徐耀晖, 朱福文, 高彩霞,等.永磁直线同步电机力角特性偏移研究[J].河南理工大学学报（自然科学版）,2025,44(3):138-146.

XU Y H, ZHU F W, GAO C X, et al. Study on force-angle characteristics of permanent magnet linear synchronous motor[J]. Journal of Henan Polytechnic University(Natural Science) , 2025, 44(3): 138-146.

永磁直线同步电机力角特性偏移研究

徐耀晖1,2, 朱福文1, 高彩霞2, 赵宝森3, 王翰4, 缪庆彬5

1.焦作煤业（集团）有限责任公司 机电部，河南 焦作  454000；2.河南理工大学 电气工程与自动化学院，河南 焦作  454000；3.焦作煤业（集团）赵固（新乡）能源有限责任公司，河南 新乡  453000；4.焦作煤业（集团）新乡能源有限公司 机电科，河南 新乡  453000；5.焦作煤业（集团）有限责任公司 中马村矿，河南 焦作 454171

摘要: 目的 力角特性是永磁直线同步电机（permanent magnet linear synchronous motor，PMLSM）运行稳定性的重要特性，是评价电机性能和控制电机的依据。但在低频工况下，PMLSM的力角特性因电枢电阻的影响而存在偏移现象，进而导致利用现有忽略电枢电阻的力角特性分析计算电机低速运行特性会存在较大的偏差。为此，对PMLSM低频低速下的力角特性偏移原因及其影响规律展开深入研究，并确定力角特性偏移的临界条件。  方法 首先，建立考虑电枢电阻的PMLSM力角特性的解析模型，分析力角特性产生偏移的原因；其次，基于建立的解析模型，通过峰值推力及其对应的功角研究不同因素对推力特性的影响规律，并建立有限元模型对分析结果进行验证。然后，利用解析法确定PMLSM力角特性产生偏移的临界条件，即当力角偏移系数k（k=X_t/R_a）≥11.43可以近似认为峰值推力对应的功角等于90°，可以忽略力角偏移现象；最后，搭建PMLSM样机测试平台，将有限元结果、实验结果与理论分析进行比较，验证推力特性曲线产生偏移的原因和临界条件。  结果 研究发现，与常用的忽略电枢电阻的力角特性相比，PMLSM力角特性向左偏移。力角特性偏移现象会导致两方面的影响，一是导致推力和电枢电流的关系不单调，出现小负载的电流比大负载的还要大的现象，二是低频运行时峰值推力减小，因此低频时不能保持恒推力运行。 结论 研究结果对PMLSM的设计和精确控制具有重要的参考价值。

关键词:永磁直线同步电机;力角特性;力角特性偏移;临界条件

doi: 10.16186/j.cnki.1673-9787.2023060026

基金项目:国家自然科学基金资助项目（52177039）；河南省自然科学基金资助项目（252300421328）；河南省高校基本科研业务费专项资金资助项目（NSFRF240306）

收稿日期:2023/06/09

修回日期:2023/10/27

出版日期:2025-04-18

Study on force-angle characteristics of permanent magnet linear synchronous motor

XU Yaohui1,2, ZHU Fuwen1, GAO Caixia2, ZHAO Baosen3, WANG Han4, MIAO Qingbin5

1.Mechanical and Electrical Department， Jiaozuo Coal Industry（Group）， Jiaozuo  454000， Henan， China；2.School of Electrical Engineering and Automation， Henan Polytechnic University， Jiaozuo  454000， Henan， China；3.Jiaozuo Coal（Group） Zhaogu（Xinxiang） Energy Co.， Ltd.， Xinxiang  453000， Henan， China；4.Mechanical and Electrical Department， Jiaozuo Coal（Group） Xinxiang Energy Co.， Ltd.， Xinxiang  453000， Henan， China；5.Zhongmacun Mine， Jiaozuo Coal（Group） Co.， Ltd.， Jiaozuo  454171， Henan， China

Abstract: Objectives The force angle characteristic is an important characteristic to analyze the operation stability of permanent magnet linear synchronous motor （PMLSM）， and it is the basis of designing and controlling motor. The influence of armature resistance was generally ignored in the existing calculation of force angle characteristics. However， due to the influence of armature resistance at low speed， PMLSM force angle characteristic has obvious deviation phenomenon. Therefore， using the existing force angle characteristics to calculate the performance of PMLSM will have a large deviation， which cannot meet the actual work needs of the motor. Hence， in this paper， the basic reasons and critical conditions for the deviation were investigated， and the critical conditions of the force angle characteristic offset were determined. Methods Firstly， an analytical model of PMLSM force angle characteristics considering armature resistance was established， and the reason for the deviation of force angle characteristics was analyzed. Secondly， based on the established analytical model， the influence of different factors on the force angle characteristics was studied by the peak thrust and its corresponding power angle， and the finite element model was established to verify the analysis results. Finally， the critical condition of PMLSM force angle characteristic offset was determined by analytical method. When the force angle offset coefficient k（k=X_t/R_a） is ≥ 11.43， it can be approximated that the force angle corresponding to the peak thrust is equal to 90°， and the phenomenon of force angle offset can be ignored. The causes of the deviation of the force angle characteristic curve and the correctness of the critical conditions were verified by finite element simulation and experimental results verify. Results This study found that compared with the commonly used force angle characteristics that ignore armature resistance， the force angle characteristics of PMLSM are shifted to the left. The phenomenon of force angle characteristic deviation can lead to two effects. One is that the relationship between thrust and armature current is not monotonic， resulting in a phenomenon where the current of small loads is larger than that of large loads. The peak thrust decreases during low-frequency operation， so constant thrust operation cannot be maintained at low frequencies. Conclusions The research in this paper has important reference value for the design and precise control of PMLSM.

Key words: permanent magnet linear synchronous motor; force angle characteristics; force angle characteristic offset; critical conditions