Mechanical Damping Coefficient Research Articles

Power absorption and flow-field characteristics analysis for oscillating coaxial twin-buoy wave energy converter by using CFD

The energy conversion capacity of wave energy conversion devices highly depends on the hydrodynamic characteristics of the energy-harvesting structure. To investigate the effect of hydrodynamic performance on the power conversion characteristics, a twin-buoy wave energy converter (WEC) was investigated by using a three-dimensional numerical wave pool based on the Computational Fluid Dynamics (CFD) method. Several factors are examined, including the elasticity coefficient of the anchor chain, the bottom configuration of the floating body, and the power take-off (PTO) damping coefficient. The heave displacement, heave velocity, and heave force of the converter are calculated under specific wave parameters, and the flow field cloud diagram during the heave motion is analyzed. The results indicate that a wave energy converter with a hemispherical floating body exhibits the best kinematic performance. The influence of the mechanical damping coefficient on the energy conversion performance of the device is studied. By appropriately reducing the mechanical damping coefficient, the energy capturing capability of the device can be increased to a certain extent. These findings can serve as a theoretical basis for the application of deep-water wave energy conversion in engineering and the optimization of future WEC designs.

Stochastic dynamics of a nonlinear vibration energy harvester subjected to a combined parametric and external random excitation: The distinct cases of Itô and Stratonovich stochastic integration

The Stratonovich and Itô interpretations of a stochastic integral are mathematically consistent, distinct representations that yield contrasting response characteristics for stochastic dynamical systems subjected to multiplicative noise, such as parametric random excitation. The contrasting dynamics from the two interpretations currently remain unexplored in vibration energy harvester dynamics. We analytically investigate the dynamics of a generic piezoelectric, nonlinear vibration energy harvester simultaneously subjected to stochastic damping and external random excitation, focusing on the contrasting dynamics engendered by the two interpretations. Numerically solving the Stratonovich and Itô stochastic differential equations in the nonequilibrium regime of harvester dynamics, we find that the Stratonovich version yields significantly higher root mean square values of the harvester voltage output, for lower values of the mechanical damping coefficient. Furthermore, we find positive values for the leading Lyapunov exponent indicating instabilities in the harvester response unique to the Stratonovich interpretation. Additionally, comparing the results for the harvester electrical output between the cases of external excitation represented by the white noise and the Ornstein–Uhlenbeck noise processes, we find lower root mean square values of the voltage output in the latter case. Moreover, the results indicate that the averaged voltage output becomes progressively lower with increasing correlation time of the Ornstein–Uhlenbeck process. Studying the equilibrium dynamics by deriving Fokker–Planck equations for the response amplitude of the harvester using the harmonic balance method and stochastic averaging techniques, we solve for the stationary probability densities to find that the harvester is more likely to attain a well-defined equilibrium state under the Itô interpretation. In summary, the results contribute to the theoretical understanding of the fundamental contrast between the Stratonovich and Itô interpretations in vibration energy harvester dynamics and are expected to motivate advances in harvester design for various applications.

Dynamic mechanical properties and ageing studies of coir-sisal yarn reinforced polypropylene commingled composites

This work investigates the dynamic mechanical properties (DMA) and ageing behavior of coir-sisal yarn reinforced polypropylene commingled composites. Moreover, the fibres were subjected to various chemical treatments and their effects on DMA and ageing studies were investigated. DMA reveals that the chemical treatment, especially MAPP treatment, enhances the storage and loss modulus values on the other hand it diminishes the mechanical damping coefficient (tan δ) of the composite. Diffusion studies indicates that treated composites shows a much lower apparent percentage weight gain compared to other treated ones. Solar ageing studies shows that accelerated solar ageing deteriorated tensile strength and modulus of PP/coir-sisal yarn composite.

