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中型 拖拉机 机耕 传动系统 设计

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中型船式拖拉机（机耕船）传动系统设计,中型,拖拉机,机耕,传动系统,设计

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华中农业大学本科毕业论文(设计)中期进展情况检查表 2012 年 3 月 20 日课题名称中型船式拖拉机（机耕船）传动系统设计学生姓名沈瑞东学 号2008307202893专 业农业机械化及自动化指导教师夏俊芳职 称教授主要研究内容及进展主要研究内容针对我国南方水田和旱地耕整的农艺要求，设计一种既可进行水田水耕，又可进行水田旱耕、旱田旱耕的中型船式拖拉机。设计的中型船式拖拉机具有动力输出装置，可在简易公路运输和田间作业转移，有3个前进挡位和1个后退挡位。进展查阅并学习相关资料，完成了任务书、外文翻译、开题报告以及文献综述；拟定并论证了传动方案，初步计算了各档总传动比及其分配，绘制了传动路线图；尚须完成的任务零部件性能和结构计算；零部件草图绘制及修订；完成总装图及零件图的绘制；撰写设计说明书及修改设计图样；整理资料准备毕业答辩；存在的主要问题及解决措施主要问题由于传动要求的非通用性，变速箱与分动箱不能进行选用；解决措施自行设计计算，选用齿轮进行组合装配；指导教师审查意见设计初步分析本设计中，分动器位于变速器之后。发动机的动力经变速器第二轴，通过花键套筒联轴器传至分动器第一轴。分动器兼有副变速器的作用，因此分动器将发动机动力分配给前后桥的同时进一步提高了传动比。分动器传动方案如图5-1。图分动器传动方案根据总传动方案的设计要求，分动器第一轴与变速器第二轴同轴，分动器第二轴与变速器中间轴同轴。动力输出从动轴同时穿过变速器中间轴和分动器第二轴。由此可知分动器第一轴与第二轴中心距A=168mm，第二轴为空心轴。分动器为中央传动，按照系统中传动比的分配，分动器的传动比为3。如图5-1，齿轮11为分动器主动齿轮，齿轮13为分动器从动齿轮，z13/z11=3。为满足总体结构设计的要求，加装齿轮12作为中间惰轮，使动力输出从动轴与分动器传动不产生干涉。综上所述，为满足中心距与传动比的要求，可取分动器主从动齿轮与动力输出主从动齿轮取相同的齿数与模数，同时得到齿轮12与齿轮13拥有相同的齿数与模数。齿轮设计分动器齿轮的设计校核方法与变速器齿轮设计方法相同。分动器齿轮采用渐开线圆柱直齿轮。因传递扭矩较大，材料均选40Cr，调质处理，硬度240280HBS。材料热处理质量可达到MQ要求。取齿轮的精度等级为887FH GB1009588。设计的齿轮参数及校核结果见表5-4。设计参数及校核结果齿轮编号111213齿数216363模数(mm)444齿宽(mm)888484材料40Cr40Cr40Cr热处理调质调质调质硬度(HBS)255255255接触强度计算应力(MPa)958.3638.2638.2许用应力(MPa)971.3971.3971.3疲劳极限(MPa)724.9724.9724.9安全系数1.0弯曲强度计算应力(MPa)252.1206.5206.5许用应力(MPa)1016.21016.21016.2疲劳极限(MPa)591.8591.8591.8安全系数1.4很显然，校核结果满足设计要求。轴的设计计算按扭转强度初选最小直径。第一、第三轴为实心轴，按式（423）进行设计计算，第二轴为空心轴，按式（424）设计计算。具体结构与尺寸参见设计图纸。分动器第一轴。材料40Cr，最小直径dmin=40mm，轴承选择单列深沟球轴承6028。分动器第二轴。材料45钢，内径d1=44mm，外径d=84mm，轴承选择单列深沟球轴承6217。分动器第三轴。材料45钢，最小直径dmin=65mm，轴承选择单列深沟球轴承6313。3华中农业大学本科毕业设计外文翻译本科毕业设计外文翻译 题 目动力换挡农用拖拉机的传动控制设计与最终自动调整姓 名沈瑞东学 号2008307202893专 业农业机械化及其自动化指导教师夏俊芳职 称教 授中国武汉二一二 年 二 月动力换挡农用拖拉机的传动控制设计与最终自动调整 Mara Tanelli , Giulio Panzani , Sergio M. Savaresi , Carlo Pirolaa Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, Italyb SAME Deutz-Fahr Group, Viale F. Cassani, 15, 24047 Treviglio (Bergamo), Italy摘 要：本文涉及大功率变速农用拖拉机传动控制系统的分析和设计。