Proof Mass Research Articles

Theoretical and experimental research on a Quasi-Zero-Stiffness-Enabled nonlinear piezoelectric energy harvester

Piezoelectric material provides a convenient and efficient avenue to convert ambient vibration energy into electrical energy to power wireless sensor network nodes of Internet of Things. However, the design of effective ultralow-frequency and low-amplitude harvesters using piezoelectric materials remains a challenge. To address this challenging problem, this paper devises a quasi-zero-stiffness-enabled (QZSE) piezoelectric energy harvester based on a geometrical nonlinear structure. The basic configuration and operation principles of the QZSE piezoelectric energy harvester ware elaborated firstly, then the nonlinear electromechanical coupling equation is derived, whose solution informs on both the dynamic and electrical responses of the harvester. The electromechanical-coupled equations are solved with the aid of the fourth-order Runge-Kutta algorithm. The energy harvesting performance is then investigated with respect to the parameter effects of excitation, damping and proof mass. For validating numerical results and demonstrating the advantages of the proposed design, a prototype is fabricated and experimentally tested. The results confirm the ability of the QZSE piezoelectric energy harvester in producing effective vibration-to-electricity energy conversion in ultralow frequency range. This study provides new impetus to energy harvesting from ultralow frequency ambient vibration using piezoelectric materials.

A laterally sensitive quartz vibrating beam accelerometer for inertial navigation application

To improve the sensitivity and stability of a quartz vibrating beam accelerometer (QVBA), a laterally sensitive structure was developed that utilizes the force-frequency characteristics of a quartz double-ended tuning fork (DETF) to realize quasi-digital measurement of acceleration. Two DETFs were purposely designed for the sidewalls of the proof mass, and the hinge of the spring-mass structure was along the proof-mass thickness, which improved the sensitivity. Laterally sensitive structures can also solve the fabrication problems of hinges, including accuracy, deformation, and residual stress. A femtosecond laser was used to release the anchor between the out-of-frame and the proof mass to protect the hinge. The isolation structure was designed to float both the DETFs and hinge to reduce the interference of external stress. Electrodes were deposited on the four surfaces of the vibrating beam in a three-segment configuration to excite the DETF into the antiphase in-plane vibration model. As a result, an accelerometer prototype is fabricated, and the performance characterization results exhibit the sensitivity and stability of 188.61 Hz/g and 7.81 ppm, respectively, and the bias instability (Allan deviation) of 1.26 μg, which proves the design rationality of laterally sensitive QVBA.

Reversible nonlinear energy harvester tuned by titling angle or clamping distance

This paper proposes a reversible nonlinear energy harvester to realize broadband vibration energy harvesting. Especially, the softening and hardening nonlinear responses of an M-shaped piezoelectric beam could occur by tuning the clamping distance or titling angle, which is unlike previous efforts to institute nonlinearity. The proposed M-shaped beam consists of a pre-bent steel beam, a piezoelectric patch, and a proof mass without magnetic components. According to the numerical and experimental results, the proposed harvester could achieve a broader operation bandwidth than its linear counterpart. Under the low forward sweep excitation level (3 m/s2), the proposed reversible nonlinear energy harvester can cover the wide low-frequency range of 13.4–27.6 Hz (or 18.1–28.8 Hz) by changing the clamping distance (or the tilting angle). Exploiting this tunable nonlinear phenomenon makes it more suitable to harvest energy from broadband vibration efficiently.

Design and performance evaluation of a pendulous piezoelectric rotational energy harvester through magnetic plucking of a fan-shaped hanging composite plate

Over the past decade, there has been significant interest in harvesting energy from rotational motion through piezoelectric transduction, with the aim of providing energy-autonomous structural health monitoring systems for rotating machinery. Unlike most existing separated-type magnetically plucked piezoelectric rotational energy harvesters (PREHs) where a separate stationary support is frequently required to place either exciting or excited magnets, we proposed a pendulous piezoelectric rotational energy harvester (P-PREH) which was characterized by the structural integration and simultaneous motion of the piezoelectric transducer and actuator to harvest energy from rotating machines without stationary support. Structure simulation, fabrication, and experimental testing were performed to verify the structural feasibility and investigate the effect of structure and exciting parameters. The results showed that the P-PREH can generate relatively stable output voltage within a wide range of rotary speeds because of the random swing of exciting disk. Besides, the load resistance-dependent power indicated that P-PREH with swing radius of proof mass of 160 mm and the exciting magnet quantity ratio of 0.82 could yield a maximum output power of 0.65 mW at 20 kΩ and 1120 r/min. Also, 50 blue LEDs, array of different color LEDs and a low-power light strip could be lighted by the P-PREH.

