圆柱形推拉式电磁铁的电磁力数值算法

Numerical Algorithm of Electromagnetic Force of Cylindrical Push-Pull Electromagnet

电磁力是推拉式电磁铁非常重要的参数,但由于磁场的非线性变化,解析计算困难。针对这一问题,利用柱状坐标系下的磁矢量势理论求解圆柱形推拉式电磁铁的电磁力。将整个螺线管磁场划分为多个子域并明确边界条件得到可求数值解的子域磁矢量方程组,再通过MATLAB软件编程实现磁矢量势、电感和电磁力等电磁特性数据的计算。对比有限元中铁芯磁导率分别为恒定值10 000和电工软铁的B-H曲线两种情况,说明了该数值算法的计算准确度及误差变化趋势,并分析了误差形成的原因。随着电流的加大铁芯会发生磁饱和,当磁饱和问题不严重时,数值算法的计算结果具有高准确度;随着电流的增加,铁芯发生磁饱和后误差迅速增加。实验中给圆柱形推拉式电磁铁施加不同大小的励磁电流,得到的输出推力结果与理论分析相符。

Electromagnetic force is a very important parameter for push-pull solenoids,but it is difficult to calculate analytically due to the nonlinear variation of the magnetic field.Aiming at this problem,To address this problem,the use of magnetic vector potential theory in a columnar coordinate system was investigated to solve the electromagnetic force of a cylindrical push-pull electromagnet.The whole solenoid magnetic field was divided into several sub-domains and the boundary conditions were defined to obtain the sub-domain magnetic vector equations which can be solved numerically,and then the electromagnetic characteristic data such as magnetic vector potential,inductance and electromagnetic force were calculated by MATLAB programming.Comparing the two cases of B-H curves of iron core permeability in finite element with constant value of 10 000 and electric soft iron respectively,the calculation accuracy and error variation trend of this numerical algorithm were illustrated,and the reason for the formation of the error were analyzed.With the increase of current the core will be magnetically saturated,when the magnetic saturation problem is not serious,the calculation result of numerical algorithm has high accuracy.With the increase of current,the error increases rapidly after the core is magnetically satura-ted.In the experiment,different sizes of excitation currents were applied to the cylindrical push-pull electromagnet,and the output thrust results obtained were consistent with theoretical analysis.