Resonance Frequency Of Transducer Research Articles

A Hybrid Actuator Model for Efficient Guided Wave based Structural Health Monitoring Simulations

Abstract Simulation has been recognized as a promising option to reduce the time and costs associated with determining Probability of Detection (POD) curves to demonstrate the performance of Guided Wave based Structural Health Monitoring (GW-SHM) systems. Time domain transient spectral finite element schemes have been used for large GW-SHM simulation campaigns, but the most common piezoelectric transducer model used for actuation, the pin force model, has limitations in terms of its range of validity. This is because the excitation frequency for the pin force model has only been validated far below the first electromechanical resonance frequency of the piezoelectric transducer mainly due to not considering the normal stress and dynamics of the transducer. As a result, the value of simulation tools for performance demonstrations may be limited. To address this limitation, this paper introduces a Hybrid Actuator Model that integrates frequency-dependent complex interfacial stresses in both the shear and normal directions, computed using finite elements. These surface stresses are compatible with time domain transient spectral finite element schemes, enabling their seamless integration without compromising the required performance for conducting intensive simulation campaigns. The proposed hybrid actuator model undergoes validation through a combination of simulation and experimental studies. Additionally, a comprehensive parametric study is conducted to assess the model's validity across a wide range of excitation frequencies. The results demonstrate the accurate representation of the transduction signal above the piezoelectric transducer's first free electromechanical resonance frequency.

Investigation of the equivalent circuit and performance of an ultrasonic transducer under a force load

In ultrasonic processing technology applications, the force load can cause a drift in the resonance frequency of the ultrasonic transducer and significantly reduce its mechanical quality factor. The traditional equivalent circuit of an ultrasonic transducer can only be used to calculate performance parameters without a force load but not with a force load. Based on Mason’s equivalent circuit, a new equivalent circuit for ultrasonic transducers under a force load is derived while considering the effects of the force load on the material parameters and various types of losses in piezoelectric ceramics. Furthermore, performance parameters are analyzed, such as the resonance frequency, effective electromechanical coupling coefficient, and mechanical quality factor. The ultrasonic transducer sample is produced and the experimental platform is constructed for applying force loads on the ultrasonic transducer. The theoretical model is verified by static loading on the ultrasonic transducer. The proposed equivalent circuit provides theoretical guidance for tracking the exact resonance frequency and performance parameters of force-loading ultrasonic transducers.

Metamaterial‐Augmented Head‐Mounted Audio Module

AbstractRecent developments in metamaterial research have shown promising progress in overcoming the fundamental physical limitations of acoustics. While the majority of this research is curiosity‐driven and focused on fundamental physics, there has been a scarcity of acoustic metamaterials research that can have a direct and immediate impact on real‐world applications. In this study, an acoustic metamaterial inside a head‐mounted audio module is incorporate to achieve a 3–7 dB broadband sound pressure level (SPL) improvement in the bass range (50–700 Hz), which is the most challenging frequency range for radiation enhancement. The adoption of the acoustic metamaterial not only enhances voltage sensitivity near the intrinsic metamaterial resonance frequency, but also extends the broadband enhancement to a lower transducer resonance frequency by carefully engineering the metamaterial‐transducer resonant coupling. The improvement of the audio module is demonstrated through fully coupled electrical‐mechanical‐acoustical numerical simulations using finite element analysis, which are validated against comprehensive measurements including electrical impedance analysis, speaker diaphragm displacement analysis, voltage sensitivity and power sensitivity analysis, and spectrogram. This study not only offers a promising path to improve the audio module quality without increasing the size, but also represents an important milestone toward using acoustic metamaterial research to solve audio industry challenges.

