Analysis of nonaxisymmetric vibration mode piezoelectric annular plate and its application to an ultrasonic motor

The development of an ultrasonic motor using nonaxisymmetric vibration modes of a piezoelectric annular plate is described. A piezoelectric annular plate is analyzed to find its mode patterns, elliptic motions of displacement for the motor, and the distributions of the induced charge on the plate surface, and to calculate electromechanical coupling factors. On the basis of the analyzed results, motors using the annular plate have been built and their characteristics measured. The construction and characteristics of these motors are discussed.     

电刷式纵扭型超声电机结构设计中的关键技术

详细阐述了在电刷式纵扭型超声电机设计中所遇到的三个关键技术：电机结构型式的选择、纵、扭模态频率一致性和压电陶瓷的安装位置的合理性。分别论证了这些技术的关键所在以及作者提出解决的办法。据此，设计和制造了一台纵扭型超声电机原型机，并获得了较为满意的整机性能。     

Piezoelectric ultrasonic motor using longitudinal-torsional composite resonance vibration

A piezoelectric ultrasonic motor, which uses longitudinal and torsional composite vibration, is examined in order to obtain high torque characteristics with small diameter. Piezoelectric ceramic elements, oscillating in both longitudinal and torsional modes, respectively, are used as piezoelectric stiffened modes having high electromechanical coupling factors k(33) and k(15), respectively. It is found that the resonant frequencies for longitudinal mode and torsional mode could coincide with each other in the ultrasonic motor, according to finite element method analysis and experimental measurement. The motor operating in both resonant vibrations indicated good performance. The 20-mm diameter motor exhibited 4 kgfcm maximum torque, 450 r/min maximum rotational speed, 40% maximum efficiency, and quick responsiveness, within 2.5 ms.     

Theoretical, numerical, and experimental investigation on resonant vibrations of piezoceramic annular disks

In this study, vibration characteristics of thin piezoceramic annular disks with stress-free boundary conditions are investigated by theoretical analysis, numerical simulation, and experimental measurement. The nonaxisymmetric, out-of-plane (transverse), and axisymmetric in-plane (tangential and radial extensional) vibration modes are discussed in detail in terms of resonant frequencies, mode shapes, and electrical currents. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), as well as the electrical impedance measurement are used to validate the analytical results. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be determined by the impedance analysis; hence, only resonant frequencies of extensional vibration modes are presented from the impedance analyzer. The LDV system is used to measure the resonant frequencies of transverse vibrations. However, both the transverse and extensional vibration modes and resonant frequencies of piezoceramic annular disks are obtained by the AF-ESPI method, and the interferometric fringes are produced instantly by a video recording system. Numerical results obtained by finite-element calculations are compared with those from theoretical analysis and experimental measurements. It is shown that the theoretical predictions of resonant frequencies and the corresponding mode shapes agree well with the experimental results. Good agreement between the predicted and measured electrical impedance also is found. The dependence of resonant frequencies and dynamic electromechanical coupling coefficients on the inner-to-outer radius ratio also is analyzed and discussed in this study.     

Same phase drive-type ultrasonic motors using two degenerate bending vibration modes of a disk

Same-phase drive-type ultrasonic motors, using two degenerate bending vibration modes of a disk, are presented. The distinctive feature of the motor is in using the standing wave modes. The motor is not driven by two input signals with different phases, but by input signals with the same phase. Therefore, only one amplifier is sufficient to drive the motor. The experimental results have proved that the motor can yield stable operational characteristics at low speed and high torque.     

Performance evaluation of dual-frequency driving plate ultrasonic motor based on an analytical model

An analytical model is presented to explain the effects of dual-frequency drive on the plate ultrasonic motor in this paper. The experimental prototype is a plate ultrasonic motor using single-phase asymmetric excitation, which can work under a single vibration or multiple vibration modes. Based on the linear superposition of vibrations with two different excitation frequencies, an analytical model is established using the classic Coulomb friction model, and the non-load rotation speed and maximum stall torque are deduced. Moreover, some crucial parameters such as preload and dead-zone in dual-frequency superposition model are identified or modified automatically by searching for the maximum correlation coefficient between simulation and experimental data using single-frequency drive. It is found that simulation and experiment results agree well when no excitation frequency component is at resonance.     

