Proof Mass Research Articles

Structural Design and Optimization of a Resonant Micro-Accelerometer Based on Electrostatic Stiffness by an Improved Differential Evolution Algorithm.

This study designed an in-plane resonant micro-accelerometer based on electrostatic stiffness. The accelerometer adopts a one-piece proof mass structure; two double-folded beam resonators are symmetrically distributed inside the proof mass, and only one displacement is introduced under the action of acceleration, which reduces the influence of processing errors on the performance of the accelerometer. The two resonators form a differential structure that can diminish the impact of common-mode errors. This accelerometer realizes the separation of the introduction of electrostatic stiffness and the detection of resonant frequency, which is conducive to the decoupling of accelerometer signals. An improved differential evolution algorithm was developed to optimize the scale factor of the accelerometer. Through the final elimination principle, excellent individuals are preserved, and the most suitable parameters are allocated to the surviving individuals to stimulate the offspring to find the globally optimal ability. The algorithm not only maintains the global optimality but also reduces the computational complexity of the algorithm and deterministically realizes the optimization of the accelerometer scale factor. The electrostatic stiffness resonant micro-accelerometer was fabricated by deep dry silicon-on-glass (DDSOG) technology. The unloaded resonant frequency of the accelerometer resonant beam was between 24 and 26 kHz, and the scale factor of the packaged accelerometer was between 54 and 59 Hz/g. The average error between the optimization result and the actual scale factor was 7.03%. The experimental results verified the rationality of the structural design.

Analysis of Energy Harvesting Enhancement in Piezoelectric Unimorph Cantilevers.

Environmental energy harvesting is a major operation in research and industries. Currently, researchers have started analyzing small-scale energy scavengers for the supply of energy in low-power electrical appliances. One area of interest is the use of piezoelectric materials, especially in the presence of mechanical vibrations. This study analyzed a unimorph cantilever beam in different modes by evaluating the effects of various parameters, such as geometry, piezoelectric material, lengths of layers, and the proof mass to the energy harvesting process. The finite element method was employed for analysis. The proposed model was designed and simulated in COMSOL Multiphysics, and the output parameters, i.e., natural frequencies and the output voltage, were then evaluated. The results suggested a considerable effect of geometrical and physical parameters on the energy harvesters and could lead to designing devices with a higher functional efficiency.

Rotational multi-beam energy harvester with up-conversion mechanism in an extremely low frequency scenario

We propose a novel frequency-up converting device in an extremely low frequency rotating scenario based on a multi-beam piezoelectric energy harvester and multiple impacts. The rotating multi-beam structure consists of a piezoelectric sheet added to a top beam, a large seismic mass added to a bottom beam and an elastic stop which can be eventually replaced by a buzzer. At half of the rotating cycle, the bottom beam impacts the top beam by means of a spring generating energy by a frequency up-conversion mechanism. At the other half of the cycle, the up and bottom beam separate from each other and the bottom beam impacts an elastic stop or a buzzer which are used to simultaneously recover the kinetic energy of the collision, generate energy (buzzer) and prevent possible damage to the structure. An analytical model that governs the electromechanical equations and the impact dynamics is proposed to provide a means to predict the generated output energy. The model is based on the Euler-Bernoulli structural theory for the beams and a piezoelectric nonlinear constitutive model. Two different energy generation possibilities are studied, depending on the selection of the elastic stop or the buzzer. When the elastic spring acts as stop, the collision between the bottom beam and the stop is more elastic. Replacing the spring stop with a piezo buzzer adds to the system an additional mechanism of energy conversion. By making several experimental tests, the analytical model is validated by computing the cumulated energy. The results demonstrate that the buzzer element significantly improves the harvested power when it replaces the elastic stop. To estimate the usable power of the device, rectifier circuits coupled to the piezo elements are built and test. The results show that in the case of the buzzer used as a stop, a rectified power that overcomes 6.4 times in average other previous designs is harvested in the range of 0.8–2.2 Hz over an electrical load of 10 kΩ. The amount of collected power is suitable for autonomous sensing of wind turbines of 30 kW with rotational speeds of between 50 and 150 rpm.

