Modeling nonlinear behavior in a piezoelectric actuator

A piezoelectric tube actuator is employed as a sample positioning device in Nanocut, a cutting instrument conceived to study the mechanics of nanometric cutting. Extension of functionality of the instrument as a nanometric machine tool motivates the search for an accurate model of the actuator for implementing feedback control. A simple nonlinear model describing longitudinal expansion of the piezoelectric tube actuator is presented in this paper. The model derivation is based on a non-formal analogy with nonlinear viscoelastic materials under uniaxial extension, for which the responses to a step input are similar to the piezoelectric tube. Suitability of the model structure for arbitrary inputs is tested by cross-verification between time and frequency domains. Two parameter estimation procedures are examined and the results of the experimental work for characterization, estimation and validation are presented.     

Dynamic analysis of a train-bridge system under multi-support seismic excitations

A numerical solution for the dynamic responses of a train-bridge interaction system subjected to multi-support seismic loads was studied. The train vehicle was modeled by the rigid-body dynamics method, and the bridge was modeled by the finite element method. The vertical and lateral wheel-rail interaction forces were defined according to the wheel-rail corresponding assumption and the simplified Kalker creep theory. Three-dimensional seismic accelerations were incorporated using the large mass method. In a case study, the dynamic responses were simulated for a high-speed train traversing a steel truss cable-stayed bridge with different seismic intensities and different train speeds, and train safety was evaluated.     

Modeling and flow analysis of piezoelectric based micropump with various shapes of microneedle

Micropumps have been investigated as drug delivery and disease diagnostic devices. Many of these micropumps have been designed, considering primarily, available micro fabrication technologies rather than appropriate pump performance analysis. Piezoelectric and silicon based micro pumps are more popular as compared to other smart materials being explored. The microneedle is an integral part of these micropumps providing an interface between the drug reservoir and the patient’s body for extracting the blood for investigation. Blood collected in the pump chamber passes through the biosensor and gives the required investigation report. It is aimed to minimize the pain while the microneedle is inserted in the body without having any effect on the flow characteristics. Several factors affect the pain while inserting the needle, out of which shape and size of the microneedle are two important parameters. In this study we have investigated the effect of shape of the microneedle on the flow inside the micropump. A micropump design is based on the required flow at the biosensor point. All computations were carried out with water (Newtonian fluid) as the working fluid after carrying out a comparative analysis with human blood (non-Newtonian fluid). For the pentagonal shaped microneedle, the velocity at the top of the microneedle was minimum, which is beneficial in that fluid should remain in contact with the sensor for longer time.

     

Modeling and performance analysis of a novel M-shaped piezoelectric energy harvester employing magnets

Journal of Mechanical Science and Technology - Piezoelectric energy harvesters convert the vibration energy of a mechanical system into the electrical energy. Among them, cantilever type is the...     

Modeling and analysis of curved beams with debonded piezoelectric sensor/actuator patches

In this paper, a mathematical model for thin-walled curved beams with partially debonded piezoelectric actuator/sensor patches is presented for investigating the effect of debonding of the actuator/sensor on their open- and closed-loop behaviors. The actuator equations and the sensor equations of the curved beam in perfectly bonded and debonded regions are derived. In the perfect bonding region, the adhesive layer is modeled to carry constant peel and shear stresses; while in the debonding area, it is assumed that there is no peel and shear stress transfer between the host beam and the piezoelectric layer. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the bonded and debonded regions. Based on the model and the sensing equation of the sensor, a closed-loop vibration control for the curved beams is performed. To obtain the frequency response from the presented model, a solution scheme for solving the complex governing equations is given. Using this model and the solution scheme, the effects of the debonding of actuator and sensor patches on open- and closed-loop control are investigated through an example. The results show that edge debonding of the piezoelectric patch has a significant side effect on the closed-loop control of the curved beams.     

压电驱动器迟滞非线性的分数阶建模及实验验证

存在于压电陶瓷全工作范围内的迟滞非线性特性,往往会导致压电陶瓷执行器的系统精度下降、振荡,甚至造成系统的不稳定。针对周期性的正弦输入信号,提出一种基于分数阶算子的迟滞建模方法。首先,在分析压电特性和分数阶算子特性的基础上,采用结构简单参数少的分数阶算子来描述压电陶瓷的迟滞特性;然后,搭建了基于dSpace的压电驱动微位移定位实验平台;最后,将基于分数阶算子的迟滞建模方法应用于压电驱动微位移定位平台中,对压电陶瓷的迟滞非线性特性进行辨识。实验结果表明采用基于分数阶的迟滞模型(FOM)比传统的Prandtl-Ishlinskii模型(PIM)及其改进的增强型Prandtl-Ishlinskii模型(EPIM)更有优势;在低频段,FOM模型比PIM模型和EPIM模型精度略有提高,但是在高频段,FOM模型比PIM模型和EPIM模型精度则提高显著。在输入频率为100HZ的情况下,所提出的FOM模型较PIM模型的均方根误差(RMSE)值精度提高69.84%,较EPIM模型的RMSE值精度提高68.88%。     

