Heat generation by internal loss factors of piezoelectrics is one of the critical issues for high power density piezoelectric applications, such as ultrasonic motors, piezoelectric actuators and transducers. There are three types of internal losses in piezoelectric materials, namely dielectric, elastic and piezoelectric losses. In this paper, a decoupled equivalent circuit is proposed to emulate a piezoelectric disk in radial vibration mode considering all three types of internal losses. First, the decoupled equivalent circuit is derived according to the conventional electromechanical equivalent circuit model. Then, a piezoelectric disk configuration in radial vibration mode is explored and simulated. The resonance and antiresonance frequencies and their corresponding mechanical quality factors are achieved by the proposed circuit. In order to verify the accuracy of the simulation results, the piezoelectric disk is fabricated and tested. Simulation results with the new circuit exhibit a good agreement with experimental results. Finally, the equivalent circuit with only dielectric and elastic losses are simulated and compared which further validates the accuracy improvement of the new equivalent circuit considering all three losses.

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Electromechanical Equivalent Circuit Model of a Piezoelectric Disk Considering Three Internal Losses

Of great importance is modeling for transducer design and application to predict its performance and simulate key characteristics. The equivalent circuit modeling (ECM), one of the most powerful tools, has been widely used in the transducer industry and academia due to its outstanding merits of low simulation cost and easy usage for multi-field simulation in both time and frequency domains. Nevertheless, most of the existing equivalent circuit models for Terfenol-D transducers normally ignore three material losses, namely elastic loss, piezomagnetic loss, and magnetic loss. Additionally, the magnetic leakage due to the intrinsic poor magnetic permeability of Terfenol-D is rarely considered into the piezomagnetic coupling. Both loss effects will produce substantial errors. Therefore, an improved SPICE model for a high-power Terfenol-D transducer considering the aforementioned three losses and magnetic flux leakage (MFL) is proposed in this article, which is implemented on the platform of LTspice software. To verify the usefulness and effectiveness of the proposed technique, a high-power Terfenol-D tonpilz transducer prototype with a resonance frequency of around 1 kHz and a maximum transmitting current response (TCR) of 187.1 dB/1A/ μ Pa is built and tested. The experimental results, both in the air and water of the transducer, are in excellent agreement with the simulated results, which well validates our proposed modeling methods. 

SPICE Modeling of a High-Power Terfenol-D Transducer Considering Losses and Magnetic Flux Leakage

Mechanical vibrations have been an important sustainable energy source, and piezoelectric cantilevers operating at the resonant frequency are regarded as one of the effective mechanisms for converting vibration energy to electricity. This paper focuses on model and experimental investigations of multiple attached masses on tuning a piezoelectric cantilever resonant frequency. A discrete model is developed to estimate the resonant frequencies’ change of a cantilever caused by multiple masses’ distribution on it. A mechanism consisted of a piezoelectric cantilever with a 0.3 g and a 0.6 g movable mass along it, respectively, is used to verify the accuracy of the proposed model experimentally. And another mechanism including a piezoelectric cantilever with two 0.3 g attached masses on it is also measured in the designed experiment to verify the discrete model. Meanwhile, the results from the second mechanism were compared with the results from the first one in which the single attached mass is 0.6 g. Two mechanisms have wildly different frequency bandwidths and sensitivities although the total weight of attached masses is the same, 0.6 g. The model and experimental results showed that frequency bandwidth and sensitivity of a piezoelectric cantilever beam can be adjusted effectively by changing the weight, location, and quantity of attached masses.

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Modeling and Analysis of Multiple Attached Masses Tuning a Piezoelectric Cantilever Beam Resonant Frequency

The properties of giant magnetostrictive material (GMM) are very sensitive to external compressive stress. Knowledge of these key properties is of essential importance in practical applications such as high-power underwater transducers. Although the parameters of GMM have been extensively studied, characterization and analysis of magnetic, elastic, and piezoelectric losses under different compressive stresses are rarely reported due to the difficulty in experimentally realizing the ideal mechanical free or clamped boundary conditions. In this study, we designed a longitudinal transducer for complex parameters characterization of GMM. We successfully characterize the key three losses in GMM using a multi-degree-of-freedom (MDOF) lumped parameter equivalent circuit model (LECM), meticulously incorporating the surface contact damping, stiffness, and structural losses. MDOF LECM provides a novel idea for loss characterization of GMM under compressive stress. In contrast to prior-art parameters characterization based on the distributed parameter equivalent circuit model (DECM), the proposed characterization based on MDOF LECM shows apparent superiority in terms of global sensitivity. The intensive losses of GMM for ten-time characterizations show high stability and are all positive. Statistical analysis of intensive losses’ dependency on the compressive stress is performed. A longitudinal transducer is designed for experimental verification. Finally, 95% prediction and confidence intervals for the variation trend of the intensive losses in relationship with compressive stress are obtained.

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Loss Characterization of Giant Magnetostrictive Material Under Compressive Stress

The vibration isolation system is now indispensable to high-precision instruments and equipment, which can provide a low vibration environment to ensure performance. However, the disturbance with variable frequency poses a challenge to the vibration isolation system, resulting in precision reduction of dynamic modeling. This paper presents a velocity self-sensing method and experimental verification of a vibration isolation system. A self-sensing actuator is designed to isolate the vibration with varying frequencies according to the dynamic vibration absorber structure. The mechanical structure of the actuator is illustrated, and the dynamic model is derived. Then a self-sensing method is proposed to adjust the anti-resonance frequency of the system without velocity sensors, which can also reduce the complexity of the system and prevent the disturbance transmitting along the cables. The self-sensing controller is constructed to track the variable frequency of the disturbance. A prototype of the isolation system equipped with velocity sensors is developed for the experiment. The experiment results show that the closed-loop transmissibility is less than -5 dB in the whole frequency rand and is less than -40 dB around, adding anti-resonance frequency which can be adjusted from 0 Hz to initial anti-resonance frequency. The disturbance amplitude of the payload can be suppressed to 10%.

https://www.mdpi.com/1424-8220/21/6/1941/pdf

Design and Experimentation of a Self-Sensing Actuator for Active Vibration Isolation System with Adjustable Anti-Resonance Frequency Controller.

The self-sensing technique allows a single piece of piezoelectric element to function simultaneously as an actuator and a sensor in a closed-loop system. This study proposes an improved vibration suppression system using the piezoelectric self-sensing technique whose usefulness is experimentally verified in a cantilever beam. A single piezoelectric element is bonded to the root of the beam and functions as an actuator and a sensor simultaneously. A mirror circuit constructed with two charge driver circuits is used to pick up the sensing signal from the driving voltage signal. Then, a closed-loop control strategy based on the proportion integration differentiation (PID) algorithm can adjust the sensing signal precisely to suppress the vibration of the cantilever beam quickly. The first mode of vibration is suppressed, and the amplitude of the vibration is actively dampened by a factor exceeding 96.4%. Moreover, the frequency sweep experiments demonstrate that with the PID feedback control circuit connected to the piezoelectric cantilever beam, the Q value of the system is greatly reduced, and the loss factor is increased from 0.053 to 0.288. The improved mirror circuit with PID control has a good suppression effect in the frequency range near the first order mode of the cantilever beam.

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Gang Qian

Papers

Self-Sensing Vibration Suppression of Piezoelectric Cantilever Beam Based on Improved Mirror Circuit