RAINBOW Actuators Research Articles

Nonlinear analysis of RAINBOW actuator characteristics

This paper discusses an investigation into deformations of rectangular RAINBOWactuators, which are classified as a type of laminated actuator. The actuators consist ofa piezoelectric active layer and a reduced passive layer formed in an elevatedtemperature reduction process. An energy-based Rayleigh–Ritz model is used toapproximate the thermally induced deformations with 23-term polynomials. Due to largeout-of-plane displacements of the RAINBOW actuators after cooling down to roomtemperature, inclusion of geometric nonlinearities in the kinematic relations istaken into consideration. Actuation characteristics of these actuators caused by aquasi-static electric field applied to the piezoelectric layer are also modeled with theRayleigh–Ritz approach. Material nonlinearities in the piezoelectric layer areincluded in the constitutive equation to capture the effects of a strong electric field.Piezoelectrically induced tip deflections of a series of RAINBOW cantilever actuators arecalculated and compared with experiment. With the geometrical and materialnonlinearities taken into account, numerical simulation reveals the computed tipdeflections agree very well with the experimental data. In addition, tip blockingforces representing the load-carrying capability of the RAINBOW actuators areapproximately evaluated by equating the magnitude of force-induced displacementto that of the piezoelectrically induced tip deflection. Again, good agreementbetween numerical results and experiment can be observed in the case of the tipblocking force. This evidently shows that the pertinent nonlinearities have verycrucial effects on the responses and performances of the RAINBOW actuators.

Structurally Graded Monolithic Piezoelectric Actuators, Modeling and Optimization with FEM

In this work, novel structurally graded piezoelectric disc actuators are proposed. The monolithic gradient actuators had nonuniform thickness profiles, which caused distribution of the electric field and resulted in bending of the discs. The geometry and clamping conditions of the actuators were varied and the displacement properties were optimized using ATILA and Comsol Multiphysics finite element modeling (FEM) softwares. The material parameters of commercial PZT-5H were used in the modeling of the actuators — 25 mm in diameter with an original thickness of 0.5mm. Additional steel layers with different thicknesses were introduced under the actuators in `unimorph-fashion' in order to study their effect on the displacements and stresses of the actuators. The modeling results showed that the bending of the monolithic actuators could be realized without any additional passive layers and also that the utilization of clamping further improved the displacement capabilities. For example, ~53 μm axial displacements were enabled with a 1 V/μm electric field (corresponding to the thinnest part of the actuator) without any passive layers. The modeled displacement results were comparable to displacements obtained by pre-stressed PRESTO (~50 μm), THUNDER (~60 μm) and RAINBOW (~70 μm) actuators of 25 mm in diameter with a 1 V/μm electric field.

Fabrication of a novel piezoelectric actuator with high load-bearing capability

A lot of piezoelectric ceramic researchers have been devoted to the development of piezoelectric actuator with enhanced axial displacement as well as excellent load-bearing capability. The piezoelectric actuator with dome-shaped structure possesses higher axial displacement, such as RAINBOW and THUNDER. In this study, a new method for producing piezoelectric actuator with enhanced load-bearing capability has been developed. The manufacturing process is better than the fabrication of the RAINBOW and THUNDER type actuator. The novel piezoelectric actuator module was made up by nickel electroplating on one side of the stainless steel substrate glued with the PZT patch on the other side. It is observed that by electroplating process the load-bearing capability is significantly enhanced while the actuating displacement is somewhat decreased. For example, with 60 min electroplating on the substrate of the actuator, the load-bearing ability is increased by 4.7 multiples whereas the maximum output displacement is only decreased by 20.2%.

