Modelling and characterization of a piezoceramic inertial actuator

An inertial actuator (also known as a proof mass actuator) applies forces to a structure by reacting them against an “external” mass. This approach to actuation may provide some practical benefits in the active control of vibration and structure-borne noise: system reliability may be improved by removing the actuator from a structural load path; effective discrete point-force actuation permits ready attachment to curved surfaces, and an inherent passive vibration absorber effect can reduce power requirements.This paper describes a class of recently developed inertial actuators that is based on mechanical amplification of displacements of an active piezoceramic element. Important actuator characteristics include resonance frequencies, clamped force, and the drive voltage to output the force frequency response function.The paper addresses one particular approach to motion amplification, the “dual unimorph,” in detail. A model of actuator dynamic behavior is developed using an assumed-modes method, treating the piezoelectrically induced stresses as external forces. Predicted actuator characteristics agree well with experimental data obtained for a prototype actuator. The validated actuator dynamic model provides a tool for design improvement.     

A curved ultrasonic actuator optimized for spherical motors: Design and experiments

Multi-degree-of-freedom angular actuators are commonly used in numerous mechatronic areas such as omnidirectional robots, robot articulations or inertially stabilized platforms. The conventional method to design these devices consists in placing multiple actuators in parallel or series using gimbals which are bulky and difficult to miniaturize. Motors using a spherical rotor are interesting for miniature multidegree-of-freedom actuators. In this paper, a new actuator is proposed. It is based on a curved piezoelectric element which has its inner contact surface adapted to the diameter of the rotor. This adaptation allows to build spherical motors with a fully constrained rotor and without a need for additional guiding system. The work presents a design methodology based on modal finite element analysis. A methodology for mode selection is proposed and a sensitivity analysis of the final geometry to uncertainties and added masses is discussed. Finally, experimental results that validate the actuator concept on a single degree-of-freedom ultrasonic motor set-up are presented.     

New breathing functions for the transverse breathing crack of the cracked rotor system: Approach for critical and subcritical harmonic analysis

The actual breathing mechanism of the transverse breathing crack in the cracked rotor system that appears due to the shaft weight is addressed here. As a result, the correct time-varying area moments of inertia for the cracked element cross-section during shaft rotation are also determined. Hence, two new breathing functions are identified to represent the actual breathing effect on the cracked element stiffness matrix. The new breathing functions are used in formulating the time-varying finite element stiffness matrix of the cracked element. The finite element equations of motion are then formulated for the cracked rotor system and solved via harmonic balance method for response, whirl orbits and the shift in the critical and subcritical speeds. The analytical results of this approach are compared with some previously published results obtained using approximate formulas for the breathing mechanism. The comparison shows that the previously used breathing function is a weak model for the breathing mechanism in the cracked rotor even for small crack depths. The new breathing functions give more accurate results for the dynamic behavior of the cracked rotor system for a wide range of the crack depths. The current approach is found to be efficient for crack detection since the critical and subcritical shaft speeds, the unique vibration signature in the neighborhood of the subcritical speeds and the sensitivity to the unbalance force direction all together can be utilized to detect the breathing crack before further damage occurs.     

悬线式力矩器磁路设计中的有限元分析应用

光学头力矩器的空间磁场分布直接决定了力矩器的动态性能,对磁场进行准确分析是力矩器设计的前提。分析了悬线式力矩器的空间磁场产生机理,并采用有限元分析法进行了理论推导。以一款动线圈式二维对称型只读悬线式力矩器为例,采用有限元仿真软件（ANSYS）分析并设计了其空间磁场分布,对影响力矩器空间磁场分布的相关因素进行了分析。将采用有限元法对悬线式力矩器空间磁场仿真计算得出的力矩器动态特性参数与实测力矩器动态特性参数相比,其结果均符合力矩器的设计要求,证明基于有限元分析法的悬线式力矩器空间磁场设计是可行的。     

空间望远镜分块式主镜建模与面形控制方法

空间望远镜分块式主镜的面形是由其背后布置的若干致动器控制的,是一个复杂的控制系统。应用BP神经网络的方法建立了以致动器作用力作为输入、镜面形变的Zernike多项式拟合系数作为输出的镜面形变模型。利用镜面有限元分析的大量数据对该模型进行了离线训练,并在最小二乘法的基础上,设计了加入单纯形修正算法的主镜面形静态控制器。仿真结果表明,应用该控制器对空间望远镜进行在线控制,控制精度优于最小二乘控制法。     

Finite element analysis of piezoelectric actuator with PMN–PT single crystals for nanopositioning

A piezoelectric bending actuator has been used widely in areas related to precision position controlling, loudspeakers, and pressure sensing. In this paper, a fine focusing actuator is designed using a computer aided design tools, Solid Works 2004, for an optical disk drive pick-up system. The finite element analyses are performed with the software COSMOS Work 2004 and the ANSYS 5.7. The tip displacement of the piezoelectric bending actuator with PMN-PT single crystals is 46 μm at 10 V. It is 15 times larger than tip displacement of PZT ceramics for the same design. The tip displacement obtained from the finite element analyses agrees with the measured data very well.     

