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[摘要]
【目的】针对复杂槽极配合、多相配置及不同绕组形式下电机绕组排布设计依赖经验、效率低且易遗漏可行方案的问题,本文提出一种基于搜索与剪枝的绕组自动排布方法,为集中绕组、分布绕组及多相绕组的统一生成与筛选提供自动化求解思路。【方法】将绕组排布问题抽象为带约束的线圈边组合搜索问题,构建基于回溯的深度优先搜索框架,以线圈边配对方式生成候选绕组方案。采用位掩码记录槽位占用状态,实现快速冲突检测与合法性判定。利用增量复数和更新基波及谐波合成相量,避免重复全量求和。为缩减实际搜索规模,引入对称规约、三角不等式可达上界和沿当前合成相量方向的投影上界,对不可能达到目标绕组系数的分支进行剪枝。【结果】三相与五相典型算例表明,所提方法能够在不同槽极配合下自动生成基波绕组系数较高的可行绕组排布方案。相较于组合枚举方法,本文方法显著减少了搜索节点数和计算时间,典型算例剪枝率均超过95%。40槽26极五相永磁同步电机有限元仿真结果表明,本文方法所得绕组方案的平均转矩为14.570 N·m,略高于星线图法的14.547 N·m;转矩脉动率为0.067 4%,低于星线图法的0.075 6%;气隙磁密波形总谐波畸变率为9.95%,低于星线图法的11.18%。【结论】本文方法能够在保证可行解搜索完整性的基础上有效缩减实际搜索空间,并获得具有基波绕组系数高且低阶谐波含量低的绕组排布方案。该方法适用于复杂槽极组合、多相配置及多种绕组形式下的快速设计与方案对比,可为后续电磁优化、谐波抑制和转矩脉动抑制提供前端设计工具。
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[Abstract]
[Objective] To address issues of experience dependence, low efficiency, and possible omission of feasible solutions in motor winding layout design under complex slot-pole combinations, multiphase configurations, and different winding forms, a search-and-pruning-based automatic winding layout method is proposed. The method provides an automated solution framework for the unified generation and screening of concentrated windings, distributed windings, and multiphase windings. [Methods] The winding layout problem was formulated as a constrained coil-side combination search problem. A backtracking-based depth-first search framework was constructed to generate candidate winding layouts through coil-side pairing. Bit-mask representation was used to record slot occupancy, enabling fast conflict detection and feasibility checking. The synthesized fundamental and harmonic phasors were updated through incremental complex summation, which eliminated redundant full-range summation calculations. To narrow down the actual search space, symmetry reduction, a triangle-inequality reachability upper bound, and a projection upper bound along the current synthesized phasor direction were adopted to prune invalid branches that fail to satisfy the target winding factor. [Results] Representative three-phase and five-phase case studies showed that the proposed method can automatically generate feasible winding layout schemes with high fundamental winding factors under different slot-pole combinations. Compared with combinational enumeration method, the proposed method significantly reduced the number of visited search nodes and computation time, with pruning rates exceeding 95% in typical cases. Finite element simulation of a 40-slot 26-pole five-phase permanent magnet synchronous motor showed that the average torque of the winding layout obtained by the proposed method was 14.570 N·m, slightly higher than the 14.547 N·m obtained by the star diagram method. Its torque ripple of 0.067 4% was lower than 0.075 6% obtained by the star diagram method, and the total harmonic distortion of the air-gap flux density waveform reached 9.95%, also lower than the 11.18% given by the star diagram method. [Conclusion] The proposed method effectively reduces the practical search space while ensuring the completeness of feasible solution exploration, thereby yielding winding configurations with a high fundamental winding factor and low low-order harmonic content. It is applicable to rapid design and scheme comparison for complex slot-pole combinations, multiphase configurations and diverse winding forms, providing a reliable front-end design tool for subsequent electromagnetic optimization, harmonic suppression, and torque ripple mitigation.
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