Stress‐Biased Cymbals Using Shape Memory Alloys

Cymbals and other flextensional transducers demonstrate high effective displacements due to the amplifying nature of the metal endcaps, while stress‐biased RAINBOW actuators display high displacements due to enhanced 90° domain wall translational processes that result from the tensile stress in the surface region of the lead zirconate titanate (PZT) layer created during manufacturing. A new class of transducers, called stress‐biased cymbals (SBC), was developed that couples the operational principles of cymbal and stress‐biased actuators. Pre‐stressing the PZT in the cymbal was accomplished using a flat‐trained shape memory alloy endcap. Hysteresis loops were measured using a Sawyer–Tower circuit for different pre‐stress levels. Enhancements in the differential dielectric constant of more than 70% and the effective d33 of the cymbal by ∼57% were observed, suggesting greater 90° domain wall motion in the SBC compared with the standard cymbal device. The stresses developed during the fabrication process were measured and compared with theoretical models. Additional performance characteristics including dynamic dielectric constant, loss, and radial resonance frequency of the devices are also reported.

Displacement Properties of Newly Developed 3-Dimensional Piezoelectric Actuator at Various AC Frequencies

The electromechanical properties of a newly proposed 3-dimensional piezoelectric actuator have been investigated. Especially, the effects of 3-dimensional geometry on the maximum tip displacement were carefully investigated. As a result, it was found that the maximum strain of the 3-dimensional piezoelectric device was significantly enhanced up to 4.5 times higher than that of a disk shape device. This data was in good agreement with the finite element model analysis of strains and vibration modes. Moreover, the field -induced displacement stability of dome-shaped 3- dimensional piezoelectric actuator at various ac freguencies was superior to Rainbow actuator.

Poling Conditions of Pre-Stressed Piezoelectric Actuators and Their Displacement

The poling procedure has always been the key issue in producing piezoelectric actuators with optimised performance. This is also true with the relatively new category of pre-stressed bender actuators, where mechanical bias achieved with a passive layer is introduced in the actuators during manufacturing. Due to these factors, the behaviour of the actuator under poling is different compared to its bulk counterparts. In this paper, two different thicknesses of commercial PZT 5A and PZT 5H materials were used in bulk actuators and pre-stressed benders realised by new method. Pre-stress was introduced by using a post-fired biasing layer utilising sintering shrinkage and difference in thermal expansion. The hysteresis loop of the actuators was measured under 0.5–7.0 MV/m electric fields at 25–125∘C temperatures, providing information about their remnant polarisation and coercive field before poling. The results showed that high electric field and 25∘C temperatures in poling provided higher remnant polarisation and coercive electric field than using 125∘C temperature at poling. Difference was especially significant in coercive electric field values where up to 114.8% difference was obtained for PZT 5H bulk actuator and 65.9% for pre-stressed actuators. Higher coercive fields can be utilized as increased operating voltage range of piezoelectric devices. The differences in results obtained here and by others can be explained by the different pre-stress level, stronger clamping of the thicker passive layers of the RAINBOW and THUNDER actuators and passive ring area introducing high tensile stresses. The same conditions were used to pole the actuators, after which the displacement and dielectric constant of the actuators were measured. The displacement measurements showed that remnant polarisation has good correlation with displacement. This fact can be used in estimating pre-stressed actuator performance before actual poling. The dielectric constant measurements with a small signal after poling gave even better correlation than the remnant polarisation.

Characterization and modelling of 3D piezoelectric ceramic structures with ATILA software

In this paper, the correspondence between ATILA-simulated and measured values of two piezoelectric ceramic structures, bulk and RAINBOW actuators, was determined. Modelling was started by creating a 2D wire model of the structures, after which a 3D model was created and simulation parameters were introduced (electric potentials, polarizations and boundary conditions). Harmonic type analysis was used in the simulations. The results obtained from the simulations contained information about displacements in the z-axis direction. Displacements of the measured structures behaved nonlinearly as a function of the electric field. Accordingly, effective piezoelectric coefficients (i.e. d 31, d 33) calculated from the electric field and the displacement also changed nonlinearly. However, the displacement results acquired from simulations are linear, since the ATILA program uses a linear approach for in the calculation. This causes the modelling results to differ from the measurement results, especially when large voltages are used. The problem was solved by modifying the constant parameters used in the simulations. In the study reported here, relative permittivity K 33, piezoelectric coefficient d 33 and approximated piezoelectric coefficient d 31 were used to obtain more accurate modelling results corresponding to the measurement results. The differences in the z-axis displacements between the modelling (using the original material parameters) and measurement results obtained with bulk and RAINBOW actuators were 6.5–17.7% and 6.0–27.9%, respectively. With modified material parameters, the differences were 1.1–1.6% and 3.1–8.5%, respectively.

