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传统上的机械设计考虑积层，高速，内置永磁同步机转子爱德华c拉雷丝美国电气和电子工程师协会会员 Jahns托马斯m 朗博士杰弗里h Keim托马斯a Abstract-This机械设计的考虑。本文讨论了对传统所特有(例如,径向)永磁同步电机的转子内部层机器。重点是放在的应用场合,在那里,径向力由于高速运行的主要途径是机械的限制设计的因素。适当设计的分层桥梁或肋骨,在转子外径是指在词语解释的是兼而有之资料的思路和电磁性能影响。与性能的权衡复杂的联系在一起使用加强肋磁铁蛀牙进行了探讨。这灵敏度的rotor-shaft机械设计的限制的越来越多的机制,突出了。这些效应,然后利用有限元分析的一种方法分析了m / 6-kW 150-N先发投手/发电机设计集成运行到6000股r /分钟环形转子来容纳变矩器或离合器总成。这个例子,证明了这是有可能的对显著提高转子的结构完整性使用摘要叙述技术只有一个非常谦逊的冲击在放映的机械驱动成本。指数Terms-Electrical钢、有限元分析(FEA),高速度、室内永磁(IPM)同步机、片、磁饱和。I.介绍OTOR设计和施工的室内永久的,磁铁(IPM)机是很有挑战性的任务到期一种矛盾的特点,改了系统性能转子的复杂性。IPM的机器是感兴趣的,因为他们是非常有吸引力的表演的立场在牵引和主轴应用1、2。机器设计可以(IPM)用宽,从理论上无限,速度范围为常数具有优良的逆变器利用权力运作。这是通过使用一凸实现转子几何有限 论文发表于IPCSD 03-084 2001年,IEEE国际电气机械与驱动研讨会,6月17 - 20日剑桥,麻萨诸塞州,和批准发表在中华民国的工业应用电机委员会正则化方法的工业应用的社会。手稿提交审查并公布了11月5日,2002年1月出版20日,2004年。 这项工作是由麻省理工学院的财团支持先进汽车电子/电气元件和系统。 拉雷丝与SatCon e . c的高新技术公司,剑桥,麻萨诸塞州美国(电子邮件件: 02142l)。t . m . Jahns与威斯康辛大学电机与电力电子联合体,电气连接,计算机工程部门,大学的威斯康辛州麦迪逊、作业指导书,美国(电子邮件: 53706-1691)。t . a . Keim和j . h .朗与实验室的磁力部门或电子系统、电气工程和计算机科学、麻省理工学院、剑桥,MA 02139美国(电子邮件:,)。10.1109 / TIA.2004.827440数字对象标识符。 从磁通,里面藏贡献转子结构谱。达到理想的程度的凸极、特殊纹理策略是典型的设计和组装要求比较对那些需要为竞争对手的机器类型诸如表面点和异步电机。转子设计策略机器一般可(IPM)轴向及径向划分,每层合结构以其自身优势3,4。转子的轴向的层使用多种交替层构造软、硬磁纸上的,还是放在沿主轴的机器,每个弯曲和个人的大小与转子磁极形成1。该设计方法可以达到high-inductance凸极率超过10:1。然而,合轴转子相对昂贵制造由于分类切割,塑造和组装的许多不同的片那一定是就业。此外,一个约束转子的袖子可能是必要的,以防止纹理高速运作入侵到气隙。这种袖子通常减少由于他们的凸极有限厚度和经常增加由于涡流损失当高强度不锈钢(例如,Inconel)是超套筒材料。相比之下,属于典型的层合转子径向设计以1 - 4层的硬磁材料在每个极。每个纹理,这一点与其他类型机器,是传统穿孔或削减作为一个单一的单一块为横截面上的转子。蛀牙是穿孔或剪切成转子片,和磁性材料插入这些蛀牙。这求购,最多可以放置,以便使用传统的方法转子是属于比较容易制造比它的轴叠层IPM翻版。摘要本文检视传统机械设计的问题(也称横向或径向)胶布等IPM转子。只有离心力被认为是这可能是占统治地位的机械应力的来源在高-速度的设计。每个设计特征的几个关键转子进行了考核反过来对他们的影响结果表明,在转子弯曲故障的压力苏:拉雷丝等传统层合、高速,IPM同步机转子图1 .12-pole IPM的横截面的机器。国家和电磁性能。设计策略与就功能,可以有效减少合成机械应力状态进行了研究。辩论的证实通过有限元分析(FEA)来验证的观点。一个IPM转子设计一个集成起动/发电机(ISG)应用是用来在整个论文以说明该方法的意义这些机械方面的技术问题5-7。一个横截面双层结构设计12-pole图1显示的是。特别需要指出的是,转子的机械应力状态,这是一种极限设计约束由于具有较高的转子变速运行,是必需的环形旋转音圈汽车机械。相关的设计规范设计技术：每分钟6000-r最大操作速度;设计000-r /分钟10个破裂速度;转子内径最小165mm;最大的定子外径300mm;永磁材料II机械设计的IPM转子为了这个讨论,机械设计点所对应的应用进行说明,而产生的在最坏的情况下,转子的机械应力(IPM)。假设在这个发展过程中采用如下:只是稳态速度情况忽略温度效应29-gage基线芯材:M19电气钢产量帮助中的小应变分析表明平面应力电磁起源的力量可以忽略不计振动和转子轴动力部队被忽略了与这些假定的基础上,对转子的力量支配着通过稳态离心力在恒定的速度。因此,机械设计点所对应的稳态破裂的手术设计速度值,10基米-雷克南/分钟。与这些假定的基础上,对转子的力量支配着通过稳态离心力在恒定的速度。因此,机械设计点所对应的稳态破裂的手术设计速度值,10基米-雷克南/分钟。峰值应力的解析计算由于离心一时径向力机转子是一层合(IPM)具有挑战性的任务,那是不尝试过在本文由于复杂的转子分层设计特点。然而,这些峰值应力影响的边界上的优化变量,确定出最优的系统设计,所以定性讨论的合力由于惯性负载是合适的。讨论了著名的原则,采用材料在描述的行为静载荷8,9。图2。素描的内力有着坚实的转子图3。在草图合力转子在一个magnet-filled(IPM)空腔内。图2显示一个坚实的转子截面与标示注明主要力量的核心由于离心加载。从最简单的水平,而忽略了磁铁的蛀牙、转子就像一个环不变的前提下,离心加载。在这些一种元素的条件下,转子的成员在切向张力和径向压缩。我们可以为薄壁箍近似建模转子由于窄深的转子ISG相比较于转子的ID。作为一个结果,转子的细分市场主要经验切向张力的力量。使用这个假设,主要影响因素的峰值应力的平均值“环”的半径和转速。帮助中的小应变分析根据应力增加的平方每个这些因素。如果转子腔现在视为图3中,哪个只含有一腔层、钢杆件集中这连接到轴是,现在只剩下的纹理薄的钢桥在各个末端。因此,离心加载在电线杆上一篇文章并不是均匀的分布在图4。在草图合力IPM转子在多种层次。“箍、转子径向导演”,导致实质性的惯性两个保留上的负荷之间的桥梁。 应该指出的是,该保税点资料洞里也将有助于这个装载,因为它是更少吗钢的硬度比,因此,贡献,将额外的加载攻击的内侧边缘杆件。因此,磁铁的等效质量, 图3中,必须的总和钢杆两件作品,磁铁(阴影部分的图3)。保税磁性材料不提供任何磁体和钢显著之间的融洽,因此,不传递力与服事的杆件。面临的挑战,就可建模思路,并在这在很大程度上取决于具体桥的形状。如果桥梁(主要是直的,然后梁弯曲近似的吗适当的。当多个图层都被看作是图4中每一层能被视为独立的载入如果inter-cavity钢截面大得足够分配任何胁迫浓度相邻的桥。负荷在每座桥是再后末期由于负载在干熄炉径向方向其惯性负载上剩余的部分杆件这座桥正在考虑之间和轴。如果桥梁每一层都有相同的规模,将桥最长结束的时候将在最高的空腔压力。如果空腔的目的都是圆形的,如图5秒,然后每个“梁有效长度”降低,而简单的光束上述近似不再是合理的。每个现在就像一个圆锥形桥缺口应力集中造成的元件下侧作用力,如图5精确定位的峰值应力在每座桥组态会要求重大分析来确定的不诉诸数值解。特别需要指出的是,安装(固定或简单等价的两头各)“梁”为straight-bridge模型是不明确的。 如果两端的各自的经验比较。最小弯曲桥梁其余的桥,这是一个合理的假设高峰压力会被发现在两端。相比之下,峰值应力圆形腔结构模型的可预期的图5。在草图合力转子在多个腔(IPM)层圆润的小费。在这一阶段,可以使一些概述转子设计决策,IPM恶化或改进了机械应力条件。speed-A减小10%最大转子在机械设计点的速度将降低峰帮助中的小应变分析应力降低近20%转子OD-Similarly,减免10%的半径转子表面,此处的桥梁所在位置,也会减少了20%的应激因素圆形的bridges-The”束“压力被减少“梁”变得更短和所有其它密度的平等。的特点,在此基础上切口的应力集中圆形桥循环模型,形状应该将近减少应力峰值pieces-A减小10%的小杆钻具杆件轴向长度单位质量将会减少压力几乎线性的。这可以达到降低分数撑竿的程度,以致于空间跨度。增加磁极数量的机器能产生同样的效果一根肋骨加强rib-Adding重新分配的离心从杆位片负荷导致在一个具有很重要的意义改进的应力状态。一根肋骨,加入到纹理几何穿过轴的每一腔抵抗离心运动通过撑竿的群众张力而不是弯曲 另一个因素的合力所引起的惯性加载量是影响,整个转子径向的偏转对组件的大小和环应力拉伸。在桥的投篮张力是由于拉伸,作为转子扩展到气隙在更高的速度。隐含的边界条件是,在箍应力计算转子ID和OD界限是无约束。作为一个结果,减少不必要的在任何一个边界将会减少变形的扩张转子在斯坦福桥球场进行的,因此也降低半径篮筐加载应力的组成部分。转子OD是有问题的制约,因为它将要求比其它材料钢大幅减少惯性载荷下的径向变形。此外,添加任何资料气隙中,影响电磁力将原有的转子的凸极的降解性能这台机器。苏:拉雷丝等传统层合、高速,IPM同步机转子图6。设计采用鸠转轴毂关节之间的枢纽和转子的ID图7 .转轴毂设计采用轴螺栓通过堆栈结束板身份证是制约转子更可行的解决方案提高转子的结构完整性。既然有那必须附上已一个集线器转子曲轴,在那里是一种机会,专门设计中心保留转子吗径向非。通常情况下,一个集线器只是设计传递的力矩在圆周方向会发生在一个毂转子是压合内。一个压合,虽然,什么也不做约束的转子ID,也就不会减轻的最大值机械设计点的应力。如果没有空间限制内转子的身份证,各种各样不同的枢纽装置可能在安理会的考虑范围。一个焊接中心可以工作,但却可以改变磁特性的核心。一种选择是一种轴向缸,伴侣的转子的ID表面采用鸠,如图6。另一个替代方案来建造一个终板和螺栓分布在吗终板的周长(1 /杆),如图7。将下降,片带孔沿每个轴地核是宽的地方。这个螺栓系统是唯一可行的螺栓的张力。如果足够能够发展和维持这样的径向载荷被掳去了由终板。如果足够的螺栓张力并不发达,在那里将会是有意义的,这将side-loading钉可能导致剪切掉钉在细胞表面的结束盘子里。相吻合的优势夹具(图6)或任何夹具表面沿转子的ID是它的结构与鲁棒性如果近对称径向基板部分中心所在地附近的中点处轴转子叠加。它的主要缺点那是一个有限的枢纽锡厚度,可以吗使它需要减少对转子的可用空间求购。相比之下,终板结构的优势的(图7)那径向板的尽头堆栈和不使用任何内在房地产里面的ID,否则可能被保留对于一个离合器或变矩器。作为一个结果,这种方法也许产生最紧密ISG配置。此外,缺席的情况下允许转子内部中心被设计以最小ID和里程计所测量,这可能会降低峰值应力的影响(应力)的平方。然而,任何终板方法必须解决实际安装相关的问题与大量求购加载螺栓和压缩。第三章,在终板中心结构分析结合转子截面修改提出展示一种合理的解决方案,为机械设计的自动售货机的应用IPM ISG。侧板的设计是选作分析,因为它允许最小机转子直径一致与给定的约束提供的。问题空间内转子ID为变矩器。机械设计的考虑以上讨论的影响设计性能优化机器的几个。(IPM方法6,7,10。