MEMS capacitive accelerometer: A review

Micro-electro-mechanical systems sensors are integrated systems used in many fields such as consumer electronics, the automobile industry, and biomedical, and their dimensions change between micrometers and millimeters. MEMS capacitive accelerometers are the most widely used sensor type among MEMS accelerometer sensors. As a result of the external force applied to the capacitive accelerometer sensor, the proof mass inside the sensor moves, and the capacitive change is measured as an electrical signal using reading circuits. In this review paper, general information about MEMS sensors is given, and a comprehensive review is made of MEMS capacitive accelerometers. In the study, the dynamic circuit of the MEMS capacitive accelerometer is given, and the calculation of the important values for the mechanical and electronic structure during the design of the capacitive MEMS accelerometer is explained. In addition, information about the readout circuits used to convert the capacitive change to voltage is given. Finally, the fabrication processes used to produce the final product are explained, and the studies on sample fabrication processes found in the literature are mentioned.

Two-axis multiple masses resonator with frequency and Q-factor matching

This paper reports a design and experimental results of a two-axis symmetric dynamically balanced resonator based on a triple mass system, whose frequency and Q-factor can be independently tuned. Two dynamically equivalent proof masses are connected by four coupling springs, and four coupling proof masses are implemented between them. The frequency and Q-factor of the anti-phase modes can be tuned independently of each other. The frequency is tuned by electrostatically softening the suspensions stiffness, and the Q-factor is adjusted by controlling the squeeze film damping through the mode coupling between the anti-phase and in-phase modes. The changes of frequency and mode coupling under different DC bias tunings are studied by FEA, which reveals the modification of the suspension stiffness only decreases the frequency and the modification of the inner stiffness of the coupling proof masses exerts a large effect on the mode shape, i.e. Q-factor, while a minor effect on the frequency. The as-fabricated frequency and Q-factor mismatches were evaluated as 5% and 7.7% in a fabricated device, respectively. A large adjustment of the Q-factor by 21% was observed by adding a 27 V DC voltage on the tuning electrodes inside the coupling proof masses, while the frequency was only decreased by as small as 810 ppm. A mode matching was achieved by electrostatic softening the suspensions of both main proof masses. Thanks to the decoupling between frequency and Q-factor, a frequency matching under 10 ppm and a Q-factor matching under 650 ppm were experimentally proved.

Analysis of the Frequency-Dependent Vibration Rectification Error in Area-Variation-Based Capacitive MEMS Accelerometers.

The presence of strong ambient vibrations could have a negative impact on applications such as high precision inertial navigation and tilt measurement due to the vibration rectification error (VRE) of the accelerometer. In this paper, we investigate the origins of the VRE using a self-developed MEMS accelerometer equipped with an area-variation-based capacitive displacement transducer. Our findings indicate that the second-order nonlinearity coefficient is dependent on the frequency but the VRE remains constant when the displacement amplitude of the excitation is maintained at a constant level. This frequency dependence of nonlinearity is a result of several factors coupling with each other during signal conversion from acceleration to electrical output signal. These factors include the amplification of the proof mass's amplitude as the excitation frequency approaches resonance, the nonlinearity in capacitance-displacement conversion at larger displacements caused by the fringing effect, and the offset of the mechanical suspension's equilibrium point from the null position of the differential capacitance electrodes. Through displacement transducer and damping optimization, the second-order nonlinearity coefficient is greatly reduced from mg/g2 to μg/g2.

Passively Tuning the Resonant Frequency of Kinetic Energy Harvesters Using Distributed Loaded Proof Mass

The inability to tune the frequency of MEMS vibration energy-harvesting devices is considered to be a major challenge which is limiting the use of these devices in real world applications. Previous attempts are either not compatible with microfabrication, have large footprints, or use complex tuning methods which consume power. This paper reports on a novel passive method of tuning the frequency by embedding solid microparticle masses into a stationary proof mass with an array of cavities. Altering the location, density, and volume of embedded solid filler will affect the resonant frequency, resulting in tuning capabilities. The experimental and computational validation of changing and tuning the frequency are demonstrated. The change in frequency is caused by varying the location of the particle filler in the proof mass to alter the center of gravity. The goal of this study was to experimentally and numerically validate the concept using macro-scale piezoelectric energy-harvesting devices, and to determine key parameters that affect the resolution and range of the frequency-tuning capabilities. The experimental results demonstrated that the range of the frequency tuning for the particular piezoelectric cantilever that was used was between 20.3 Hz and 49.1 Hz. Computational simulations gave similar results of 23.7 Hz to 49.4 Hz. However, the tuning range could be increased by altering the proof mass and cantilever design, which resulted in a tuning range from 144.6 Hz to 30.2 Hz. The resolution of tuning the frequency was <0.1 Hz.

