Study On The Theory And Application Of Magnetic Force And Magnetic Stiffness Of NdFeB Permanent Magnets

NdFeB permanent magnet(PM)is a kind of rare earth functional material with higher residual magnetic flux density,larger coercivity and magnetic energy product,as well as excellent service performance and high-cost performance,and is widely employed in aerospace,defense and military industry,rail transit,equipment manufacturing,lithography machine,new energy,electronic information,precision measurement,medical equipment,5G supporting applications and other strategic high-tech fields.The magnetic force and magnetic stiffness between PMs are one of the basic problems in the application of PMs.The magnetic force and magnetic stiffness affect the working performance and stability of the system,and are important parameters for system design and control.Therefore,it is very important to accurately evaluate the magnetic force and magnetic stiffness between PMs,and it is necessary to establish an accurate and easyto-calculate mathematical theoretical formula model of the magnetic force and magnetic stiffness.However,due to ignoring some parameters,the existing magnetic force mathematical theory formula model has some shortcomings,such as inaccurate model,many restrictions on use,and difficulty in solving.The mathematical theoretical model of the main magnetic stiffness and cross-coupling magnetic stiffness between PMs is not perfect.It brings inconvenience and even difficulties to the calculation and evaluation of magnetic force and magnetic stiffness in PMs’ applications.Thus,in order to evaluate the magnetic force and magnetic stiffness accurately between NdFeB PMs,the mathematical theoretical formula model and calculation method of the magnetic force and magnetic stiffness between NdFeB PMs are given in this paper.On this basis,the applications of PMs are discussed in PM spring and magnetic microrobot drive.The main research work includes:(1)Based on the static magnetic field analysis method,a parameterized mathematical theoretical model of the magnetic force and magnetic stiffness between NdFeB PMs is established,and the effect of the PM’s relative magnetic permeability on the surface magnetic charge density is explained.On this basis,the mathematical theoretical models of magnetic force and magnetic stiffness between two cylindrical PMs,two cuboid PMs,cylindrical and cuboid PMs,with parallel and perpendicular magnetization directions,are deduced in detail.In principle,the internal relationship among the shape,size,position,magnetization direction,relative permeability,residual magnetic flux density and other parameters of NdFeB PM and the magnetic force and magnetic stiffness is revealed.Finally,the efficient solution method to solve the magnetic force and magnetic stiffness mathematical theoretical model is introduced.(2)The magnetic force measurement experimental device is developed.Using this measuring device and the electromagnetic analysis finite element software,the magnetic forces are measured,simulated,and calculated between two cylindrical PMs,two cuboid PMs,cylindrical PM and cuboid PM with parallel and perpendicular magnetization directions.By comparing the magnetic force and magnetic stiffness’ s mathematical theoretical model calculation results,finite element simulation and experimental measurement results,the correctness of magnetic force and magnetic stiffness mathematical theoretical model is verified.The time of magnetic force mathematical theoretical model calculation and finite element simulation is compared,proving the high efficiency of the magnetic force mathematical theoretical model calculation.(3)Aiming at the magnetic force and magnetic stiffness characteristics between two cylindrical PMs,two cuboid PMs,cylindrical PM and cuboid PM whose magnetization directions are parallel and perpendicular to each other,the effect of the PMs’ relative displacement along the three-degree-of-freedom direction on the magnetic force and magnetic stiffness is analyzed by employing the established mathematical theoretical models of magnetic force and magnetic stiffness.Then,the relationship between the PMs’ geometric dimensions and the magnetic force and magnetic stiffness is discussed.The influence of relative displacements and sizes between PMs of different shapes on the magnetic force and magnetic stiffness characteristics is revealed.(4)A variable stiffness PM spring is designed and trial-manufactured by using annular PMs.Firstly,the mathematical theoretical model of the PM spring’s magnetic force and magnetic stiffness is established.The PM spring’s magnetic force and axial magnetic stiffness mathematical theoretical models are verified by finite element simulation and experimental test.Then,the effects of ring PMs’ size,relative displacement,relative permeability,and residual magnetic flux density on the PM spring’s magnetic force and magnetic stiffness are analyzed at different axial displacements,and the PM spring’s magnet size is optimized.Finally,the theoretical analysis of vibration isolation dynamics is carried out for the PM spring.The dynamic model of the massdamping-nonlinear magnetic stiffness system is established,and the steady-state displacement response of the system is solved.The vibration isolation performance of variable stiffness PM spring and conventional constant stiffness mechanical spring is compared and analyzed,and the vibration isolation advantages of PM spring are analyzed.(5)Using the magnetic interaction force between PMs,the reciprocating motion of the pipe magnetic microrobot driven by PMs is studied,and a method of using reciprocating magnetic microrobot to dredge pipe blockage is proposed.The corresponding test device is built.The cylindrical and cuboid PMs are used to drive the magnetic microrobot to reciprocate in horizontal and vertical pipelines,respectively.The magnetic microrobot’s dynamic equation and magnetic driving force mathematical theoretical model are established.The magnetic microrobot’s motion trajectory is obtained by the image processing technology.The effects of driving frequency,liquid flow rate,viscosity,and driving distance on the reciprocating motion characteristics of magnetic microrobots are discussed.Finally,the impact and move blockage tests are carried out by using the cuboid PM to drive a bullet-shaped magnetic microrobot to reciprocate in the pipe,and the impact and movement of pipe blockage are realized.