【作者】 刘峰；

【导师】 王秀和；

【作者基本信息】 山东大学 ， 电气工程， 2025， 博士

【摘要】 内置式永磁同步电机凭借高效率、高功率/转矩密度、宽调速范围和强容错能力等诸多优异的特性在传统装备制造业和现代综合交通运输体系中得到了广泛应用。然而,受限于复杂拓扑结构,内置式永磁同步电机在多物理场的快速精确计算和协同优化设计上仍然面临诸多严峻的挑战。一方面,在现有计算内置式永磁同步电机电磁场、温度场和应力场的方法中,有限元法和计算流体力学具有较高的计算精度,但建模工作量较大且计算耗时较长;解析法计算耗时较短且易与优化设计模型进行拓展,但在对复杂拓扑结构进行处理时存在明显的过度等效现象,无法准确计及结构复杂性和材料非线性等多种因素的影响,难以满足高精度计算需求;尚缺乏能够有效兼顾快速性和准确性的计算方法。另一方面,内置式永磁同步电机的优化设计需要全面考虑多物理场的综合表现以及需要充分计及不同物理场之间存在的深度强耦合特征,但现有优化设计模型严重受限于多物理场计算方法的局限性,无法实现高效的多场协同优化设计。针对现有研究的不足,本文围绕内置式永磁同步电机提出了电磁场、温度场和应力场快速精确解析计算模型,在准确计及结构复杂性、材料非线性、传热多变性和应力集中性的同时实现了关键电磁、温度和应力特性的快速精确解析计算。进一步,在此基础上,与智能机器学习语言和先进多目标优化算法相结合,提出了能够充分计及多场深度强耦合特征的多物理场高效高品质协同解析优化设计模型,克服了现有优化设计模型多场耦合实现困难且优化效率低下等诸多弊端,为实现高效的多场协同优化设计奠定了坚实的理论基础和技术支撑。主要研究工作概要如下:(1)开发新型主从子域细分技术,通过主子域和从子域交替连接而成的组合型扇形子域最大程度地还原复杂转子结构,进而提出基于改进子域法的电磁场计算模型,在准确计及结构复杂性和材料非线性的同时实现关键电磁特性的快速精确解析计算。针对有限元法建模工作量较大且计算耗时较长以及子域法难以有效应对复杂转子结构的问题,提出了基于改进子域法的电磁场快速精确解析计算模型。首先,为全面考虑内置式永磁同步电机的复杂转子结构,开发了新型主从子域细分技术:将永磁体的径向极沿径向均匀地细分为多个组合型扇形子域,每个组合型扇形子域均由一个主子域和一个从子域交替连接而成,并且每个主子域内半径上的左右两侧端点与原始拓扑中的对应边界相重合,以避免对于复杂转子结构的过度等效,保障精确子域模型的计算精度;基于面积守恒和定位半径不变的原则,将永磁体的切向极、中间磁桥和双边磁桥细分成单层扇形子域,并且在永磁体的切向极与径向极以及永磁体的切向极与中间磁桥的连接处分别设置从子域和辅助连接域,以保障精确子域模型的顺利构建和求解。其次,基于精确子域模型,再根据磁场连续性定理,对各个子域上矢量磁位的通解进行了推导。在此基础上,引入等效磁路法和等效面电流法,充分计及了转子磁桥和定子铁心的饱和效应。然后,采用基于改进子域法的电磁场计算模型对电机电磁场进行了计算,实现了内置式永磁同步电机磁密、反电动势和转矩等关键电磁特性的快速精确解析计算。最后,采用有限元法和样机电磁场实验对计算结果进行了验证,并对精确子域模型在不同拓扑结构下的普适性进行了讨论,证实了提出的电磁场计算模型的准确性、有效性和实用性。(2)鉴于热传递的强三维空间特征,开发新型多层热域细分技术,精准捕获x-y平面上关键部件的复杂几何特征以及z轴截面旋转变化的随机性,进而提出基于改进热域法的三维温度场计算模型,充分计及电磁场与温度场之间的深度强耦合特征以及热源非均匀分布和不确定节点信息等因素的影响,实现关键温度特性的快速精确解析计算。针对计算流体力学建模工作量较大且计算耗时较长以及集总参数热网络和解析法计算能力有限的问题,提出了基于改进热域法的三维温度场快速精确解析计算模型。首先,为全面考虑复杂拓扑结构,同时鉴于热传递具有很强的三维空间特征,开发了新型多层热域细分技术:在x-y平面上,将新型多层热域细分技术与新型主从子域细分技术相结合,以精准捕获永磁体和槽内绕组等关键部件的复杂几何特征;在z轴截面上,将不同旋转角度下的永磁体和端部绕组等关键部件沿径向细分为多层热域,以精准捕获实际运行过程中z轴截面随旋转角度变化的随机性;针对绕组的复杂构成,将铜线与绝缘漆、浸渍漆、空隙、槽绝缘和槽楔等其他非导体成分等同视为均匀分布的各向同性导热介质,以保障精确热域模型的计算精度,提升建模和分析效率。其次,基于精确热域模型,再根据热传递理论,对各个热域上的温度分布函数的通解进行了推导。在此基础上,引入等效热路概念和迭代求解策略,并结合有限元法在计算电磁损耗方面的特有优势,充分计及了电磁场与温度场之间的深度强耦合特征以及热源非均匀分布和不确定节点信息等因素的影响。然后,采用基于改进热域法的三维温度场计算模型对电机温度场进行了计算,实现了内置式永磁同步电机全局温度分布、温度变动曲线和部件温度等关键温度特性的快速精确解析计算。最后,采用计算流体力学和样机温度场实验对计算结果进行了验证,并对精确热域模型在不同运行工况下的稳健性进行了讨论,证实了提出的三维温度场计算模型的准确性、有效性和实用性。(3)将质心等效环法、铁木辛柯梁理论和等效弹簧进行创新性结合,开发新型力域细分技术,有效避免精确力域细分过程中对于复杂几何特征的忽略,进而提出基于改进质心等效环法的应力场计算模型,并引入提出的三维温度场计算模型,充分计及转子发热和温度非均匀分布等因素的影响,实现关键应力特性的快速精确解析计算。针对有限元法建模工作量较大且计算耗时较长以及解析法过度依赖应力集中系数的问题,提出了基于改进质心等效环法的应力场快速精确解析计算模型。首先,为全面考虑复杂转子结构,将质心等效环法、铁木辛柯梁理论和等效弹簧进行创新性结合,开发了新型力域细分技术,对内置式转子进行了精确力域细分:将中间磁桥视为长方体模型,结合牛顿第三定律得到关于中间磁桥的形变函数;将双边磁桥视为直梁模型,通过分析形变过程中的受力情况得到关于双边磁桥的形变函数;将转子极靴视为弹簧模型,通过捕捉径向刚度和切向刚度得到关于转子极靴的形变函数;进而得到中间磁桥、双边磁桥与转子极靴之间的受力平衡方程,有效避免了精确力域细分过程中对于复杂几何特征的忽略。其次,基于精确力域模型,再根据位移情况,对各个力域上的应力应变函数的通解进行了推导。在此基础上,引入提出的三维温度场计算模型,充分计及了转子发热和温度非均匀分布等因素的影响。然后,采用基于改进质心等效环法的应力场计算模型对电机应力场进行了计算,实现了内置式永磁同步电机转子最大机械应力等关键应力特性的快速精确解析计算。最后,采用有限元法、材料力学拉伸实验和样机应力场实验对计算结果进行了验证,并对精确力域模型在不同参数配置下的灵敏性进行了讨论,证实了提出的应力场计算模型的准确性、有效性和实用性。(4)将提出的多物理场快速精确解析计算模型与智能机器学习语言和先进多目标优化算法进行创新性结合,提出能够充分计及多场深度强耦合特征的多物理场高效高品质协同解析优化设计模型,实现高效的多场协同优化设计。在现有关于多物理场的优化设计模型中,仍然有很多亟需改进的地方。例如,在数据采集阶段,也严重受限于现有方法在计算内置式永磁同步电机电磁场、温度场和应力场时所面临的诸多局限。这不可避免的导致优化设计过程较为繁琐,难以兼顾出色的优化效果和较低的优化成本,无法实现高效的多场协同优化设计,特别是在计及内置式永磁同步电机不同物理场之间存在的深度强耦合特征时。为此,围绕内置式永磁同步电机多物理场高效高品质协同解析优化设计展开了创新性研究。首先,深入探究了内置式永磁同步电机不同物理场之间的耦合作用机制,在提出的电磁场、温度场和应力场计算模型之间搭建信息传递通道,充分计及了多场深度强耦合特征的影响。然后,构建了基于精确子域模型、精确热域模型和精确力域模型的多物理场快速精确耦合分析模型,实现了多重因素影响下内置式永磁同步电机多物理场表现的快速精确计算和全方位评估。进一步,在此基础上,与智能机器学习语言和先进多目标优化算法相结合,提出能够充分计及多场深度强耦合特征的多物理场高效高品质协同解析优化设计模型。进而在兼顾出色的优化效果和较低的优化成本的同时,实现了高效的多场协同优化设计,全面提升了内置式永磁同步电机多物理场的综合表现。最后,采用有限元法、计算流体力学、基于分段田口法的多物理场协同优化设计模型和样机实验验证了提出的多物理场协同解析优化设计模型的准确性、有效性和实用性。更多还原

