Magnetic Spring Research Articles

Design study of a nonlinear electromagnetic converter using magnetic spring

In this paper, an experimental and theoretical study for designing a nonlinear electromagnetic converter-based magnetic spring is performed. The governing equation of the converter is investigated. A special focus is given to the magnetic force acting on the moving magnet in dependence of its volume and the geometry of the two fixed magnets, i.e., disc or ring. For the developed analytical and numerical model, the same converter volume has been used for all conducted investigations. Several parameters have been studied that can be used to tune the nonlinearity behavior. Further, the coil axial position was investigated analytically and experimentally. An energy harvesting prototype consisting of an oscillating cylindrical magnet levitated between two stationary magnets is fabricated and evaluated through experiments. The open-circuit voltage obtained through the analytical model has been compared to the experiment and solutions to tune the harvester resonant frequency while maintaining its output power density were proposed.

Lever-type quasi-zero stiffness vibration isolator with magnetic spring

Unlike the tuning of the vibration isolation band through stiffness and geometric parameters in traditional quasi-zero stiffness (QZS) vibration isolators (VIs), this study presents a lever-type QZS vibration isolator (L-QZS-VI) to improve the vibration isolation performance. The QZS characteristic is realized with a magnetic spring. Eddy current damping (ECD) is used to eliminate the jump phenomenon and improve the vibration isolation performance. A theoretical model of L-QZS-VI with ECD is developed and the corresponding governing equation is obtained using the Lagrange equation. The displacement transmissibility is derived using the harmonic balance method. The effects of the tip mass of the lever, lever ratio, nonlinear stiffness of the magnetic spring and excitation amplitude on the vibration isolation performance of the L-QZS-VI are analyzed numerically and experimentally. The vibration isolation performance can be largely improved by tuning the lever ratio, tip mass of the lever, and nonlinear stiffness of the magnetic spring. The ECD can produce tunable damping to further improve the vibration suppression performance in the resonance region. This study provides a guideline to design, model, and optimize L-QZS-VI.

Equivalent Electronic Circuit of a System of Oscillators Connected with Periodically Variable Stiffness

In this paper, we have shown an electronic circuit equivalence of a mechanical system consisting of two oscillators coupled with each other. The mechanical design has the effects of the magnetic spring force resistance force, and the spring constant of the system is periodically varying. We have shown that the system’s state variables, such as the displacements and the velocities, under the effects of different forces, lead to some nonlinear behaviors, like a transition from the fixed point attractors to the chaotic attractors through the periodic and quasi-periodic oscillations. We have verified those numerically obtained phenomena using the analog electronic circuit of this mechanical system.

Fabrication and preliminary evaluation of alginate hydrogel-based magnetic springs with actively targeted heating and drug release mechanisms for cancer therapy

In this study, we developed calcium alginate hydrogel-based magnetic springs containing magnetically aligned Fe 2 O 3 magnetic nanoparticles (MNPs) to render them responsive toward magnetic fields. Under a low-frequency magnetic field, a torque was exerted on the springs propelling them along their long axis. In contrast, under a high-frequency alternating magnetic field (AMF) of 200 kHz, the temperature of the spring increased up to 45 °C, making them suitable for magnetic hyperthermia. Moreover, the heat caused thermal stresses, resulting in the spring's mechanical deformation (shrinkage) that accelerated the drug release. Based on the observation of CO 2 using mass spectra, we verified the boundary conditions prevailing during thermal deformation and thermal cracking. In the AMF condition, a spring temperature of 43 °C was attained, and the drug release was about 35% higher than that of physiological temperature (37 °C). In addition, the mechanical and thermal properties of the magnetic hydrogel were investigated based on the concentration and alignment of MNP, because these properties affect the locomotion the drug release mechanism of the hydrogel. Ultimately, the viability of the spring for active targeted heating and drug release was verified via various in-vitro tests.