Resonant Transducers Consisting of Graphene Ribbons with Attached Proof Masses for NEMS Sensors.

The unique mechanical and electrical properties of graphene make it an exciting material for nanoelectromechanical systems (NEMS). NEMS resonators with graphene springs facilitate studies of graphene's fundamental material characteristics and thus enable innovative device concepts for applications such as sensors. Here, we demonstrate resonant transducers with ribbon-springs made of double-layer graphene and proof masses made of silicon and study their nonlinear mechanics at resonance both in air and in vacuum by laser Doppler vibrometry. Surprisingly, we observe spring-stiffening and spring-softening at resonance, depending on the graphene spring designs. The measured quality factors of the resonators in a vacuum are between 150 and 350. These results pave the way for a class of ultraminiaturized nanomechanical sensors such as accelerometers by contributing to the understanding of the dynamics of transducers based on graphene ribbons with an attached proof mass.

Finite element modeling of piezoelectric cantilever-beam energy harvester

Piezoelectric energy harvesting from mechanical vibrations has attracted considerable attention during the last decade. The homogeneous harvesters were studied experimentally or numerically by various models such as single degree of freedom (SDOF) modeling, finite element (FE) modeling as well as using analytical solutions. In this work, FE models for simulating a piezoelectric beam bimorph power harvester consisting of a laminated piezoelectric beam, a proof mass, and an electrical load (series or parallel connections) configurations are developed. The effects of the material and size of the substrate, the proof mass have been studied on the resonance frequencies and the output parameters of the piezoelectric generator (PEG). Numerical results obtained using the proposed procedure for piezoelectric bimorph power harvesters are in good agreement with the experimental data available in the literature. The proposed method can be used for modeling accurately this class of energy harvesting devices.

First asteroseismic analysis of the globular cluster M80: multiple populations and stellar mass-loss

ABSTRACT Asteroseismology provides a new avenue for accurately measuring the masses of evolved globular cluster (GC) stars. We present the first detections of solar-like oscillations in 47 red giant branch (RGB) and early asymptotic giant branch (EAGB) stars in the metal-poor GC M80; only the second with measured seismic masses. We investigate two areas of stellar evolution and GC science: multiple populations and stellar mass-loss. We detect a distinct bimodality in the EAGB mass distribution. We suggest that this could be due to sub-population membership. If confirmed in future work with spectroscopy, it would be the first direct measurement of a mass difference between sub-populations. A mass difference was not detected between the sub-populations in our RGB sample. We instead measured an average RGB mass of $0.782\pm 0.009~\mathrm{M}_{\odot }$, which we interpret as the average of the sub-populations. Differing mass-loss rates on the RGB have been proposed as the second parameter that could explain the horizontal branch morphology variations between GCs. We calculated an integrated RGB mass-loss separately for each sub-population: $0.12\pm 0.02~\mathrm{M}_{\odot }$ (SP1) and $0.25\pm 0.02~\mathrm{M}_{\odot }$ (SP2). Thus, SP2 stars appear to have enhanced mass-loss on the RGB. Mass-loss is thought to scale with metallicity, which we confirm by comparing our results to a higher metallicity GC, M4. Finally, our study shows the robustness of the Δν-independent mass scaling relation in the low-metallicity (and low surface gravity) regime.

The first distributed-mass high-performance programmable optoelectromechanical steerable motion-wave sensors focused on sophisticated biomedical applications

