Theoretical Study Of Giant Magnetostrictive Micromachined Cantilever System

Micromachined cantilever is of great importance in the modern physics and material science. With the development of the microminimization of the devices,the microcantilevers are being used in the magnetic resonance force microscopy and in various micro-electromechanical system (MEMS) devices.In recent years,the successful fabrication of giant magnetostrictive materials offer reliable materials for designing new types of MEMS devices with remote operation.The wide range application of giant magnetostricitive film-substrate cantilever in the magnetic microelectromechanical system(MAGMEMS) makes such a system be one of the most important apparatus in the MEMS.However,the theoretical discussion of the giant magnetostrictive film-substrate cantilever is lagging all along,and some most basic problems are still point in issue. Therefore,this article focuses on the basic theory of bending and loading as well as the twisting deformation of the magnetostrictive micromachined multilayer cantilever,and based on this theory, the further discussion on application and optimization of the cantilever systems in MEMS devices are presented.Firstly,based on the principle of minimal free energy(PMFE) and the mechanical equilibrium equation which is equivalent to the PMFE,a general theory is established using a four parameter bending mechanism.The theory is applicable to the bending problem of the film-substrate cantilever with arbitrary film-to-substrate thickness ratio under an arbitrary point load. With the aid of mechanical equilibrium equation,the bending and loading problem of the film-substrate cantilever is solved analytically.And then,the cantilever bending problem due to isotropic and anisotropic expansion is accommodated into a unified framework.Secondly,the proposed theory is applied to the bending and loading issue of the magnetically isotropic GMF bilayer and trilayer cantilevers.Considering the physical and the geometrical parameters of the cantilever system,the application and optimization of the cantilever system in such micro-electromechanical devices as sensors and actuators are discussed,and then the optimal conditions for MEMS application is presented.Furthermore,the deficiencies that are present in the prevailing theoretical treatment of the actuators are corrected.Some corresponding numerical results are compared with the existing experimental and finite element simulation result.Both of these results are in close agreement,which suggests that the new cantilever theory presented in this paper is reasonable.Thirdly,the bending and the twisting deformation of a film-substrate cantilever with in-plane uniaxial anisotropy is discussed by combining the theory of magnetization reversal and the four parameter model for the cantilever system.For a relatively soft substrate,the mechanical damping is not considered in the discussion.Therefore,the bending and twisting procedure is almost determined by the magnetization reversal.The torsional hystersis of the cantilever calculated by this model qualitatively agrees with the recent experimental result.This fact suggests that our theory is effective in characterizing the bending and twisting effect of the cantilever with uniaxial anisotropy. The torsion angle is much sensitive to the magnitude and direction of the external field,when the field is greater than its coercivity and applied around the hard axis.This property can be applied to enhance the sensitivity of the MAGMEMS devices,which is also pointed out by Tiercelin et al.in their theoretical prediction and experiment.This fact demonstrates again the validity of our formulation developed in this article.Finally,the bending problem of a cantilever composed of thick film Giant MagnetoStrictive Composites(GMSC) and a non-magnetic substrate is studied by using the four parameter model. There may be a magnetostrictive strain gradient in the GMSC films,and hence we adopted the polynomial expansion methods that have been developed to depict the residual strain and corresponding gradient in the epitaxial films.And an effective bending theory for the cantilever actuated by GMSC thick film is presented for the first time.The results indicate that the strain gradients are favorable for the thick films in enhancing bending deflection of the cantilever,namely the resolution of the corresponding MAGMEMS devices.An experimental method for measuring the magnetostriction strain and its gradient is proposed on the basis of curvature measuring technique of the bent cantilever.By modulating the thickness of the substrate of the cantilever(for instance,etching),one can measure the magnetostrictive biaxial strain(stress) and its gradient definitely.