转子diameter-Constraining转子直径和电线杆可清楚地减少了块尺寸的设计空间优化转子material-The转子的纹理选择材料基于许用应力状态影响材料的产量力量,但它也影响到核心损失11-14。自从场的基本转子直流,虽然,在核心的损失谐波大为局限于介绍吗纹理的几何形状。转子材料也影响所需的磁铁强度flux-linkage对于一个给定的点因为选择的合金化设计资料内容饱和磁通密度改变了。饱和磁通密度,反过来,影响了磁铁的磁通的比例是通过桥梁和加强增值税由生产型改为消费型肋骨吗桥和肋骨geometry-The几何学的桥梁和加强肋直接影响磁性性能。对于给定的转变,由IPM机械设计直走到曲面型腔小费具有相同的最低限度桥的宽度增加流量/罗纹,分流通过的桥梁和肋骨。加强肋添加额外的也增加了比例的分流磁铁助焊剂。所有这些桥和肋骨因素服务来减少可用从气隙磁永久磁铁,因而减少图8。straight-edge径向位移与桥梁10基米-雷克南/分钟对于一个给定的设计优化从最初逆变器利用立场改变设计随后介绍了转变的机械原因机械设计点远离电磁达到全局最优。最终,这些改变通常表现为成本和/或大小增加为machine-inverter组合与其他值相比,当机器对于优化电磁性能孤单III. 转子的非线性有限元分析设计。一个（IPM）确认结构有限元分析进行了定性的理解上述15。这些结果也使用作为一个基线进行缩放到其他IPM机的设计提供了参考空间差异,有足够的基线小。利用有限元ANSYS进行了二维软件包。图8显示预测的径向位移,双-机器在10层(IPM)基米-雷克南/分钟而不考虑任何转子由于ID挠度约束(即附加枢纽,一个自由的转子ID边界)。该断面从一个ISG 12杠和一个转子有straight-edged 246毫米外径桥梁和隧道在没有额外的加强肋两个磁铁蛀牙。故事情节的表示在入力轴外最大挠度表面的mm,那是高达0.42的60%的名义指定ISG情节,确认了大部分的挠度梯度(所观测到的变化在桥梁阴影)自杆件外转子轭和偏转都是统一的。这是合情合理的,因为轭和杆件是太多了厚的桥梁、所以不应该非常弯曲。有限元计算结果的分析表明,在保税磁性材料几乎连续的接触和内在边界的两个入力轴杆片。相关的切向应力的情节展现出来的在图9预计到2030年的峰值应力2.6 GPa结束的时候桥的最大的(内部)终止腔。定性,这些结果预期的趋势比赛很好。不幸的是,峰值应力超过屈服应力的7倍的典型电钢。比较。airgap。图9。(Pa)切向应力与straight-edged桥梁10基米-雷克南/分钟对应于径向位移如图。8图10。预测转子在终板挠度的R -设计中心。平面(axi-symmetric)。有助于减轻压力、终板预测枢纽设计分析了作为一种手段,减少了径向载荷。此外,这台机器是re-optimized随转子ID固定最低规定极限(165毫米),这座桥型材被捕获的肋骨在补充说,加强在中点取得最大值的吗每个空腔内。图10显示变形位移的总和hub-rotor结构平面(通过曲轴中心线显示在左边。从身体上来说,这是一半的有限元模型民族结构的显示在图七部分。潜在的axi-symmetric导致这个挠度模型情节,可旋转在曲轴中心线。图中最大挠度。10个结构在10基米-雷克南/分钟是0.045 mm的一端从转子栈板上。这是大约65%少偏差比预期的转子身份证前配置在图8与一个无约束转子的ID图11。帮助中的小应变分析应力在10基米-雷克南/分钟转子ID挠度约束条件下中心。表I比较优化应用IPM为一个ISG和没有机械转子的考虑应用该计算边界条件后去的转子ID的转子模型飞机,帮助中的小应变分析压力进行了计算结果显示于图11。这转子模型包含了结构设计的改进;圆形腔小费和加强在中点的肋骨这个蛀牙。与这些款式及边界条件的变化,其主峰压力在10基米-雷克南/分钟机械设计观点已经被降低6.4个因子相比,图9的设计。作为结果,最大应力的边缘,圆形的桥梁和肋骨只有17%以上的屈服应力与钢(408 M19吗350兆帕)。这样做只会导致局部塑性屈服,因为该应力值以上产量不是贯穿宽度的桥梁和肋骨。虽然这里没有给出,分析通过指定的同时进行偏转的零的吗转子ID表面,并由此产生帮助中的小应变分析应力在这种情况下大约13%低于M19钢的屈服强度。分析与无转子ID挠度约束发达的最大值应力87%的高于M19屈服强度钢(一共655 MPa)。 (IPM)的比较,优化设计应用。ISG既有也没有额外的机械considera转子是对的(IPM)显示在表i。优化这种比较目标雇用了一个系统的成本模型这台机器加转炉那些先前报道了5,7,10。设计# 1是ISG设计转子呆板了。(IPM)行为表现在无花果。8和9,而设计2号这re-optimization有额外的机械设计的约束代表在无花果里。10号机和11号机。表我表明调查小组的设计转变为机械因素造成未成年人牺牲为当前等级和制度成本作为交换在小机器信封和一个机器设计能承受得起高设计破裂速度,而不是诉诸更多昂贵的高强度合金作转子片。这些结果都支持的结论(IPM)应用自动售货机的设计应与问题圆形桥和肋骨型材,是最小化直径以及额外的加强肋内磁铁蛀牙。此外,结果表明,附加的步骤可能会被要求为了进一步减少的峰值应力M19的范围内钢。人身破裂速度的要求,是另一种形式雇用一个中心来替代产生制约转子的ID偏斜。在机械设计减少点速度将提供一个有效的方式满足机械吗强度约束限制,如果汽车应用即可修改。为转子采用分析(设计)、2号需要在机械设计点的变化来满足M19屈服应力范围可以没有任何塑性屈服估计如下:这相当于27%下降最快的速度行驶要求。deflection-constraining枢纽的附件只有7%的速度减少机械设计(9262 r /分),必须消除忍让。另外,不同的纹理材料,具有更高的产量优势比M19钢也可能被考虑为了满足原来的尺寸10基米-雷克南/分钟破裂速度的要求。材料对比较成本具有足够的屈服强度,但是较高的核心的损失,有被证实为高速机械14。IV. 结论摘要首先分析了的力学行为和设计传统的启示与层合IPM转子求购高速切削应用统一。设计技术介绍了能有效减轻的机械应力峰值转子在高速行驶时的抓地力。它已被证明稳健设计,都离不开具有很重要的意义通过适当选择性能下降转子的维度、桥梁和肋骨设计,shaft-to-rotor附件,和材料的选择。一列高速行驶的例子申请已被使用环形ISG通过有限元分析来证实这些结论。进一步的工作应该包括的原型结构力学性能的测试,评价的温度效应,发展和结构复合参数模型合并优化设计过程中通过直接。参考1 w .宋楚瑜,“设计与造型的axially-laminated室内永久的为field-weakening磁铁电动机驱动的应用程序,“博士论文,部门。电子。选举的人。材料科学与工程,大学学历。格拉斯哥、格拉斯哥、英国,1993年2 Vagati李晓岚、Franceschini福神,Fratta,下午3点红色的,“交流 电机对高性能驱动:一个基于设计的比较,在09/10/1997。”运动。Annu IEEE-IAS。 会议。725-733,1995年,页3 :Fratta f,a . Vagati,Villata,“设计标准的IPM的机器适合field-weakened操作”,陈鹰。 1990年,页,革新。1059-10654 t . a脂,t . j . e米勒,a . Vagati ,即Boldea Malesani,和t . Fukao,“同步磁阻驱动教程中,发表在Annu IEEE-IAS。 会议,丹佛,CO,10月2胜7负,1994年5 e . c拉雷丝、八宝饭m . Jahns、李佳玲Kirtley Jr,j . h .朗,”的内饰起动/发电机的点在汽车上的应用”,陈鹰。革新,页。三、土耳其的伊斯坦布尔。1802-1808 1998年,页。6 e . c拉雷丝、八宝饭m . Jahns h .朗,”一个饱和集中参数模型内部永磁同步机”,陈鹰。IEEEIEMDC,西雅图,华盛顿州,1999年,第1 - 11页。553-5557 拉雷丝”,即优化的c型饱和室内每-manent-magnet同步机械驱动,“博士,部门。选举的人。英格。计算。科学,麻萨诸塞州研究。1995,16(2),剑桥,麻萨诸塞州,20008 小j . e和c,r . Mischke、机械工程设计、5号艾德。纽约:天下,1989年。9 l . s .标志,t Baumeister、标志的标准手册机械工程师。纽约:天下,1986年。10 e . c拉雷丝、八宝饭m . Jahns朗,“影响之饱和度和变频器在内线成本优化、永磁同步机器驱动”在09/10/1997。 运动。Annu IEEE-IAS。 会议上,第一卷。、菲尼克斯、阿兹,1999年,页。125-131。11 Nonoriented钢板为磁应用,美国钢铁,匹斯堡,PA,1978年版。12 合金钢纹理的产品,Armco钢、匹斯堡,PA,1999年。13 木匠合金钢产品选择指南、木工钢,读书,爸爸,1997年。14 w . l .宋楚瑜李晓岚、b Kliman约翰逊,r,r的n -米勒,白色的,j .“小说高速异步电动机为一家商业离心式压缩机,”在09/10/1997。 运动。Annu IEEE-IAS。 会议上,第一卷。、菲尼克斯、阿兹,1999年,页。494-501。15 应用ANSYS有限元软件ANSYS Multiphysics集团公司、Canonsburg、PA,1999年。爱德华c拉雷丝(S 00)收到了96-M蔓延至S.B.丁镛,学位,1988年和1996年分别为:从机械工程学系,博士学位和丁镛,1996年和2000年,分别从国防部电气工程和计算机科学,麻萨诸塞州理工学院(麻省理工学院),剑桥。于2000年5月,他加入了SatCon技术公司、剑桥,麻萨诸塞州,它执行研究和开发在电力和能源产品,而且目前是在探讨了直通式/电磁学小组长。从1988年到1996年,他与通用电气(GE)飞机的引擎,明美,马,在那里他加入了发展先进的发动机控制系统设计,军事和商业数据通信系统和地面和飞行测试流体力学并数字控制引擎系统。当他回到麻省理工学院在1994年,他继续专门从事设计和控制电机驱动运输等领域。他现在的技术研究发展先进的兴趣是机电一体化、机械设计、控制系统、和运输等领域。拉雷丝收到一满三年患病的德怀特D奖学金。艾森豪威尔奖学金计划(美国交通部,美国联邦公路行政ISTEA助学金和奖学金计划)为他的博士研究。来自麻省理工学院进一步赞助/行业汽车财团对先进电气/电子部件和系统他为一家研究助理研究集中在汽车电子产品吗在过渡到一个42-Vdc汽车平台。他也是服务奖的受奖人技术和政策计划库克公共服务奖和最好的论文陈述口服建筑作品奖。托马斯m . Jahns(S 91-F 73-M 79-SM 93年)收到蔓延至S.B.,交通大学学位在1974年和博士学位于1978年在麻省理工剑桥,所有技术,在电子工程。在1998年,他加入了大学的师资队伍威斯康辛州麦迪逊,作为一个教授,在整个部门然而电子计算机工程,在那里他也是一个威斯康辛州的副主任电机与电力电子财团(WEMPEC)。 在加入大学的威斯康辛州、就与通用电器研究发展,Schenectady,纽约,在过去的15年间,在那里他追赶新电源电子、电机驱动技术在各种各样的研究和管理现需要招聘所述职位。他的研究兴趣包括永磁同步机器,由于各种各样的应用,包括从高性能的机器工具向低成本电器驱动器。在他进行了一项研究,从市场在麻省理工学院的休假,期间他执导的研究活动在该地区的国际先进的汽车电气系统及配件作为一个industry-sponsored汽车协会主任。