Determination of the Temperature-Dependent Resonance Behavior of Ultrasonic Transducers Using the Finite-Element Method

PurposeLangevin transducers are ultrasonic transducers that convert electrical into mechanical energy through the piezoelectric effect. This class of transducers achieves the highest efficiency in their mechanical resonance. Studies have shown that the resonant frequency changes with temperature. The aim of this contribution is to reproduce this temperature-dependence resonance frequency as accurately as possible with FEM simulations.MethodsTherefore, the temperature-dependent resonance behavior of Langevin transducers is examined experimentally. A FEM model is created on the basis of temperature-dependent measured material coefficients. Using parameter correlations and optimization algorithms, the FEM model is fitted and validated by experimental results. Six variants of Langevin transducers are examined in the range from 30 °C to 80 °C with resonance frequencies between 34 and 38 kHz. They differ in three geometries and two materials.ResultsThe experimental results show that the resonance frequencies decrease with increasing temperatures by 5.0–19.4 Hz/°C, depending on the material and geometry. As decisive parameters for the model fitting of the FEM results, three function-dependent stiffness coefficients of the piezoelectric material PZT8 and the Young’s moduli of the metallic materials are determined by parameter correlation.ConclusionThrough the targeted fitting of these function-dependent parameters, the calculation of the resonance frequencies of Langevin transducers can be qualitatively and quantitatively improved, independent of shape and material.

Towards a MEMS Force Sensor via the Electromagnetic Principle.

Force measurement is a science discipline that experiences significant progress with the introduction of new materials and evaluation methods. Many different sensor types, working on different principles, have been developed and reviewed and have found use in medicine as well as many other industries. New trends and demands require a size reduction and simple applicability, with the use of, for example, micro electromechanical systems (MEMS). For purposes of this study, the initial MEMS body is supplemented by its scaled version. Force measurement in this study works on the force to time-delay conversion principle. A compact compliant mechanical body (CCMB) with an embedded parallel resonant circuit (PRC) acting as a transducer realizes the conversion. Depending on the resonant frequency of the transducer (CCMB or MEMS), we have measured the applied force based on the reverse influence of the transducer on the surrounding EM field. The analysis shows that the transducer's resonant frequency has a detectable reverse influence on the voltage-controlled oscillator (VCO) DC supply current. The force influencing the transducer is determined by the DC supply current ripple position during the VCO frequency sweep. The study presents the method proposal and mathematical analysis, as well as its function verification by simulation and prototype measurements. The proposed principle was validated on a CCMB prototype capable of measuring forces up to ∼2.5 N at a sampling frequency of ∼23 kHz, while the measured time-delay ranges from 14.5 µs to 27.4 µs.

Double-armed cone-shaped flexoelectric transducer

Compared with a single energy harvester, this tuning fork double-armed cone-shaped flexure transducer can fundamentally solve the problems of high resonance frequency, low output efficiency, and narrow bandwidth of the flexure transducer. Since the transducer limits the clamping losses of the cantilever beam, it provides sufficient stiffness-mass balance to lower the resonance frequency of the system and extend the bandwidth. The tapered structure provides sufficient strain gradient for the flexoelectric effect, improving the output efficiency of the whole system. The vibration frequency of the tuning fork structure and the derivation of the bandwidth formula are analyzed theoretically, and then the electrode width and thickness of the cone structure are studied through simulation to analyze the transducer output response, resonant frequency, bandwidth, and output impedance.

Research on correlation model between transducer temperature and acoustic performance parameters of ultrasonic machining system

In the process of ultrasonic vibration cutting (UVC), the acoustic performance parameters of ultrasonic machining system change because of systems heating up and cutting loads. The changes of acoustic performance parameters will affect resonant frequency, impedance, and power match of the ultrasonic machining system, and stability of the amplitude of UVC system. It is hard to monitor the acoustic performance parameters online. Based on the analysis of the correlation mechanism between transducer temperature and acoustic performance parameters, the correlation models between transducer temperature and resonance frequency, static capacitance, and dynamic resistance of ultrasonic vibration machining system are established by curve regression analysis modeling method. The acoustic performance parameters of an ultrasonic vibration machining system are determined by transducer temperature using the correlation models. The effectiveness of the model is verified by experiments. It gives the information for the stability evaluation of the ultrasonic vibration machining process, the dynamic impedance matching of the ultrasonic machining system, and the power matching adjustment of the ultrasonic power supply.