Stabilization Control of a MEMS Accelerometer With Tuned Quasi-Zero Stiffness

In this paper, a novel MEMS accelerometer with tuned quasi-zero stiffness stabilized and operated in a closed-loop is proposed. By using the electrostatic softening effect of the double-sided comb-finger capacitors and the triangular capacitors, the effective stiffness of the accelerometer can be adjusted to quasi-zero. The variation of the electrostatic stiffness arising from the thermal drift of the proposed quasi-zero stiffness accelerometer can be greatly reduced when utilizing the double-sided comb-finger capacitors. For a high-sensitivity and high-linearity acceleration measurement, a traditional proportional-integral-derivative (PID) controller and a proportional-integral sliding mode (PISM) controller are designed for the stabilization near the border of pull-in. The parameters of the controller are tuned to ensure that the proof mass is stably positioned at the desired position. Both the simulation and experiment validate the feasibility of two controllers, showing distinct transient characteristics and long-term stability performance. Compared to the open-loop accelerometer with untuned stiffness, the sensitivity of the closed-loop accelerometer is increased over 40 times while the long-term stability of the closed-loop accelerometer with quasi-zero stiffness is remarkably improved for both controllers. The PID-controlled accelerometer with quasi-zero stiffness has an Allan bias instability as low as 22.51 ng and narrow bandwidth of 0.36 Hz. The PISM controlled accelerometer with quasi-zero stiffness has a linearly varied Allan bias instability from 37 ng to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.02 ~\mu \text{g}$ </tex-math></inline-formula> depending on the switching gain which determines the acceleration input range. However, the bandwidth of the PISM control system exhibits a nonlinear and wide-range variation with respect to the switching gain.

Vibration Energy Harvester Based on Torsionally Oscillating Magnet.

Most of the miniaturized electromagnetic vibrational energy harvesters (EVEHs) are based on oscillating proof mass suspended by several springs or a cantilever structure. Such structural feature limits the miniaturization of the device’s footprint. This paper presents an EVEH device based on a torsional vibrating magnet over a stack of flexible planar coils. The torsional movement of the magnet is enabled by microfabricated silicon torsional springs, which effectively reduce the footprint of the device. With a size of 1 cm × 1 cm × 1.08 cm, the proposed EVEH is capable of generating an open-circuit peak-to-peak voltage of 169 mV and a power of 6.9 μW, under a sinusoidal excitation of ±0.5 g (g = 9.8 m/s2) and frequency of 96 Hz. At elevated acceleration levels, the maximum peak-to-peak output voltage is 222 mV under the acceleration of 7 g (±3.5 g).

Multiple spring-mass oscillator for wide bandwidth piezoelectric energy harvester

This work proposed a design of unique wideband piezoelectric energy harvester. The solution toward broadband response was achieved by using multiple spring-mass oscillators integrated with piezoelectric energy harvester array. The harvester was demonstrated to harvest continuous power from vibration source under various frequencies in the range of 0-250 Hz. It is shown that the stable output power of the harvester over a wide range of source frequency was achieved. The maximum output voltage and power of each beam were 4, 3.6, 9.8, 10 V and 0.01, 0.07, 0.45, 0.52 mW for 15, 30, 45 gm of the proof masses and the superimposed case, respectively. The resonant frequencies of the harvester were in the low ambient vibration frequency range. Expanded in resonance frequency was achieved in this new design harvester.

Analysis and compensation for nonlinearity of sandwich MEMS capacitive accelerometer induced by fabrication process error

The effect of fabrication process error on the nonlinearity of sandwich MEMS capacitive accelerometer is analyzed in the paper. Firstly, after the packaging of the accelerometer, the displacement offset and torsion angle of the sensitive proof mass are obtained by CV testing. The gravitational field rolling four-position testing method is used to calibrate the bias, the scale factor, and the second-order nonlinearity coefficient of the accelerometer under different compensation capacitance. Testing results show that the second-order nonlinearity coefficient has a linear relationship with the compensation capacitance. A physical model of the accelerometer is built to analyze the effect of fabrication process error on the nonlinearity of the accelerometer, justifying the experimental linear relationship. Using the relationship, the capacitance compensation method is optimized, thus improving the efficiency of compensation. In the optimal case, the second-order nonlinearity coefficient of the accelerometer can be reduced to the order of 10−4 only by three capacitance compensations.

Modelling vibrations of axial piezoelectric generator with active base

Modelling of an axial-type piezoelectric generator (PEG) is considered. PEG is an integral part of the system for converting mechanical vibration energy from the environment into electrical energy. The energy generator has an axial type of the configuration of elements, aimed on using bending and compressive loads simultaneously on piezoelectric elements. The base of the generator is made as an active pinching. A feature of PEG is that the generator has two types of piezoelectric elements: (1) elements located on the substrate in the form of a bimorph and (2) piezoelectric elements of a cylindrical shape, fixing the generator base, located on the same axis. PEG has a symmetrical structure about the center of proof mass. The results of modal and harmonic analysis of vibrations are given for vibration excitation of the PEG base in a certain frequency range. The analysis of the output characteristics is given.

