Coupled tangential-axial resonant modes of piezoelectric hollow cylinders and their application in ultrasonic motors

This paper describes a tangential-axial eigen-mode of a piezoelectric hollow cylinder. A new type of piezoelectric ultrasonic motor using this oscillation mode has been developed. The motor is a traveling-wave-type motor. The stator of such a motor consists of a solid piezoelectric hollow cylinder, which, excited in the tangential-axial resonant mode by a three-phase electrical signal, will exhibit elliptical displacement and transfer rotation to the rotor. The behavior of the stator has been simulated with finite element method (FEM) software. The simulation results have been checked with single-point contact measurements on the surface of the ultrasonic motors. The paper closes with the introduction of new ultrasonic motors based on this oscillation mode.     

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。     

Analysis of a disk-type piezoelectric ultrasonic motor using impedance matrices

The dynamic behavior and the performance characteristics of the disk-type traveling wave piezoelectric ultrasonic motors (USM) are analyzed using impedance matrices. The stator is divided into three coupled subsystems: an inner metal disk, a piezoelectric annular actuator with segmented electrodes, and an outer metal disk with teeth. The effects of both shear deformation and rotary inertia are taken into account in deriving an impedance matrix for the piezoelectric actuator. The impedance matrices for each subsystem then are combined into a global impedance matrix using continuity conditions at the interfaces. A comparison is made between the impedance matrix model and the three-dimensional finite element model of the piezoelectric stator, obtaining the resonance and antiresonance frequencies and the effective electromechanical coupling factors versus circumferential mode numbers. Using the calculated resonance frequency and the vibration modes for the stator and a brush model with the Coulomb friction for the stator and rotor contact, stall torque, and no-load speed versus excitation frequencies are calculated at different preloads. Performance characteristics such as speed-torque curve and the output efficiency of the USM also are estimated using the current impedance matrix and the contact model. The present impedance model can be shown to be very effective in the design of the USM.     

Flextensional ultrasonic motor using the contour mode of a square piezoelectric plate

This paper presents the design, fabrication, and characterization of a new type of standing wave piezoelectric ultrasonic motor. The motor uses a metallic flextensional amplifier, or cymbal, to convert the contour mode vibrations of a square piezoelectric ceramic plate into flexural oscillations, which are further converted to produce rotary actuation by means of an elastic-fin friction drive. The motor operates on a single-phase electrical supply. A beryllium copper rotor design with three-fin configuration was adopted, and the geometry was varied to include different material thicknesses, fin lengths, and inclinations. The best stall torque and no load speed for a 25-mm square motor were 0.72 Nmm and 895 r/minute, respectively. The behavior of the stator structure was analyzed by ANSYS finite element software using harmonic and modal analyses. The vibration mode estimated by finite element modeling (FEM) was confirmed by laser Doppler vibration measurements.     

Rotor Design and Finite Element Analysis of Traveling Wave Rotaty Ultrasonic Motor

The dynamic transfer mechanism of the traveling wave rotary ultrasonic motor rotor-stator' s contact surface is studied in the paper and the key parts stator and cone flexible rotor of ultrasonic motor are designed.The three-dimensional contact model and finite element model considering the radial sliding between the rotor and the stator are established. The relation between the stator surface particle that amplitude frequency characteristics,resonance speed,radial displacement of ultrasonic motor and the tooth height are analyzed. Mass point radial relative displacement of contact surface between the cone flexible rotor,flexible rotor and the stator are contrasted. The cone flexible rotor is better placed on the surface of the stator tooth through its elastic deformation is interpreted. The cone flexible rotor reduces the radial slip between the stator and the output efficiency of ultrasonic motor is improved. The displacement trajectory of the stator surface is synthesized in a row wave cycle. The method of the stator mass point elliptical motion drives the rotor rotation is verified.     

A piezoelectric motor using flexural vibration of a thin piezoelectric membrane

This paper describes a new implementation of a disk-type piezoelectric motor, whose stator is a commercial available piezomembrane composed of a nickel alloy disk to which a piezoceramic disk is bonded. The two disks are concentric, and the total thickness is very small. Ultrasonic motors are based on the concept of driving a rotor by mechanical vibration excited on a stator, via the piezoelectric effect. The rotor is in contact with the stator, and the driving force is the frictional force between rotor and stator. To transform the mechanical vibration of the stator in the rotor rotation, a traveling wave must be excited on the stator surface. The proposed motor can be regarded as a disk-type, single wavelength motor in which the traveling wave is due to the natural flexural vibration of the piezomembrane at low frequency. The behavior of the stator is analyzed both theoretically, by using the theory of isotropic and homogeneous vibrating plates, and by means of a commercial finite element computer code, finding a good agreement with the experimental results. The main features of the motor are very small thickness, appreciable torque, and high speed, obtained with low input power at low voltage; the intended application is to substitute the moving-coil in analogic instrumentation.     

