汽车磁流变制动器设计的多学科设计优化【中文8000字】
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汽车磁流变制动器设计的多学科设计优化Edward J. Park, Luis Falcao da Luz, Afzal Suleman维多利亚大学机械工程系，P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6 2007年4月3日在线提供摘要本文介绍了使用磁流变（MR）流体的新型机电制动系统的开发。所提出的制动系统包括浸没在MR流体中并封闭在电磁体中的旋转盘，其中流体的屈服应力随电磁体施加的磁场而变化。可控的屈服应力引起旋转盘表面上的摩擦，从而产生减速扭矩。只需改变施加在电磁铁上的电流即可精确控制制动力矩。介绍了汽车MR制动器初始设计中涉及的关键问题，如MR流体选择，磁路设计，扭矩要求，重量限制，尺寸和温度。进行多学科有限元分析，包括静磁，流体流动和传热分析，以研究系统的行为，并作为多学科设计优化程序的基础。给出了优化过程的结果，并详细讨论了所得到的最终设计。关键词：磁流变液;汽车制动器;有限元分析;计算流体动力学;多学科设计优化;电动制动执行器1.简介这项工作涉及使用采用磁流变（MR）流体的机电制动器（EMB）开发用于汽车的新型线控制动系统。线控制动取代了每个车轮上的制动执行器和带有电气元件的制动踏板之间的机械连接。与传统的液压制动（CHB）系统相比，使用纯电子控制的制动系统有许多优点。只需更改软件参数和电气输出而不是调整机械组件，即可轻松调整制动器的性能和行为。这还可以更容易地集成现有和新的控制功能，如防抱死制动系统（ABS），车辆稳定性控制（VSC），电子驻车制动器（EPB）等，以及车辆底盘控制（VCC）和自适应巡航控制（ACC）。诊断功能和消除水污染制动液是额外的好处1，以及少量组件，简化布线和通用优化布局。在本文中，我们提出了一种用于每个车轮制动器的MR执行器设计。执行器由浸入MR流体中的旋转盘组成，封装在电磁铁中。原则上，可以通过改变施加到电磁铁的DC电流来控制制动扭矩。磁流变液-一种含有悬浮铁细颗粒的化合物 - 在磁场存在的情况下固定。MR流体的两个重要特征是：（i）它们表现出近似线性响应，即，增加的强度与施加的磁场强度成正比，（ii）它们提供快速响应，即MR流体变化在暴露磁场的毫秒内，从流体状态到近固态。 CHB系统在驾驶员踩下制动踏板的时间内表现出大约200-300ms的延迟，并且由于液压管路内的压力积聚而在车轮处观察到相应的制动响应。电动制动系统有可能大大减少这种时间延迟，从而减少制动距离。最近，德尔福2推出了一种性能类似于现有盘式制动器的EMB，其中制动垫由电动机驱动，而不是液压致动器。虽然MR流体在汽车中的应用多年来一直很有前途，但最近才有基于MR流体的机电设备开始取代全机械或液压机械设备。例如，通用汽车公司最近在Corvette和凯迪拉克塞维利亚STS和XLR上推出了磁力控制3，这是一种由德尔福开发的基于MR流体的悬架控制系统。这些新系统的重要意义在于车辆控制正在迅速摆脱传统机械部件的限制，例如弹簧，制动器，减震器和舵机。相反，实时传感器和高速直接电动驱动现在可以根据驾驶条件调整所有这些系统4。在这方面，MR制动器（MRB）致动器是用于具有高商业价值的汽车工业的有前途的技术。这个文章的概述如下。在第2节中，详细解释了MR流体现象。在第3节中，我们提出的汽车MRB设计进行了描述和建模。第4节和第5节介绍了提出的MRB的多学科有限元分析和后续设计优化。第6节介绍了设计优化结果，瞬态温度模拟以及最终MRB设计的最终尺寸和参数。第7节总结了论文。2.MR流体MR流体是通过将微米级铁颗粒添加到适当的载体流体（如油，水或硅图标）中而创建的。当没有外部磁场时，它们的流变行为几乎与载流子的流变行为相同。然而，当暴露于磁场时，铁粒子获得与施加的磁场对齐的偶极矩，以形成平行于场的线性链6。这可以将自由液体可逆地改变为具有可控屈服强度的半固体，这取决于所施加的磁场的大小。图1.宾汉塑料模型。尽管MR流体已知数十年，但它们已经经历了商业应用的稳定性和寿命问题。然而，最近这些问题已经解决并且商业应用开始出现，最明显的是上述汽车悬架中的可控阻尼器4以及用于地震响应控制的民用工程应用5。在文献中，发现MR流体的基本磁场依赖性流体特征可以通过简单的Bingham塑性模型来描述6。如图1所示，在该模型中，总剪切应力由下式给出其中是由于施加的磁场H引起的屈服应力，是恒定的塑性粘度，其被认为等于流体的非现场粘度，是剪切应变速率。在这里，塑性粘度定义为剪切应力和剪切应变率之间的斜率，这是牛顿流体的传统关系。在没有磁场的情况下，MR流体的真实行为表现出与Bingham模型的一些显着偏差（即，7。其他研究人员尝试了更精细的模型，如Herschel-Bulkely模型8,9，以适应流体中剪切应变率依赖的剪切稀化和剪切增稠现象。但是，如果正确使用式（1）为基于MR流体的设备10的设计提供了有用的基础，简单的Bingham模型仍然非常适合初始设计阶段5。此外，Lord Corporation的基于碳氢化合物的MRF-132AD和水基MRF-241ES在本文中进行了分析和比较，具有近似线性的实验应力 - 剪切速率曲线（见图2），这些曲线很接近于Bing-ham模型。表1总结了这两种最适合汽车制动应用的MR流体的一些关键特性。从表中可以看出，水基MRF-241ES具有比MRF-132AD更高的屈服应力，但磁导率更低。图2.在没有施加磁场的情况下剪切应力作为剪切应变速率的函数：（a）MRF-132AD和（b）MRF-241ES。表1 Lords MRF-132AD和MRF-241ES的主要特性属性 MRF-132AD MRF-241ES基础流体 烃 水工作温度 -40至+ 130 -10至+70最大屈服应力sy 44.5 kPa 69 kPa粘度g（无磁性 0.090.02 Pa之间 2.20.4 Pa现场应用） 500和800 503.汽车MR流体制动器图3所示为本文提出并分析的MR制动（MRB）执行器设计的基本结构的三维图示。 它包含一个在静态套管内封装的MR流体内旋转的圆盘。 在图3中，已经进行了切割以突出显示和分析的横截面。 图中的图例表示MRB的各种组件，MR流体除外，MR流体位于旋转圆盘（第3号）和定子（第5号）周围的窄通道（第7部分）中。图3.提出的MR制动器的基本配置。基于式（1）和图1所示的给定几何结构，延迟转矩或制动转矩 - 由MR流体与MRB内固体表面之间的界面上的摩擦引起 - 可写为11 其中n是与MR流体接触的制动盘的表面数量（例如，2个用于1个盘，其中MR流体覆盖两侧，4个用于2个盘等）; rz和rw分别是制动盘的外半径和内半径;和其中x是旋转盘的角速度，h是MR流体间隙的厚度，H是磁场强度，k和b是近似于磁场强度和屈服应力之间关系的常数参数。对于MR流体。然后，式。（2）可以改写为式（3）是比12中使用的Lord公司的低扭矩MRB更准确的形式，因为它可以考虑非恒定的磁场分布。这种改进是必要的，以便使用更大量的MR流体（导致磁场强度变化更大），而12用于交流感应电机制动。式（3）提供了对MRB动力学的一些了解，并显示了改善制动扭矩的可能方法，包括使用多个磁盘表面（增加n）或具有高屈服应力（增加k和/或b）的流体。通过放大积分中的第一项来提高制动扭矩，即增加塑性粘度g或减小间隙厚度h，是不希望的，因为这会导致更大的残余扭矩（即使没有施加制动也会增加阻力） ）。式（3）表明，携带单盘配置（因此，n = 2）在MRB的设计，制造和重量的简单性方面是理想的，具有多个盘产生更多的制动扭矩。因此，选择总共四个配置进行详细分析，包括两种不同几何配置，一个磁盘或两个磁盘，两个不同的MR流体，MRF-241ES或MRF-132AD流体之间的所有可能组合。考虑到磁盘表面的数量，影响MRB性能的其他参数是其组件的物理尺寸。现在，可以针对性能和重量优化图4中所示的MRB的物理尺寸。但是，必须限制其整体尺寸，以便制动器可以像典型的CHB一样安装在轮辋内。例如，考虑到车轮轮辋与制动器之间的一般建议最小间隙为3 mm，最大可接受的MRB1600轮的半径约为20厘米11。在第6节中，使用第5节中描述的多学科设计优化（MDO）程序优化图4中表示的各种尺寸参数。图4. MR制动器尺寸设计参数。最后，当电流i被提供给环绕MR流体的电磁体时，所施加的磁场H可以在MRB内产生，即，其中a是比例增益。然后，由于由施加的磁场引起的屈服应力而产生的制动扭矩的两个贡献和由于MR流体的摩擦和粘度引起的T1，可以通过执行式中的积分来导出（3）代替式（1），即其中h是盘的旋转速度，b = 1.注意在MRB内磁路周围驱动磁流的磁动势由13给出。下标（）f和（）分别表示MR流体和钢制部件; N是线圈中的匝数; h是MR流体间隙的长度;和Ls是钢套管中的流动路径的平均长度。然后，为了最大化制动扭矩，必须最大化Hf（最大化MR流体间隙中的磁场能量），同时必须最小化Hs（最小化钢路径中的能量损失）。方程中的比例增益a （4）和（5）然后可以从式（7）。4.有限元建模使用ANSYS开发了MRB的有限元模型（FEM），以准确表征制动器的行为。该模型是一个多物理场模型，它考虑了磁流变，MR流体流动，传热，MRB内的结构响应。由于MRB的多学科性质，存在非线性 - 例如磁饱和和非牛顿流体行为以及没有封闭形式的解决方案，有限元建模和分析是必不可少的设计步骤。我们的有限元分析程序包括磁静力学研究，然后在ANSYS中进行计算流体动力学（CFD）模拟。前者在整个MR制动器中提供磁场分布，这允许确定屈服应力sy。然后将磁场分布提供给CFD模型，该模型计算壁剪应力 - 施加在壁和盘表面上的摩擦力 - 以及MRB内的温度分布。有限元建模的第一步是确定基本的制动几何形状。由于我们的问题是轴对称的，意味着几何形状，材料属性和载荷沿切线方向都是一致的，因此只对横截面进行了建模。这样，解决方案成为二维问题的解决方案，允许使用ANSYS的平面元素（即用于静磁模型的PLANE13元素和用于CFD建模的FLUID141元素）和轴对称配置，以及从而大大降低了每次模拟的计算成本。对于静磁模拟，两个MR流体的B-H（磁流密度与施加的磁场）曲线是从制造商的规格和钢制元件（SAE 1010钢）的B-H曲线得到的。从ANSYS材料库获得套管和圆盘。钢是理想的低磁阻（或高磁导率）流体导管，可以引导和聚焦磁流体进入MR流体间隙13。图5包含这些B-H曲线，它们表明MR流体（MRF-132AD作为代表）和钢都具有非线性磁特性（即饱和）。在钢的情况下，饱和曲线的拐点开始出现在大约1.6T，这应该是钢的最大工作点，以便Hs in 式。 （7）根据图5b中钢的B-H曲线接近零，从而使制动扭矩最大化。图5. MRB设计中使用的材料的B-H曲线：（a）MRF-132AD（由Lord Co.提供）和（b）ANSI 1010钢。图6.使用MRF-241ES的单盘配置中的磁通密度分布：（a）薄外壳和（b）厚外壳。在有限元建模中，线圈中的电流被用作面积负载。图6显示了使用MRF-241ES流体的单盘配置中的磁通密度分布，其中（a）薄壳和（b）厚套管，其中表示磁流密度方向的箭头如下钢套管周围的预定路径。