Displacement, stiffness and load behaviour of laser-cut RAINBOW actuators

Commercial piezoceramic PZT 5A discs were reduced in air at 750 °C to produce RAINBOW actuators using graphite as the reduction substrate and ZrO 2 powder for protection. After the reduction process, the RAINBOW actuators were cut to desired shapes with a Nd–YAG laser. The effect of the laser cutting on the load, displacement, stiffness and dielectric constant characteristics of the actuators was studied for different sizes. Load capabilities of the actuators reduced as the amount of active material decreased but almost 30% of the active material could be removed without significant change in load properties. Results showed the possibilities to shape and decrease the size of the actuators and perform application specific modifications in load, displacement and stiffness properties. The effect of the laser cutting on the dielectric constant was insignificant compared with the de-poling effect of high electric field driving. Manufactured actuators were modelled with the ATILA program. Modelling gave accurate results with the original RAINBOW actuator and with sliced actuators 15 and 10 mm in width.

Estimation of the Effective d31 Coefficients of the Piezoelectric Layer in Rainbow Actuators

We have analyzed the performance of Rainbow (reduced and internally biased oxide wafer) actuators by assuming that the key difference between these devices and unimorph actuators is the presence of internal stress that alters the extrinsic (domain switching) contribution to electromechanical response, and thus, the effective d31 coefficient of the piezoelectric layer. Based on this assumption, we calculated the d31 coefficient as a function of device geometry and electric field and found that the coefficients ranged from approximately −300 to −600 pm/V. The highest d31 value was obtained for a Rainbow actuator that was fabricated by reducing 1/3 of the piezoelectric layer; other studies indicated that this device possessed the highest tensile stress in the surface region of the piezoelectric. We observed that geometric effects on calculated d31 coefficients were as significant as voltage effects. The analytical approach utilized also permitted estimation of the relative contributions of mechanical and stress effects to the performance of these devices, which were determined to be dependent on field and geometry. Although the estimated d31 coefficient for certain geometries is twice the typical low field value, it must be remembered that this value represents an “average” value for the entire piezoelectric layer, which is under a stress gradient; i.e., the lower region of the piezoelectric is in lateral compression, while the upper region is in lateral tension. This suggests that the true electromechanical coefficients of the lead zirconate titanate composition utilized in these devices would display an even broader range of d31 values, if d31 was characterized as a function of uniform lateral stress.

Mechatronic design and control of singly and doubly curved composite mesoscale actuator systems

Recently, the design of curved mesoscale actuators (deflections from 1 to 15 mm) has been a topic of study for many researchers. The work in this paper deals with the development of a comprehensive modeling technique for dealing with curved actuators. First, the formulation begins with the equations of motion for a general shell surface. Second, relationships for reducing the equations to those for known actuators are given. The technique can be applied to a broad array of curved actuators. These actuators include but are not limited to rainbow actuators, thunder actuators, and basic C-block actuators. Next, the technique is then experimentally verified on a stack of rainbow actuators. Finally, the system is controlled using both classical and intelligent control techniques. In addition, hardware and circuitry issues are explored.

Design optimization of dome actuators

This paper reports the conceptual design, analysis, and modeling of the electromechanical behavior of dome actuators. The geometric parameters of the actuator (dome thickness, width, radius, and depth), poling direction, electric field, and material properties (elastic compliance, piezoelectric constants, and dielectric permittivity) have been taken into account in the modeling work. The results of the analysis indicate that a dome actuator with a tangentially alternating poling direction and electric field (Case C) exhibits much larger displacement and force responses than dome actuators with other poling directions and electric fields. The first mode of natural frequency of the Case C dome actuator also was investigated, and its predicted performance was compared with that of moonie and rainbow actuators. The findings of this research clearly demonstrate the merit of design optimization of electromechanical devices.