Feedforward correction of nonlinearities in piezoelectric scanner constructions and its experimental verification

Piezoelectrical actuators widely used in scanning devices for highly resolved displacement generation exhibit a number of known nonlinear effects as hysteresis and creep. This article describes an attempt to minimize those nonlinearities by recognizing the relation between scan range and voltage magnitude in a scanner specific function. In addition, by utilizing a strain gauge sensor system, a forward displacement correction is realized. The mathematical procedure behind the hysteresis correction is described in detail. The dependence of the higher order correction factors on parameters such as scan speed, scan range, or center position is studied carefully to extract their influence on the result. Finally, integral nonlinearities of about 1% are proven in experiments with an atomic force microscope.     

Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities

This paper aims to investigate the nonlinear dynamics of a thin-plate workpiece during milling process with cutting force nonlinearities. By modeling the thin-plate workpiece as a cantilevered thin plate and applying the Hamilton’s principle, the equations of motion of the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations. Using the Galerkin’s approach, the equations of motion are reduced to a two-degree-freedom nonlinear system. The method of Asymptotic Perturbation is utilized to obtain the averaged equations in the case of 1:1 internal resonance and foundational resonance. Numerical methods are used to find the periodic and chaotic oscillations of the cantilevered thin-plate workpiece. The results show that the cantilevered thin-plate workpiece demonstrate complex dynamic behaviors under time-delay effects, the external and parametric excitations.     

Modeling and identification of an electrostatic motor

The present study describes modeling and parameter identification for a high-power electrostatic motor. The motor is a synchronous motor with six phases that is modeled by a six-terminal capacitance network. A method to measure the capacitance coefficient matrix of a network using an LCR tester is proposed and demonstrated. The thrust force of the motor is shown analytically using the proposed model, which shows good agreement with empirical measurements of the motor behavior. Based on the proposed model, the effect of electrode skew is analyzed for force ripple reduction. Using the analysis, a skew motor is fabricated and tested, with the results demonstrating that a skewing electrode with a skew factor π can considerably reduce thrust force ripple.     

非线性压电振动能量采集器与非线性接口转换 电路的耦合动力学特性研究

压电振动能量采集器是实现低功耗电子产品无线自供电的核心部件,其与非线性接口转换电路的耦合机理是提升无线 自供电系统输出性能的关键理论。 以非线性三稳态压电振动能量采集器及其 4 种非线性接口转换电路为对象,建立动力学模 型,利用谐波平衡方法求解不同接口电路下系统耦合动态响应的稳态解;仿真分析了系统参数对接口电路输出特性的影响。 研 究结果表明,当机电耦合系数较小时,串联同步电感开并接口电路(S-SSHI)适合于频率小于 7 Hz、负载电阻小于 7. 4×10 6 Ω 的 场合,而并联同步电感开关接口电路( P-SSHI) 则相反;当机电耦合系数较大时,直流电( DC) 电路具有优势,功率达到 4. 5×10 -3 mW;交流电(AC)电路和 DC 电路具有较宽的机电耦合系数范围,而 P-SSHI 电路和 S-SSHI 电路却较窄但输出功率高, 最大输出功率可达到 19. 0×10 -3 和 14. 3×10 -3 mW。 实验验证了仿真结果的正确性。     

Modeling and analysis of nonlinear damping mechanisms in vibrating systems

A damping mechanism is universally seen in vibrating systems, such as flexible structures and robotic manipulators. However, its nature is still little understood and the modelling technique so far has been primitive. This work, by introducing the Method of Energy Approximation (MEA), provides a unified approach to nonlinear damping modeling and random response analysis of single-d.f. vibrating systems. By the MEA, one can easily find the approximate but closed-form stationary probability density function (i.e. the stationary solution of the Fokker-Planck equation) of any nonlinearly damped vibration subject to white noise excitation. Various results validating the MEA are obtained. The central result of this work is the establishment of an efficient method for the modeling of a nonlinear damping mechanism based upon free response data. It is also found that, among all choices of nonlinear damping models, energy type nonlinear damping models of the form play a central role and their relation to all other nonlinear damping models is thoroughly studied.     

