高精度TMR加速度计中圆柱磁体空间磁场线性区间的计算与仿真

Spatial magnetic field distribution of cylindrical permanent magnet for high resolution tunneling magnetoresistive accelerometer

基于高灵敏隧道磁电阻的高精度加速度计中,圆柱磁体数学模型的确定和探寻磁体空间磁场分量线性分布区间是实现加速度高精度测量的关键。针对这个问题,采用磁体空间磁场分布的理论解析计算方法,对磁体空间磁场的分布进行了矢量分解,重点分析计算了磁体外空间磁场的线性分布范围。采用MATLAB软件,获得了磁场各分量在轴向和径向上的变化规律,找出了线性分布的最佳空间位置,并运用COMSOL软件进行验证。依据计算结果,总结出了磁体空间磁场分量的线性区间宽度、径向分量最大值、灵敏度这三者与磁体尺寸、磁化强度、空间位置之间的变化关系,为高精度隧道磁电阻加速度计的设计提供理论依据。

Permanent magnet is the core part of the tunnel magnetoresistive （TMR） accelerometer, in which the spatial magnetic field distribution of the permanent magnet is essential to achieve high resolution performance. In order to construct an optimized magnetic field distribution in a TMR accelerometer, the mathematical modeling of cylindrical permanent magnets and the analysis of the magnetic field linearity are presented in this paper. The equivalent current model was established for the axially magnetized cylindrical permanent magnet and the mathematical formula of the magnetic induction intensity of any point outside the cylinder was derived using the Biot-Savart law and the superposition principle of magnetic field. Based on the mathematical model, the magnetic induction intensity was calculated by MATLAB. The axial and radial magnetic field distribution of a cylindrical permanent magnet was obtained and verified by COMSOL software. Based on the calculated results, the dependence between the spatial characteristics of the magnetic field generated by the cylindrical magnets and the magnets’ dimensions and magnetization intensities was summarized, which provide a theoretical basis for the design of high precision TMR accelerometer.