Novel modeling technique for the stator of traveling wave ultrasonic motors

Traveling wave ultrasonic motors (TWUM) are a promising type of piezoelectric transducers, which are based on the friction transmission of mechanical propagating waves. These waves are excited on the stator by using high Q piezoelectric ceramics. This article presents a modeling strategy, which allows for a quick and precise modal and forced analysis of the stator of TWUM. First-order shear deformation laminated plate theory is applied to annular subdomains (super-elements) of the stator. In addition to shear deformations, the model takes into account the effect of rotary inertia, the stiffness contribution of the teeth, and the linear varying thickness of the stator. Moreover, the formulation considers a more realistic function for the electric field inside the piezoelectric ceramic, i.e., a linear function, instead of the generally assumed constant electric field. The Ritz method is used to find an approximated solution for the dynamic equations. Finally, the modal response is obtained and compared against the results from classical simplified models and the finite element method. Thus, the high accuracy and short computation times of the novel strategy were demonstrated.     

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.     

Design and performance testing of an ultrasonic linear motor with dual piezoelectric actuators

In this work, design and performance testing of an ultrasonic linear motor with dual piezoelectric actuator patches are studied. The motor system consists of a linear stator, a pre-load weight, and two piezoelectric actuator patches. The piezoelectric actuators are bonded with the linear elastic stator at specific locations. The stator generates propagating waves when the piezoelectric actuators are subjected to harmonic excitations. Vibration characteristics of the linear stator are analyzed and compared with finite element and experimental results. The analytical, finite element, and experimental results show agreement. In the experiments, performance of the ultrasonic linear motor is tested. Relationships between velocity and pre-load weight, velocity and applied voltage, driving force and applied voltage, and velocity and driving force are reported. The design of the dual piezoelectric actuators yields a simpler structure with a smaller number of actuators and lower stator stiffness compared with a conventional design of an ultrasonic linear motor with fully laminated piezoelectric actuators.     

Design and implementation of spherical ultrasonic motor

We present a mechanical design and implementation of spherical ultrasonic motor (SUSM) that is an actuator with multiple rotational degrees of freedom (multi-DOF). The motor is constructed of 3 annular stators and a spherical rotor and is much smaller and simpler than conventional multi-DOF mechanisms such as gimbals using servomotors. We designed a novel SUSM using experimental data from a single annular stator and a finite element method. The SUSM using a spherical rotor of diameter 20 mm without any reduction gear has demonstrated advantages of high responsiveness, good accuracy, and high torque at low speed. The dynamic implementation of SUSM was consistent with the driving model of SUSM based on a friction drive.     

基于HHT的超声电机噪声源分析

对超声电机的噪声信号做希尔伯特一黄变换(HHT)，发现噪声中从始至终都含有10kHz左右的成分。在分析了电机运动机理后，以转子为对象建立碰撞摩擦模型，从系统的加速度响应中，同样分解出10kHz左右的成分。说明系统运动非线性产生的分数次谐波，是诱发噪声的直接原因。对定子作有限元分析，得到定子的一阶模态频率为10．74kHz，与噪声频率非常接近，表明分数次谐波激发了定子共振，为噪声输出提供了能量源。为了降低噪声，可以考虑降低定子、转子的碰撞强度或改进定子、转子的结构。     

微振动输送中圆盘型压电振子的动力学分析

目的研究压电陶瓷振动给料器的双晶片压电振子,求出其力学表达式,为振动给料器的双压电晶片的优化设计奠定理论基础。方法以螺旋式压电振动给料器的圆盘型压电振子为例,对圆盘型压电双晶片进行动力学分析,建立振动模型及动力学方程,对激振力进行求解。结果运用Rayleigh-Ritz法推导出在简支边界条件下,双压电晶片振子的弯曲振动的共振频率以及激振力表达式,得出最大误差出现在160 V处,理论计算与实验验证数据的误差为10%左右,有限元分析与实验验证数据的误差为5%左右。结论通过实验可以看出在实际应用中,要综合考虑其电压输入与压电陶瓷层的变形程度,选择最佳的电能输入,才能使压电双晶片获得最大的激励位移。     