Finite element analysis of a deformable array transducer

Deformable array transducers have previously been described to implement 2-D phase aberration correction of near-field aberrators with only a 1xN or 2xN array configuration. This transducer design combines mechanical phase correction using an actuator with electronic phase correction for a 2-D correction with significantly fewer elements than a full 2-D array. We have previously reported the fabrication and results of a 1x32 deformable array fabricated with a RAINBOW (Reduced And INternally Biased Wafer) actuator. Because of the complicated construction of deformable arrays, we propose to use finite element analysis (FEA) as a design tool for array development. In this paper, we use 2-D and 3-D FEA to model the experimental results of the deformable array as the first step toward development of a design tool. Because the deformable array combines a mechanical actuator with a medical ultrasound transducer, improvement in performance must consider both the ultrasound characterization along with the low frequency actuator characterization. For the ultrasound characterization, time domain FEA simulations of electrical vector impedance accurately predicted the measurements of single array elements. Additionally, simulations of pulse-echo sensitivity and bandwidth were also well matched to measurements. For the low frequency actuator characterization, time domain simulation of the low frequency vector impedance accurately predicted measurement and confirmed the fundamental flexure resonance of the cantilever configuration at 1.3 kHz. Frequency domain FEA included thermal processing effects and predicted actuator curvature arising during fabrication. Finally, frequency domain FEA simulations of voltage-induced displacement accurately predicted measured displacement.

Real-time feedforward control of low-frequency interior noise using shallow spherical shell piezoceramic actuators

This paper demonstrates the use of RAINBOW and THUNDER actuators as acoustic control sources in the real-time control of low frequency harmonic interior noise. The former actuator drives a flat acoustic piston while the latter drives a conventional speaker cone. The low-profiled and lightweight nature of these actuators makes them suitable for aircraft applications. The two devices have been used successfully for active noise cancellation inside a duct and a cylindrical enclosure. This paper presents results of the real-time noise control experiments.

Piezoelectrically driven speakers for active aircraft interior noise suppression

This paper presents results from an experimental study of light weight piezoelectrically driven speakers developed in the Smart Trim Technology Laboratory (SMARTTLAB) at University of Delaware. The speakers are of direct radiator type and are driven by shallow spherical shell piezoceramic actuators. Two implementations – an acoustic piston and a cone – have been tested. Results from small signal characteristics measurements performed in a semi-reverberant environment are presented. While most of the tests have been performed using RAINBOW actuators as driving elements, some results for the THUNDER actuator are also presented. The possible use of these devices as controllable acoustic sources in active noise control applications is discussed. The low weight of these actuators makes them highly suitable for aircraft interior noise control applications with severe space and weight restrictions.

Tip Deflection and Blocking Force of Soft PZT‐Based Cantilever RAINBOW Actuators

A piezoelectric/electrostrictive RAINBOW actuator is a monolithic bending device consisting of an electromechanically active layer and a reduced passive layer formed in a high‐temperature reduction treatment. When the piezoelectric or electrostrictive layer is driven under an electric field or when the environmental temperature changes, bending deflection is produced because of the constraint of the reduced inactive layer or because of the thermal expansion coefficient difference of the two layers. In this study, general analytical expressions relating tip deflection, blocking force, and equivalent moment with an applied electric field and temperature change are derived for a cantilevered RAINBOW actuator. It is shown that optimal actuator performance can be achieved in the RAINBOW actuator by choosing a suitable thickness ratio of the reduced layer to the PZT layer. A series of RAINBOW cantilever actuators have been experimentally prepared from high‐density, soft, lead zirconate titanate (PZT) ceramics. Different reduction layer thickness is obtained by adjusting the processing parameters, such as reduction temperature and time. The measured results on tip deflection and blocking force agree well with theoretical prediction under a weak electric field. However, when a high driving electric field is used, deviation is observed, which can be attributed to a nonlinear piezoelectric response and a nonlinear elastic behavior associated with soft PZT materials under high driving electric fields.