The collapse margin ratio of steel frames considering the vertical component of earthquake ground motions

The FEMA P695 methodology does not consider the application of the vertical component of ground motions in nonlinear response history dynamic analyses for obtaining collapse margin ratios. The vertical component of earthquake affects the demand on the steel moment frame and flexural capacity of the columns in interaction with the fluctuating axial load. This paper investigates the effect of the vertical component of far- and near-field ground motions on the seismic collapse capacity of low-, mid-, and high-rise buildings. Various span lengths, story heights, and seismic mass ratios have been taken into account to cover the significant parameters in amplifying vertical earthquake damages. More than 50,000 nonlinear response history dynamic analyses are performed to obtain seismic collapse margin ratios considering (1) the horizontal components of ground motion, (2) the horizontal plus vertical components of the earthquake, (3) the horizontal components of ground motion along with dead load factors suggested by ASCE7–16 to represent the vertical earthquake loading. Results are compared numerically, and the robustness of the procedure suggested by ASCE7–16 is assessed. It is shown that the adverse effect of the vertical component of the earthquake on the collapse capacity of the considered archetype buildings increases with the increase in the fundamental vertical period of buildings. Finally, adjusting equations using dimensionless parameters are developed for estimating the seismic collapse margin ratio of structures considering the vertical component of the ground motion. The proposed equations adjust the corresponding collapse margin ratio obtained using the horizontal components of ground motion.

Design and development of frequency tuneable vibration based piezoelectric energy harvester

This paper presents the design and development of manual frequency tuneable energy harvester. The energy harvester consists of beam, piezoelectric materials, proof mass, charging circuit, storage device and enclosure box. The design of beam and proof mass was made using the output of previous work and other parts were designed in this work. The energy harvester was developed based on the design and placed into the enclosure box. The fabricated model was tested to know the performance of energy harvester by analysing the output voltage, current, power and charging time of the battery. The distance of proof mass was varied from the fixed end of the cantilever beam to tune the frequency of energy harvester. From the experiment, it was found that the proof mass of energy harvester at 115 mm produced 88.77% more power compared to the proof mass placed at 85 mm from the fixed end. The operating range of energy harvester is about 5 Hz to 30 Hz. The proof mass placed at a distance of 155 mm from the fixed end charge the 60 mAh battery at 65.14% faster compared to the proof mass placed at 85 mm from the fixed end.

Design, modeling, and testing of a bidirectional multi-threshold MEMS inertial switch

We present a MEMS inertial switch with multiple, non-latching acceleration thresholds in two directions, that consumes no power in its inactive state. The design implements a suspended proof mass, with stationary electrodes placed at different positions in its sensitive direction so that different shock-induced displacements of the proof mass will result in contact/actuation at the stationary electrodes corresponding to the applied acceleration levels. This allows for automatic acceleration-based action, as a switch, or categorization for acceleration as a binary sensor. The designs were modeled using a finite-element simulation. The device was fabricated through SOIMUMPS and then tested using a drop-table shock system. The experimental results were close to the performed simulations with acceleration thresholds of 69 g and 121 g.

Design and modeling of a novel multi-beam piezoelectric smart structure for vibration energy harvesting

Vibration energy harvesting holds great potential to achieve long-lifetime autonomous operation of low-power electronic devices. This work is concerned with analytical and numerical modeling and analysis of a unimorph beam and a novel multi-beam energy harvesting systems. Several of the former device and two identical proof masses are utilized to design the multi-beam harvester, aiming to propose a scavenger with resonance frequency of less than 100 Hz. Accuracy of the models are verified, and extensive parametric studies are presented. Results demonstrate that the proposed multi-beam harvester is capable of generating several milliwatts of power under harmonic base acceleration of 0.4 g.

Design and Analysis of AC14 Ship Anchor

A Ship’s anchor makes a ship to be at a fixed location against currents and winds when ship is in rest position. Purpose of anchor is to restrict the drifting of ship, which is occurs due to the currents. Even though there are many different types of anchor, present paper intended to do design and analysis on stockless anchor AC14 type. Project aims to determine the equivalent von-mises stress and maximum deformation in anchor when subjected to proof test. Proof test load is decided based on the mass of the anchor. (Reference is taken for the relationship of proof test load and mass of the anchor. Solid modeling of Stockless ship anchor model is carried out on NX 11.0 and modal analysis of ship anchor is carried out using ANSYS 16.0

A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling.