Y形旋转超声波马达的设计与动态特性分析

为了探索和丰富旋转超声波马达的结构,使其满足响应精准且速度快以及控制简便的要求,设计了Y形旋转超声波马达,并对其结构及动态特性进行了分析。Y形旋转超声波马达将3组压电陶瓷片的横向振动复合成驱动足端面对转子的微幅驱动,通过摩擦耦合在惯性作用下推动转子顺时针或逆时针旋转。运用Workbench软件中的Design Exporation组件对Y形旋转超声波马达定子组件的结构尺寸进行了优化设计,提升了定子组件的性能。构建优化后Y形旋转超声波马达定子组件的有限元仿真模型,并通过模态分析获得了定子组件工作所需的固有振型,通过谐响应分析获得了定子组件的幅频特性曲线,通过瞬态分析获得了1个激励周期内定子组件的振动模态,验证了Y形旋转超声波马达的驱动机理。结果表明,Y形旋转超声波马达压电陶瓷片表面施加电压的最佳频率为20 739 Hz,对应的驱动足端面的振幅为6.95 μm。Y形旋转超声波马达结构简单且具有对称性,能效利用率高,对拓宽超声波马达的应用领域有重要参考价值。     

Novel method for driving the ultrasonic motor

This paper reports a novel driving method for an annular plate-type ultrasonic motor. Instead of the direct current/alternating current (DC/AC) converter type driver using a conventional electromagnetic transformer, a compact disc-type piezoelectric transformer is used to obtain a high voltage output for driving the ultrasonic motor. The piezoelectric transformer is operated in the radial vibration mode at resonance frequency close to the resonance frequency of the ultrasonic motor. Later, it was found that the piezoelectric transformer could drive the ultrasonic motor, even if their resonance frequencies are not exactly the same by incorporating a matching network in the circuit. The maximum speed of the ultrasonic motor obtained by using this driving method is over 300 rpm. It is believed that the results of this study will have impact on the integration and miniaturization of the ultrasonic motor and its driving circuit.     

Ultrasonic stepping motor using spatially shifted standingvibrations

This paper proposes a novel configuration of ultrasonic stepping motor. It is based on the simple phenomena that an object on a vibrating body moves to the nodal position of the vibration mode and rests there. The use of standing flexural vibrations of a ring simplifies both the structure of the motor itself and the driving circuit. To move the nodal point, several standing modes spatially shifted with respect to each other are excited one after another by switching the driving position on the stator ring at the timing of stepping clock. In this paper, a 60-step stepping motor is designed and fabricated for trial, where an optimum combination of the order of the mode used and the number of the spatial phase shifts is discussed. The basic characteristics of the prototype motor is also studied experimentally     

纵振换能器式圆筒型超声电机振动特性的研究

以纵振夹心换能器式圆筒型超声电机为研究对象,对换能器的振动状态进行了分析,给出了换能器弯曲振动的产生原因;研究了耦生弯振对电机机电耦合系数以及圆筒中弯振行波质量所带来的影响,耦生弯振的存在使得定子模态特征频率偏离换能器谐振频率,并使得定子圆筒中的弯振行波产生了畸变。最后,提出一种采用换能器弯振激励圆筒径向弯振的模态组合方式。     

Performance improvement of rectangular-plate linear ultrasonic motors using dual-frequency drive

To improve the performances of a rectangular-plate linear ultrasonic motor for specific applications, a dual-frequency drive has been proposed and investigated. Through careful design of the rectangular piezoelectric ceramic plate, its first longitudinal resonant frequency coincides with its second lateral bending resonant frequency and is one-third of its higher lateral bending resonant frequency. When a square-wave voltage is used to drive the motor, its first longitudinal and second bending and the higher bending vibration modes are excited. Experimental results show that the maximum thrust force and maximum velocity of the motor are over 170% of those obtained from the single-frequency sine-wave drive when the voltage performance of the motor becomes saturated.     