如图6所示，基于磁流体连续性的原理，较厚的套管在钢套管中表现出较低的磁通密度。图7a显示了使用MRF-241ES流体在同一配置中磁场强度的分布。图6b示出了所施加的磁场H与所得屈服应力sy之间的关系。当MR流体的场强（Hf）达到约130kA / m时，屈服应力开始饱和。结果，MRB的制动扭矩的增加变得有限。对于CFD模型的传热分析，指定了移动盘的速度，以及线圈中电流流动产生的热量（所谓的焦耳效应）。由流体和固体表面之间的摩擦产生的热量由CFD求解器计算。由于制动器由壳体周围的外部空气流冷却，因此还根据基于努塞尔数的经验关系确定了对流系数。图8显示了再次使用MRF-241ES流体从CFD分析获得的初步结果。图8a示出了双盘配置的壁剪切应力的分布，其发生在旋转盘与固定壳体和定子（中间盘）之间的MR流体间隙中。当使用基于烃的MRF-132AD流体代替时，虽然流体中的磁场强度值较高，但由于其较低的粘度值，壁剪切应力值实际上较低（参见表1）。与基于MRF-241ES的MRB相比，这导致更低的制动扭矩。图8b显示了与适度减速时的恒定制动相关的稳态温度分布（0.05 g，与长下坡路上的制动相对应）。5.多学科设计优化图7.使用MRF-241ES的单盘配置中的磁场强度分布：（a）磁场强度和（b）磁场强度与屈服应力。图8.使用MRF-241ES的双盘配置的CFD分析：（a）壁面剪切应力分布和（b）稳态温度分布。在开发描述MRB行为的有限元模型之后，编写了一个优化程序以获得最佳设计。为了成功将MRB用于乘用车，考虑到MRB的钢制部件很重并且可能会增加车辆的重量，因此需要最大改进的因素被认为是重量。制动扭矩也是一个重要的参数，但在这个设计阶段，只要满足最小扭矩要求，就认为它不如重量重要。因此，通过指定更大的标量加权因子（0.9-0.1），定义了优化的目标函数，使得重量比制动扭矩更重要。制动扭矩的最小可接受值和制动重量的最大可接受值分别选择为1010Nm和65kg。这些数字是优化问题的约束。在这个初始MRB设计阶段，虽然最小制动扭矩值与典型CHB的最小制动扭矩值相对应，但是最大重量的值被大大放宽，这样它将允许优化程序寻找更宽的设计空间。此外，每个MRB可能比同类车轮CHB具有更大的重量，因为它不再具有CHB的液压部件承载的额外重量：主缸，制动液管和泵。优化问题表示为最小化以上是优化的目标函数，受两个约束的约束，其中x包含设计变量，这些设计变量是图4中先前和下面表2中所示的尺寸设计参数。选择Tref = 1200 Nm和Wref = 30 kg作为扭矩和重量的参考值，xmin和xmax表示每个设计变量的所选最小值和最大值。表2显示了这些值的允许范围。表2每个变量的设计空间设计变量x 允许值，xmin-xmax（cm）th_磁盘 1.0-5.0（1个磁盘）0.5-2.5（2个磁盘）rad_磁盘 13.0-18.5 rad_th_线圈 0.25-2.5rad_th_套管 1-5（1个磁盘）0.5-2.5 （2个磁盘）ax_th_套管 0.25-2.5length_磁盘 3.0-8.0fl_gap 0.1图9.实施的模拟退火过程。针对上述问题应用了三种不同的优化方法：前两个（子问题近似和第一阶）是ANSYS的内置功能，第三个是模拟退火。后者是一种更强大的技术，为MRB的设计定制编程，但代价是计算时间。这是一种随机搜索方法，可以找到方程中目标函数f（x）的全局最小值。（8）两种ANSYS内置方法，可以使用并且需要较少的计算时间，可以快速了解每个优化变量的效果。在使用这两种方法进行评估后，将它们的结果与更精确的模拟退火方法进行比较，以获得具有最低目标函数值的最佳MRB设计。两种ANSYS内置方法背后的理论的深入描述见14，而模拟退火背后的理论见15。图9概述了MRB的实施模拟退火过程。6. 设计优化的结果表3每种设计配置的目标函数的最佳值设计配置 近似子问题 一阶法 模拟退火一个磁盘，MRF-132AD一个磁盘，MRF-241ES 101.7301 101.7311两个磁盘，MRF-132AD 100.8975 100.9598 100.7905两个磁盘，MRF-241ES 100.7144 100.5946 100.4547计算时间 20分钟 4小时 100小时式中优化函数优化方法的实现。（8）导致表3中列出的值，其中短划线表示没有找到满足所有规定约束的解决方案。表3的最后一行比较了每种方法在获得解决方案时所花费的计算时间。可以看出，与其他两种方法相比，模拟退火方法对于双磁盘配置和单磁盘配置的类似结果给出了最佳结果（最低目标函数值）。然而，这种改进的结果是一个很大的计算费用（即100小时）。第一阶方法似乎在良好结果和计算时间之间产生了良好的折衷。子问题近似方法产生最快的结果，但是对于单磁盘配置没有获得可行的解决方案。图10显示了在双盘MRF-241ES流体配置中使用三种方法的目标函数的收敛图。很明显，模拟退火方法产生最好的结果，而子问题近似和第一阶方法收敛到相似的值。图10.目标函数值的收敛性。从表3中可以清楚地看出，采用MRF-241ES流体的双盘配置是最佳设计解决方案-其产生的模拟制动扭矩为1025 N m，重量约为18 kg（相比之下，10 10 N m和64 kg最坏的情况设计）。但是，下面第6.1节中的后续传热分析显示了该设计中潜在的热量积聚问题。考虑到基于碳氢化合物的MRF-132AD比水基MRF-241ES具有更高的耐温性（见表1），我们为汽车制动应用选择的最终设计是采用MRF-132AD的双盘配置FL UID。最终设计在6.2节中有详细描述。6.1 动态温度分析回想一下表1，MR流体的工作温度范围是有限的。因此，我们还进行了重复使用MRB的温度分布分析;为此目的，进行了瞬态模拟，如图12所示。这模拟了按下和释放制动踏板的重复循环。当踩下踏板时，MR流体表现出最大粘度，从而产生完全的制动力;当踏板释放时，意味着车辆加速或翘曲，没有施加磁场并且表现出最小粘度。由于在ANSYS中无法明确定义时变材料属性，因此通过改变边界条件找到了另一种解决方案：当释放踏板时，盘速度设置为零，因此MR流体粘度对温度没有影响（制动器通过对流冷却。这种近似解决方案可以深入了解MRB中随时间变化的粘度效应。双盘MRB中反复制动 - 释放循环的温度随时间的变化如图11所示。图11.双盘MRB中的瞬态温度分析。注意，在图12中，按下制动器的持续时间设定为3.2秒，这是典型汽车从100公里/小时达到完全停止所需的平均时间。准确地假设制动器释放的持续时间是制动持续时间的六倍，即19.2秒。从图12a可以看出，在这些条件下，基于MRF-132AD的MRB内的最高温度在压制和释放制动器12个循环后开始收敛到约100（或373K），其中均衡达到温度，其中在制动循环期间由摩擦产生的热量等于在非制动循环期间通过对流消散的量。另一方面，图12b显示基于MRF-241ES的MRB的该平衡温度为约127（或400K），其显着高于MR流体的操作温度范围（-10至+ 70）。6.2.最终的 MRB设计使用Lord公司基于碳氢化合物的MRF-132AD流体得到的最佳MRB设计及其参数（使用模拟退火）在表4中给出。如图6所示，双盘配置（即，n = 4），在旋转盘之间有一个定子，是最佳的制动器设计，使目标函数最小化。这种设计产生的最大制动扭矩为1013 N，制动重量为27.9 kg，其本身（不考虑整个制动系统）的重量是同等性能CHB的两倍。表5列出了模拟使用或获得的其余设计参数。图13是具有适当物理尺寸的最终MRB设计的图示。图12.双盘MRB在重复制动 - 释放循环时的最大温度变化：（a）使用MRF-132AD和（b）使用MRF-241ES。表4最佳MRB设计参数设计变量 最佳值磁盘数量 2最大电流 12 A线圈数 约80th磁盘 1.2厘米rad磁盘 16.8厘米Rad_th_线圈 1.4厘米Rad_th_套管 0.5厘米ax_th_套管 1.6厘米length_磁盘 5.5厘米Fl_gap（h） 0.1厘米图13.最佳双磁盘MRB配置。7.结束语已经提出并设计了一种新的机电式汽车制动器。设计过程包括MRB的数学建模和有限元分析，以研究其在应用的磁场中的MR流体行为以及由此产生的传热现象。包括静磁，流体流动和传热分析在内的有限元分析形成了优化程序的基础，其中使用了三种不同的优化方法并进行了比较以获得制动器的理想尺寸，从而使足够的制动扭矩成为可能。由轻型MRB提供。使用这三种方法获得的结果在最终输出值和所需的计算时间方面进行了比较。正如预期的那样，发现模拟退火产生了最好的结果，尽管是计算成本。提议的MRB自然是纯电子控制的制动系统，它使用字节和安培代替杆和压缩制动液。这样可以轻松实现先进的制动控制功能，只需更少的元件，简化布线，改善制动响应并优化布局。在这项工作中，表明所提出的MRB可以在制动扭矩，温度和重量方面满足设计目标。未来的工作必须集中在生命周期测试上，以评估流体和系统的可靠性和使用寿命，并确保它能够有效地取代现有的液压制动技术。此外，通过在旋转盘中引入槽/孔或使用具有更好温度特性的水基MR流体，所提出的MRB可以在制动转矩，结构重量和散热方面得到进一步改善。致谢这项工作得到了加拿大自然科学和工程研究委员会（NSERC）的战略计划STPGP 246515-01的支持。参考文献1 dSPACE Gmbh。制动最佳在线。可从以下网站获取：www.dSPACE.com。2 Delphi Co. Delphi电动卡尺在线。特洛伊，密歇根州。可从以下网站获取：。3 Gilbert R，Jackson M. Magnetic ride control。 GM Tech Link 2002; 4（1）：1-2。4 McCosh D.工程学在NAIAS的趋势是serachlights背后的技术 - 北美国际。 2003年车展在线。可从：www.fi 获得。5 Yang G，Spencer BF，Carlson JD，Sain MK。大型MR流体阻尼器：建模和动态性能考虑因素。 Eng Struct 2002; 24（3）：309-23。6 Phillips RW。具有可变屈服应力的流体的工程应用。博士论文，加州大学伯克利分校，1969年。7 Kormann C，Laun M，Klett G. Actuator 94.在：Borgmann H，Lenz K，编辑。第四届新型执行器会议论文集。 Axon Technologies Consult GmbH; 1994年。 271。8 Lee DY，Wereley NM。使用Herschel-Bulkley模型分析电流和磁流变模式阻尼器。在：SPIE智能结构和材料会议论文集，加利福尼亚州纽波特海滩，2000年。 244-52。9 Wang X，Gordaninejad F.使用Herschel-Bulkely理论研究流动模式下的现场可控，电磁和磁流体流体阻尼器。在：2000年加利福尼亚州纽波特海滩的SPIE智能结构和材料会议论文集。 232-43。10 Lord Corporation。工程说明：使用MR流体进行设计在线，Cary，NC，可从以下网站获取：。11 Falcada Luz L.磁流变制动系统的设计。M.A.Sc. 论文，维多利亚大学，维多利亚，BC，加拿大，2004年。