This paper presents a systematic and efficient design approach for the two degree-of-freedom (2-DoF) capacitive microelectromechanical systems (MEMS) accelerometer by using combined design and analysis of computer experiments (DACE) and Gaussian process (GP) modelling. Multiple output responses of the MEMS accelerometer including natural frequency, proof mass displacement, pull-in voltage, capacitance change, and Brownian noise equivalent acceleration (BNEA) are optimized simultaneously with respect to the geometric design parameters, environmental conditions, and microfabrication process constraints. The sampling design space is created using DACE based Latin hypercube sampling (LHS) technique and corresponding output responses are obtained using multiphysics coupled field electro–thermal–structural interaction based finite element method (FEM) simulations. The metamodels for the individual output responses are obtained using statistical GP analysis. The developed metamodels not only allowed to analyze the effect of individual design parameters on an output response, but to also study the interaction of the design parameters. An objective function, considering the performance requirements of the MEMS accelerometer, is defined and simultaneous multi-objective optimization of the output responses, with respect to the design parameters, is carried out by using a combined gradient descent algorithm and desirability function approach. The accuracy of the optimization prediction is validated using FEM simulations. The behavioral model of the final optimized MEMS accelerometer design is integrated with the readout electronics in the simulation environment and voltage sensitivity is obtained. The results show that the combined DACE and GP based design methodology can be an efficient technique for the design space exploration and optimization of multiphysics MEMS devices at the design phase of their development cycle.

Highly Efficient Piezoelectrets through Ultra-Soft Elastomeric Spacers.

Piezoelectrets are artificial ferroelectrics that are produced from non-polar air-filled porous polymers by symmetry breaking through high-voltage-induced Paschen breakdown in air. A new strategy for three-layer polymer sandwiches is introduced by separating the electrical from the mechanical response. A 3D-printed grid of periodically spaced thermoplastic polyurethane (TPU) spacers and air channels was sandwiched between two thin fluoroethylene propylene (FEP) films. After corona charging, the air-filled sections acted as electroactive elements, while the ultra-soft TPU sections determined the mechanical stiffness. Due to the ultra-soft TPU sections, very high quasi-static (22,000 pC N−1) and dynamic (7500 pC N−1) coefficients were achieved. The isothermal stability of the coefficients showed a strong dependence on poling temperature. Furthermore, the thermally stimulated discharge currents revealed well-known instability of positive charge carriers in FEP, thereby offering the possibility of stabilization by high-temperature poling. The dependences of the dynamic coefficient on seismic mass and acceleration showed high coefficients, even at accelerations approaching that of gravity. An advanced analytical model rationalizes the magnitude of the obtained quasi-static coefficients of the suggested structure indicating a potential for further optimization.

Nonlinear dynamics of new magneto-mechanical oscillator

This study presents modelling and analysis of a new magneto-mechanical (MM) oscillator (Wiercigroch et al., 2020), which pays a special attention to mechanical and magnetic nonlinearities for large amplitude responses. The oscillator is comprised of a box structure made of two parallel leaf springs with one end fixed and the other clamped with a proof mass, and an electromagnetic actuator. A solenoid and a permanent magnet are the main parts of the actuator, which acts directly on the proof mass providing an accurate and versatile excitation by varying intensity and frequency of the input current. The new model for a beam of large deflection is based up the constitutive relation of nonlinear beam theory. A new design of the electromagnetic actuator with a pair of identical solenoids and a new concept of quasi-constant force (QCF) are proposed, which aims to generate a nearly constant amplitude force for a constant input current. The mathematical model of the MM oscillator is systematically developed and discussed for different types of excitations depending on designs and parameters of the electromagnetic actuator. The undertaken nonlinear dynamics analysis demonstrates versatility of the electromagnetic actuator to generate a wide spectrum of excitations. The prediction from the modelling were validated by the previous work (Costa et al., 2020). The study exemplify that the electromagnetic actuator provides a wide range of excitation patterns and can be used to study experimentally subtle nonlinear phenomena.

(Invited) A Highly Sensitive MEMS Accelerometer Module for Measuring Micro Muscular Sounds

This paper introduces a high-sensitivity accelerometer module to measure micro muscular sounds. The feature of our microelectromechanical systems (MEMS) accelerometer is the use of high-density gold proof mass structure fabricated by the multi-layer metal technology for reducing the Brownian noise. The noise floor of the proposed module is 10-dB better than that of a commercial one. The measurement results showed that our module can capture small muscular sounds which are buried in the noise of the commercial accelerometer.