Methodology for Shape Optimization of Magnetic Designs: Magnetic Spring Characteristic Tailored to Application Needs

Topology and shape optimization are still rarely applied to problems in electromagnetic design due to the computational complexity and limited commercial tooling, even though components such as electrical motors, magnetic springs or magnetic bearings could benefit from it, either to improve performance (reducing torque ripple and losses through shaping harmonic content in back electromotive force) or reduce the use of rare-earth materials. Magnetic springs are a fatigue free alternative to mechanical springs, where shape optimization can be exploited to a great degree—allowing for advanced non-linear stiffness characteristic shaping. We present the optimization methodology relying on a combination of several approaches for characteristic shaping of magnetic springs through either a modular design approach based on: (i) Fourier order decomposition; (ii) breaking conventional design symmetry; or (iii) free shaping of magnets through deviation from a nominal design using problem formulations such as spline and polynomials for material boundary definitions. Each of the parametrizations is formulated into a multi-objective optimization problem with both performance and material cost, and solved using gradient free optimization techniques (direct search, genetic algorithm). The methodology is employed on several benchmark problems—both academic and application inspired magnetic spring torque characteristic requirements. The resulting designs fit well with the requirements, with a relatively low computational cost. As such, the methodology presented is a promising candidate for other design problems in 2D shape optimization in electrical motor research and development.

Exploiting Cyclic Angle-Dependency in a Kalman Filter-Based Torque Estimation on a Mechatronic Drivetrain

Torsional vibrations play a critical role in the design and operation of a mechanical or mechatronic drivetrain due to their impact on lifetime, performance, and cost. A magnetic spring allows one to reduce these vibrations and improve the actuator performance yet introduces additional challenges on the identification. As a direct torque measurement is generally not favourable because of its intrusive nature, this paper proposes a nonintrusive approach to identify torsional load profiles. The approach combines a physics-based lumped parameter model of the torsional dynamics of the drivetrain with measurements coming from a motor encoder and two MEMS accelerometers in a combined state/input estimation, using an augmented extended Kalman filter (A-EKF). In order to allow a generic magnetic spring torque estimation, a random walk input model is used, where additionally the angle-dependent behaviour is exploited by constructing an angle-dependent estimate and variance map. Experimental validation leads to a significant reduction in bias in the load torque estimation for this approach, compared to conventional estimators. Moreover, this newly proposed approach significantly reduces the variance on the estimated states by exploiting the angle dependency. The proposed approach provides knowledge of the torsional vibrations in a nonintrusive way, without the need for an extensive magnetic spring torque identification. Further, the approach is applicable on any drivetrain with angle-dependent input torques.

Research on mathematical modeling of the servo valve torque motor considering the variation of working air-gaps leakage flux

In the current research of the magnetic circuit model of the servo valve torque motor, the magnetic flux leaking from working air-gaps is regarded as constant. However, the working air-gaps leakage flux varies with the armature rotation angle, which affects the accuracy of the existing mathematical model of the torque motor. To solve this problem, a new mathematical model of the torque motor with two working air-gaps is built. First, different from the previous model, the variation of the working air-gaps leakage flux is considered in the magnetic circuit model. A more detailed mathematical model of the torque motor is established based on the magnetic circuit model. Second, the finite element method is used to reveal that there is a linear relationship between working air-gaps leakage flux and armature rotation angle in a certain range of rotation angles. Then, the new model is validated by numerical calculation, which indicates that the theoretical results calculated by this new model show better agreement with the simulation results compared to the previous model when the armature rotation angle increases. Further, the theoretical results of the electromagnetic torque constant and magnetic spring stiffness acquired by the new model and the previous model are compared. The comparison shows that the variation of the working air-gaps leakage flux has the greatest influence on the magnetic spring stiffness. Finally, the experiments on the torque motor are conducted to verify the accuracy of the new model. The theoretical results obtained by this new model are better consistent with the experimental results than that obtained by the previous model. This study shows that considering the variation of working air-gaps leakage flux is valuable to improve the accuracy of the magnetic circuit model of the torque motor, which provides an effective guidance for the structural optimization and performance prediction of the torque motor.

Reproduction of Intrinsic Localized Modes by Prototype Experiments of Nonlinear Magnetic Rotary Springs

Reproduction of Intrinsic Localized Modes by Prototype Experiments of Nonlinear Magnetic Rotary Springs

Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation

Paralleling magnetic negative stiffness mechanism (NSM) with positive stiffness serves as an effective way to resolve the inherent contradiction between high load capacity and ultra-low frequency vibration isolation ability. Nevertheless, the stiffness nonlinearity and oversize of common magnetic NSMs restrict their further applications. In this paper, a novel compact arrayed-magnetic-spring with negative stiffness (AMS-NS) is proposed. The AMS-NS, which consists of cuboidal magnets arranged as a rectangular array, possesses high negative stiffness density and ameliorative nonlinearity. An analytical model of the AMS-NS is established based on the magnetic charge model and validated by static experiments. Parametric studies are conducted to provide guidelines for the optimal design of the AMS-NS. In addition, the nonlinear displacement transmissibility of an isolator with the AMS-NS and positive stiffness in parallel (APSP) is derived utilizing the harmonic balance method, and effect of stiffness characteristic of the AMS-NS on the isolation performance are furtherly investigated. Finally, dynamic experiments were conducted on a prototype with APSP, the results demonstrated that the proposed AMS-NS has high negative stiffness density and can effectively reduce the resonance frequency to broaden the vibration isolation band; and the analytical results showed good agreements with the experimental results.

Magnetoelastic coupling enabled tunability of magnon spin current generation in two-dimensional antiferromagnets

We theoretically investigate the magnetoelastic coupling (MEC) and its effect on magnon transport in two-dimensional antiferromagnets with a honeycomb lattice. MEC coeffcient along with magnetic exchange parameters and spring constants are computed for monolayers of transition metal trichalcogenides with N\'eel order ($\text{MnPS}_3$ and $\text{VPS}_3$) and zigzag order ($\text{CrSiTe}_3$, $\text{NiPS}_3$ and $\text{NiPSe}_3$) by $ab$ $initio$ calculations. Using these parameters, we predict that the spin-Nernst coefficient is significantly enhanced due to magnetoelastic coupling. Our study shows that although Dzyaloshinskii-Moriya interaction can produce spin Nernst effect in these materials, other mechanisms such as magnon-phonon coupling should be taken into account. We also demonstrate that the magnetic anisotropy is an important factor for control of magnon-phonon hybridization and enhancement of the Berry curvature and thus the spin-Nernst coefficient. Our results pave the way towards gate tunable spin current generation in 2D magnets by SNE via electric field modulation of MEC and anisotropy.

Design and Control of a Novel Compact Nonlinear Rotary Magnetic SEA (MSEA) for Practical Robotic Gripper Implementation

In this letter we present a novel design of a nonlinear series elastic actuator based on magnetic repulsive forces. The primary application of the actuator is for simple robotic grippers that operate in close proximity to the environment and are exposed to hazards of collision frequently. The design of the rotary magnetic spring proposes a unique configuration that maximizes the torque profile range while minimizing size and weight, which makes it practically implantable in robotic gripper applications. The torque profile of the proposed configuration was verified with FEM simulations and a series of experiments. The proposed SEA (MSEA) was controlled with a gain scheduling method which adjusts the gains of a PID controller based on the estimated stiffness of the spring in real-time. MSEA performance characteristics to accurately track torque and absorb shocks were evaluated and verified through a series of experiments.

Intrinsic Localized Mode in a Multiple Mass Dynamic Vibration Systems Using Nonlinear Magnetic Springs

AbstractIntrinsic localized mode (ILM) can be generated in multiple mass‐spring systems using nonlinear springs, and ILM has attracted a lot of attention due to its special vibration modes that are not found in linear systems. However, the difficulty of creating nonlinearity remains a barrier to ILM research. In this paper, we propose a rotating magnetic spring based on magnetic nonlinearity. The nonlinear restoring properties of the proposed magnetic spring are confirmed by finite element method (FEA). Finally, using the restoring properties obtained from FEA, it is shown that ILM can be excited by MATLAB numerical analysis. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Modelling and Optimization of a Magnetic Spring Based Electromagnetic Vibration Energy Harvester

This paper presents the development of an AA battery size electromagnetic vibration energy harvester with an aim to maximize the output power density. A tube shape and stacked opposing permanent magnets with magnetic spring were used to suit the shape constraint as well as to achieve high flux linkages. An initial prototype of electromagnetic vibration harvester with AA battery size was built and tested on a controllable shaker to obtain its output voltage and power level at different frequencies for fixed accelerations. A single magnet was fixed at the bottom of the harvester to provide levitation force in this development in order to lower the resonant frequency. A special time-domain based analytical model was also developed using both Finite Element Analysis and Simulink simulation. The time-domain analytical model is easier to implement than other frequency domain based analytical models which generally applied in literatures for modelling of the electromagnetic vibration energy harvesters. The analytical model was verified by the measured results obtained from the initial prototype. The validated analytical model was successfully applied to optimize the harvester. Two more generator prototypes were further built and tested after the optimization study. The optimized harvester using three stacked opposing permanent magnets could achieve a normalized power density of 12,655 μWcm−3 g−2 at 9.9 Hz frequency with 0.22 g acceleration, which is significantly higher than other reported electromagnetic vibration energy harvesters.