Dynamic responses of the 2DOF electromagnetic vibration energy harvester through different electrical coil connections

This work investigated the dynamic responses and evaluated the performance of a two-degree-of-freedom (2DOF) coupled coil-magnet electromagnetic vibration harvester excited at low frequencies. Three different connection modes with individual, in-series, and in-parallel configurations of the transduction coils were considered. Such approach was taken to identify the most suitable mode for usage because different sensor nodes have different power, current and impedance ratings and the optimum load associated with each connection mode differs. The above reasons also lead to the need for impedance matching of the sensor and the harvesters optimum load, as otherwise, the power deliverable to the sensor would be significantly lower than those achievable under a matched impedance condition. The mathematical model was established and verified experimentally, and a 97.8 % agreement is shown across the connection types at resonance of 9.69 Hz and 0.30 g excitation level. At optimum loads, the individual and series connections output the highest power at 497.50 mW and 410.40 mW, respectively. The optimum power peaked at densities of 223.13 Wm3, 1216.36 Wm3, 1009.03 Wm3, and 658.38 Wm3 for coils 1 and 2 (individual), series and parallel connections, respectively. Overall analysis concludes that the optimum harvestable power using in-series and individual coil 2 connection is higher by 47.41 % and 36.25 %, respectively, over the in-parallel connection and 81.77 % and 77.90 % over individual 1 connection. A comparison of the 2DOF harvester with an equivalent two SDOF harvesters at same resonance, excitation level and mechanical damping coefficient shows that that 2DOF series and individual coil 2 connections perform consistently well in preference to the equivalent two SDOF systems in terms of the power harvested, bandwidth, and normalized power density while associated optimum load resistance dichotomized the practical operational impedance into the high and low on the series and individual coil 2, respectively in the operational bandwidth corresponding to each design.

Frequency response locking of electromagnetic vibration-based energy harvesters using a switch with tuned duty cycle

Abstract It is proposed to tune linear electromagnetic vibration-based energy harvesters so that they will achieve an optimum case regardless of the base amplitude or excitation frequency of the environment. The author designed the optimum coil and load parameters as well as the optimum acceleration amplitude and vibration frequency of the magnet for known values of three mechanical parameters (spring constant, mass, and mechanical damping coefficient) so that the optimum parameters will remain constant upon switching. As the vibration frequency of the magnet deviates from the optimal value, the switch turns on and off to compensate for the deviation so that the maximum power entering the electrical domain does not change. The deviation is limited to frequency or base amplitude acceleration. Other optimum parameters are fixed values. They are designed so that they can handle the maximum power that is delivered to the electrical domain.

Power optimization of a magnetoelectric wireless power transfer system with volume constraint

We present a general framework for maximizing the power delivered to a load resistance of a magnetoelectric wireless power transfer system, especially under a volume constraint condition. We derive an analytical solution to a power optimization problem, both for a given transducer geometry and when the geometric dimensions are subject to change. We investigate the relationships between the output power and the chosen operating frequency in various circumstances when the mechanical damping coefficient or the mechanical quality factor is kept constant independent of the change in the receiver geometry. We discuss the essential roles of the magneto-elastic transduction factor and a resonator figure of merit and show how to obtain the optional thickness ratio between the two constitutive materials, magnetostrictive and piezoelectric. Examples with particular sets of system parameters are given to demonstrate the general theoretical analysis.

Modelling, simulation, and experimental verification of a pendulum-flywheel vibrational energy harvester

Vibration energy harvesting has been a popular topic in recent years. This technology is promising in developing self-powered sensor nodes for health condition monitoring of machines or structures, especially in remote areas. This study proposes a pendulum-flywheel vibration energy harvester based on the electromagnetic energy conversion mechanism. The harvester has two motion modes, namely the pendulum mode and eccentric flywheel mode, and can switch between the two modes automatically in response to external excitations.We first establish a theoretical model and fabricate a prototype of the harvester for evaluating its performance. Then, experimental and theoretical methods are employed to estimate the parameters of the model, such as the dipole moment of magnets, the mechanical damping coefficients, and the optimal resistance of the external electrical load. The typical trajectories of different motion modes, the frequency response characteristics, and the influence factors on the basins of attraction of the harvester are studied with the theoretical model. It is found that the small magnet distance can broaden the frequency band and enlarge the amplitude of the dynamic responses of the system. This finding provides us with an approach to control the performance of harvester and enables it to have stronger adaptability to variant ambient vibration in nature. Finally, laboratory tests are performed to validate the theoretical model. The experimental data verified the assumption that the rotation speed of the pendulum and the induced electromotive voltage have a linear relationship. Experimental and numerical simulation results show that the errors between them in most cases are less than 10% when the excitation displacement is small and have a slight increase with the excitation displacement. In the experiments, this harvester achieves a maximum power of 16.3 mW, exhibiting good performance in comparison with the-state-of-the-art pendulum-based harvesters.

