Calculation Method of Magnetic Force of Hybrid Electromagnets Based on Nonlinear Inductance
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摘要:
为提高混合电磁铁磁力计算的准确性和效率，综合考虑解析法计算速度快和有限元法计算精度高的优势，提出一种基于非线性电感的混合电磁铁磁力计算方法. 首先，分析混合电磁铁电感与电流的关系，建立考虑磁饱和的非线性电感模型；然后，采用等效面电流法，将 2 种典型的混合电磁铁结构（结构a、结构b）等效为多电磁线圈的纯电磁铁结构，进而利用能量平衡法推导出通用于串联磁路型混合电磁铁磁力表达式，其中非线性电感的参数变量由有限元仿真法拟合得到. 研究结果表明：结构 a 和结构 b 利用本文所述方法得到的电磁力计算结果与传统有限元仿真结果的平均偏差为2.54%和2.37%，结构a与实验测量的平均偏差为2.63%，且与传统有限元法相比，计算效率极大提升，即本文所述方法通过较少任务的有限元仿真得到远高于现有解析公式准确性的电磁力计算结果.
Abstract:In order to improve the accuracy and efficiency of the magnetic force calculation of hybrid electromagnets, this paper took into account the advantages of fast calculation speed of the analytical method and high calculation accuracy of the finite element method and proposed a calculation method of the magnetic force of hybrid electromagnets based on the nonlinear inductance. The paper first analyzed the relationship between the inductance and current of the hybrid electromagnet and established a nonlinear inductance model considering magnetic saturation. Then, the equivalent surface current method was used to equate two typical hybrid electromagnet structures (structure a, structure b) into pure electromagnet structures with multi-electromagnetic coils. The magnetic force expression of the series magnetic circuit type hybrid electromagnet was derived by using the energy balance method, in which the parameter variables of the nonlinear inductance model were fitted by the finite element simulation method. The research results show that the average deviations between the electromagnetic force calculation results of structures a and b obtained by the proposed method and the traditional finite element simulation are 2.54% and 2.37%, and the average deviation between structure a and experimental measurement is 2.63%. Compared with the traditional finite element method, the calculation efficiency is greatly improved. In other words, the proposed method obtains electromagnetic force calculation results that are much more accurate than the existing analytical formulas through finite element simulation with fewer tasks.
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图 7 气隙z运动到z1时线圈磁链-电流曲线
Figure 7. Flux-current curves of coil when the air gap z moves to z1
图 11 系统xOz平面磁感应强度分布
Figure 11. Magnetic induction intensity distribution of system on xOz plane
图 12 工作气隙为5～15 mm时电磁力随气隙高度的变化曲线
Figure 12. Variation curves of electromagnetic force with air gap height at working air gap of 5–15 mm
图 14 工作气隙为8～15 mm时电磁力随气隙高度的变化曲线
Figure 14. Variation curves of electromagnetic force with air gap height at working air gap of 8–15 mm
表 1 仿真参数
Table 1. Simulation parameters
参 数 数 值 hpm/mm 6 N/匝 550 Hc/（A·m−1） 5.8 × 105 额定电磁线圈电流 I/A 2 等效线圈a（b）电流/A 2.67 额定气隙/mm 10 
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