被授予博士Jahns威廉e纽尼尔奖由分散型电源电子产品针对社会是在1999年。()他被认为是一位杰出的讲师由IEEE工业应用的社会(IAS)在1994 - 1995年针对在1996年。他一直担任总统(1995-1996),针对常规作为一个成员之间IAS执行委员会患有急性心梗。他被选为导演/代表名牌”、“服务之2002至2003年期间模块董事会。托马斯。a . Keim(M 90)接受医生的科学从麻省理工学院的学位(麻省理工学院),剑桥。毕业后,他在麻省理工学院几年成为会员的科研工作人员,超导电机。他然后工作,与一般的超过10年电气公司的研究和杰弗里h .朗(S 95-F 78-M 79-SM 98年)收到蔓延至S.B.,交通大学电子工程的学位博士学位,麻萨诸塞州理工学院(麻省理工学院),剑桥,在1975年,1977年,1980年,分别。他是教授的电机工程麻省理工学院和麻省理工学院实验室副主任对电磁和电子系统。他麻省理工学院成员一直是自1980年以来。他的主要研究和教学领域兴趣着重分析,设计及控制的机电系统在旋转机械上与一个重音,微传感器和致动器、灵活的结构。他单独140多个学术论文,而且是5件专利持有人在以下领域的机电、电力电子,应用控制。所有的花都朗博士被授予了三个最佳论文奖由各种各样的IEEE的社会群体。他是前赫兹基金会院士和前任副主编传感器和执行器的自诊断。806IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 3, MAY/JUNE 2004MechanicalDesignConsiderationsforConventionallyLaminated, High-Speed, Interior PM SynchronousMachine RotorsEdward C. Lovelace, Member, IEEE, Thomas M. Jahns, Fellow, IEEE, Thomas A. Keim, Member, IEEE, andJeffrey H. Lang, Fellow, IEEEAbstractThis paper discusses mechanical design consid-erations that are particular to conventionally (i.e., radially)laminated rotors of interior permanent-magnet synchronousmachines. Focus is placed on applications where the radial forcesdue to high-speed operation are the major mechanically limitingdesign factor. Proper design of the lamination bridges, or ribs,at the rotor outer diameter is explained in terms of the bothmaterial considerations and electromagnetic performance impact.The tradeoff of complexity versus performance associated withusing strengthening ribs in the magnet cavities is discussed. Thesensitivity of the mechanical design limitations to the rotor-shaftmounting mechanism is also highlighted. These effects are thenanalyzed using finite-element analysis for a 150-N m/6-kWintegrated starter/alternator designed for operation up to 6000r/min with an annular rotor to accommodate a torque converteror clutch assembly. This example demonstrates that it is possibleto significantly improve the rotors structural integrity using thetechniques described in this paper with only a very modest impacton the projected machine drive cost.Index TermsElectrical steel, finite-element analysis (FEA),highspeed,interiorpermanent-magnet(IPM)synchronousmachine, laminations, magnetic saturation.I. INTRODUCTIONROTOR DESIGN and construction of interior perma-nent-magnet (IPM) machines is a challenging task dueto the conflicting characteristics of improved performance androtor complexity. IPM machines are of interest because they areparticularly attractive from a performance standpoint in tractionandspindle applications1,2.IPMmachinescanbedesignedwith wide, and theoretically infinite, speed ranges for constantpower operation with excellent inverter utilization. This isachieved through use of a salient rotor geometry with limitedPaper IPCSD 03084, presented at the 2001 IEEE International Electric Ma-chines and Drives Conference, Cambridge, MA, June 1720, and approved forpublication in the IEEE TRANSACTIONS ONINDUSTRYAPPLICATIONSby theElectric Machines Committee of the IEEE Industry Applications Society. Man-uscriptsubmittedforreviewNovember5,2002andreleasedforpublicationJan-uary 20, 2004. This work was supported by the MIT Consortium on AdvancedAutomotive Electrical/Electronic Components and Systems.E. C. Lovelace is with SatCon Technology Corporation, Cambridge, MA02142l USA (e-mail: ).T. M. Jahns is with the Wisconsin Electric Machines and Power ElectronicsConsortium,DepartmentofElectricalandComputerEngineering,UniversityofWisconsin, Madison, WI 53706-1691 USA (e-mail: ).T. A. Keim and J. H. Lang are with the Laboratory for Electromagneticand Electronic Systems, Department of Electrical Engineering and ComputerScience, Massachusetts Institute of Technology, Cambridge, MA 02139 USA(e-mail: , ).Digital Object Identifier 10.1109/TIA.2004.827440flux contribution from PMs buried within the rotor structure.To achieve the desired degree of saliency, special laminationdesign and assembly strategies are typically required comparedto those required for competing machine types such as surfacePM and induction machines.TherotordesignstrategiesforIPMmachinescangenerallybedivided into axially and radially laminated configurations, eachwith its own advantages 3, 4. The axially laminated rotor isconstructed using many alternating layers of soft and hard mag-netic sheets that are laid along the axis of the machine, eachbent and individually sized to form the poles of the rotor 1.This design approach can achieve high-inductance saliency ra-tiosin excess of 10:1. However, the axially laminatedrotorisrelativelyexpensivetomanufactureduetothesortedcut-ting, shaping, and assembly of the many different laminationsthatmustbeemployed. Furthermore, aconstrainingrotorsleevemay be necessary for high-speed operation to prevent lamina-tion intrusions into the air gap. Such sleeves typically reducethe saliency due to their finite thicknesses and often increaselosses due to eddy