This paper introduces the first high-performance distributed-mass acoustic sensor made of cascaded differential phase shift suspended slot waveguide sections in a Mach–Zehnder interferometer optical transducer circuit. The heavyweight seismic mass used in traditional optoelectromechanical sensors is replaced by an fg lightweight coupling arm yielding an extra compact fast responding structure enabling utilizing over 64\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$64$$\\end{document} cascaded sections and resulting in enhancing the performance by hundreds of times. The transducer operation relies on converting the acoustic vibration into phase modulation of the light for a splendid performance. The novel sensor architecture challenges achieving optical sensitivities higher than 33×103%/g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$33\ imes {10}^{3} \\%/\\mathrm{g}$$\\end{document} (33 times supersensitive), operating at ultrasonic acoustic speeds higher than 27 MHz, and recognizing resolutions in the 1 ng order. The programmable sensor is voltage-controlled supporting the operation in multimodes. Four operation modes are elucidated including the natural aspiration force, turbo electrostatic force open-loop voltage control, zero-force closed-loop voltage control, and dynamic turbo-force closed-loop voltage control. Wide dynamic ranges for controlling the optical sensitivity and maximum measurable acceleration up to 115.5 dB are reported. Steering capabilities of the acoustic beam in the azimuth plane are demonstrated utilizing two-spoke and three-spoke directional architectures supporting 116.64∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$116.64^\\circ$$\\end{document} and 360∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$360^\\circ$$\\end{document} of respective steering angles. Potential acoustic biosignal-based applications in the medical field are outlined.

Clapping triboelectric nanogenerators as self-powered, frequency-insensitive and gravity-independent vibration sensors

Self-powered vibration sensors have the potential to greatly improve vibration monitoring of remote and hard-to-access structures by providing cost-effective and energy-efficient solutions. One promising type of sensors based on the triboelectric generator mechanism has shown significant advantages over other self-powered sensors, including better energy conversion efficiency and high output voltage. However, the majority of the recently reported triboelectric powered sensors exhibit strong frequency dependence, being mostly effective under low frequency vibrations. To address these issues, herein we present a novel design of self-powered vibration sensors based on the clapping mode of a triboelectric nanogenerator (TENG). The sensor, consisting of two tribo-layers made of regular copy paper and PTFE that are clamped together by springs, is able to achieve a high sensitivity of 10.8 mV/g and a broad frequency range from 50 to 8000 Hz with a flat frequency response of ±5 dB, regardless of the inclination angle between the contacting surfaces and gravity. The sensor exhibits high linearity (0.9999) and stability over six days and 400,000 cycles. Furthermore, computational modelling has been conducted to understand the nonlinear clapping phenomenon and the influence of clamping force, proof mass and spring stiffness on the sensor's performance. The potential of the clapping TENG sensor is demonstrated through two different applications such as music recording and diagnosis of the loosing of bolts in a rotating machine. Its superior performances, along with low cost, compact design, and electromagnetic shielding, make it a promising candidate for battery-free high-frequency vibration sensors in practical vibration measurement applications.

Novel method for measuring non-stationary pitch and roll angles with a pendulous accelerometer in the presence of vibrations

We developed a novel universal method to solve an important mechanics problem arising during wind tunnel tests of aircraft models: the measurement of non-stationary pitch and roll angles of aircraft models and strain-gauge balances using a pendulous accelerometer. The method is based on a physical model in which the accelerometer pendulum is replaced by a proof mass and its hinge is replaced by a spring with damping. This model makes it possible to measure non-stationary pitch and roll angles in a wide range of vibration frequencies, including the accelerometer’s eigenfrequency. We propose a method for determining the accelerometer’s natural frequency in the absence of damping (resonance frequency) as well as the ratio of the damping coefficient to the pendulum’s mass. We also conducted experimental studies in which an acceleration similar in form to the Heaviside function was applied to the accelerometer; the results verify the proposed method.

The effect of magnetic proof masses on the energy harvesting bandwidth of piezoelectric coupled cantilever array

In order to explore the ability of magnetic force in improving energy harvesting bandwidth, a novel energy harvester of piezoelectric coupled cantilever array (PCCA) was proposed which introduces nonlinear magnetic force (damping) to differentiate the natural frequencies of PCCs and widen energy harvesting bandwidth of PCCA. Meanwhile, the design of PCCA can increase the number of voltage peaks of each PCC at the cost of decreasing the voltage peaks of its neighbouring PCCs at resonance. The effect of some significant factors, such as PCC interval, PCS length, PCC number, and PCC substrate thickness, on PCC voltage, PCC natural frequency, and PCCA bandwidth are deeply studied and analyzed by experiments and simulations. The results demonstrate that the bandwidth for the proposed PCCA can achieve 73 Hz by the standard of >15 V pp. voltage in the excitation of 1 g acceleration amplitude. Based on the experiment and simulation results, a series of theoretical models are derived to compute PCC voltage, PCC natural frequency, and bandwidth of PCCA with different design parameters, these theoretical models give a reliable instruction for the design of PCCAs to match environmental vibration with different frequency such as machine, wind, wave, and so on.