A lumped parameter model of the longitudinal NiMnGa transducer based on piezomagnetic equations.

The NiMnGa alloy is a typical magnetic shape memory alloy with up to 6% immense strain, high energy density, and low effective elastic modulus. These comprehensive characteristics make it possible to realize a low-frequency underwater acoustic transducer. To describe the field-induced dynamic strain, an equivalent circuit model (ECM) of a longitudinal NiMnGa transducer is presented as a lumped parameter model, which couples magnetics, mechanics, and acoustics. In this paper, we focus on the piezomagnetic equations as the constitutive relationship of the NiMnGa element with a dynamic magnetic field. Furthermore, combined with the dynamic kinetic equation, the equivalent circuit is derived, and it has the advantage of containing acoustical terminals. The proposed model can predict the resonance frequency, effective stiffness, and input impedance of the NiMnGa transducer. Finally, a finite element model (FEM) is developed to verify the lumped parameter model. The results indicate that the spring's stiffness increases the resonance frequency, while the mass load is on the contrary, and they both agree well with the results of ECM. In addition, the FEM and ECM can also predict the dynamic responses, which provide a guideline for the design of longitudinal NiMnGa transducers.

Comparison of the performance characteristics of the tonpilz transducers fabricated from 0.60PMN-0.40PT & PZT piezoceramics

In this study, tonpilz transducers based on 0.60Pb(Mg1/3Nb2/3)O3-0.40PbTiO3 (60PMN-PT) and commercially available lead zirconate titanate (PZT) compositions (PZT 4, PZT 5H, PZT 8 and PZT 5A) were designed, fabricated, characterized and compared for their underwater performance. Each stack is composed of two rings of PZT or PMN-PT ceramics. Transducers were designed and analyzed using the commercial ATILA finite elements analysis (FEA) code. Commercially available powders were used for PZT, whereas 60PMN-PT powders with pure perovskite phase were synthesized using solid-state reaction route. Ceramic rings have been produced using dry pressing. Dielectric, piezoelectric and electromechanical properties of the rings were calculated using the resonance method. Vibration modes of the rings and transducers constructed from various types of piezoceramics were analyzed using FEA. The main resonance frequency of the tonpilz transducer belonging to the longitudinal piston mode was measured in the mid-frequency range between 30 and 35 kHz. Underwater acoustic measurements were conducted on polymer-coated transducers, and their performances were compared for possible underwater acoustic applications. Transducers fabricated from 60PMN-PT were found to have comparable underwater performance with that of PZT 4, where the Transmitting Voltage Response (TVR) reached 135 − 136 dB re 1 µPa/V @1 m range with a −3dB bandwidth of 4 kHz. These results indicated the viability of using 60PMN-PT ceramics in active device applications in an array form.

A New Method to Detect and Track the Resonance Frequency of Piezoelectric Transducers in Ultrasonic Power Supplies

In this paper, a new method is developed to detect and track the resonance frequency of ultrasonic transducers. In order to have an acceptable performance of transducers, power supplies should be able to detect and track the resonance frequency. Different methods have been used for this purpose. In this research, the voltage of the transducer and the phase difference between the voltage and current are used to find the resonant frequency. The maximum voltage of a transducer is founded in a predefined frequency interval. Afterward, the minimum phase difference between the voltage and current is obtained in a smaller interval around it. The simultaneous use of the voltage and phase shift increases the accuracy and speed of the algorithm. Since the transducer's voltage variations are relatively large near the resonant frequency, it is a versatile parameter compared to the current used in other methods to indicate the resonance frequency. The algorithm is implemented within a microcontroller. An FPGA is used to generate accurate frequency using the Direct Digital Synthesis (DDS) method. The algorithm can detect the resonant frequency under free conditions. Applying force to transducers or emerging the transducer's head to the water changes the resonant frequency. The experimental tests showed that the algorithm could find and track the resonant frequency automatically under loading conditions.