currents when high-strength stainless steel(e.g., Inconel) is chosen for the sleeve material.By contrast, radially laminated rotors are typically designedwith 14 layers of hard magnetic material in each pole. Eachlamination, as with other conventional machine types, ispunched or cut as a single unitary piece for the cross section ofthe rotor. Cavities are punched or cut into the rotor laminations,and the magnet material is inserted into these cavities. Thelaminations can be stacked using conventional means so thatthe rotor is generally easier to manufacture than its axiallylaminated IPM counterpart.However, adoption of the radially laminated rotor comes atthe expense of saliency with typical inductance ratios rangingfrom 1.5 up to 10:1, depending on the number of magnet cavitylayersand theirconfiguration.Forgoodelectromagneticperfor-mance, it is necessary to minimize thesteel bridges surroundingthe magnetic cavities that are necessary to link the rotor ironsegments into a unitary lamination. Each bridge effectively cre-atesamagneticshortciruitacrossthePMs,therebyreducingthemagnets contribution to the overall air-gap flux.This paper examines the mechanical design issues of con-ventionally (also referred to as transverse or radially) laminatedIPM rotors. Only the centrifugal force is considered as this islikely to be the dominant source of mechanical stress in high-speed designs. Each of several key rotor design features are ex-amined in turn with respect to their influence on the rotor stress0093-9994/04$20.00 2004 IEEELOVELACE et al.: CONVENTIONALLY LAMINATED, HIGH-SPEED, IPM SYNCHRONOUS MACHINE ROTORS807Fig. 1.Cross section of a 12-pole IPM machine.state and electromagnetic performance. Design strategies withrespect to features that can mitigate the resultant mechanicalstress state are also presented. The discussion is substantiatedthrough finite-element analysis (FEA) to verify the arguments.An IPM rotor design for an integrated starter/generator (ISG)application is used throughout the paper to illustrate the signif-icance of these mechanical issues 57. A cross section for a12-pole two-layer design is shown in Fig. 1. In particular, themechanical stress state of this rotor is a limiting design con-straint due to the high rotor tip speed operation that is requiredof annular direct-drive automotive machinery.The pertinent design specifications for this ISG design are: 6000-r/min maximum operating speed; 10000-r/min design burst speed; minimum rotor inner diameter (ID)mm; maximum stator outer diameter (OD)mm; bonded PM material in cavities.II. MECHANICALDESIGN OFIPM ROTORSFor the purpose of this discussion, the mechanical designpoint corresponds to the application specification that producesthe worst case mechanical stress in the IPM rotor. The assump-tions employed in this development are as follows: steady-state speed conditions only; temperature effects neglected; baseline core material: M19 29-gage electrical steel; yield indicated by planar Von Mises stress; forces of electromagnetic origin considered negligible; vibration and rotor shaft dynamical forces neglected.With these assumptions, the forces on the rotor are dominatedby the steady-state centrifugal forces at constant speed. There-fore, the mechanical design point corresponds to steady-stateoperation at the design burst speed value, 10 kr/min.Analytical calculations of the peak stresses due to centrifugalforces acting on a radially laminated IPM machine rotor is achallenging task that is not attempted in this paper due to thecomplexity of the rotor lamination design features. However,these peak stresses affect the boundaries of the optimizationvariables that determine the optimal system design, so a quali-tative discussion of the resultant forces due to inertial loadingis appropriate. The discussion is conducted employing well-Fig. 2.Sketch of resultant forces on a solid rotor.Fig. 3.Sketch of resultant forces on an IPM rotor with one magnet-filledcavity.known principles that describe the behavior of materials understatic loading 8, 9.Fig. 2 shows a solid rotor cross section with annotations toindicate the major forces on the core due to centrifugal loading.At the simplest level, neglecting the magnet cavities, the rotorresemblesahoopwithconstantcentrifugalloading.Undertheseconditions,an elementalmember oftherotor isundertangentialtension and radial compression.Thin-walled hoop approximations can be justified for mod-eling the rotor because of the narrow depth of the ISG rotorin comparison to the rotor ID. As a result, the rotor segmentsmainly experiencetangentialtension forces. Using this assump-tion, the major factors affecting the peak stress are the averageradius of the “hoop” and the rotational speed. The Von Misesstress increases according to the square of each of these factors.If the rotor cavities are now considered as in Fig. 3, whichonly contains one