【Abstract】 The interior permanent magnet synchronous motor(IPMSM)has been widely used in the traditional equipment manufacturing and modern integrated transportation system with many excellent characteristics such as high efficiency,high power/torque density,wide speed range,and strong fault tolerance.However,limited by the complex topology,IPMSM still faces many serious challenges in the fast and accurate calculation as well as cooperative optimization design of multi-physics fields.On the one hand,among the existing methods for calculating the electromagnetic,temperature,and stress fields of IPMSM,the finite element method and computational fluid dynamics have higher computational accuracy,but the modeling workload is larger and the computation is time-consuming.The analytical method is less time-consuming and easy to expand with the optimization design model,but there is an obvious over-equivalence phenomenon in the processing of complex topologies,which cannot accurately account for the influence of various factors such as structural complexity and material nonlinearity,and it is difficult to meet the demand for high-precision calculations.Calculation methods that effectively balance speed and accuracy are lacking.On the other hand,the optimization design of IPMSM needs to comprehensively consider the integrated performance of multi-physics fields and needs to fully account for the deep and strong coupling characteristics between different physical fields.But the existing optimization design models are severely limited by the limitations of the multi-physics field calculation method,which cannot achieve the efficient multi-field cooperative optimization design.To address the shortcomings of existing research,this paper proposes the fast and accurate analytical calculation model of electromagnetic,temperature,and stress fields around IPMSM.The fast and accurate analytical calculations of critical electromagnetic,temperature,and stress characteristics are realized while accurately accounting for structural complexity,material nonlinearity,heat transfer variability,and stress concentration.Further,on this basis,an efficient and high-quality cooperative analytical optimization design model for multi-physics fields that can fully account for the multi-field deep and strong coupling characteristics is proposed in combination with the intelligent machine learning language and advanced multi-objective optimization algorithm.It overcomes many drawbacks of the existing optimization design model,such as the difficulty of achieving multi-field coupling and the low efficiency of optimization.It lays a solid theoretical foundation and technical support for achieving efficient multi-field cooperative optimization design.The main research work is summarized below:(1)A novel master-slave subdomain subdivision technique is developed.The complex rotor structure is maximally restored by the combined fan-shaped subdomain consisting of alternately connected master and slave subdomains.In turn,a calculation model of the electromagnetic field based on the improved subdomain method is proposed.The fast and accurate analytical calculation of key electromagnetic characteristics is realized while accurately accounting for structural complexity and material nonlinearity.Aiming at the problems of large modeling workload and long calculation time of the finite element method as well as the difficulty of the subdomain method to effectively deal with the complex rotor structure,a fast and accurate analytical calculation model of electromagnetic field based on the improved subdomain method is proposed.First,a novel master-slave subdomain subdivision technique is developed to fully consider the complex rotor structure of IPMSM.The radial pole of the permanent magnet is uniformly subdivided into a plurality of combined fan-shaped subdomains along the radial direction.Each combined fan-shaped subdomain consists of a master subdomain and a slave subdomain connected alternately.Moreover,the left and right endpoints on the radius in each main subdomain