压电悬臂梁发电装置的建模与仿真分析

为提高一定尺度压电复合悬臂梁（简称压电梁）的发电能力,建立了单、双晶压电梁发电能力的仿真分析模型,研究了结构尺寸、激励方式及材料性能等对其发电能力的影响规律。研究表明,在基板材料及激励条件相同时,存在不同的最佳厚度比使单／双晶压电梁发电能力最大,双晶梁的最大发电量约为单晶梁的2倍。基板材料不同时,最佳厚度比随（基板与压电材料的）杨氏模量比的增加而减小,铝、钼基板构成的单／双晶压电梁的最佳厚度比分别为（0.7,0.32）和（0.45,0.2）。在相同的厚度比（0.5）及外界激励条件下,杨氏模量比对两种电梁发电能力的影响不同,杨氏模量低于3.3时,双晶梁的发电量均大于单晶梁。     

Direct descent curvature optimal control with a modification algorithm and its application to nonlinear process

This paper presents a direct descent second order or direct descent curvature algorithm with some modifications for the optimal control computations. This algorithm is compared with Hamiltonian methods in the literature. The proposed algorithm has generated numerically robust solutions with respect to conjugate points. The weighting matrix updating scheme was developed to improve the second-order optimal control algorithm, tested the performance of the algorithm, and shown on the benchmark and industrial process. The time-varying optimal feedback (TVOFB) gains are also generated along the trajectory as byproducts. If the trajectory deviates from the optimal trajectory for any reason (i.e., changing of system parameters, step disturbance into the plant, changing of initial conditions), it is held on the optimal trajectory by means of the optimal feedback. Simulations have been given for controlling the Van der Pol and bioreactor system, which are nonlinear benchmark systems.     

Analysis of nonlinear vibration response of a functionally graded truncated conical shell with piezoelectric layers

The nonlinear vibration response of a functionally graded materials (FGMs) truncated conical shell with piezoelectric layers is analyzed. The vibration amplitude is suppressed by the positive and inverse piezoelectric effects. And the bifurcation phenomenon is described to reveal the motion state of the conical shell. Firstly, a truncated conical shell composed of three layers is described. And the effective material properties of the FG layer are defined by the Voigt model and the power law distribution. Next, the electric potentials of piezoelectric layers are defined as cosine distribution along the thickness direction. Meanwhile, the constant gain negative velocity feedback algorithm is used to suppress the vibration amplitude by the electric potential produced by the sensor layer. Thereafter, considering the first-order shear deformation theory and the von Karman nonlinearity, the relationship between the strain and displacement is defined. And the corresponding energy of the conical shell is calculated. After that, the motion equations of the conical shell are derived based on the Hamilton principle. Again, the nonlinear single degree of freedom equation is derived by the Galerkin method and the static condensation method. In the end, the nonlinear vibration response of FGMs truncated conical shell with piezoelectric layers under the external excitation is analyzed via using the harmonic balance method and the Runge-Kutta method. The effects of various parameters, such as ceramic volume fraction exponent, external excitation’s amplitude, control gain and geometric parameters on the nonlinear vibration response of the system are evaluated by case studies. Results indicate that the control gain plays an important role on the suppression of the vibration amplitude. The ceramic volume fraction exponents are not sensitive to the nonlinear vibration response compared with other parameters. The bifurcation behavior is observed under different parameters. The FGMs truncated conical shell with piezoelectric layers has three types of motion state, such as periodic motion, multi-periodic motion, and chaos motion.

     

压电式振动发电机的建模及应用

振动式压电发电机是一种可为旋转机械故障诊断中的无线传感节点供电的微能源。本文设计了由压电悬臂梁、质量块和固定装置组成的振动式压电发电机,并建立了安装在恒速旋转机械上的悬臂梁式发电机的数学模型。分析了轴向分力对悬臂梁刚度和发电机频率的影响,在考虑悬臂梁受到轴向力影响的基础上,给出了发电机固有频率、输出电压和输出功率的公式。对一个安装于转动框架上的振动式压电发电机进行了测量,结果表明,当框架转动频率为14.25 Hz时,发电机的输出功率约为35 μW,随着旋转机械转动频率偏离发电机固有频率,发电机的输出功率很快降低。     

Comparison of electrostatic fins with piezoelectric impact hammer techniques to extend impulse calibration range of a torsional thrust stand

