A Novel Motion Amplifier Using an Axially Driven Buckling Beam

For active materials such as piezoelectric stacks, which produce large force and small displacement, motion amplification mechanisms are often necessary—not simply to trade force for displacement, but to increase the output work transferred through a compliant structure. Here, a new concept for obtaining large rotations from small linear displacements produced by a piezoelectric stack is proposed and analyzed. The concept uses elastic (buckling) and dynamic instabilities of an axially driven buckling beam. The optimal design of the buckling beam end conditions was determined from a static analysis of the system using Euler’s elastica theory. This analysis was verified experimentally. A stack-driven, buckling beam prototype actuator consisting of a pre-compressed PZT stack (140 mm long, 10 mm diameter) and a thin steel beam (60 mm × 12 mm × 0.508 mm) was constructed. The buckling beam served as the motion amplifier, while the PZT stack provided the actuation. The experimental setup, measuring instrumentation and method, the beam preloading condition, and the excitation are fully described in the paper. Frequency responses of the system for three preloading levels and three stack driving amplitudes were obtained. A maximum 16° peak-to-peak rotation was measured when the stack was driven at an amplitude of 325 V and frequency of 39 Hz. The effects of beam preload were also studied.

Optimization of Electrical Output in Response to Mechanical Input in Piezoceramic Laminated Shells

The piezoelectric ceramic, Lead Zirconate Titanate (PZT), is capable of producing large voltages in response to an applied mechanical stress when employed in a laminate manufactured using the THUNDER process. This study addresses the issue of optimizing mechanical parameters in a PZT unimorph to maximize charge generated due to mechanical strain. The PZT unimorph structure is initially curved and generates a surface charge when vertically loaded. In the analysis, the principles of shallow shell and linear piezoelectric laminate theories are employed to obtain an expression for charge in terms of geometry, material properties and loading. Analytical relationships are then derived that can be used to optimize the charge produced from these generators. Numerical parametric studies are then conducted to maximize the charge generation by manipulating dimensions of the components. Experimental results show a “convergence” to a theoretically predicted ‘applied force vs. deformation’ relationship when the PZT unimorph is subjected to a pressure load. Finally, a charge collecting circuitry for harvesting the charge produced is designed and presented.

Harmonic Wave Propagation of Ultrasonic Arc Stators

A piezoelectric curvilinear arc stator designed for an ultrasonic curvilinear motor is studied in this research. Design of piezoelectric curvilinear arc stator is proposed and its governing equations and vibration behavior are investigated. Then, analysis of forced vibration response or driving characteristics to harmonic excitations in the modal domain is conducted. Finite element modeling and analysis of the arc stator are also discussed. Analytical results of free vibration characteristics are compared favorably with the finite element results. Harmonic analyses of the three finite element models reveal changes of dynamic behaviors of three models and also imply operating frequencies with significant traveling wave component. Study of mathematical and finite element simulation results suggests that stable traveling waves can be generated to drive a motor on the proposed curvilinear arc stator system.

Micro-Structronics and Control of Hybrid Electrostrictive/Piezoelectric Thin Shells

Certain ferroelectric materials possess dual electrostrictive and piezoelectric characteristics, depending on their specific Curie temperatures. These materials exhibit piezoelectric characteristics in the ferroelectric phase when the temperature is below the Curie point. However, they become electrostrictive in the paraelectric phase (non-polar phase) as the temperature exceeds the Curie point. The (direct) electrostrictive effect is a quadratic dependence of stress or strain on applied electric field. The nonlinear electromechanical effect of electrostrictive materials provides stronger actuation performance as compared with that of piezoelectric materials. Due to the complexity of the generic ferroelectric actuators, micro-electromechanics and control characteristics of generic electrostrictive/piezoelectric dynamics system deserve an in-depth investigation. In this study, electro-mechanical dynamic system equations and generic boundary conditions of hybrid electrostrictive/piezoelectric double-curvature shell continua are derived using the energy-based Hamilton’s principle, elasticity theory, electrostrictive/piezoelectric constitutive relations, and Gibb’s free energy function. Moreover, the second converse electrostrictive effect and the direct piezoelectric effect are all considered in the generic governing equations. Simplifications of the generic theory to other common geometries or specific materials are demonstrated and their electromechanical characteristics are also evaluated.

The Design Tradeoffs of Linear Functionally Graded Piezoceramic Actuators

It is common practice to reduce the voltage level within piezoelectric actuators by utilizing multiple layers, typically bonded together. Unfortunately, this has a tendency to result in device failure due to delamination. For example, with benders the typical lifetime is 105 to 106 cycles, limiting its use in practical applications. This poses an interesting design tradeoff: the stroke is increased due to sharper gradients between material layers; however, the higher gradients lead to high stress concentrations at those interfaces. One approach to reducing these stresses is to grade the material properties through a monolithic piece of piezoceramic so that no interfaces or bonding elements exist, but this comes at the cost of stroke. This paper explores the design tradeoff inherent to monolithic functionally graded piezoelectrics. An analytical free-displacement model for a monolithic piezoceramic beam with a generic gradient is derived. Key to this is the inclusion of the complex electric field distribution which rises from the non-homogeneous material properties. This model is used along with finite element models to examine the effect of continuous linear and stepwise material gradients on the displacement performance as well as the stress levels. The study shows that using monolithic functionally graded piezocermics can significantly reduce the stresses with only a minor impact on the device stroke.