12 Bydon，S。采用磁流变制动器的感应电机轴定位系统仿真。 参见：2003年第28届ASR 2003仪器与控制研讨会论文集，波兰俄斯特拉发，2003年。28-34。13 Lord Corporation。 工程说明：磁路设计在线，卡里，北卡罗来纳州。 可从以下网站获取：。14 ANSYS Incorporated。 ANSYS理论参考。 宾夕法尼亚州卡农斯堡，2003年。15 van Laarhoven PJM，Aarts EHL。 在：模拟退火：理论和应用。 荷兰多德雷赫特：D。Reidel Publishing Co;1987年。Available online at Computers and Structures 86 (2008) 207216/locate/compstrucMultidisciplinary design optimization of an automotive magnetorheological brake designEdward J. Park, Luis Falcao da Luz, Afzal Suleman *Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6Available online 3 April 2007AbstractThis paper presents the development of a new electromechanical brake system using magnetorheological (MR) uid. The proposed brake system consists of rotating disks immersed in a MR uid and enclosed in an electromagnet, where the yield stress of the uid varies as a function of the magnetic eld applied by the electromagnet. The controllable yield stress causes friction on the rotating disk surfaces, thus generating a retarding torque. The braking torque can be precisely controlled by simply changing the current applied to the elec- tromagnet. Key issues involved in the initial design of the automotive MR brake are presented such as the MR uid selection, magnetic circuit design, torque requirements, weight constraints, dimensions and temperature. A multidisciplinary nite element analysis is per- formed involving magnetostatics, uid ow, and heat transfer analysis to study the behaviour of the system, and to serve as basis for a multidisciplinary design optimization procedure. The results of the optimization procedure are presented and the nal design obtained is discussed in detail.。 2007 Elsevier Ltd. All rights reserved.Keywords: Magnetorheological uid; Automotive brake; Finite element analysis; Computational uid dynamics; Multidisciplinary design optimization; Electric brake actuator1. IntroductionThis work is concerned with the development of a new brake-by-wire system for automotive vehicles, using an electromechanical brake (EMB) that employs magnetorhe- ological (MR) uid. Brake-by-wire replaces the mechanical connection between the brake actuator on each wheel and the brake pedal with electrical components. There are many advantages of using a pure electronically controlled brake system over a conventional hydraulic brake (CHB) system. The properties and behaviour of the brake will be easy to adapt by simply changing software parameters and electrical outputs instead of adjusting mechanical com- ponents. This also allows easier integration of existing and new control features such as anti-lock braking system (ABS), vehicle stability control (VSC), electronic parking* Corresponding author. Tel.: +1 250 721 6039; fax: +1 250 721 6051.E-mail address: sulemanuvic.ca (A. Suleman).brake (EPB), etc., as well as vehicle chassis control (VCC) and adaptive cruise control (ACC). Diagnostic fea- tures and the elimination of the water polluting brake uids are additional benets 1, as well as a small number of components, simplied wiring and generalized optimized layout.In this paper, we propose a MR actuator design for the brake in each wheel. The actuator consists of a rotating disk immersed in a MR uid, enclosed in an electromagnet. In principle, the brake torque can be controlled by changing the DC current applied to the electromagnet. Magnetorhe- ological uid a compound containing ne iron particles in suspension stiens in the presence of a magnetic eld. Two important characteristics of MR uids are: (i) they exhibit approximately linear response, i.e., the increase in stiness is directly proportional to the strength of the applied mag- netic eld and (ii) they provide fast response, i.e., MR uid changes from a uid state to a near-solid state within milli- seconds of exposing a magnetic eld. CHB systems exhibit about 200300 ms of delay between the time the brake pedal0045-7949/$ - see front matter 。 2007 Elsevier Ltd. All rights reserved. doi:10.1016/pstruc.2007.01.035208E.J. Park et al. / Computers and Structures 86 (2008) 207216is pressed by the driver and the corresponding brake response is observed at the wheels due to pressure build- up within the hydraulic lines. An electric brake system has the potential to drastically reduce this time delay, conse- quently bringing a reduction in braking distance. Recently, Delphi 2 introduced an EMB with performance similar to the existing disk brakes, with the brake pads actuated by an electrical motor, instead of the hydraulic actuator.While the application of MR uid in automotive vehi- cles has been promising for years, it is only recent that MR uid-based electromechanical devices have started to displace all-mechanical or hydraulic counterparts. For instance, General