With the progression of high-power electric propulsion and high thrust-to-power propulsions system, thrust stand diagnostics require high-fidelity calibration systems that are accurate over a large-range of thrust levels. Multi-mode and variable I(sp) propulsion devices also require that a single stand be capable of measuring thrust from 10's of uNs to 100's of mNs. While the torsional thrust stand mechanic and diagnostics are capable of operating over such a large range, current pulsed calibration schemes are typically limited to a few orders of magnitude of dynamic range. In order to develop a stand with enough dynamic range, two separate calibration methods have been examined and compared to create a combined system. Electrostatic fin (ESF) and piezoelectric impact hammer (PIH) calibration systems were simultaneously tested on a large scale torsional thrust stand system. The use of the these two methods allowed the stand to be calibrated over four orders of magnitude, from 0.01 mNs to 750 mNs. The ESF system produced linear results within 0.52% from 0.01 mNs to 20 mNs, while the PIH system extended this calibration range from 10 mNs to 750 mNs with an error of 0.99%. The two calibration methods agreed within 4.51% over their overlapping range of 10-20 mNs.     

压电陶瓷执行器迟滞非线性补偿与最优控制

为提高空间望远镜精密稳像系统中压电驱动快摆镜(FSM)的摆动精度,对压电陶瓷执行器迟滞非线性补偿和控制技术进行研究。针对压电迟滞的非对称性以及Duhem模型求逆过程复杂的问题,对Duhem模型中的微分方程进行变换,直接建立Duhem非对称逆迟滞模型作为迟滞前馈补偿器,并利用免疫差分进化算法辨识模型参数。在Duhem逆模型补偿压电静态迟滞非线性的基础上,引入基于优化参考跟踪的线性二次型高斯(LQG-ORT)控制方法进一步提高压电执行器的动态定位精度,采用动态迟滞率相关自回归各态历经模型(ARX)建立状态空间方程,用于卡尔曼滤波器预测状态变量和控制器计算状态变量的最优控制系数矩阵。实验结果表明：直接建立的Duhem非对称逆迟滞模型能有效描述压电执行器非对称逆迟滞曲线,拟合均方根误差为0.635 9 V(0.5 Hz),相对误差为0.79%(0.5 Hz);实时跟踪幅值为24μm,频率范围1～80 Hz的目标位移信号,LQG-ORT算法的跟踪误差为0.065 5μm,相对误差为0.27%。     

Passive suppression of nonlinear panel flutter using piezoelectric materials with resonant circuit

In this study, a passive suppression scheme for nonlinear flutter problem of composite panel, which is believed to be more reliable than the active control methods in practical operations, is proposed. This scheme utilizes a piezoelectric inductor-resistor series shunt circuit. The finite element equations of motion for an electromechanically coupled system is derived by applying the Hamilton’s principle. The aerodynamic theory adopted for the present study is based on the quasi-steady piston theory, and von-Karrnan nonlinear strain-displacement relation is also applied. The passive suppression results for nonlinear panel flutter are obtained in the time domain using the Newmark-β method. To achieve the best damping effect, optimal share and location of the piezoceramic (PZT) patches are determined by using genetic algorithms. The effects of passive suppression are investigated by employing in turn one shunt circuit and two independent shunt circuits. Feasibility studies show that two independent inductor-resistor shunt circuits suppresses flutter more effectively than a single shunt circuit. The results clearly demonstrate that the passive damping scheme that uses piezoelectric shunt circuit can effectively attenuate the flutter.     

Modeling of piezoelectric actuator for compensation and controller design

This work proposes a novel method for describing the hysteretic non-linearity of a piezoelectric actuator. The hysteresis behavior of piezoelectric actuators, including the minor loop trajectory and the residual displacement near zero input, are modeled by a set of hysteresis operators, including a gain and an input-dependent lag, as well as the parameter scheduling method. A hysteresis model, using the identified parameters, and containing only the dominant hysteresis operator, is presented herein. Based upon a simplified hysteresis model, tracking is controlled to reduce the non-linear effects in the characteristics of the piezoelectric actuator. A proportional-integral (PI) controller, with inverse model feed-forward, suppresses the tracking error to within ±1% full span range (FSR) of the actuator, noticeably improving the tracking performance of the piezoelectric actuator.     

Induction ultrasonic piezoelectric transducers: Theoretical analysis of the operation of a piezoelectric transducer

The main expressions for the coefficients of electroacoustic transformation and the electric and acoustic impedances of a new type of ultrasonic transducers—induction piezoelectric transducers—have been obtained as functions of their geometric and electromagnetic parameters.