A velocity decomposition approach for moving interfaces in viscous fluids

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier–Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier–Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.     

Finite element modelling of dielectric elastomer minimum energy structures

This paper presents an experimentally validated finite element model suitable for simulating the quasi-static behaviour of Dielectric Elastomer Minimum Energy Structure(s) (DEMES). A DEMES consists of a pre-stretched Dielectric Elastomer Actuator (DEA) adhered to a thin, flexible frame. The tension in the stretched membrane causes the frame to curl up, and when a voltage is applied, the frame returns to its initial planar state thus forming a useful bending actuator. The simulation method presented here incorporates a novel strain energy function suitable for simulating general DEA actuator elements. When compared against blocked force data from our previous work, the new model provides a good fit with an order of magnitude reduction in computational time. Furthermore, the model accurately matched experimental data on the free displacement of DEMES formed with non-equibiaxially pre-stretched VHB4905 membranes driven by 2500 V. Non-equibiaxially pre-stretching the membranes allowed control of effective frame stiffness and bending moment, this was exploited by using the model to optimise stroke at 2500 V in a hypothetical case study. Dielectric constant measurements for non-equibiaxially stretched VHB4905 are also presented.     

A miniaturization of the multi-degree-of-freedom ultrasonic actuator using a small cylinder fixed on a substrate

Multi-degree-of-freedom ultrasonic actuator has been studied for robot arms and multidimensional precision table and so on because of its simple structure, silent operation, and holding force. In this study, we aim to miniaturize multi-degree-of-freedom ultrasonic actuator for fabrication on a substrate. This actuator consists of a stainless steel cylinder and a PZT ring. The cylinder is fixed on a substrate and the PZT ring is glued to the substrate near the cylinder. The 1st longitudinal vibration and the 2nd bending vibration are simultaneously excited in the cylinder to make elliptical motion at the top of the cylinder and a ball rotor placed on the cylinder rotates because of the friction force. Length of the cylinder was decided so as to tune the resonance frequency of the 1st longitudinal vibration to the 2nd bending one. Actuator performances are evaluated experimentally using a 14 mm height and 7 mm diameter stainless steel cylinder with a 0.5 mm thickness PZT ring. The rotation about the cylinder axis is tested using the two orthogonal bending vibrations with 90 degrees phase difference. Also, the rotation about horizontal axes were investigated using the combination of the longitudinal vibration and one of two bending vibrations. We measured the rotation speed of a steel ball and obtained 15.8 rps using a 6 mm diameter ball rotor.     

The use of roving discs and orthogonal natural frequencies for crack identification and location in rotors

A variety of approaches that have been developed for the identification and localisation of cracks in a rotor system, which exploit natural frequencies, require a finite element model to obtain the natural frequencies of the intact rotor as baseline data. In fact, such approaches can give erroneous results about the location and depth of a crack if an inaccurate finite element model is used to represent an uncracked model. A new approach for the identification and localisation of cracks in rotor systems, which does not require the use of the natural frequencies of an intact rotor as a baseline data, is presented in this paper. The approach, named orthogonal natural frequencies (ONFs), is based only on the natural frequencies of the non-rotating cracked rotor in the two lateral bending vibration x–z and y–z planes. The approach uses the cracked natural frequencies in the horizontal x–z plane as the reference data instead of the intact natural frequencies. Also, a roving disc is traversed along the rotor in order to enhance the dynamics of the rotor at the cracked locations. At each spatial location of the roving disc, the two ONFs of the rotor–disc system are determined from which the corresponding ONF ratio is computed. The ONF ratios are normalised by the maximum ONF ratio to obtain normalised orthogonal natural frequency curves (NONFCs). The non-rotating cracked rotor is simulated by the finite element method using the Bernoulli–Euler beam theory. The unique characteristics of the proposed approach are the sharp, notched peaks at the crack locations but rounded peaks at non-cracked locations. These features facilitate the unambiguous identification and locations of cracks in rotors. The effects of crack depth, crack location, and mass of a roving disc are investigated. The results show that the proposed method has a great potential in the identification and localisation of cracks in a non-rotating cracked rotor.     