Motors recently introduced the Magnetic Ride Control 3, which is a MR uid-based suspensionTotal Shear Stresst (Pa)ty h1Shear Strain Rate g (s-1)Fig. 1. Bingham plastic model.control system developed by Delphi, on the Corvette and Cadillac Seville STS and XLR. The signicance with these new systems is that the vehicle control is quickly evolving away from the limitations of traditional mechanical com- ponents, such as springs, brakes, shocks and steering gear. Instead, real-time sensors and high-speed, direct electric actuation can now adjust all these systems depending on driving conditions 4. In this regard, a MR brake (MRB) actuator is a promising technology for the automotive industry with high commercial values.The outline of this paper is as follows. In Section 2, the MR uid phenomenon is explained in detail. In Section 3, our proposed automotive MRB design is described and modelled. Sections 4 and 5 present the multidisciplinary nite element analysis and subsequent design optimization of the proposed MRB. Section 6 presents design optimiza- tion results, along with transient temperature simulations, and the resulting dimensions and parameters of the nalparticles acquire a dipole moment aligned with the applied magnetic eld to form linear chains parallel to the eld 6. This reversibly changes the free owing liquid to semi-sol- ids that have a controllable yield strength, which depends on the magnitude of the applied magnetic eld.Although MR uids have been known for decades, they had been experiencing stability and longevity issues for commercial applications. Recently, however, these prob- lems have been solved and commercial applications are starting to appear, most notably as controllable dampers in the afore-mentioned car suspensions 4 and in civil engi- neering applications for seismic response control 5.In the literature, it is found that the essential magnetic eld dependent uid characteristics of MR uids can be described by a simple Bingham plastic model 6. As illus- trated in Fig. 1, in this model, the total shear stress s is given byMRB design. Section 7 concludes the paper.s syH gc_12. MR uidswhere sy is the yield stress due to the applied magnetic eldH, g is the constant plastic viscosity, which is consideredequal to the no-eld viscosity of the uid, and c_ is theMR uids are created by adding micron-sized iron par- ticles to an appropriate carrier uid such as oil, water or sil- icon. Their rheological behaviour is nearly the same as that of the carrier uid when no external magnetic eld is pres- ent. However, when exposed to a magnetic eld, the ironshear-strain rate. Here, the plastic viscosity is dened as the slope between the shear stress and shear-strain rate, which is the traditional relationship for Newtonian uids. True behaviour of MR uids exhibits some signicant departures from the Bingham model in the absence of aFig. 2. Shear stress as a function of shear-strain rate with no magnetic eld applied: (a) MRF-132AD and (b) MRF-241ES.E.J. Park et al. / Computers and Structures 86 (2008) 207216209Table 1Key properties of Lords MRF-132AD and MRF-241ESPropertiesMRF-132ADMRF-241ESBase uidHydrocarbonWater Operating temperature40 to +130 。C10 to +70 。C Maximum yield stress, sy44.5 kPa69 kPaMRB with the exception of the MR uid, which is located in the narrow channel (part no. 7) surrounding the rotating disk (no. 3) and the stator (no. 5).Based on Eq. (1) and the given geometrical congura- tion shown in Fig. 1, the retarding torque or brakingtorque which is caused by the friction on the interfacesViscosity, g (no magneticeld applied)0.09 0.02 Pa s between500 and 800 s 12.2 0.4 Pa s 50 s 1between the MR uid and the solid surfaces within the MRB can be written as 11magnetic eld (i.e., lp lp c_ ; H ) 7. Other researchers have tried more elaborate models such as the HerschelT b 2pnZ rzrwsr2dr 2pnZ rzrwgc_ sH r2dr2Bulkely model 8,9 to accommodate the shear-strain rate dependent shear thinning and shear thickening phenomena in the uid. However, if used properly Eq. (1) provides a useful basis for the design of MR uid-based devices 10,where n is the number of surfaces of the brake disk(s) in contact with the MR uid (e.g., 2 for 1 disk with MR uid covering the both sides, 4 for 2 disks, etc.); rz and rw are the outer and inner radii of the brake disk, respectively; andand the simple Bingham model is still very suitable forthe initial design phase 5. In addition, the Lord Corpora- tions hydrocarbon-based MRF-132AD and water-basedc_ rxbhand sy kHMRF-241ES, which are analyzed and compared in this paper, have nearly linear experimental stress-shear rate curves (see Fig. 2) that are well approximated by the Bing- ham model. Table 1 summarizes some of the key properties of these