coincide with the corresponding boundaries in the original topology to avoid the over-equalization for the complex rotor structure as well as to guarantee the computational accuracy of the exact subdomain model.Based on the principle of area conservation and constant positioning radius,the tangential pole of the permanent magnet,the middle magnetic bridge,and the bilateral magnetic bridge are subdivided into single-layer fan-shaped subdomains.Moreover,the slave subdomain and auxiliary connection domain are set up at the connection between the tangential pole and radial pole of the permanent magnet as well as the tangential pole of the permanent magnet and the middle magnetic bridge,respectively.So as to guarantee the smooth construction and solution of the exact subdomain model.Secondly,based on the exact subdomain model and then on the magnetic field continuity theorem,the general solution of the vector magnetic potential on each subdomain is derived.On this basis,the equivalent magnetic circuit method and the equivalent surface current method are introduced,which fully account for the saturation effect of the rotor magnetic bridge and stator core.Then,the motor electromagnetic field is calculated using the electromagnetic field calculation model based on the improved subdomain method.The fast and accurate analytical calculation of key electromagnetic characteristics of IPMSM,such as flux density,back electromotive force and torque,is realized.Finally,the computational results are validated using the finite element method and prototype electromagnetic field experiments,and the universality of the exact subdomain model in different topologies is discussed,confirming the accuracy,validity,and practicality of the proposed electromagnetic field calculation model.(2)A novel multi-layer thermal domain subdivision technique is developed in view of the strong three-dimensional spatial features of heat transfer.The complex geometric feature of critical components in the x-y plane and the randomness of rotational changes in the z-axis section are accurately captured.In turn,a calculation model of the three-dimensional temperature field based on the improved thermal domain method is proposed.The fast and accurate analytical calculation of key temperature characteristics is realized by fully accounting for the deep and strong coupling characteristics between the electromagnetic and temperature fields,as well as the effects of the nonuniform distribution of the heat source and the uncertain node information.Aiming at the problems of large modeling workload and long calculation time of the computational fluid dynamics as well as the limited computational capability of the lumped parameter thermal network and the analytical method,a fast and accurate analytical calculation model of three-dimensional temperature field based on the improved thermal domain method is proposed.First,a novel multi-layer thermal domain subdivision technique is developed to fully consider the complex topology and also in view of the fact that heat transfer has strong three-dimensional spatial features.In the x-y plane,the novel multi-layer thermal domain subdivision technique is combined with the novel master-slave subdomain subdivision technique in order to accurately capture the complex geometric feature of critical components such as the permanent magnet and the in-slot windings.In the z-axis section,the critical components such as the permanent magnet and end windings at different rotation angles are subdivided into multi-layer thermal domains along the radial direction in order to accurately capture the randomness of the z-axis section with the rotation angle during the actual operation.For the complex composition of the windings,the copper wire is regarded as a uniformly distributed isotropic