cavity layer, the steel pole piece centered ontheaxis is now only attached to the rest of the laminationby the thin steel bridges at each end. Therefore, the centrifugalloading on the pole piece is not evenly distributed around the808IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 3, MAY/JUNE 2004Fig. 4.Sketch of resultant forces on an IPM rotor with multiple layers.rotor “hoop,” causing a substantially radially directed inertialload on the two retaining bridges.It should be noted that the bonded PM material in the cavitywill also contribute to this loading because it is generally lessstiff than the steel and will, therefore, contribute additionalloading against the inside edge of the pole piece. Therefore,the equivalent magnet mass,in Fig. 3, must be the sum ofboth the steel pole piece and the magnet (the shaded portionof Fig. 3). The bonded magnet material does not provide anysignificant bonding between magnet and steel and, therefore,does not transmit force from the yoke to the pole pieces.The challenge then reduces to modeling the bridges, and thisis largely dependent on the specific bridge shape. If the bridgesare principally straight, then beam bending approximations areappropriate. When multiple layers are considered as in Fig. 4,each layer can be considered as being independently loadedif the inter-cavity steel sections are wide enough to distributeany stress concentrations between adjacent bridges. The loadon each bridge is then the end load in the radial direction due tothe inertial loading on the remaining section of the pole piecebetween the bridge under consideration and theaxis.If the bridges on each layer have the same dimensions, thebridge at the end of the longest cavity will be under the higheststress. If thecavityends are roundedas shown inFig.5, then theeffectivelengthofeach“beam”is reduced,and thesimplebeamapproximations described above are no longer reasonable. Eachtaperedbridgenowresemblesaroundnotchstressconcentrationelement under side loading as shown in Fig. 5.The precise location of the peak stress within each bridgeconfiguration would require significant analysis to determinewithout resorting to numerical solutions. In particular, theequivalent mounting (fixed or simple) at the ends of each“beam” for the straight-bridge model is not clearly defined. Ifthe ends of each bridge experience minimal bending comparedto the rest of the bridge, it is reasonable to assume that the peakstress will be found at the ends. In contrast, the peak stress inthe rounded cavity structural model would be expected at theroot of the stress concentration, corresponding to the midpointof each bridge.Fig. 5.Sketch of resultant forces on an IPM rotor with multiple cavity layerswith rounded tips.At this stage, some general observations can be made aboutIPM rotor design decisions that would worsen or improve themechanical stress conditions. Maximum rotor speedA 10% reduction in the mechan-ical design point speed would reduce the peak Von Misesstress by almost 20%. Rotor ODSimilarly, a 10% reduction in the radius at therotor surface, where the bridges are located, would alsoreduce the stress by a 20% factor. Rounded bridgesThe “beam” stresses are reduced asthe “beam” gets shorter with all other dimensions equal.Based on the characteristics of the notch stress concen-tration model, a circularly rounded bridge shape shouldnearly minimize the peak stress. Smaller pole piecesA 10% reduction of the deflectingpole piece mass per unit axial length will reduce the stressalmost linearly. This can be achievedbyreducingthe frac-tion of the pole pitch that the cavities span. Increasing thenumber of machine poles can produce the same effect. Strengthening ribAdding a rib redistributes the cen-trifugal load from the pole piece resulting in a significantimprovement in the stress state. A rib that is added tothe lamination geometry across theaxis of each cavityresists the centrifugal motion of the pole masses throughtension rather than bending.Another factor in the resultant forces caused by the inertialloading is the effect that the radial deflection of the entire rotorhas on the magnitude of the tensile component of hoop stress.The hoop tension in the bridge is due to stretching as the rotorexpandsinto the air gap at higher speeds. Theimplicit boundaryconditions in hoop stress calculations are that the rotor ID andOD boundaries are unconstrained. As a result, reduction of thedeflection at either boundary will reduce the expansion of therotor at the bridge radius and therefore also reduce the hoopstress component of loading.Constraining the rotor OD is problematic since it would re-quire a material substantially stiffer than steel to decrease theradial deflection under inertial load. Furthermore, adding anyLOVELACE et al.: CONVENTIONALLY LAMINATED, HIGH-SPEED, IPM SYNCHRONOUS MACHINE ROTORS809Fig. 6.Rotor hub design using dovetailed