讨。对二自由度球面压电马达进行了接触静力学分析,通过推导,明确了马达定转子间的力传递关系,建立了马达输出转矩的表达式,获得了马达输出转矩的影响因素。通过对平板形压电马达的设计与实践,基本形成了平板形压电马达的设计理论。
4、平板形二自由度压电马达的试验研究
分析了现有的球面多自由度运动的测量方法;在此基础上,提出采用鼠标器测量原理的球面多自由度运动测量方法;给出了两种接触式测量方案和一种非接触式测量方案,设计了各方案的测量电路;讨论了非接触式测量方案通过单次测量获取二自由度运动的测量原理,给出了该方案的测量步骤;搭建了三种测量方案的试验测试系统,对三种测量方案进行了试验研究,结果表明三种测量方案的误差均较小,可用于马达球面运动的测量。利用所搭建的测试系统对基于B_(23)与B_(32)模态、B_(43)与B_(34)模态的两种压电马达样机分别进行了运动能力及驱动性能测试;获得了两种马达的输入频率、输入电压与马达转速之间的关系,马达的瞬态响应特性及机械特性;通过对试验结果的分析,反映出在压电振子的制作过程中,应重点保证凸起间距的加工精度;经测试,马达主要的性能指标为:基于B_(23)与B_(32)模态的压电马达,当驱动电压为90V,驱动频率为43.8kHz时,马达绕压电振子长度方向的转速为37.7r/min,堵转力矩为1.15mNm;基于B_(43)与B_(34)模态的压电马达,当驱动电压为90V,驱动频率为99.5kHz时,马达绕压电振子宽度方向的转速为89.35r/min,堵转力矩为1.34mNm。分析了影响马达工作性能的外界环境和马达内部的因素,为提高马达的性能提供了参考。
5、平板形二自由度压电马达驱动控制电路的研究
设计了一种满足平板形压电马达工作要求的驱动控制电路,该电路能实现稳定的频率、相位、电压输出,且可以根据马达运动的需要,调整驱动信号,跟踪马达的工作频率。讨论了驱动电路与马达的电学匹配问题,通过合理设置放大电路中电感、电容的相互关系,设置占空比为1/3,可有效减少电路中的寄生谐波。讨论了采用PLL锁相环技术实现马达最佳工作频率跟踪的方法。
本文的研究内容涉及压电学、机械学、力学、振动分析、电学、控制学等多学科交叉的知识。论文的研究工作为多自由度压电驱动机构的研究提供了新的思路,为全向驱动轮、机器人的驱动关节、全景摄像系统等方面的应用提供了研究基础,对相近机械结构的研制也具有借鉴参考意义。
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 2~3 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 motor
Based 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 B_(23) and B_(32) modal, B_(43) and B_(34) 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 vibrator
The 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 B_(23), B_(32), B_(34) and B_(43) 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 motor
The 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 motor
Based 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 B_(23) and B_(32) modes, B_(43) and B_(34) 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 B_(23) and B_(32) 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 B_(43) and B_(34) 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 motor
A 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.
引文
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