Effect of Concave Stave on Class I Barrel-Stave Flextensional Transducer

To meet the requirements of low frequency, high power, small size and light weight, a type of Class I barrel-stave flextensional transducer employing improved concave stave is presented. As the key component of flextensional transducer, concave stave plays an important role in vibrating efficiently to radiate acoustic energy. The structure of concave stave has a great effect on its behavior. In this paper, the main parameters of concave stave are discussed, especially the effect of radius on flextensional transducer. Both concave stave and transducer are analyzed through finite element method, including mechanical transformation behavior of concave stave and performances of flextensional transducer. On the basis of finite element design, five prototypes employing concave staves with different radii are manufactured and measured. The simulations and tests reveal that concave stave can affect performances of flextensional transducer. A larger radius of concave stave will result in a greater amplification of vibration and a lower resonance frequency of transducer. This can be a feasible way to optimize the resonance frequency or source level of flextensional transducer through adjusting the radius of concave stave in a small range. According to the electrical and acoustical tests, our Class I barrel-stave flextensional transducer is capable of being used as underwater low-frequency small-size projector.

Analytical model and spectral characteristics of acoustic emission signal produced by localized fault of rolling element bearing

The accurate description of acoustic emission signals produced by the localized fault of a rolling element bearing plays an important role in its feature extraction and analysis. This paper analyzes the excitation mechanisms and develops the analytical model of acoustic emission signals produced when the rolling element bearing passes across the localized fault on the inner or outer race. Based on the analytical model, the spectral characteristics are discussed substantially. Simulations and experiments are carried out to validate the efficacy of the model developed in the paper. The experimental results show that the response signal thus produced has two parts. The first one is produced by the entry of the rolling element bearing, while the other is produced by the departure of the rolling element bearing. The energy of both parts is concentrated around the resonance frequency of the acoustic emission transducer. Generally, the interval of adjacent acoustic emission events is not equivalent to each other and the corresponding spectrum is continuous in the high frequency band.

Particle separation in microfluidics using different modal ultrasonic standing waves

Microfluidic technology has great advantages in the precise manipulation of micro and nano particles, and the separation of micro and nano particles based on ultrasonic standing waves has attracted much attention for its high efficiency and simplicity of structure. This paper proposes a device that uses three modes of ultrasonic standing waves to continuously separate particles with positive acoustic contrast factor in microfluidics. Three modes of acoustic standing waves are used simultaneously in different parts of the microchannel. According to the different acoustic radiation force received by the particles, the particles are finally separated to the pressure node lines on both sides and the center of the microchannel. In this separation method, initial hydrodynamic focusing and satisfying various equilibrium constraints during the separation process are the key. Through numerical simulation, the resonance frequency of the interdigital transducer, the distribution of sound pressure in the liquid, and the relationship between the interdigital electrode voltage and the output sound pressure are obtained. Finally, the entire separation process in the microchannel was simulated, and the separation of the two particles was successfully achieved. This work has laid a certain theoretical foundation for the rapid diagnosis of diseases in practical applications.

Experimental study on the choice of transducer resonance frequency in downhole flow measurement

In the process of downhole layered oil recovery, it is necessary to measure the liquid production of each layer in real time, so as to control the oil production plan of each layer in real time according to the oil production plan. Need to use ultrasonic time difference flowmeter to measure the flow in the process of injection and production. Due to the complex and changeable downhole environment, impurities such as sand and bubbles often appear in the process of downhole flow measurement. How to choose a suitable ultrasonic transducer frequency is of great significance to the flow measurement results. At present, common transducer resonance frequencies on the market mainly include 1MHz, 500KHz, 180KHz, and 40KHz. In this paper, the attenuation characteristics of the resonant signal of the transducer in the medium containing impurities are studied through simulation and experiment. The experimental data shows that in the stratified oil recovery system, the receiving effect of the system is best when the transducer frequency is 1MHz.