heat conducting medium together with other non-conducting components such as insulating varnish,impregnating varnish,void,slot insulation,and slot wedge,in order to guarantee the computational accuracy of the exact thermal domain model as well as to enhance the modeling and analysis efficiency.Secondly,based on the exact thermal domain model and then on the heat transfer theory,the general solution of the temperature distribution function on each thermal domain is derived.On this basis,the concept of equivalent heat circuit and the iterative solution strategy are introduced in combination with the unique advantages of the finite element method in calculating electromagnetic losses,which fully account for the deep and strong coupling characteristics between the electromagnetic and temperature fields,as well as the effects of the nonuniform distribution of the heat source and the uncertain node information.Then,the motor temperature field is calculated using the three-dimensional temperature field calculation model based on the improved thermal domain method.The fast and accurate analytical calculation of key temperature characteristics of IPMSM,such as global temperature distribution,temperature variation curve and component temperature,is realized.Finally,the computational results are validated using the computational fluid dynamics and prototype temperature field experiments,and the robustness of the exact thermal domain model in different operating conditions is discussed,confirming the accuracy,validity,and practicality of the proposed three-dimensional temperature field calculation model.(3)A novel force domain subdivision technique is developed by the innovative combination of the center-of-mass equivalent ring method,Timusinko beam theory,and equivalent spring.The neglect of complex geometrical features during accurate force domain subdivision is effectively avoided.In turn,a calculation model of the stress field based on the improved center-of-mass equivalent ring method is proposed.Moreover,the proposed three-dimensional temperature field calculation model is introduced to fully account for the effects of rotor heating and nonuniform temperature distribution.The fast and accurate analytical calculation of key stress characteristics is realized.Aiming at the problems of large modeling workload and long computation time of the finite element method as well as the over-reliance on stress concentration coefficients of the analytical method,a fast and accurate analytical calculation model of the stress field based on the improved center-of-mass equivalent ring method is proposed.First,in order to fully consider the complex rotor structure,a novel force domain subdivision technique is developed by the innovative combination of the center-of-mass equivalent ring method,Timusinko beam theory,and equivalent spring,which provides accurate force domain subdivision for the interior rotor.The middle magnetic bridge is considered as a rectangular model,and the deformation function about the middle magnetic bridge is obtained by combining with Newton’s third law.The bilateral magnetic bridge is considered as a straight beam model,and the deformation function about the bilateral magnetic bridge is obtained by analyzing the force during the deformation process.The rotor pole shoe is considered as a spring model,and the deformation function about the rotor pole shoe is obtained by capturing the radial and tangential stiffnesses.The force equilibrium equations between the middle magnetic bridge,the bilateral magnetic bridge,and the rotor pole shoe are then obtained,which effectively avoids the neglect of complex geometrical features during the accurate force domain subdivision.Secondly,based on the exact force domain model and then on the displacement,the general