joints between the hub and rotor ID.Fig. 7.Rotor hub design using axial bolts through the stack to an end plate.material in the air gap that adversely affects the electromagneticsaliency of the original rotor would degrade the performance ofthe machine.Constraining the rotor ID is a more feasible solution forimproving the structural integrity of the rotor. Since there isalready a hub that must attach the rotor to the crankshaft, thereis an opportunity to specially design the hub to retain the rotorradially. Typically, a hub is only designed to transmit the torquein the circumferential direction as would occur with a hub thatis press fit inside the rotor. A press fit, though, does nothing toconstrain the rotor ID and so would not mitigate the maximumstress at the mechanical design point.If there are no space constraints inside the rotor ID, a varietyof different hub fixtures might be considered. A welded hubmay work but could alter the magnetic properties of the core.One alternative is an axial cylinder that mates with the rotor IDusingdovetailedsurfacesasshowninFig.6.Anotheralternativeis to construct an end plate with studs distributed around thecircumference of theend plate (oneperpole)as shown inFig.7.The laminations would be cut with a hole along eachaxiswhere the core is widest (i.e., there no cavities along theaxis),and then assembled onto the studs.This bolted system is only practical if sufficient bolt tensioncan be developed and maintained so that the radial load is takenup by the end plate. If adequate bolt tension is not developed,there will be significant side-loading on the studs that wouldlikely result in shearing off the studs at the surface of the endplate.The advantage of the dovetail fixture (Fig. 6) or any fixturealong the rotor ID surface is that it is structurally robust andnearly symmetric if the radial plate portion of the hub is lo-cated axially near the midpoint of the rotor stack. Its chief dis-advantageis that thehubcylinderhas a finitethickness thatmaymake it necessary to reduce the available space for the rotorlaminations.In contrast, the advantage of an endplate structure (Fig. 7) isthat the radial plate is at the end of the stack and does not useany internal real estate inside the ID that might otherwise be re-servedforaclutchortorqueconverter.Asaresult,thisapproachmay yield the most compact ISG configuration. Furthermore,the absence of the internal hub allows the rotor to be designedwith the smallest possible ID and OD, which will reduce thepeak stress (squared impact on stress). However, any endplateapproach must solve the practical installation problems associ-ated with heavily loaded studs and compressed laminations.In Section III, the endplate hub structure is analyzed incombination with proposed rotor cross-section modifications todemonstrate a plausible solution for the mechanical design ofan IPM machine for the ISG application. The endplate design ischosen for analysis because it allows the smallest machine rotordiameter consistent with the given ISG constraint to providespace inside the rotor ID for a torque converter.The mechanical design considerations discussed above affectthe design performance optimization of IPM machines in sev-eral ways 6, 7, 10. RotordiameterConstrainingtherotordiameterandpolepiece sizes clearly reduces the available design space foroptimization. Rotor materialThe choice of rotor lamination materialaffects allowable stress state based on the material yieldstrength, butit alsoaffectsthecorelosses 1114.Sincethe fundamental rotor field is dc, though, the core lossesare substantially confined to harmonics introduced by thelamination geometry. The rotor material also influencesthe required magnet strength for a given PM flux-linkagedesign because the choice of alloying material contentalters the saturation flux density. The saturation flux den-sity, in turn, affects the proportion of the magnet flux thatis shorted through the bridges and strengthening ribs. Bridge and rib geometryThe geometry of the bridgesand strengthening ribs directly affects magnetic perfor-mance. For a given IPM machine design, changing fromstraight to curved cavity tips with the same minimumbridge/rib width increases the flux that is shunted throughthe bridges and ribs. Adding additional strengthening ribsalso increases the proportion of shunted magnet flux. Allthese bridge and rib factors serve to reduce the availableair-gap flux from the permanent magnets, thereby re-ducing the magnet torque component for a given designor requiring the introduction of larger, stronger magnets.810IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 3, MAY/JUNE 2004Fig. 8.Radial displacement with straight-edge bridges at 10 kr/min.For a given design that was initially optimal from an inverterutilization standpoint (i.e.,) 1, design changessubsequently introduced for mechanical reasons shift themachine