A study of a speed amplified linear generator for low-frequency wave energy conversion

This paper proposes a new method of speed amplification for a direct drive ocean wave energy converter. The relative speed of the stator and translator of a linear generator is doubled through a fixed pulley wheel mechanism. Analytical and simulation models of the system have been developed and simulated considering the mechanical damping and electrical damping coefficients. The models have been simulated in both the regular waves and irregular waves where hydrodynamic parameters for different heaving buoys are calculated from hydrodynamic boundary element analysis simulation using the ANSYS AQWA software. The relative displacement, output voltage and harvested power of the speed amplified wave energy converter system have been obtained in the frequency and time domains. The frequency and time domain models were validated through comparing the peak output power values at different frequencies. The generator parameters of electromagnetic coupling coefficient, or the power take-off (PTO) electrical damping coefficient and external resistance were studied to ensure an optimal wave-energy converter (WEC) design.

Study on a heat-driven thermoacoustic refrigerator for low-grade heat recovery

Recovering low-grade heat from renewable energy sources and waste heat is crucial for improving energy utilizing efficiency as well as reducing CO2 emissions. Conventional thermoacoustically-driven refrigerators have a high onset temperature and low cooling efficiency, which significant limit their capacity for low-grade heat utilization. This paper investigates a novel thermoacoustically-driven refrigerator with gas-liquid resonators which enable a lower onset temperature and better cooling performance for harvesting low-grade heat. Theoretical analyses were performed on multi-stage systems to explore the onset characteristics and steady performance. Onset characteristics analysis was conducted by using a transfer matrix method. The effects of mean pressure, liquid volume ratio and the expected liquid mechanical damping coefficient on the onset temperature difference and working frequency were studied for systems with different numbers of stages. A comparison of system onset performance was made with conventional systems containing a gas-only resonator. The research illustrated that for a mean pressure of 1 MPa, the proposed system can significantly reduce the onset temperature difference from 144.1 K to below 35.5 K. In addition, an analysis was then conducted to study the parametric sensitivity of the thermodynamic performance. Calculation results show that the proposed system can achieve a baseline cooling power of 2.7 kW and a thermal-to-cooling efficiency of 0.67 at a heating temperature of 420 K and a cooling temperature of 270 K. This represents significant increases by a factor of 5.6 in cooling power and 1.5 in efficiency from a gas-only to a gas-liquid resonator.

Nonlinear analysis of axially loaded piezoelectric energy harvesters with flexoelectricity

In this work, nonlinear electromechanical models for energy harvesters based on axially preloaded piezoelectric beams incorporating flexoelectric effect are presented. Depending on the amplitude of the applied axial load, the proposed energy harvester could operate in either prebuckling or postbuckling configuration. According to the theory of flexoelectricity and the Hamilton's principle, the nonlinear electromechanical coupling equations of the proposed energy harvesters under base excitations are derived. For a simply-supported piezoelectric beam, the expression of the static buckling load is analytically determined. Then, for energy harvesters in the prebuckling and postbuckling configurations, we obtain the discrete nonlinear governing equations by employing the Galerkin's method. These coupling equations are solved numerically by the Runge–Kutta method. Case studies are provided to show the steady-state output voltage and power of the energy harvesters. Results indicate that the frequency response curves show a typical hardening nonlinear behavior in the prebuckling configuration and a softening nonlinear behavior in the postbuckling configuration. Such nonlinear behaviors of energy harvesters imply a wider frequency operation bandwidth of the proposed energy harvesters. We also find that the energy harvesters utilizing flexoelectricity have a better performance than those based on piezoelectricity in the prebuckling configuration. Moreover, we examine the influences of resistive load, mechanical damping coefficient and the amplitude of the base excitation on the performance of the energy harvesters as well as the size effect due to flexoelectricity. It is also interesting to observe that both intrawell and interwell oscillations of the energy harvesters could occur in the postbuckling configuration. This work provides an efficient route to design energy harvesting systems at micro- and nano-scales with enhanced performance.