solution of the stress-strain function on each force domain is derived.On this basis,the proposed three-dimensional temperature field calculation model is introduced,which fully accounts for the effects of factors such as rotor heating and nonuniform temperature distribution.Then,the motor stress field is calculated using the stress field calculation model based on the improved center-of-mass equivalent ring method.The fast and accurate analytical calculation of key stress characteristics of IPMSM,such as rotor maximum mechanical stress,is realized.Finally,the computational results are validated using the finite element method,material mechanics tensile experiments and prototype stress field experiments,and the sensitivity of the exact force domain model in different parameter configurations is discussed,confirming the accuracy,validity,and practicality of the proposed stress field calculation model.(4)The proposed fast and accurate analytical calculation model for multi-physics fields is innovatively combined with the intelligent machine learning language and advanced multi-objective optimization algorithm.An efficient and high-quality cooperative analytical optimization design model for multi-physics fields that can fully account for the multi-field deep and strong coupling characteristics is proposed.The efficient multi-field cooperative optimization design is achieved.There are still a lot of much needed improvements in the existing optimization design models about multi-physics fields.For example,the data acquisition phase is also severely limited by the many limitations that existing methods face in calculating the electromagnetic,temperature,and stress fields of IPMSM.This inevitably leads to a cumbersome optimization design process,making it difficult to combine excellent optimization results with low optimization costs.The efficient multi-field cooperative optimization design cannot be achieved,especially when accounting for the deep and strong coupling characteristics that exist between different physical fields of IPMSM.To this end,an innovative research is carried out around the efficient and high-quality cooperative analytical optimization design of multi-physics fields for IPMSM.First,the coupling mechanism between the different physical fields of IPMSM is explored in depth.The information transfer channel between the proposed electromagnetic field,temperature field,and stress field calculation models is constructed to fully account for the influence of the multi-field deep and strong coupling characteristics.Then,the fast and accurate coupled analytical model of multi-physics fields based on the exact subdomain model,the exact thermal domain model,and the exact force domain model is constructed.The fast and accurate calculation as well as the all-round evaluation of the multi-physics field performance of IPMSM under the influence of multiple factors are realized.Further,on this basis,combined with the intelligent machine learning language and advanced multi-objective optimization algorithm,an efficient and high-quality cooperative analytical optimization design model for multi-physics fields that can fully account for the multi-field deep and strong coupling characteristics is proposed.Thus,while balancing excellent optimization results and low optimization costs,it achieves efficient multi-field cooperative optimization design,and comprehensively improves the comprehensive performance of multi-physics fields of IPMSM.Finally,the finite element method,computational fluid dynamics,multi-physics field cooperative optimization design model based on the segmented Taguchi method,and prototype experiments are used to validate the accuracy,validity,and practicality of the proposed multi-physics field cooperative analytical optimization design model.更多还原