Evolution of some newer flextensional transducer designs

Flextensional transducers, such as the classic oval Class IV, have provided a means for magnified high output at low frequencies from a small size, when compared with Tonpilz piston transducers. We present here a transition to other newer flextensional types and shapes, such as the cylindrical Trioid and LCAT transducers and the piston cantilever mode transducer, CMX. We will show that these transitions came about after a flextensional X-spring design was realized. Although the X-spring was originally conceived to increase the output and also lower the resonance frequency of Tonpilz piston transducers, it also turned out to provide a significant means for the development of newer flextensional transducer designs. Examples of these newer designs and their operation, as well as an initially unexpected improved lower frequency performance from an array of CMX transducers, will be presented. [Work supported in part by Office of Naval Research.]

Analytical and Numerical Study of Pre-Stress Effect in Piezoelectric Sandwich Type Ultrasonic Transducer

In this paper, the effect of pre-stress condition on the resonance frequency of the transducer is studied by using numerical and analytical methods. To compare the obtained results, two sandwich-type transducers with nominal frequency of 25 kHz and 30 kHz are considered. Experimental determination of pre-stress value in transducer is described and measured. Then resonance frequency of transducers in the presence of pre-stress is determined by impedance analyser. Numerical analysis is conducted by modelling three-dimensional transducer in details at ABAQUS software. The resonance frequency is determined with and without pre-stress. The FE results show that by applying pre-stress on the transducers, the resonance frequency of transducers decreased. Furthermore, the FE results are very close to experimental results. Furthermore, a systematic analytical solution is presented based on one-dimensional wave propagation. The resultant displacement for each sub-section of the transducer is calculated and then all of them are assembled and solved by considering the continuity conditions of displacement and force components. It is found that pre-load condition that is produced by central bolt reduces resonance frequency of the transducer. The obtained analytical results provide fast and reliable model for predicting resonance frequency of transducer.

The High Frequency Flexural Ultrasonic Transducer for Transmitting and Receiving Ultrasound in Air

Flexural ultrasonic transducers are robust and low cost sensors that are typically used in industry for distance ranging, proximity sensing and flow measurement. The operating frequencies of currently available commercial flexural ultrasonic transducers are usually below 50 kHz. Higher operating frequencies would be particularly beneficial for measurement accuracy and detection sensitivity. In this paper, design principles of High Frequency Flexural Ultrasonic Transducers (HiFFUTs), guided by the classical plate theory and finite element analysis, are reported. The results show that the diameter of the piezoelectric disc element attached to the flexing plate of the HiFFUT has a significant influence on the transducer's resonant frequency, and that an optimal diameter for a HiFFUT transmitter alone is different from that for a pitch-catch ultrasonic system consisting of both a HiFFUT transmitter and a receiver. By adopting an optimal piezoelectric diameter, the HiFFUT pitch-catch system can produce an ultrasonic signal amplitude greater than that of a non-optimised system by an order of magnitude. The performance of a prototype HiFFUT is characterised through electrical impedance analysis, laser Doppler vibrometry, and pressure-field microphone measurement, before the performance of two new HiFFUTs in a pitch-catch configuration is compared with that of commercial transducers. The prototype HiFFUT can operate efficiently at a frequency of 102.1 kHz as either a transmitter or a receiver, with comparable output amplitude, wider bandwidth, and higher directivity than commercially available transducers of similar construction.