Optimisation of Heat Treatment Process for Damping Properties of Mg-13Gd-4Y-2Zn-0.5Zr Magnesium Alloy Using Box–Behnken Design Method

High damping magnesium alloys have poor mechanical properties, so it is necessary to investigate the damping properties of high-strength wrought magnesium alloys to effectively reduce vibration and noise in mechanical engineering. The aim of this work is to improve the mechanical damping performance of a novel high-strength Mg-13Gd-4Y-2Zn-0.5Zr magnesium alloy by optimising the heat treatment process. The mechanical damping coefficient, considering not only damping capacity but also the yield strength, is selected as one of the evaluation indexes. The other evaluation index is the tensile strength. The solid solution and ageing treatment were optimised by Box-Behnken method, an efficient experimental design technique. Heat treatment experiments based on the optimal parameters verified that the best process is a solution at 520 °C for 10 h followed by ageing at 239 °C for 22 h. The damping coefficient reaches 0.296, which is 73.1% higher than that before heat treatment. There was a good agreement between the experimental and Box-Behnken predicted results. The microstructure, morphology and composition of the second phases after heat treatment were analysed by SEM, XRD and EDS. Due to the high content of alloying elements in Mg-13Gd-4Y-2Zn-0.5Zr alloy, there are a large number of second phases after heat treated. They mainly include layer, short rod-shaped, bulk long period stacking order (LPSO) Mg12YZn and granular Mg5Gd phases. It was found that the area fraction of the second phases has an extreme effect on the damping capacity and short rod-shaped LPSO can effectively improve the damping capacity of heat-treated Mg-13Gd-4Y-2Zn-0.5Zr alloy. The volume fraction of the second phases was analysed by ImageJ software. It was concluded that the smaller the area occupied by the second phases, the better the mobility of the dislocation, and the better the damping performance of the alloy. The statistical analysis results obtained using ImageJ software are consistent with the experimental results damping capacity.

Evaluation of two-step transformation in Ni-rich titanium-nickel alloys using thermal and internal friction analyses

The use of Ti-Ni memory alloys covers several fields of application such as medicine, dentistry, actuators, sensors among others. Because of the thermomechanical behavior of these materials, they are an object of continuous studies and their properties are related to the occurrence of thermoelastic martensitic phase transformations. The thermal analyzes were performed using dilatometry and differential scanning calorimetry to determine the temperatures that occurred transformations during the cooling and heating, as well as to evaluate the influence of the thermal treatments performed by dilatometry. The thermomechanical behavior was also evaluated by the internal friction that measured behavior damping considering the structural and microstructural changes. The calorimetry measurements indicated suppression of the R phase through decomposition of precipitates of Ti3N4after the thermal treatments, that were corroborated by dilatometry and microhardness. This phase was also studied by the technique of internal friction, which showed that the mechanical damping coefficient increased as a function of temperature, due to the movement of the defects induced by tension. Keywords: Ti-Ni, shape-memory effect, internal friction, dilatometry, calorimetry.

Anomalous Behavior During Nano‐Compression Superelastic Tests on Cu‐Al‐Ni Shape Memory Alloy Micro Pillars

Shape memory alloys are one of the most important families of functional materials due to superelasticity and shape memory properties. In particular Cu‐Al‐Ni alloys exhibit these properties at nanoscale, becoming potentially useful to design new smart MEMS. In this work, an anomalous behavior observed during nano‐compression superelastic tests on Cu‐Al‐Ni shape memory alloy micro pillars is reported. The study is approached by nano‐compression tests on micro and nano pillars milled by focused ion beam. The anomalous behavior on the superelastic effect is manifested by a sudden stabilization of the stress‐induced martensite, which does not undergo the reverse transformation. A transition, from superelastic to pseudoelastic‐twinning behavior, takes place during the nano‐compression tests, and is evaluated through the load‐depth curves and quantified by the mechanical damping coefficient η, which undergoes a sharp change from ultra‐high damping, η > 0.1, down to η ≈ 0.01. The stabilization of the martensite occurs under two different experimental conditions, along cycling and by applying a very high stress during superelastic tests. In both cases, a further recovery of the initial superelastic behavior is registered. The mechanisms responsible for the observed stabilization and recovery are discussed, together with the implications and further requirements for technological applications in MEMS.