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet was proposed in this paper. The proposed motor contains a horizontal transducer and two vertical transducers. The horizontal transducer includes two exponential shape horns located at the leading ends, and each vertical transducer contains one exponential shape horn. The horns of the horizontal transducer and the vertical transducer intersect at the tip ends where the driving feet are located. Longitudinal vibrations are superimposed in the motor and generate elliptical motions at the driving feet. The two vibration modes of the motor are discussed, and the motion trajectories of driving feet are deduced. By adjusting the structural parameters, the resonance frequencies of two vibration modes were degenerated. A prototype motor was fabricated and measured. Typical output of the prototype is no-load speed of 854 mm/s and maximum thrust force of 40 N at a voltage of 200 V(rms).     

大力矩径向驻波型超声波电机有限元分析与实验研究

提出了一种大力矩径向驻波型超声波电机,在实现电机大力矩输出的同时保持结构紧凑的特点。首先设计并分析了电机的结构和工作原理,采用有限元法分析了电机定子的振动特性。接着制作了超声波电机样机,样机直径为32 mm。采用激光测振仪测量了定子的共振频率及径向振动的振幅,测量结果与理论分析结果相吻合。最后,搭建了电机输出特性测试平台,测量了电机在不同电压下的转矩-转速特性。实验测试结果显示,定子工作模态的共振频率为73.3 kHz,当施加的电压幅值为100 V、频率为74 kHz时,电机的空载转速为45 r/min,堵转力矩达到0.41 N·m。与其他同尺寸的超声波电机相比,所提出的径向驻波型超声波电机具有更大的堵转力矩。     

Transducer for high speed and large thrust ultrasonic linear motor using two sandwich-type vibrators

A transducer for an ultrasonic motor using two sandwich-type vibrators has been proposed and designed. The vibrators cross at right angles with each other at the tip. The transducer has two vibration modes; one is a symmetrical mode and the other is anti-symmetric. The normal direction motion of the transducer tip is excited by the symmetrical mode. The lateral motion of the tip is excited by the anti-symmetrical mode. The transducer is designed so that these vibration modes are degenerated. To obtain high output force and high power, materials were carefully selected. Heat-treated high strength chromium manganese steel bolts were used for binding the PZT elements. A zirconia ceramics plate was bonded on the transducer tip as frictional material. The no-load maximum speed was 3.5 m/sec. The output force was 39 N at the driving voltage of 500 V(rms) and the preload of 150 N. At this condition the maximum efficiency was 28%, and the velocity was 0.55 m/sec. The maximum output force was 51 N, which was 17 times of the transducer weight. The maximum output power per unit weight was 76 W/kg.     

A single vibration mode tubular piezoelectric ultrasonic motor

A novel tubular ultrasonic motor is presented that uses only a single vibration bending mode of a piezoelectric tube to generate rotation. When the piezoelectric tube bends, the diagonal motion of points on selected areas at the ends of the tube generates forces with tangential components along the same circumferential direction, driving the rotors to rotate. Bi-directional motion is achieved by simply switching the direction of bending. Because only one vibration mode is used, the motor requires only one driving signal and no vibration mode coupling is needed, simplifying the design, fabrication, assembly, and operation of the device. Two prototypes [one with cut-in lead zirconate titanate (PZT) teeth and one with added metal teeth] were built and tested using PZT tubes available to the authors. The tubes have an outside diameter of 6.6 mm, inner diameter of 5.0 mm, and length of 25.4 mm. The working frequencies of the two motors are 27.6 and 23.5 kHz. The motors achieved a maximum no-load speed of 400 rpm and a stall torque of 300 μN·m.     