design point away from the electromagnetic optimum.Ultimately, these changes typically manifest themselves as costand/or size increases for the machineinverter combinationcompared to their comparable values when the machine isoptimized for electromagnetic performance alone.III. FEAOF ANIPM ROTORDESIGNStructural FEA was conducted to confirm the qualitative un-derstandings presented above 15. These results are also usedas a baseline for scaling to other IPM machine designs pro-vided that the dimensional differences with the baseline are suf-ficiently small. The FEA was carried out using the ANSYS 2Dsoftware package.Fig. 8 shows the predicted radial displacement of a double-layer IPM machine at 10 kr/min without considering any rotorID deflection constraint due to an attached hub (i.e., a free rotorID boundary). This cross section is from an ISG with 12 polesand a rotor OD of 246 mm having straight-edged bridges andno additional strengthening ribs within the two magnet cavities.The plot indicates a maximum deflection on the-axis outersurface of 0.42 mm, which is 60% of the nominal specified ISGairgap.The plot confirms that the bulk of the deflection gradients(observed by the change in shading) are in the bridges since therotor yoke and outer pole piece are both uniformly deflected.This is reasonable because the yoke and pole piece are muchthicker than the bridges and so should not bend very much bycomparison.The FEA results show that the bonded magnet material is innearly continuous contact with the inner boundaries of the two-axis pole pieces. The associated tangential stress plot shownin Fig. 9 predicts a peak stress of 2.6 GPa at the end of thebridge terminating thelargest (inner)cavity. Qualitatively,theseresults match the expected trends quite well. Unfortunately, theFig. 9.Tangential stress Pa with straight-edged bridges at 10 kr/mincorresponding to the radial displacement shown in Fig. 8.Fig. 10.Predicted deflection of the rotor with endplate hub design in the?plane (axi-symmetric).peak stress is more than seven times the yield stress of typicalelectrical steel.To mitigate the predicted stress, the end plate hub design wasanalyzed as a means of reducing the radial loading. Further-more, the machine was re-optimized with the rotor ID fixedto the minimum specified limit (165 mm), the bridge profileswere rounded, and strengthening ribs were added at the mid-point of each cavity. Fig. 10 shows the deflection of the com-bined hubrotorstructure in theplane (with thecrankshaftcenterline shown on the left. Physically, this FE model is half ofthe structure shown in Section A-A of Fig. 7. The underlyingaxi-symmetric model leads to this deflection plot that can be re-volved around the crankshaft centerline.The maximum deflection in the Fig. 10 structure at 10 kr/minis 0.045 mm at the far end of the rotor stack from the endplate.This is about 65% less deflection at the rotor ID than predictedLOVELACE et al.: CONVENTIONALLY LAMINATED, HIGH-SPEED, IPM SYNCHRONOUS MACHINE ROTORS811Fig. 11.Von Mises stress at 10 kr/min with rotor ID deflection constrained byhub.TABLE ICOMPARISON OFOPTIMIZEDIPMFOR ANISG APPLICATIONWITH ANDWITHOUTMECHANICALROTORCONSIDERATIONSfor the previous configuration in Fig. 8 with an unconstrainedrotor ID.After applying this calculated boundary condition to therotor ID of anplane rotor model, the Von Mises stresswas calculated and the results are shown in Fig. 11. Thisrotor model incorporates the structural design improvements;rounded cavity tips and strengthening ribs at the midpoint ofthe cavities.With these design and boundary condition changes, the peakstressatthe10kr/minmechanicaldesignpointhasbeenreducedby a factor of 6.4 compared to the Fig. 9 design. As a result, themaximum stress on the edge of the rounded bridges and ribsis only 17% above the yield stress of M19 steel (408 versus350 MPa). This may only result in localized plastic yielding be-cause this stress value above yield is not present throughout thewidthofthebridgeandtherib.Thoughnotshownhere,analyseswere also conducted with a specified deflection of zero on therotor ID surface, and the resulting Von Mises stress in this casewas about 13% lower than the M19 steel yield strength. Ana-lyzes with no rotor ID deflection constraints developed max-imum stress 87% higher than the yield strength of M19 steel(655 MPa).The comparison of optimized IPM design for the ISG appli-cation both with and without additional mechanical considera-tions for the IPM rotor is shown in Table I. The optimizationtarget employed for this comparison is a system cost model ofthe machine plus converter that was previously reported on 5,7, 10. Design #1 is the ISG design with the IPM rotor me-chanical behavior shown in Figs. 8 and 9, while Design #2 isthe re-optimization with the additional mechanical design con-straintsrepresentedinFigs.10and11.TableIdemonstratesthatthe ISG design