two MR uids that are most suitable for the auto- motive brake application. As can be seen from the table,where x is the angular velocity of the rotating disk, h is thethickness of the MR uid gap, H is the magnetic eld inten- sity, and k and b are constant parameters that approximate the relationship between the magnetic eld intensity and the yield stress for the MR uid. Then, Eq. (2) can be rewritten asthe water-based MRF-241ES has a higher yield stress than MRF-132AD, but lower magnetic permeability.T b 2pnZ rzrwrg r xkH hb,r2dr33. Automotive MR uid brakeShown in Fig. 3 is a three-dimensional illustration of the basic conguration of the MR brake (MRB) actuator design that is proposed and analyzed in this paper. It con- sists of a disk rotating within MR uid enclosed in a static casing. In Fig. 3, a cut has been made to highlight the cross-section that was modelled and analyzed. The legend in the gure indicates the various components of theFig. 3. Basic conguration of the proposed MR brake.Eq. (3) is a more accurate form than that of the Lord Cor- porations low torque MRB used in 12, because it can take into account non-constant magnetic eld distribu- tions. This improvement is necessary in order to use a greater amount of MR uid (which causes greater varia- tions in the magnetic eld intensity) than that of 12, which was used for AC induction motor braking. Eq. (3) provides some insight into the dynamics of an MRB and shows pos- sible ways to improve the braking torque, including the use of multiple disk surfaces (increasing n) or uids with high yield stresses (increasing k and/or b). Improving the brak- ing torque by amplifying the rst term in the integral, i.e., increasing the plastic viscosity g or decreasing the gap thickness h, is not desired as this would lead to a greater residual torque (increasing the drag even without the brakes applied).Eq. (3) indicates that, while carrying a one-disk congu- ration (hence, n = 2) would be ideal in terms of the simplic- ity of the design, manufacturing and weight of the MRB, having multiple disks generates more braking torque. Hence, a total of four congurations were selected for detailed analysis, involving all possible combinations between two dierent geometry congurations, one disk or two disks, and two dierent MR uids, MRF-241ES or MRF-132AD uids. Given the number of disk surfaces, additional parameters that inuence the performance of the MRB are the physical dimensions of its components.Now, the physical dimensions of the MRB shown in Fig. 4 can be optimized for performance and weight. How- ever, its overall dimensions must be restricted so that the210E.J. Park et al. / Computers and Structures 86 (2008) 207216Fig. 4. MR brake dimensional design parameters.brake can be tted inside a wheel rim as the typical CHB does. For example, considering the fact that the general recommended minimum clearance between the wheel rim and the brake is 3 mm, the maximum acceptable MRBradius for a 1600 wheel is about 20 cm 11. In Section 6,the various dimensional parameters represented in Fig. 4 are optimized using a multidisciplinary design optimization (MDO) procedure described in Section 5.Finally, the applied magnetic eld H can be produced within the MRB when current i is supplied to the electro- magnet encircling the MR uid, i.e.,H ai4where a is a proportional gain. Then, the two contributions of the resulting braking torque, Ty due to the yield stress induced by the applied magnetic eld and Tl due to the friction and viscosity of the MR uid, can be derived by performing the integration in Eq. (3) and substituting Eq. (1), i.e.,the average length of the ux path in the steel casing. Then to maximize the braking torque, Hf has to be maximized (maximizing the magnetic eld energy in the MR uid gap), while Hs has to be minimized (minimizing the energy lost in the steel path). The proportional gain a in Eqs. (4) and (5) then can be obtained from Eq. (7).4. Finite element modellingA nite element model (FEM) of the MRB was devel- oped using ANSYS to accurately characterize the brakes behaviour. This model was a multiphysics model that accounted for magnetostatics, MR uid ow, heat transfer, structural response within the MRB. Due to the multidisci-plinary nature of the MRB, with the presence of nonlinear- ities such as magnetic saturation and non-newtonian uid behaviour and the absence of closed-form solutions, nite element modelling and analysis were an essential design step.Our nite element analysis procedure consisted of a magnetostatics study followed by a computational uid dynamics (CFD) simulation in ANSYS. The former gives the magnetic eld distribution throughout the MR brake, which allows the determination of the yield stress sy. The magnetic