Dynamic and contact analysis of a bimodal ultrasonic motor

A bimodal ultrasonic motor, which operates with only one power amplifier, uses two simultaneously excited modes to drive the rotor; a longitudinal mode and a flexural mode. The equations of motion describing the vibrations and contact behavior are derived by Hamilton's principle and the geometry constraint. The Lagrange multiplier method is used to treat the frictional contact problem. The finite element method and numerical integration scheme are used to simulate the dynamic responses of this system with and without contact. Some important factors are studied for the bimodal ultrasonic motor design. The factors include structure design, amplitude of input voltage, phase displacement, exciting frequency, and contact behavior.     

确定轴向冲击下薄壁圆柱壳第二临界速度的新方法

研究薄壁圆柱壳的动态屈曲模式，有助于构造具有高吸能率的抗冲击结构。根据轴向冲击下的薄壁圆柱壳存在使其屈曲模式由轴对称转换为非轴对称的第二临界速度，且当冲击速度大于第二临界速度时薄壁圆柱壳的屈曲模式先呈现轴对称形式，然后随着冲击响应时间逐渐由轴对称形式转化为非轴对称形式这一理论，基于有限元仿真，比较撞击系统动能的时间历程和屈曲变形的时间历程，提出了用以确定第二临界速度的能量迭代法。应用此方法设计薄壁圆柱壳的动力屈曲结构可有效地减少试验次数，降低实验成本。该方法的可行性和正确性利用落锤实验得到了验证。     

Curved PVDF airborne transducer

In the application of airborne ultrasonic ranging measurement, a partially cylindrical (curved) PVDF transducer can effectively couple ultrasound into the air and generate strong sound pressure. Because of its geometrical features, the ultrasound beam angles of a curved PVDF transducer can be unsymmetrical (i.e., broad horizontally and narrow vertically). This feature is desired in some applications. In this work, a curved PVDF air transducer is investigated both theoretically and experimentally. Two resonances were observed in this transducer. They are length extensional mode and flexural bending mode. Surface vibration profiles of these two modes were measured by a laser vibrometer. It was found from the experiment that the surface vibration was not uniform along the curvature direction for both vibration modes. Theoretical calculations based on a model developed in this work confirmed the experimental results. Two displacement peaks were found in the piezoelectric active direction of PVDF film for the length extensional mode; three peaks were found for the flexural bending mode. The observed peak positions were in good agreement with the calculation results. Transient surface displacement measurements revealed that vibration peaks were in phase for the length extensional mode and out of phase for the flexural bending mode. Therefore, the length extensional mode can generate a stronger ultrasound wave than the flexural bending mode. The resonance frequencies and vibration amplitudes of the two modes strongly depend on the structure parameters as well as the material properties. For the transducer design, the theoretical model developed in this work can be used to optimize the ultrasound performance.     

Dynamics of an ultrasonic transducer used for wire bonding

The vibration displacement distributions along a transducer used in ultrasonic wire bonding were measured using a heterodyne interferometer, and many nodes and anti-nodes were found. A mechanical finite element method (FEM) was used to compute the resonant frequencies and vibration mode shapes. The displacement distributions of the dominant 2nd axial mode agreed well with the measured values. Undesirable nonaxial modes, including the higher order flexural and torsional modes, also were excited at frequencies very close to the working frequency (2nd axial mode) of the transducer. Hence, the measured displacements were the resultant of all the allowable modes being excited. However, the excitation of these nonaxial modes were small enough not to affect the formation of consistent and high quality wire bonds. Results of the present study were used to determine a suitable location for installing a piezoelectric sensor to monitor the bond quality.     

面内模态方形压电超声电机的工作机理与实验

针对利用面内模态的方形压电超声电机工作机理进行研究,利用有限元方法得出了方形超声电机定子的振动模态振型,以此为基础,分析了电机定子内圈小齿在平面内模态(3,1)和(R,1)下的位移特点,给出了一个周期内电机定子内圈6个小齿切向运动与法向运动的分析结果,得出了在定子平面内模态(3,1)和(R,1)下,定子内圈6个小齿能够推动转子转动的结论.制作了电机样机并完成了电机运转试验,得出了相应的电机特性曲线,对上述分析进行了验证.根据上述分析结果,可以进一步研制一种方形驻波超声电机.