Power Electronics Control of an Energy Regenerative Mechatronic Damper

This paper presents the development of a power electronics controller for a proof-of-concept energy regenerative damper in vehicular applications. The damper consists of an efficient motion conversion mechanism to convert translational base vibration into reciprocating rotary motion, a brushless three-phase permanent-magnet rotary machine, and a three-phase power converter. A power electronics boost controller is developed to capture the generated electrical power and store it into a battery that allows overcoming kinematic nonlinearities in the motion conversion stage. To this end, a sliding-mode controller that can enforce a resistive behavior across the terminals of the rotary machine by regulating the converter's input current in real time is presented. Through the proposed approach, the mechanical damping coefficient of the system can be controlled, on demand, with an energy regenerative function. The performance of the developed system is evaluated under sinusoidal excitation inputs and transient conditions when operating with a damping coefficient of 650 $\hbox{N}\cdot\hbox{s/m} $ synthesized through power electronics and control. Experimental results that evaluate the performance of the proposed energy regenerative damper are presented.

An Online Measurement Approach of Generators’ Torsional Mechanical Damping Coefficients for Subsynchronous Oscillation Analysis

The series compensation capacitor and HVDC are widely used in Chinese power grids to increase the transmission capability of long distance lines, which might cause subsynchronous oscillation (SSO) between the turbine generators and power systems. The torsional mechanical damping coefficient of a turbine generator reflects the inherent damping level of the shaft and, thus, is a critical factor in SSO analysis. However, the torsional mechanical damping coefficient under practical operating conditions is difficult to obtain from the design parameters. In this paper, a novel approach is developed for online torsional mechanical damping coefficient measurements. The torsional interaction mechanism of identical parallel connected turbine generators is investigated, and then the characteristics of in-phase mode (IPM) and anti-phase mode (APM) are described. From this analysis, an active stimulating method for APM is presented, and a practical scheme for online torsional mechanical damping coefficient measurement is designed. This approach takes advantage of the APM features and decouples the generators from the grid. Moreover, the proposed approach has been implemented in the Yimin power plant in Inner Mongolia to realize online measurement of the torsional mechanical damping coefficient. Field test results are presented to demonstrate the effectiveness of the proposed approach.

Development of a 3 kW double-acting thermoacoustic Stirling electric generator

In this paper, a double-acting thermoacoustic Stirling electric generator is proposed as a new device capable of converting external heat into electric power. In the system, at least three thermoacoustic Stirling heat engines and three linear alternators are used to build a multiple-cylinder electricity generator. In comparison with the conventional thermoacoustic electricity generation system, the double-acting thermoacoustic Stirling electric generator has advantages on efficiency, power density and power capacity. In order to verify the idea, a prototype of 3kW three-cylinder double-acting thermoacoustic Stirling electric generator is designed, built and tested. Based on the classic thermoacoustic theory, numerical simulation is performed to obtain the thermodynamic parameters of the engine. And distributions of key parameters are presented for a better understanding of the energy conversion process in the engine. In the experiments, a maximum electric power of about 1.57kW and a maximum thermal-to-electric conversion efficiency of 16.8% were achieved with 5MPa pressurized helium and 86Hz working frequency. However, we find that the mechanical damping coefficient of the piston is dramatically increased due to the deformation of the cylinder wall caused by high thermal stress during the experiments. Thereby, the system performance was greatly reduced. Additionally, the performance differences between three engines and three alternators are significant, such as the heating temperature difference between three heater blocks of the engines, the piston displacement and the output electric power differences between three alternators. These problems need further investigation. This work presents a new thermal-to-electric conversion technology, which can be utilized in many energy area, such as solar energy, industrial waste heat and so on.