Integrated mechatronic design of an industrial piezoelectric vibration energy harvester

Increased consumption of non-renewable energy sources, such as batteries, have led to increased environmental pollution and critical energy crises. Harvesting energy from vibration sources, using piezoelectric cantilevers, may be one of the main solutions to extending the life of the battery of some autonomous devices and either reducing or eliminating the need to replace them in service. This would make sensors self-powered, for instance. To minimize the volume of the Energy Harvester, a configuration with a circular frame supporting a radial set of bimorph piezoelectric beams with a proof mass at the tip is proposed. An analytic model is first developed to investigate the behavior of the electromechanical coupling, preliminarily sizing the design parameters, and to estimate the maximum power converted. A numerical model is then developed, in the COMSOL® Multiphysics software, to analyze all of the system details. Some FEM analyses allow for verifying the accuracy of the analytic model and predicting the dynamic system behavior under different load conditions. A critical issue in properly predicting the performance of such device is the electric circuit which is coupled to extract the charge produced. Therefore, the design of this read-out circuit is herein addressed. The LTspice XVII® software is then used to model the charge readout circuit. The electronic components interconnected within the circuit are first determined, and their electrical dynamic behavior is studied when coupled with the mechanical system. The efficiency of charge production and energy storage is evaluated by integrating the whole electromechanical system, including the readout circuit with the numerical model. The performance looks compatible with the required values proposed for some practical industrial applications, being also described.

Development of Membranes for Use as the Seismic Mass in a Fiber Optic-Accelerometer

Development of Membranes for Use as the Seismic Mass in a Fiber Optic-Accelerometer

Design and Considerations: Microelectromechanical System (MEMS) Vibrating Ring Resonator Gyroscopes

Microelectromechanical system (MEMS) vibrating gyroscope design considerations are always intriguing due to their microscale mechanical, electrical, and material behavior. MEMS vibrating ring gyroscopes have become important inertial sensors in inertial measurement units (IMU) for navigation and sensing applications. The design of a MEMS vibrating ring gyroscope incorporates an oscillating ring structure as a proof mass, reflecting unique design challenges and possibilities. This paper presents a comprehensive design analysis of the MEMS vibrating ring gyroscope from the mechanical, electrical, and damping perspectives. The mechanical design of the MEMS vibrating ring gyroscope investigates the various frame designs of the vibrating ring structure, as well as the various beam structures, including rectangular and semicircular beam structures, which are analyzed using mathematical models and finite element analysis (FEA) simulations that provide an in-depth analysis of the stiffness and deflection of the vibrating structures. The electrical designs of the MEMS vibrating ring gyroscope are analyzed using various electrode configurations, electrostatic actuation, and capacitive detection mechanisms. The design analysis of various forms of damping, including viscous, structural, thermoelastic, and anchor damping, is discussed. The variety of design structures is investigated for MEMS vibrating ring gyroscopes’ mechanical, electrical, and damping performance.

Development of SQUID detection technology for a superconducting gravimeter.

In this paper, we present research on the development of SQUID (Superconducting QUantum Interference Device) detection technology for a superconducting gravimeter (SG), aiming to achieve precise real-time measurements of gravity. We provide an introduction to the composition and internal details of the SQUID-based superconducting gravimeter (SSG). The internal components of the SSG are designed based on theoretical calculations to optimize the system and enhance its sensitivity. With the current in the levitation coil set to persistent mode, a unique proof mass is levitated through electromagnetic force. We demonstrate the equilibrium position of the levitated proof mass by assessing the change in the coil inductance. Furthermore, we present preliminary experimental results of earth tidal measurements using the developed SQUID detection technology and compare these outcomes with measurements from an absolute gravimeter (FG5X) and with theoretical calculations. These comparisons confirm the potential of the proposed new gravity measurement technology.

Design and experimental verification of the working mode of an electrostatic suspension accelerometer

An electrostatic suspension accelerometer is an important instrument for measuring quasi-steady micro-acceleration. A reasonable working mode is the premise to ensure acquisition and stable control of the accelerometer in-orbit and then to carry out high-precision linear measurement. Based on the dynamic model analysis of the electrostatic suspension accelerometer, and taking the force balance of inertial proof mass as the fundamental requirement, the design of the acquisition working mode and measurement working mode based on displacement sensing output and feedback control output is proposed. The rationality and feasibility of the proposed working mode design are verified by the ground drop tower test of the Taiji-1 accelerometer prototype and in-flight test of the actual product.