Micromechanics for energy generation

The emergence and evolution of energy micro-generators during the last 2 decades has delivered a wealth of energy harvesting powering solutions, with the capability of exploiting a wide range of motion types, from impulse and low frequency irregular human motion, to broadband vibrations and ultrasonic waves. It has also created a wide background of engineering energy microsytems, including fabrication methods, system concepts and optimal functionality. This overview presents a simple description of the main transduction mechanisms employed, namely the piezoelectric, electrostatic, electromagnetic and triboelectric harvesting concepts. A separate discussion of the mechanical structures used as motion translators is presented, including the employment of a proof mass, cantilever beams, the role of resonance, unimorph structures and linear/rotational motion translators. At the mechanical-to-electrical interface, the concepts of impedance matching, pre-biasing and synchronised switching are summarised. The separate treatment of these three components of energy microgenerators allows the selection and combination of different operating concepts, their co-design towards overall system level optimisation, but also towards the generalisation of specific approaches, and the emergence of new functional concepts. Industrial adoption of energy micro-generators as autonomous power sources requires functionality beyond the narrow environmental conditions typically required by the current state-of-art. In this direction, the evolution of broadband electromechanical oscillators and the combination of environmental harvesting with power transfer operating schemes could unlock a widespread use of micro-generation in microsystems such as micro-sensors and micro-actuators.

Seismic acceleration demand and fragility assessment of storage tanks installed in industrial steel moment-resisting frame structures

Recent seismic events highlighted the importance of non-structural elements in seismic assessment and performance-based earthquake engineering. When referring to industrial facilities, storage tanks represent one of the most critical components for the continuous functionality of industrial and building plants after seismic events. At the same time, the dispersion of dangerous or inflammable materials, due to their collapse, could become a safety issue in terms of both human life and environmental impact. This study focuses on the seismic performance assessment of a liquid-storage tank installed in an industrial steel moment-resisting frame building. The performance is assessed in terms of fragility curves, that are provided for the meaningful limit states that affect the liquid-storage tank and considering several intensity measures. The results related to the structural performance are also discussed in detail in terms of fragility functions and floor response. The assessment is performed through nonlinear dynamic analyses using two different modelling approaches to evaluate the structural and non-structural performance. The first modelling approach explicitly accounts for the tank-structure interaction, while in the second one the tank is only modelled considering its seismic mass. The results show the importance of the modelling assumptions to accurately estimate the seismic demand on liquid-storage tanks and corresponding fragility, which is calculated in terms of different intensity measures (IM): average ground spectral acceleration, peak floor acceleration, and floor spectral accelerations. Peak floor acceleration, drift profiles, and absolute acceleration and relative displacement floor response spectra are instead scrutinised for what concerns demand. The comparison with the code formulations available in the literature for estimating the seismic demand to non-structural elements pointed out their inaccuracy for the analysed liquid-storage tank and the need for further efforts to develop more accurate procedures. Furthermore, the outcomes indicate that the IM adopted for secondary components, i.e. peak floor acceleration, may not always be the optimal one hence additional attention should also be paid to the definition of updated fragility curves for non-structural elements, identifying and adopting more suitable IMs.

Resource Allocation in Vibration Energy Harvesters

This paper studies the optimization of mechanics and resource allocation in linear vibration energy harvesters operating under an overall size constraint. In such harvesters, the volume aspect ratio and the stroke direction should be carefully selected to maximize output power and power density. Further, because the proof mass and spring stroke must share the available size along the stroke direction, a mass-stroke design trade-off results; the trade-off is optimized here. The optimization further leads to a universal metric the enables the comparison of linear vibration energy harvesters designed to operate in a limited volume. Examination of this metric results in guidelines and best practices for selecting harvester dimensions and shape for a given volume constraint, all based on the dimensional harvester optimization for maximum size-constrained output power. This paper offers several key contributions. First, it provides an evaluation and optimization of the impact that volume shaping and volumetric resource allocation have on the output power of linear vibration energy harvesters. Second, it develops a “universal normalized surface” relating output power to dimensional harvester design. The surface expresses the performance limit of space-constrained linear vibration energy harvesters in terms of their output power density. This leads to universal guidelines for harvester design. Finally, benchmarking harvesters reported in the literature against the universal surface demonstrates that their output performances lie on or below the surface, despite large variations in their exogenous design variables such as vibration amplitude, frequency, volume etc. Thus, this paper offers an effective method to evaluate mechanical design and optimization in state-of-the-art linear vibration energy harvesters under volume constraints, a scenario suited for IoT applications. [2021-0074]