Correlation of the coercive field and reduced layer thickness in piezoelectric RAINBOW ceramics

RAINBOWs are a relatively new type of high-displacement, piezoelectric actuator produced by selectively removing oxygen from one side of a lead-containing ceramic using a high-temperature chemical reduction process. This process yields devices which contain a piezoelectric layer and a metallic layer (i.e., the reduced layer). In this study, piezoelectric RAINBOW actuators with reduced layer-to-total-thickness ratios ranging from 0.05 to 0.8 were produced from five soft-piezoelectric formulations. The ferroelectric hysteresis properties of each specimen were then measured while taking the total thickness of the device to be ferroelectric. Because of this assumption and the metallic nature of the reduced layer, the resulting coercive field measurements were found to correlate strongly with the thickness of the piezoelectric portion of each device. A simple, non-destructive method for estimating the reduced layer thickness in RAINBOW ceramics was devised based on this relationship.

Design and development of smart microstrip patch antennas

The major weakness of a microstrip patch antenna is its narrow bandwidth characteristic. One method that has been investigated to increase bandwidth is the addition of a parasitic element to the microstrip patch antenna. In an active microstrip patch antenna, variable bandwidth can be achieved by varying the spacing between the antenna and the parasitic element, which is fixed to a dielectric plate. In this study an actuator is developed, tested and employed on an actual microstrip patch antenna and its parasite. Since a relatively large displacement (1 cm) is needed, the actuator is comprised of a stack of RAINBOW actuators. This study takes advantage of the fact that, for antennas operating at higher frequencies, smaller absolute displacements will result in significant percentage changes in antenna bandwidth. The use of the parasite and the active system accounted for up to a factor of five increase in antenna bandwidth. Various control techniques were employed to counteract the effects of hysteresis and creep on the actuator. Because the use of metal components can degrade antenna performance, emphasis was placed on synergy in the design process.

Experimental studies of shallow spherical shell piezoceramic actuators as acoustic boundary control elements

This paper presents an experimental study of the shallow spherical shell piezoceramic RAINBOW actuator, to follow up the theoretical modeling and numerical studies of this actuator reported in a previous paper. A comparison of theoretically predicted and experimentally determined natural frequencies of the RAINBOW actuator with free edge boundary conditions is presented in the paper. Also presented are results from experiments performed on a prototype of a low profile piezoelectrically driven baffled acoustic piston developed at the Smart Trim Technology Laboratory. Experimentally generated volume velocity curves of the piston are presented. The possible use of this device in active noise control applications is discussed.

Asymmetric 90° domain switching in rainbow actuators

Asymmetry in the domain switching properties of Rainbow actuators with respect to positive and negative electric field was investigated and compared with the more symmetric properties of bulk ceramic materials. The electromechanical displacement and polarization hysteresis loops were found to be asymmetric in Rainbows. Peak-to-peak displacements in Rainbows poled at +25kV/cm increased steadily from 88 to 450 μm with increasing fields of ±5 to ±24kV/cm. Rainbows poled at -25kV/cm possessed a local minimum in displacement of 95 μm at 13kV/cm (near the coercive field) indicating a change in effective slope of the displacement versus field loop. Additionally, Rainbows possessed lower +EC (coercive field) and higher +PR (remanent polarization). It was found through X-ray diffraction of the tetragonal peak splitting in these materials that Rainbows exhibited enhanced 90° reorientation of a-domains to c-domain alignment with positive applied electric field than with negative field. Bulk ceramic properties were consistent for both positive and negative applied fields. A mechanism for 90° domain switching is discussed.

Modeling shallow-spherical-shell piezoceramic actuators as acoustic boundary control elements

There has been a growing interest in the active suppression of noise in aircraft interiors in the recent past. While there are already many different technical solutions available in the form of active noise controllers using loudspeakers and structural sources, there is a need for low-profile acoustic sources that could be used for generating large volume velocities with high efficiency and low control effort. This paper presents an investigation into the potential usage of shallow-spherical-shell actuators (also known as RAINBOW actuators), made of piezoelectric materials supported on a flexible foundation along the edge, for such applications. The actuators have been modeled analytically and the effects of curvature, mount stiffness, mass and other parameters on the natural frequencies, linear stroke and volume velocity have been studied. Simulation results are presented and the potential for using the actuator as an efficient acoustic source has been discussed.