A High-Tolerance Matching Method Against Load Fluctuation for Ultrasonic Transducers

Fluctuation of acoustic load significantly weakens the performance of ultrasonic system. To address this problem in a simple way, we consider the main input and output variables related to the ultrasonic transducer's performance and propose a detailed mathematical model based on the simplest LC matching network containing only one capacitor and one inductor. In this model, a new resonance frequency ${\boldsymbol{f}_{\bf 0}}$ brought by matching components was found and defined. The optimum analysis method is used to solve the model, and a high-tolerance matching method against load fluctuation is obtained. Analysis indicates that when activated at the mechanical resonance frequency, the impedance and apparent power of the piezoelectric transducer (PT) matched by the proposed method are constant no matter how the load changes, and thereby can significantly increase the stability and robustness of ultrasonic systems. For its simple structure and high performance, the proposed matching method can be widely applied in most ultrasonic systems. The tolerance of the proposed method against other environmental factors and high-order LC matching networks were also discussed. In addition, the feasibility and advantage of the proposed matching method are also verified by experiments.

Optimal design of large-sized sandwich transducer based on two-dimensional phononic crystal

Sandwich transducers are extremely versatile, but when the lateral dimension is too large, the displacement of the radiating surface is uneven due to the coupling vibration. Due to the unique vibrational band gap characteristics of phononic crystal, vibrations in the bandgap range can be prohibited from propagating for infinite periodic structure or suppressed for finite periodic structure, which makes it widely used in the field of vibration suppression. In this paper, a two-dimensional phononic crystal structure is formed by processing periodically aligned grooves in the front cover of a large-sized sandwich transducer. Since the periodic grooves are formed in the radial direction, the radial waves cannot propagate, and thus the lateral vibration is suppressed. Subsequently, the finite element method is used to simulate the vibration transmission characteristic, resonance frequency and emission voltage response of a large-sized sandwich transducer based on two-dimensional phononic crystal. The effects of slot height and slot width on its bandgap, resonance and anti-resonant frequency, bandwidth, and displacement profile of the radiating surface are discussed. The results show that the phonon crystal structure can be optimized by using a large-sized sandwich transducer. The large-sized sandwich transducer based on two-dimensional phononic crystal has a lateral band gap. When the operating frequency of the large-sized sandwich transducer is within the band gap range, the two-dimensional phononic crystal structure can effectively suppress the lateral vibration, and the uniformity of the displacement distribution of the radiating surface of the transducer is improved. In addition, when the slot width is constant, the bandwidth of the large-sized sandwich transducer based on the two-dimensional phononic crystal increases as the slot height increases. Similarly, when the slot height is constant, the bandwidth of the large-sized sandwich transducer based on the two-dimensional phononic crystal increases as the slot width increases. The two-dimensional phononic crystal structure is processed in the front cover of the large-sized sandwich transducer, and the working frequency band of the large-sized sandwich transducer is effectively broadened.

Characterization of focused-ultrasound-induced acoustic streaming

This study aims at characterizing acoustic streaming produced by High Intensity Focused Ultrasound (HIFU) propagating in a liquid medium. Particle Image Velocimetry (PIV) technique was used to determine velocity fields in an infinite medium of water subjected to a focused ultrasonic field. The tests were carried out at a transducer resonance frequency of 550 kHz for different applied acoustic pressure at the focus (ranging from 2.6 to 18.4 bar). The experimental results allowed characterizing the mean streaming flow and its evolution with the wave amplitude: In particular, it is shown that a region where viscous effects are negligible, which leads to a linear behavior of the axial velocity with respect to the excitation pressure amplitude, does exist but is limited to the region upstream of the focal area of the transducer. A scaling analysis provides an estimate of the maximum velocity, and shows that it obeys a 4/3 power law with respect to the excitation pressure amplitude, as long as the position of this maximum velocity corresponds to the focal point, which is not the case for highest pressure amplitude, for which it is shifted downstream of the focus. In addition, the streaming flow is compared to a classical free jet flow. Similarities and differences existing between both flows are reviewed and a self-similar zone for the velocity transverse profile is identified in the expansion zone of the flow.