Resonant Frequency Reduction of Vertical Vibration Energy Harvester by Using Negative-Stiffness Magnetic Spring

This work studies the resonant frequency reduction of vibration energy harvesters so as to adapt low-frequency ambient vibrations. In a typical electromagnetic vibration energy harvester, it is common sense that the resonant frequency decreases with the spring stiffness. However, the mass gravity will result in a large initial deformation of the spring with small stiffness when the energy harvester is vertically installed. To solve the problem, this work proposes a method of resonant frequency reduction by adding a negative-stiffness magnetic spring which is arranged symmetrically at the two sides of the equilibrium point. The theoretical expression of resonant frequency is derived based on magnetic field calculation. Comparisons between the energy harvesters with and without negative-stiffness magnetic spring are implemented through simulations and experiments. The results show that the resonant frequency of the vertical energy harvester can be reduced as expected without an increase of initial spring deformation by using the negative-stiffness magnetic spring. This work can provide an effective approach to designing energy harvesters for applications with low-frequency vibrations.

Design and analysis of a non-resonant rotational electromagnetic harvester with alternating magnet sequence

This paper proposed a portable non-resonant rotational electromagnetic vibration energy harvester using magnetic spring to scavenge kinetic energy from low-frequency human motion. Lagrange equations were established to study the dynamic characteristics of the harvester. MATLAB/Simulink was adopted to analyze the output performance at different excitation frequencies. A prototype has been fabricated for experiment, and the measured results are compared with the theoretical analysis. The energy harvester could respond to diverse vibration excitation. When external excitation frequency is 6 Hz, the output voltage and power density of the electromagnetic energy harvester are 2.2 V and 0.024 W·mm−3 respectively. Four LEDs are alight when external excitation frequency is 5 Hz. It is indicated that the electromagnetic energy harvester based on the magnet spring can efficiently harvest low frequency vibration energy at low frequencies. This work made a significant step toward energy harvesting from human motions. It has potential applications in self-powered portable electronics.

Material modeling of frequency, magnetic field and strain dependent response of magnetorheological elastomer

Accurate modeling of material behavior is very critical for the success of magnetorheological elastomer-based semi-active control device. The material property of magnetorheological elastomer is sensitive to the frequency, magnetic field and the input strain. Additionally, these properties are unique for a particular combination of matrix and the filler loading. An experimental-based characterization approach is costly and time consuming as it demands a large amount of experimental data. This process can be simplified by adopting material modeling approach. The material modeling of magnetorheological elastomer is an extension of conventional viscoelastic constitutive relations coupled with hysteresis and magnetic field sensitive attributes. In the present study, a mathematical relation to represent the frequency, magnetic field and strain dependent behavior of magnetorheological elastomer is presented. The viscoelastic behavior is represented by a fractional zener element and the magnetic field and strain dependent attributes incorporated in the model by a magnetic spring and linearized Bouc-–Wen element, respectively. The proposed model comprised of a total of eight parameters, which are identified by minimizing the least square error between the model predicted and the experimental response. The variations of each parameter with respect to the operating conditions are represented by a generalized expression. The parameters estimated from the generalized expression are used to assess the ability of the model in describing the dynamic response of magnetorheological elastomer. The proposed model effectively predicted the stiffness characteristics with an accuracy, more than 94.3% and the corresponding accuracy in predicting the damping properties is above 90.1%. This model is capable of fitting the experimental value with a fitness value of more than 93.22%.

A Study on the Energy-Harvesting Device with a Magnetic Spring for Improved Durability in High-Speed Trains.

Durability is a critical issue concerning energy-harvesting devices. Despite the energy-harvesting device’s excellent performance, moving components, such as the metal spring, can be damaged during operation. To solve the durability problem of the metal spring in a vibration-energy-harvesting (VEH) device, this study applied a non-contact magnetic spring to a VEH device using the repulsive force of permanent magnets. A laboratory experiment was conducted to determine the potential energy-harvesting power using the magnetic spring VEH device. In addition, the characteristics of the generated power were studied using the magnetic spring VEH device in a high-speed train traveling at 300 km/h. Through the high-speed train experiment, the power generated by both the metal spring VEH device and magnetic spring VEH device was measured, and the performance characteristics required for a power source for wireless sensor nodes in high-speed trains are discussed.