eld distribution is then supplied to the CFD model, which computes the wall shear stresses the friction exerted on the walls and disk surfaces and the tempera- ture distribution within the MRB.The rst step in the nite element modelling was to dene the basic brake geometry. Since our problem is axi- symmetric, meaning that the geometry, material properties and loads are all consistent along the tangential direction, only the cross-section was modelled. This way, the solution becomes that of a two-dimensional problem, allowing the use of ANSYS plane elements (i.e., the PLANE13 ele- ments for the magnetostatics modelling and the FLUID141 elements for the CFD modelling) with axisymmetric for- mulation, and thus greatly reducing the computational cost of each simulation.For the magnetostatics simulation, the BH (magnetic ux density vs. applied magnetic eld) curves for the two MR uids were obtained from the manufacturers speci-cations and the BH curve for the steel element (SAE2p33T y nkarz rwi T ii51010 steel) that makes up the casing and disk(s) was3 p44obtained from the ANSYS material library. Steel is anT l 2h nlp rz rwh_ T vh_6ideal low reluctance (or high magnetic permeability) ux conduit that can guide and focus magnetic ux into thewhere h_is the rotational speed of the disk(s) and b = 1.MR uid gap 13. Fig. 5 contains these BH curves, whichNote that the magnetomotive force which drives the mag-netic ux around the magnetic circuit within the MRB is given by 13Ishow that both the MR uid (MRF-132AD as a represen- tative) and steel have a nonlinear magnetic characteristic (i.e., saturation). In the case of the steel, the knee of the sat- uration curve starts to occur at approximately 1.6 T, whichNi H dl H f h H s Ls7should be the maximum operating point of the steel so thatHs in Eq. (7) is close to zero according to the BH curve ofwhere the subscripts ()f and ()s denote the MR uid andthe steel parts, respectively; N is the number of turns in the coil; h is the length of the MR uid gap; and Ls isthe steel in Fig. 5b, thus maximizing the braking torque.In the nite element modelling, the current in the coil was applied as an area load. Fig. 6 shows the magnetic uxE.J. Park et al. / Computers and Structures 86 (2008) 207216211Fig. 5. BH curves of the materials used in MRB design: (a) MRF-132AD (courtesy of Lord Co.) and (b) ANSI 1010 steel.Fig. 6. Magnetic ux density distribution in one-disk conguration using MRF-241ES: (a) thin casing and (b) thick casing.density distribution in the one-disk conguration using the MRF-241ES uid, with (a) thin casing and (b) thick casing, where the arrows that represent the direction of the mag- netic ux density follow the intended path around the steel casing. As Fig. 6 shows, based on the principle of continu- ity of magnetic ux, thicker casing exhibits lower magnetic ux density in the steel casing. Fig. 7a presents the distribu- tion of the magnetic eld intensity in the same congura- tion using the MRF-241ES uid. Fig. 6b illustrates the relationship between the applied magnetic eld H and the resulting yield stress sy. As the eld intensity (Hf) of the MR uid reaches about 130 kA/m, the yield stress starts to saturate. As a result, the increase in the braking torque of the MRB becomes limited.For heat transfer analysis of the CFD model, the veloc- ity of the moving disks was specied, as well as the heat generated by the current ow in the coil (so-called the Joule eect). The heat generated by the friction between the uid and solid surfaces was computed by the CFD solver. Since the brake is cooled by the ow of outside air around the casing, the convection coecient was also determined, from empirical relations based on the Nusselt number. Fig. 8 presents preliminary results obtained from the CFD analysis, again using the MRF-241ES uid. Fig. 8a presents the distribution of the wall shear stress for thetwo-disk conguration, which occurs in the MR uid gap between the rotating disks and the stationary casing and stator (the middle disk). When the hydrocarbon-based MRF-132AD uid is used instead, while the magnetic eld intensity values in the uid are higher, the wall shear stress values are actually lower due to its lower viscosity values (see Table 1). This results in a lower braking torque com- pared to that of the MRF-241ES-based MRB. Fig. 8b shows the steady-state temperature distribution associated with constant braking at a modest deceleration (0.05 g, cor- responding to braking in a long downhill road).5. Multidisciplinary design optimizationFollowing the development of the nite element models describing the behaviour of the MRB, an optimization rou- tine was written to obtain the best possible design. For suc- cessful employment of the MRB into passenger