| As a new type of functional material,giant magnetostrictive materials(GMM)have been rapidly developed due to their high Curie temperature,magnetic-mechanical coupling coefficient,frequency response characteristics,and magnetostrictive strain.These characteristics have been widely used to drive electro-hydraulic servo valves,vibration control,energy harvesting,active installation,drive mirrors,and in other applications.Giant magnetostrictive actuator(GMA)is based on the Joule effect of GMM rod.Under the action of driving magnetic field,GMM rod can produce axial displacement to realize the displacement and force output of GMA.However,since the GMM rod itself has a hysteresis nonlinear phenomenon,there is a hysteresis non-linear phenomenon exists between input currents and output displacements of GMA seriously damaging the nonlinear stability of GMA.If a GMA is placed in non-linear unstable working conditions,long-term prediction and control of GMA system becomes impossible,which seriously hinders its application in many important fields.Currently,most of the researches on how to improve the stability of GMA are focused on the control strategy.There is no in-depth study on the causes of GMA instability,and there is a serious lack of complete theoretical guidance for GMA structural stability design.In this paper,a GMA is designed with the GMM rod as the core component,and the following research work has been completed around the vibration characteristics of GMA.(1)The magnetic circuit mainly provides a driving magnetic field for the superimposed excitation magnetic field and the bias magnetic field for the GMA,and the strength of the driving magnetic field directly affects the output displacement of the GMA.Therefore,the structural parameter design of GMA magnetic circuit is the key factor to improve the efficiency of electromagnetic conversion and give full play to the characteristics of GMM rod.In this study,the uniformity of magnetic field intensity on the center axis of GMM rod is regarded as the evaluation standard and main design principle by analyzing the workingprinciple of GMA.Based on the given output displacement and output force,the structural parameters of the selection of bias magnetic field,GMM rod,excitation coil and magnetic circuit are designed respectively.(2)According to the magnetic path Kirchhoff's law,Ampere's Magnetic Circuit Law,Gaussian flux law and Ohm's law,the mathematical model of the GMA magnetic circuit is established,and the influence of the structural parameters of the GMA magnetic circuit on the magnetic field intensity of the centeal axis of the GMM rod is derived.The laws existed between the structural parameters of the magnetic circuit components and the magnetic field intensity and the uniformity of the magnetic field intensity is obtained based on Ansoft Maxwell electromagnetic finite element analysis.Finally,the GMA magnetic field theoretical calculation and the finite element simulation results are compared.The results show that the magnetic field distribution of GMA is more uniform,and the uniformity rate is increased to 98.65%,which verifies the correctness of the design.(3)Non-linear hysteresis dynamic differential equation of GMA system was established according to hysteresis non-linear equation,Jiles-Atherton hysteresis non-linear model,quadratic domain rotation model and GMA structural dynamics principle by analyzing the working principle of GMA.The primary resonance of GMA non-linear hysteresis dynamic system was analyzed by multiple scales method and system amplitude-frequency response curve equation was obtained.MATLAB numerical simulation was used to evaluate the mapping between different values of damping coefficient,magnetic field strength,prestress,nonlinear stiffness and output response amplitude of GMA system.In addtion,the multiscale method and singularity theory are used to determine the bifurcation characteristics of the residual dimension 2 of the system.Then,the Melnikov function method is applied to the threshold condition of the chaotic response of the system to obtain the sense of Smale horseshoe transformation.Furthermore,the mathematical model is solved to investigate the system response to the excitation force.Accordingly,including the bifurcation diagram,Maximum Lyapunov exponential graph,the time domain waveform,phase trajectorydiagram,Poincaré map and amplitude spectrum are obtained.Finally,experimental simulation is verified using Adams software.The obtained results showed that for parameter values assumed here,GMA system showed "jump" and hysteresis phenomena under the action of disc spring and excitation coil.Under certain parameter values,chaos is observed in GMA system.(4)Under the given parameters of GMA,the system is simulated in detail.By solving the bifurcation diagram of the response of the system with the parameters in the system,to determine the range of values of each parameter when chaos is used.Finally,with the Fourth-order Runge-Kutta method,the time domain waveform,phase trajectory diagram,Poincaré map and amplitude spectrum of the parameters of the system are drawn,and the four graphs are analyzed.The results show that the system damping coefficient possesses a periodic characteristic in the intervals(0.05,0.215),(0.38,0.43),(0.51,0.55),(0.61,0.765),and(0.765,1.00).The system stiffness coefficient has a periodic property in the intervals(0.07,0.48),(0.735,0.765),(0.835,0.865),and(0.865,1.00).Moreover,the coefficient of the cubic stiffness term of the disc spring indicates a periodic behavior in the intervals(0.1,0.145)and(0.355,0.38).Furthermore,the exciting force presents a periodic property in the intervals(0.05,0.225),(0.835,0.86),and(0.88,1.00).Finally,the excitation frequency is periodic in the intervals(0.465,0.59),(0.645,0.67),and(0.72,1.00).In summary,this paper studies the design and characteristics of GMA: establishes the theoretical basis of the research on the bifurcation and chaos characteristics of GMA hysteresis nonlinear dynamics system;changing the parameters can make the system produce chaos movement,or avoid chaos movement,and can control the vibration characteristics of the system.The results provide theoretical basis and technical support for GMA structural stability design. |
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