changes for mechanical considerations result ina minor sacrifice for current rating and system cost in exchangefor a smaller machine envelope and a machine design that canwithstand higher design burst speeds without resorting to moreexpensive high-strength alloys for the rotor laminations.All of these results support the conclusion that the IPMmachine for the ISG application should be designed withrounded bridge and rib profiles, a minimized diameter, andextra strengthening ribs inside the magnet cavities. Further-more, the results indicate that additional steps may be requiredto further reduce the peak stresses within the limits of M19steel. Re-evaluating the burst speed requirements is anotheralternative to employing a hub that constrains the rotor IDdeflection. A reduction in the mechanical design point speedwould provide one effective means of meeting the mechanicalstrength limit if the automotive application constraints can bemodified. For the rotor used in this analysis (Design #2), therequired change in the mechanical design point to meet theM19 yield stress limits without any plastic yielding can beestimated as follows:r/minMPaMPar/min(1)This corresponds to 27% reduction in the maximum speedrequirement. With the deflection-constraining hub attach-ment only a 7% reduction of the mechanical design speed(9262 r/min) is required to eliminate yielding. Alternatively,different lamination materials with higher yield strengths thanM19 steel may also be considered in order to meet the original10 kr/min burst speed requirement. Materials of comparablecost with sufficient yield strength, but higher core losses, havebeen demonstrated for high-speed machinery 14.IV. CONCLUSIONThis paper has investigated the mechanical behavior and de-sign implications of conventionally laminated IPM rotors withunitary laminations for high-speed applications. Design tech-niques have been presented that are effective in mitigating thepeakrotormechanicalstressesathighspeeds.Ithasbeenshownthat structurally sound designs can be achieved without sig-nificant performance degradation through appropriate choicesof rotor dimensions, bridge and rib designs, shaft-to-rotor at-tachment, and materials selection. The example of a high-speedannular ISG application has been used with FEA to substan-tiate these conclusions. Further work should include prototypetesting of structural behavior, evaluation of temperature effects,and structural lumped parameter model development to incor-porate directly in the design optimization process.812IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 3, MAY/JUNE 2004REFERENCES1 W. Soong, “Design and modeling of axially-laminated interior perma-nent magnet motor drives for field-weakening applications,” Ph.D. dis-sertation, Dept. Electron. Elect. Eng., Univ. Glasgow, Glasgow, U.K.,1993.2 A. Vagati, A. Fratta, G. Franceschini, and P. M. Rosso, “A.C. Motorsforhigh-performancedrives:Adesign-basedcomparison,”inConf.Rec.IEEE-IAS Annu. Meeting, 1995, pp. 725733.3 A. Fratta, A. Vagati, and F. Villata, “Design criteria of an IPM ma-chine suitable for field-weakened operation,” in Proc. ICEM, 1990, pp.10591065.4 T. A. Lipo, T. J. E. Miller, A. Vagati, I. Boldea, L. Malesani, andT. Fukao, “Synchronous reluctance drives tutorial,” presented at theIEEE-IAS Annu. 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Meeting, vol. 1, Phoenix, AZ, 1999, pp.125131.11Nonoriented SheetSteelfor MagneticApplications,UnitedStates Steel,Pittsburgh, PA, 1978.12Alloy Steel Lamination Products, Armco Steel, Pittsburgh, PA, 1999.13Carpenter Alloy Steel Product Selection Guide, Carpenter Steel,Reading, PA, 1997.14 W. L. Soong, G. B. Kliman, R. N. Johnson, R. White, and J. Miller,“Novel high speed induction motor for a commercial centrifugal com-pressor,” in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, Phoenix, AZ,1999, pp. 494501.15ANSYS Multiphysics, ANSYS Corp., Canonsburg, PA, 1999.Edward C. Lovelace (S96M00) received the S.B.and S.M. degrees in 1988 and 1996, respectively,from the Department of Mechanical Engineering,and the S.M. and Ph.D. degrees in 1996 and 2000,respectively, from the Department of ElectricalEngineering and Computer Science, MassachusettsInstitute of Technology (MIT), Cambridge.In May, 2000, he joined SatCon TechnologyCorporation,Cambridge,MA,whichperformsresearch and development in electric power andenergy products, and is currently the Mechan-ical/Electromagnetics Group Leader. From 1988 to 1996, he was with GEAircraft Engines, Lynn, MA, where he was involved with developmentof advanced engine control system designs, military and commercial datacommunications systems, and ground and flight testing for hydromechanicaland digitally controlled engine systems. When he returned to MIT in 1994,he continued to specialize in the design and control of electric machinedrives for transportation applications. His current tech