vehicles, a factor requiring the most improvement was considered to be the weight, given that the steel components of the MRB are heavy and may add excessive weight to the vehi- cle. The braking torque is also an important parameter but, at this design stage, as long as a minimum torque require- ment is met, it was deemed less important than the weight. Hence, the objective function for the optimization was212E.J. Park et al. / Computers and Structures 86 (2008) 207216Fig. 7. Magnetic eld intensity distribution in one-disk conguration using MRF-241ES: (a) magnetic eld intensity and (b) magnetic eld intensity vs.yield stress.Fig. 8. CFD analysis in two-disk conguration using MRF-241ES: (a) wall shear stress distribution and (b) steady-state temperature distribution.dened so that a much greater importance is given to the weight than to the braking torque, by assigning a greater scalar weighting factor (0.90.1). The minimum acceptable value for the braking torque and the maximum acceptable value for the brake weight were chosen as 1010 N m and 65 kg, respectively. These numbers are the constraints of the optimization problem. In this initial MRB design phase, while the minimum braking torque value corre- sponds to that of typical CHBs, the value for the maximum weight was greatly relaxed such that it would allow the optimization procedures search for a wider design space. In addition, each MRB can potentially have more weight than a comparable on-wheel CHB as it would no longer have the extra weight carried by the CHBs hydraulic com- ponents: the master cylinder, brake uid lines, and pump. The optimization problem is expressed byThe above is the objective function for the optimization, subject to the two constraints, with x containing the design variables which are the dimensional design parameters ex- pressed in Fig. 4 previously and again in Table 2 below. Tref = 1200 Nm and Wref = 30 kg were chosen as the refer- ence values for the torque and weight, respectively, and xmin and xmax represent the chosen minimum and maxi- mum values for each design variable. Table 2 shows the allowed ranges of these values.Table 2Design space for each variableDesign variables, xAllowed values, xminxmax (cm)th_disk1.05.0 (1 disk)0.52.5 (2 disks)rad_disk13.018.5rad_th_coil0.252.5Minimisef x1000:1 T b T refWW 0:9refrad_th_casing15 (1 disk)0.52.5 (2 disks)ax_th_casing0.252.5subject toT b P 1010 Nm and W 6 65 kg8with xmin 6 x 6 xmaxlength_disk3.08.0_gap0.1E.J. Park et al. / Computers and Structures 86 (2008) 207216213Table 3Best values of the objective function for each design congurationDesign congurationSubproblem approximationFirst order methodSimulated annealingOne Disk, MRF- 132ADOne Disk, MRF- 241ESTwo Disks, MRF- 132ADTwo Disks, MRF- 241ES101.7301101.7311100.8975100.9598100.7905100.7144100.5946100.4547Computation time 20 min4 h100 hFig. 9. Implemented simulated annealing procedure.Three dierent optimization methods were applied to the above problem: rst two (subproblem approximation and rst order) are built-in capabilities of ANSYS and the third is simulated annealing. The latter is a more pow- erful technique, custom-programmed for the design of the MRB, but at the expense of computation time. This is a random-search method that can nd a global minimum for the objective function f(x) in Eq. (8). The two ANSYS built-in methods, being ready to be used and requiring less computation time, gave a quick insight into the eect of each optimization variable. After evaluating with the two methods, their results were compared to the more accurate simulated annealing method, in order to obtain the best MRB design with the lowest value for the objective func- tion. An in-depth description of the theory behind the two ANSYS built-in methods is found in 14, whereas the theory behind simulated annealing is presented in 15. Fig. 9 outlines the implemented simulated annealing procedure for the MRB.6. Results of design optimizationTable 3, where a dash indicates that no solution was found that met all the prescribed constraints. The last row of Table 3 compares the computation time taken by each method in obtaining a solution.It can be seen that simulated annealing method gave the best results (lowest objective function values) for both two- disk congurations and similar results for the one-disk con- gurations compared to those of the other two methods. However, this improved result comes at a great computa- tional expense (i.e., 100 h). The rst order method seems to produce a good compromise between good results and computation time. The subproblem approximation method produces the fastest results, but no feasible solution was obtained for the one-disk congurations. Fig. 10 presents a convergence plot of the objective function using the three methods in the two-disk, MRF-241ES uid conguration. It is clear that simulated annealing method produces the best results, while subproblem approximation and rst order methods converge to similar values.It is clear from Table 3 that the two-disk conguration with the MRF-241ES uid is the best design solution which produced a simulated braking torque of 1025 N m,2disks,MRF241Subproblem Approximation First OrderSimulated Annealing102101.8101.6Objective function101.4101.2101100.8100.6100.4100.2100The implementation of the optimization methods for the optimization function in Eq. (8) led to the values listed in05101520253035IterationFig. 