Design of a broadband piezoelectric energy harvester with piecewise nonlinearity

In this study, a novel broadband piezoelectric vibration energy harvester (VEH) is constructed using piecewise nonlinearity. The VEH consists of a piezoelectric cantilever beam and a cylindrical cam-roller-spring structure that can produce negative stiffness and piecewise nonlinearity. The designed piecewise nonlinear force consists of two sections. The first section keeps the nonlinear force small, so that the VEH generates a high peak power, and the second section makes the nonlinear force increase sharply, so that the VEH has a wide bandwidth. Therefore, the designed VEH has higher peak power and wider bandwidth than those VEHs based on smooth magnetic nonlinearity or spring nonlinearity. Firstly, a dynamic model is developed and the steady-state periodic responses are obtained by the average method. Then, the influences of the structure parameters of the cam-roller-spring on the performance of the VEH are studied. The results show that compared with the linear system, the piecewise nonlinearity can increase the peak voltage from 28.9 to 64.6 V, increasing by 123%; it can increase the peak power from 0.84 to 4.17 mW, increasing by 396%; and it can increase the operating frequency range from 0.99 to 6.48 Hz, increasing by 554%. Finally, the energy harvesting performance of the designed VEH is compared with the widely used magnet-type and spring-type VEHs, in which the nonlinear forces are smooth. The results show that the proposed VEH has a 9.67% increase in peak power, a 79.2% increase in the frequency band, and a 4.2% increase in maximum efficiency than the magnet-type VEH; and has a 23.5% increase in peak power, a 5.01% increase in the frequency band, and an 8.8% increase in maximum efficiency than the spring-type VEH.

Design and Preliminary Testing of a Magnetic Spring as an Energy-Storing System for Reduced Power Consumption of a Humanoid Arm

The increasing use of robots in the industry, the growing energy prices, and higher environmental awareness have driven research to find new solutions for reducing energy consumption. In additional, in most robotic tasks, energy is used to overcome the forces of gravity, but in a few industrial applications, the force of gravity is used as a source of energy. For this reason, the use of magnetic springs with actuators may reduce the energy consumption of robots performing trajectories due their high-hardness magnetic properties of energy storage. Accordingly, this paper proposes a magnetic spring configuration as an energy-storing system for a two DoF humanoid arm. Thus, an integration of the magnetic spring system in the robot is described. A control strategy is proposed to enable autonomous use. In this paper, the proposed device is modeled and analyzed with simulations as: mechanical energy consumption and kinetic energy rotational and multibody dynamics. Furthermore, a prototype was manufactured and validated experimentally. A preliminary test to check the interaction between the magnetic spring system with the mechanism and the trajectory performance was carried out. Finally, an energy consumption comparison with and without the magnetic spring is also presented.

Multi-Capsule Endoscopy: An initial study on modeling and phantom experimentation of a magnetic capsule train

Capsule endoscopy offers increased patient comfort and improved visibility of the entire gastrointestinal (GI) tract. Besides imaging, numerous literary studies on capsule endoscopy have demonstrated drug delivery, navigation strategies, tactile sensing for tumor diagnosis, and biopsy. Yet, the size limitation hampers the availability of multiple features within a single capsule. In an effort to increase the space and functionality, we propose the use of multiple capsules. All capsules together form a capsule-train, whose wagons are connected with magnetic push/pull forces. Magnets located on each capsule form the virtual magnetic spring. The presence of a preset gap allows for joint tasks on the targeted tissue. The gap in-between capsules also ensures ease of motion throughout the GI, while negating the risk of clinching of tissue parts in between the capsules. Designed capsule train with two capsules successfully traveled through straight phantom without breaking connection for typical bowel speed. Also, same experiment is repeated with higher (2 × to 16 × of expected) speeds to inspect possible abrupt conditions, where capsules traveled together without any disconnection while maintaining constant distance in-between. Experiment results successfully imitate the developed magnet spring model (10–30% mismatch) even with ignored friction forces and camera pixilation errors. As future work, we will be working on adapting the capsule train for curved trajectories and perform demonstrations on ex-vivo animal bowel models. With further development, magnetically connected multi-capsule train can be adapted to clinic for improved functionality and multitasking through the GI tract.