FINITE ELEMENT FORMULATION AND ACTIVE VIBRATION CONTROL STUDY ON BEAMS USING SMART CONSTRAINED LAYER DAMPING (SCLD) TREATMENT

This work deals with the active vibration control of beams with smart constrained layer damping (SCLD) treatment. SCLD design consists of viscoelastic shear layer sandwiched between two layers of piezoelectric sensors and actuator. This composite SCLD when bonded to a vibrating structure acts as a smart treatment. The sensor piezoelectric layer measures the vibration response of the structure and a feedback controller is provided which regulates the axial deformation of the piezoelectric actuator (constraining layer), thereby providing adjustable and significant damping in the structure. The damping offered by SCLD treatment has two components, active action and passive action. The active action is transmitted from the piezoelectric actuator to the host structure through the viscoelastic layer. The passive action is through the shear deformation in the viscoelastic layer. The active action apart from providing direct active control also adjusts the passive action by regulating the shear deformation in the structure. The passive damping component of this design eliminates spillover, reduces power consumption, improves robustness and reliability of the system, and reduces vibration response at high-frequency ranges where active damping is difficult to implement. A beam finite element model has been developed based on Timoshenko's beam theory with partially covered SCLD. The Golla-Hughes-McTavish (GHM) method has been used to model the viscoelastic layer. The dissipation co-ordinates, defined using GHM approach, describe the frequency-dependent viscoelastic material properties. Models of PCLD and purely active systems could be obtained as a special case of SCLD. Using linear quadratic regulator (LQR) optimal control, the effects of the SCLD on vibration suppression performance and control effort requirements are investigated. The effects of the viscoelastic layer thickness and material properties on the vibration control performance are investigated.     

A continuous vibration theory for rotors with an open edge crack

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free vibration has been analyzed and the critical speeds have been calculated. Results are compared with the finite element results and an excellent agreement is observed.     

Estimating ensemble average power delivered by a piezoelectric patch actuator to a non-deterministic subsystem

Engineering systems such as aircraft, ships and automotive are considered built-up structures. Dynamically they are taught of as being fabricated from many components that are classified as ‘deterministic subsystems’ (DS) and ‘non-deterministic subsystems’ (Non-DS). Structures' response of the DS is deterministic in nature and analysed using deterministic modelling methods such as finite element (FE) method. The response of Non-DS is statistical in nature and estimated using statistical modelling technique such as statistical energy analysis (SEA). SEA method uses power balance equation, in which any external input to the subsystem must be represented in terms of power. Often, input force is taken as point force and ensemble average power delivered by point force is already well-established. However, the external input can also be applied in the form of moments exerted by a piezoelectric (PZT) patch actuator. In order to be able to apply SEA method for input moments, a mathematical representation for moment generated by PZT patch in the form of average power is needed, which is attempted in this paper. A simply-supported plate with attached PZT patch is taken as a benchmark model. Analytical solution to estimate average power is derived using mobility approach. Ensemble average of power given by the PZT patch actuator to the benchmark model when subjected to structural uncertainties is also simulated using Lagrangian method and FEA software. The analytical estimation is compared with the Lagrangian model and FE method for validation. The effects of size and location of the PZT actuators on the power delivered to the plate are later investigated.     

望远镜主镜气压力驱动器设计

为了获取优异的光学图像质量,大口径天文望远镜通常采用主动支撑结构以校正主镜面形误差。对望远镜主镜支撑系统所需的气压驱动器进行了研究。基于气动原理设计了一种采用滚动膜片结构的气压力驱动器,其中滚动膜片结构用于消除摩擦力的影响,滚珠式力解耦器用于消除侧向力、弯矩的影响。进一步设计了针对气压驱动器带死区的比例-积分-微分(PID)控制算法,以实现对气压驱动器的闭环控制。实验结果表明:气压力驱动器可精确提供主镜控制所需的支撑力,在望远镜高角变化速度达到2°/s时,输出支撑力范围为0～1000N,驱动器支撑力误差仅为满量程的±0.4%。设计的气压驱动器可实现主动支撑力的快速精确输出,能满足天文望远镜主镜主动支撑需求。     

Nonlinear dynamic modeling of surface defects in rolling element bearing systems

In this paper an analytical model is proposed to study the nonlinear dynamic behavior of rolling element bearing systems including surface defects. Various surface defects due to local imperfections on raceways and rolling elements are introduced to the proposed model. The contact force of each rolling element described according to nonlinear Hertzian contact deformation and the effect of internal radial clearance has been taken into account. Mathematical expressions were derived for inner race, outer race and rolling element local defects. To overcome the strong nonlinearity of the governing equations of motion, a modified Newmark time integration technique was used to solve the equations of motion numerically. The results were obtained in the form of time series, frequency responses and phase trajectories. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The classical Floquet theory has been applied to the proposed model to investigate the linear stability of the defective bearing rotor systems as the parameters of the system changes. The peak-to-peak frequency response of the system for each case is obtained and the basic routes to periodic, quasi-periodic and chaotic motions for different internal radial clearances are determined. The current study provides a powerful tool for design and health monitoring of machine systems.     