Numerical analysis of the symmetric hybrid transducer ultrasonicmotor

In this paper, operation of a symmetric hybrid transducer ultrasonic motor with output produced by two rotors connected together via a drive shaft is numerically analyzed and compared with the traditional asymmetric hybrid transducer motor design that produces its output from only one rotor. A one-dimensional finite element model for torsional vibration in the stator and a Coulomb friction model for rotor/stator contact associated with the longitudinal vibration of the motor are introduced. The calculation results demonstrate that the symmetric design is capable of performance comparable with the traditional asymmetric design when an optimum static spring force in the rotor/stator contact interface is applied during operation     

A perturbation method for finite element modeling of piezoelectric vibrations in quartz plate resonators

When the piezoelectric stiffening matrix is added to the mechanical stiffness matrix of a finite element model, its sparse matrix structure is destroyed. A direct consequence of this loss in sparseness is a significant rise in memory and computational time requirements for the model. For weakly coupled piezoelectric materials, the matrix sparseness can be retained by a perturbation method which separates the mechanical eigenvalue solution from its piezoelectric effects. Using this approach, a perturbation and finite element scheme for weakly coupled piezoelectric vibrations in quartz plate resonators has been developed. Finite-element matrix equations were derived specifically for third-overtone thickness-shear, SC-cut quartz plate resonators with electrode platings. High-frequency piezoelectric plate equations were employed in the formulation of the finite element matrix equation. Results from the perturbation method compared well with the direct solution of the piezoelectric finite element equations. This method will result in significant savings in the computer memory and computational time. Resonance and antiresonance frequencies of a certain mode could be calculated easily by using the same eigenpair from the purely mechanical stiffness matrix. Numerical results for straight crested waves in a third overtone SC-cut quartz strip with and without electrodes are presented. The steady-state response to an electrical excitation is calculated.     

Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.     

圆盘型非接触超声波马达定子的振动模拟与测试

介绍一种圆盘型非接触超声波马达的结构。利用有限元法计算了超声波马达定子在不同振动模态下的固有频率,并用激光测振仪对定子进行了测试,结果两者吻合较好。由于振幅和非接触马达的声辐射压力密切相关,因此通过谐响应分析计算了定子的振幅与定子驱动电压的关系,从而为马达的实验研究提供了理论依据。在最优模态B21下进行转子转速测试,测得最高转速为1600rpm。     

Active control of forced vibrations in adaptive structures using a higher order model

This paper deals with a finite element formulation for active control of forced vibrations, including resonance, of thin plate/shell laminated structures with integrated piezoelectric layers, acting as sensors and actuators, based on third-order shear deformation theory. The finite element model is a single layer triangular nonconforming plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which are surface bonded or embedded in the laminate.

The Newmark method is considered to calculate the dynamic response of the laminated structures, forced to vibrate in the first natural frequency. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. The model is applied in the solution of illustrative cases, and the results are presented and discussed.     

圆柱形三自由度超声电机定子的结构动力学优化设计

在已有研究的基础上,利用结构动力学方法,对圆柱形三自由度超声电机的定子进行了优化设计。首先根据该种电机的设计要求和先前的经验,确定了其定子的结构形式。然后应用精度较高的体积单元,建立了定子的结构动力学有限元模型。在灵敏度分析、确定设计变量的基础上,建立起定子的优化设计数学模型。最后,采用约束变尺度优化方法,在M ATLAB环境下编制了计算程序,得到了定子的优化设计方案,并制作了定子。实验表明:定子的工作模态满足预期的设计要求;实验结果与理论设计结果相符。同时,运用优化设计方法大大提高了设计效率。     

一种超声手术刀推挽激励换能器的研究

设计了一种超声手术刀用的新型推挽激励换能器。它是在夹心式单晶堆压电超声换能器的经典构造基础上,把原先激励一组压电陶瓷晶片堆的方式,改为同时施加反相激励的前后两组晶堆。利用有限元方法,对该推挽激励换能器进行模态分析和频率响应分析。在相同大小的电压激励下,相对单晶堆换能器,推挽激励换能器可以获得更高的工作带宽和机电耦合系数,提高了换能器的电声转换效率。按照仿真结果加工推挽激励换能器,实现良好的动力学和电学特性,满足设计要求。     

Modeling and Simulation of a salient-pole synchronous Generator with dynamic eccentricity using modified winding function theory

This paper models and simulates a salient-pole synchronous generator using a modified winding function theory and more precise stator and rotor winding distribution with dynamic eccentricity between the stator and rotor. Air-gap permeance is also computed more accurately compared to currently available methods. Inductances with this method are compared to those obtained from other methods and it is shown that the results are closer to those obtained from finite element computations. Finally, the calculated inductances are used in a coupled electromagnetic model for simulation and studying the frequency spectrum of the stator line current in the presence of dynamic eccentricity.