Numerical investigation on a thermoacoustic heat engine unit with a displacer

A novel thermoacoustic heat engine – double-acting travelling wave thermoacoustic heat engine has been proposed by our research group recently. It consists of at least three symmetric engine and resonator units and has advantages on efficiency, power density and heat source flexibility. However, some computational and experimental results indicate a dramatic heat loss caused by the jet-flow in the thermal buffer tube due to the structures of the high temperature heat exchanger and the secondary ambient heat exchanger at its two ends. To solve this problem, a displacer locating in the thermal buffer tube is proposed to suppress the jet-flow. Moreover, the displacer is capable of isolating the hot region from room temperature, which provides an opportunity to eliminate the secondary ambient heat exchanger. In order to investigate such a double-acting thermoacoustic heat engine, a test rig of the engine unit has been developed by utilizing two linear motors to provide real operational conditions in the system. In this paper, a numerical simulation is performed to reveal the influences of the displacer on the system performance. According to the numerical results, the impact of displacer is very limited when the displacer is working under the resonant state. In addition, the influences of spring constant and mechanical damping coefficient of the displacer are analyzed in detail respectively.

Coupled optimization of tuned-mass energy harvesters accounting for host structure dynamics

A tuned-mass electromagnetic energy harvester mounted on a vibrating structure is studied here, accounting for the dynamic coupling between harvester and host structure. The latter is modeled as a modal mass–spring–dashpot system, whereas the harvester device is composed of an electromagnetic transducer and a tunable secondary mass–spring–dashpot system. A thorough analytical coupled optimization of the harvested power with respect to the harvester components is presented here. Closed-form design formulas are supplied for the optimal values of the electromagnetic damping coefficient and tuning frequency, as functions of the excitation frequency, mass ratio, and mechanical damping coefficients. The optimized parameters yield a wide effective harvesting bandwidth when proper values of the mass ratio and device mechanical damping are chosen. It is shown that neglecting in the design process the dynamic coupling between harvesting device and vibrating host structure, that is, treating the latter as a mere vibration source as generally assumed in the literature, leads to a significant degradation of the harvesting performance.

Experimental and analytical parametric study of single-crystal unimorph beams for vibration energy harvesting

This research presents an experimental and theoretical energy harvesting characterization of beam-like, uniform cross-section, unimorph structures employing single-crystal piezoelectrics. Different piezoelectric materials, substrates, and configurations are examined to identify the best design configuration for lightweight energy harvesting devices for low-power applications. Three types of piezoelectrics (singlecrystal PMN-PZT, polycrystalline PZT-5A, and PZT-5H-type monolithic ceramics) are evaluated in a unimorph cantilevered beam configuration. The devices have been excited by harmonic base acceleration. All of the experimental characteristics have been used to validate an exact electromechanical model of the harvester. The study shows the optimum choice of substrate material for single-crystal piezoelectric energy harvesting. Comparison of energy scavengers with stainless steel substrates reveals that single-crystal harvesters produce superior power compared with polycrystalline devices. To further optimize the power harvesting, we study the relation between the thickness of the substrate and the power output for different substrate materials. The relation between power and substrate thickness profoundly varies among different substrate materials. The variation is understood by examining the change of mechanical transmissibility and the variations of the coupling figure of merit of the harvesters with thickness ratio. The investigation identifies the optimal thickness of the substrate for different substrate materials. The study also shows that the densities of the substrates and their mechanical damping coefficients have significant effects on the power output.

Modelling, control and Pontryagin Maximum Principle for a two-body wave energy device

Frequency-domain analysis is applied to a wave energy device composed of two coaxial axisymmetric bodies. For each frequency optimal damping coefficient values which maximize absorbed power are obtained. Several displacement amplitude restriction scenarios are considered. A stochastic model to describe the device’s behaviour in irregular waves is developed. Optimal mechanical damping and spring coefficients are computed. Considering different sea state conditions, probability density functions are defined for relevant parameters and time-averaged absorbed power values are obtained.A time domain model is also developed for the device. A non-linear power take-off mechanism configuration, consisting in a hydraulic circuit with low-pressure and high-pressure gas accumulators, is devised. Time-averaged absorbed power is maximized in terms of characteristic mechanism parameter. A sub-optimal method of phase control by latching is applied to the device in order to improve its performance. Analytical development of Pontryagin Maximum Principle is used to establish an algorithm for device’s control.