Biomimetic Compliant System for Smart Actuator-Driven Aquatic Propulsion: Preliminary Results

Biomimetic design takes principles from nature to employ in engineering problems. Such designs are hoped to be quiet, efficient, robust, and versatile, having taken advantage of optimization via natural selection. However, the emulation of specific biological devices poses a great challenge because of complicated, arbitrary, and over-redundant designs. Compliant mechanisms are of immediate appeal in addressing the problem of complex, biomimetic deformation because of their inherent flexibility and distributed compliance. The goal of this research is to develop a biologically-inspired hydrofoil for aquatic propulsion, by assembling planar compliant mechanism building blocks to generate complex 3-D deformations. The building block is a rib structure generated from topology optimization. An ADAMS model is then created to quickly visualize motion and estimate system characteristics. System refinement is achieved through further size and shape optimization of individual ribs. Testing of a single-rib and dual-actuator system is currently in progress. The preliminary results have demonstrated the potential of this combined approach to quickly identify and evaluate new applications that may result from building blocks.

Application of a Computational Micro-Electro-Mechanical Model for the Prediction of Self-Heating of Ferroelectric Ceramic Materials

Application of ferroelectric materials in devices subject to high fields and a range of drive frequencies is becoming increasingly common. As a result, self-heating of these devices is of concern. An energy based polycrystalline model including thermal and rate effects has been developed. The model has been developed from the thermodynamics of piezoelectrics, and includes elastic, dielectric, and piezoelectric anisotropy. It captures ferroelectric and ferroelastic switching under combined loading. In the current work the model is expanded to include self-heating effects. Model results are compared to experimental data. Results from the model give insight into material behavior.

Piezoelectric Energy Harvesting Using a Clamped Circular Plate: Experimental Study

Energy harvesting using piezoelectric material is not a new concept, but its small generation capability has not been attractive for mass energy generation. For this reason, little research has been done on the topic. Recently, wearable computer concepts, as well as small portable electrical devices, are a few motivations that have reignited the study of piezoelectric energy harvesting. The theory behind cantilever type piezoelectric elements is well known, but the transverse moving circular plate elements, which can be used in pressure type energy generation is not yet fully developed. The power generation in a circular plate depends on several factors. Among them, the poling direction and the stress distribution is important as shown in previous research. Specifically, it has been shown theoretically that grouping electrodes and repoling some of the regrouped segments can lead to optimized energy harvesting in a clamped circular plate structure. This paper provides experimental validation of those results. In this paper, three circular plate piezoelectric energy generators (PEG), one unmodified and two different regrouped unimorph PEGs, were used to support the regrouped PEG energy generation theory. The experimental results of regrouped PEGs will be presented with an eye toward guidelines for design of a useful energy harvesting structure.

Optimal Design and Control of a Rotating Flexible Arm With ACLD Treatment

In this paper, the optimal design and control of a rotating clamped-free flexible arm with fully covered active constrained layer damping (ACLD) treatment are studied. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The piezo-sensor voltage is fed back to the piezo-actuator via a PD controller. Finite element method (FEM) in conjunction with Hamilton’s principle is used to derive the governing equations of motion of the system which takes into account the effects of centrifugal stiffening due to the rotation of the beam. The damping behavior of the viscoelastic material (VEM) is modeled using the complex shear modulus method. The design optimization objective is to maximize the sum of the first three open-loop modal damping ratios divided by the weight of the damping treatment. A genetic algorithm, differential evolution (DE), combined with a gradient-based algorithm, sequential quadratic programming (SQP), is used to determine the optimal design variables such as the thickness and storage shear modulus of the VEM core. Next for the determined optimal design variables, the optimal control problem is performed to determine the optimal control gains which minimize a quadratic performance index. The control performance index is normalized with respect to the initial conditions and the optimal control problem is posed to solve a min-max optimization problem. The results of this study will be useful in the optimal design and control of adaptive and smart rotating structures such as rotorcraft blades or robotic arms.

Design of a Conformable Rotor Airfoil Using Distributed Piezoelectric Actuation

In the present study, a design methodology is developed for determining the optimal distribution of a limited amount of piezoelectric material and optimal skin for a conformable rotor airfoil section. The objective of the design optimization is to generate a conformable airfoil structure that produces significant trailing edge deflection under actuation loads, but minimal airfoil deflection under aerodynamic loads. Energy functions, Mutual Potential Energy (MPE) and Strain Energy (SE), are used as measures of the deflections created by the actuation and aerodynamic loads, respectively. The design objective is achieved by maximizing a multi-criteria objective function that represents a ratio of the MPE to SE. Several design optimization techniques are evaluated including geometry and concurrent geometry-topology optimizations. The results of the study indicate that the optimized conformable airfoil section obtained using the concurrent geometry-topology optimization can produce a significant downward trailing edge deflection, and the airfoil deformation due to the aerodynamic loads alone is small. However, the optimized airfoil design is extremely complex and contains intricate network of actuators, which may be difficult to fabricate. Systematic simplification of the structure is performed to obtain a conformable airfoil design that is simple and may be easy to build. Further parametric optimization is used to find optimal values of the skin axial and bending stiffness for an optimal conformable airfoil design. The airfoil can produce a downward trailing edge deflection equivalent to 3.7° of Effective Flap Angle from the actuation loads, with the peak-to-peak deflection being nearly twice the downward deflection, and the airfoil deformation due to the airload loads is less than 1°. The optimal skin should have less axial stiffness and much more bending stiffness as compared to a conventional skin.