10. Convergence of objective function values.214E.J. Park et al. / Computers and Structures 86 (2008) 207216while weighing about 18 kg (compared to 1010 N m and 64 kg for the worst case design). However, a subsequent heat transfer analysis in Section 6.1 below showed potential heat build-up problems in this design. Considering the fact that the hydrocarbon-based MRF-132AD is higher tem- perature resistant (see Table 1) than the water-based MRF-241ES, our nal design chosen for the automotive brake application was the two-disk conguration with MRF-132AD uid. The nal design is described in detail in Section . Dynamic temperature analysisRecall from Table 1 that the operating temperature ranges of the MR uids are limited. Hence, we also carried out a temperature distribution analysis resulting from repeated use of the MRB; and for this purpose, a transient simulation was performed, as shown in Fig. 12. This simu- lates repeated cycles of pressing and releasing the brake pedal. When the pedal is pressed, the MR uid exhibits the maximum viscosity that results in full braking power; when the pedal is released, implying accelerating or cruis- ing of the vehicle, there is no applied magnetic eld and the minimum viscosity is exhibited. Since time-varying material properties cannot be explicitly dened in ANSYS, an alternate solution was found by changing the boundary conditions: the disk velocity was set to zero when the pedal is released so that the MR uid viscosity has no eect on the temperature (the brake cools o by convection). This approximate solution gave some insight into the time-vary- ing viscosity eect in the MRB. The temperature variation with time to repeated brake-release cycle in the two-disk MRB is shown in Fig. 11.Note that in Fig. 12, the duration of pressing the brake was set to 3.2 s, which is the average time that a typical automobile takes to come to a full stop from 100 km/h. The duration of the brake release was conveniently assumed to be six times the braking duration, i.e., 19.2 s. It can be seen from Fig. 12a that under these conditions, the maximum temperature within the MRF-132AD-basedFig. 11. Transient temperature analysis in two-disk MRB.MRB starts to converge to about 100 。C (or 373 K) after 12 cycles of pressing and releasing the brake, where an equilibrium in temperature is reached in which the amount of heat generated by friction during the braking cycle equals the amount dissipated by convection during the non-braking cycle. On the other hand, Fig. 12b shows thatthis equilibrium temperature is about 127 。C (or 400 K) forthe MRF-241ES-based MRB, which signicantly higher than the MR uids operating temperature range ( 10 。C to +70 。C).6.2. Final MRB designThe resulting optimal MRB design and its parameters (using simulated annealing), employing the Lord Corpora- tions hydrocarbon-based MRF-132AD uid, are given in Table 4. As shown in Fig. 6, the two-disk conguration (i.e., n = 4), with a stator between the rotating disks, was the optimal brake design that minimized the objective func- tion. This design yielded a maximum braking torque of 1013 N and a brake weight of 27.9 kg, which by itself (with- out considering the overall brake system) is twice as heavy as that of a comparable performance CHB. Table 5 lists theFig. 12. Maximum temperature variation in two-disk MRB when subjected to repeated brake-release cycle: (a) using MRF-132AD and (b) using MRF- 241ES.E.J. Park et al. / Computers and Structures 86 (2008) 207216215Table 4Optimal MRB design parametersDesign variablesOptimal valuesNumber of disks2Maximum current12 ANumber of wire turnsApprox. 80th_disk1.2 cmrad_disk16.8 cmRad_th_coil1.4 cmRad_th_casing0.5 cmax_th_casing1.6 cmlength_disk5.5 cmFl_gap (h)0.1 cmTable 5Other MRB design parametersNumber of contact surfaces, n4Outer radius of brake disk, rz0.168 mInner radius of brake disk, rw0.118 mMR uid viscosity, g0.09 Pa sMR uid thickness, h1 10 3 mElectric constant, k0.269 Pa m/AProportional gain, a12.5 103 m 1Total inertia of brake disk
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