基于气象因素的集中供热系统热负荷预测研究

为了解决直升机旋翼伺服作动器维修保障过程中训练资源有限,拆装难度高,故障率较高且难以确定故障点等难题,在直升机虚拟维修训练系统(VMTS, Virtual Maintenance Training System)的基础上,提出了应用虚拟仪器检测,确定故障点的直升机故障诊断可视化设计方法。分析了故障诊断过程中仪器、工具、环境等对故障诊断的影响,实现了动态的建立仿真模型和数据处理。通过虚拟仪器和推理机的功能配合,解决了直升机维护中复杂多变的故障诊断难题,形成一个逻辑推理能力强的故障诊断系统。最后以直升机旋翼伺服作动器故障诊断为例,验证该方法的可行性。     

Pitch-variable transmission-type bulk gratings driven by shape memory alloy actuator

This paper describes a novel pitch-variable transmission-type bulk grating fabricated by silicon micromachining technology driven by a shape memory alloy (SMA) actuator. The grating is specially designed to change the pitch easily with a small force and assured moderate stress by finite element method. Using deep reactive ion etching (deep-RIE) technology, the grating has a high aspect ratio more than 10. In the diffraction experiment, more than 10% extension ratio has been obtained. The SMA actuator has been installed to the grating. Due to the two-way shape memory effect, the translation mechanism is simple and is easily controlled.     

Finite element analysis of ionic liquid gel soft actuator

A new type of soft actuator material-ionic liquid gel(ILG),which consists of HEMA,BMIMBF4,and TiO_2,can be transformed into gel state under the irradiation of ultraviolet(UV)light.In this paper,Mooney–Rivlin hyperelastic model of finite element method is proposed for the first time to study the properties of the ILG.It has been proved that the content of TiO_2 has a great influence on the properties of the gel,and Young’s modulus of the gel increases with the increase of its content,despite of reduced tensile deformation.The results in this work show that when the TiO_2 content is 1.0 wt%,a large tensile deformation and a strong Young’s modulus can be obtained to be 325%and 7.8 k Pa,respectively.The material parameters of ILG with TiO_2content values of 0.2 wt%,0.5 wt%,1.0 wt%,and 1.5 wt%are obtained,respectively,through uniaxial tensile tests,including C_(10),C_(01),C_(20),C_(11),C_(02),C_(30),C_(21),C_(12),and C_(03)elements.In this paper,the large-scaled general finite element software ANSYS is used to simulate and analyze the ILG,which is based on SOLID186 element and nonlinear hyperelastic Mooney–Rivlin model.The finite element simulation analysis based stress-strain curves are almost consistent with the experimental stress–strain curves,and hence the finite element analysis of ILG is feasible and credible.This work presents a new direction for studying the performance of soft actuator for the ILG,and also contributes to the design of soft robot actuator.     

Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators

Finite element modelling of laminated structures with distributed piezoelectric sensor and actuator layers and control electronics is considered in this paper. Beam, plate and shell type elements have been developed incorporating the stiffness, mass and electromechanical coupling effects of the piezoelectric laminates. The effects of temperature on the electrical and mechanical properties and the coupling between them are also taken into consideration in the finite element formulation. The piezoelectric beam element is based on Timoshenko beam theory. The plate/shell element is a nine-noded field-consistent element based on first order shear deformation theory. Constant-gain negative velocity feedback, Lyapunov feedback as well as a linear quadratic regulator (LQR) approach have been used for active vibration control with the structures subjected to impact, harmonic and random excitations. The influence of the pyroelectric effects on the vibration control performance is also investigated. The LQR approach is found to be more effective in vibration control with lesser peak voltages applied in the piezo actuator layers as in this case the control gains are obtained by minimizing a performance index. The application of these elements in high-performance, light-weight structural systems is highlighted.     

ELECTRIC CIRCUIT DESIGN AND TESTING OF INTEGRATED DISTRIBUTED STRUCTRONIC SYSTEMS

Modelling distributed parameter systems (DPS) by electric circuits and fabricating the complicated equivalent circuits to evaluate system responses poses many challenging research issues for many years. Electrical modelling and analysis of distributed sensing/control of smart structures and distributed structronic systems are even scarce. This paper is to present a technique to model distributed structronic control systems with electric circuits and to evaluate control behaviors with the fabricated equivalent circuits. Electrical analogies and analysis of distributed structronic systems is proposed and dynamics and control of beam/sensor/actuator systems are investigated. To determine the equivalent circuits and system parameters, higher order partial derivatives are simplified using the finite difference method; partial differential equations (PDE) are transformed to finite difference equations and further represented by electronic components and circuits. To provide better signal management and stability, active electrical circuit systems are designed and fabricated. Electrical signals from the distributed system circuits (i.e., soft and hard) are compared with results obtained by the classical theoretical, finite element, and experimental techniques.