具体地说，对所有涉及单离合器与双离合器正确操纵换档的临界情况都进行了研究，并提出一个在所有操纵条件下能提供良好换挡性能的操控系统。深入来讲，为了适应元件公差及其在生产线上的普及，为传动控制系统中的最终调节提出了一个自动程序，用于对换挡质量进行客观分类并对其进行自动优化。该方法的适宜性在仪表化的车辆上做了彻底的测试。关键词：动力换档变速器 农用拖拉机 汽车系统 最终调整一、 简介与动机农用车要应对的工作条件比其他经验丰富的地面车辆复杂与艰巨得多10。事实上，农用车本质上是作为低速行进而提供大牵引力车辆而设计的。此外，在不平坦的土壤上轻易地移动使它们同样适合重型拖车运输。为保证个速度在运用中的最大灵活性以及在工作环境下充分利用发动机的最大功率，如今农业车辆往往配备了一个被称为动力换挡变速器的设备。这种变速器含有大量的齿轮（通常从9到30）并且能够通过执行档使发动机与驱动轮之间没有（或者至少最小）功率损失。通常，一个动力换挡变速器的特点是存在2个或更多（取决于齿轮的数量以及变速箱整体机械结构）连接到液压回路的湿离合器，液压回路的压力受比例电磁阀控制。考虑到齿轮数量之大以及要达到最佳换挡的事实，正确的处理好一些控制变量是必要的，以使这种变速器得到适当的控制。设计出如此的一个控制系统不是一件简单的事情。在科学文献中，有一些处理基于路面车辆的动力换挡或者双离合器传动控制的研究，例如，3-8,15，但是关于农用拖拉机的具体解决方案基本没有。这主要是因为广泛的工作条件以及变化的车辆载荷使农用车具有独特的性能规范，这种独特的性能规范就使得农用车最优换挡的定义不同于其他路面车辆。事实上，主要的限制因素是重复性的操作以及在所有作业路面上司机的舒适度，例如从沥青泊油路到粗糙的越野地形。另外，拖拉机上的载荷分布与其他车辆有很大的不同，产生这些不同的原因可能是前面或者后面的附加载荷，而这些附加载荷源于不同作业任务所使用的各种作业设备。最后，还要注意变化的操作条件往往是无法用车载传感器测量的，因此需要功能强大的而且容易调节的变速控制器。这些事实使得在农用拖拉机上保证最优且可重复的换档这一问题成为一项非常具有挑战性的任务。设计一个有效的传动控制系统，首先要确定影响换档品质的重要参数，例如，2,16。此外，该变速控制系统必须最佳地处理好以下相冲突要求之间的平衡：（1）、舒适换档；（2）、保证换挡过程中传到驱动轮的功率无损失；（3）、车辆传动寿命周期中造成最小的的机械零件磨损；此外，在工业背景下，一旦控制设计段完成而且控制系统成为最终产品，便开始进入处理结构公差与扩大生产的最终调整阶段，这一阶段使得最终系统不同于原始系统并用于控制验证和测试。因此，这一阶段是针对控制参数进行优化，从而保证预期的换挡性能在所有的车辆上得以实现。通常这一阶段是进行人体测试，测试者根据个人驾驶喜好与驾驶经验对控制参数进行调整。因此，最终调整很明显是一个关键而又艰难的阶段。事实上，由于没有客观的指数来评估换挡性能与舒适度，一个换档机构可能会被一个操作者认为是舒适的，但对另一个操作者来说却不是：这就意味着最终的调整可能导致不同车辆上同型换挡机构截然不同的换档行为。值得注意的是，换档特性是车辆操纵品质的一个重要组成部分，而车辆操纵品质往往被看做是制造商的商标，提供具有相同操纵特点车辆的能力可以成为使客户满意并提升顾客对该品牌忠诚度的关键。另外，该种建议性做法的另一个显著优点在于减少与最终调整有关的工业成本，这种成本的减少是通过减少每辆车调整说需要的换档次数以及使该调整程序自动化，因此就不需要经验丰富的操作者来完成了。值得注意的是，该项工作中所提出的方法在超出所研究问题之外的方面仍具有有效性，尽管它最初是针对一个特定的应用，例如，上述所提到的设计步骤构成了一个可行的范例，可应用于许多不同的生产情况。事实上，本文是旨在使具有控制系统的工业应用中的最终调整正式化的贡献之一，针对所考虑的问题提出系统的方法。在这反面，文献13，16中的结论提供了上述方法论的其他应用，分别解决了通过数据量化驾驶风格与安全、农用拖拉机设计与客观地调整运动反演控制的问题。尽管相对于本文所考虑的问题有所不同，但两者共享（所有或者部分）该项目所提出的体统方法，该方法由以下四个步骤构成：建立定义目标系统质量的性能特性评价；通过灵敏度分析实验指出待优化特征与重要变量之间的关系；定义成本函数；控制算法设计与成本函数优化基础上的最终调整程序的设计。对于所有上述那些应用，这一方法论使得本文中的结论成为大众爱好，在这些应用中，必须设计并调试好一个控制系统用于解决生产扩大与公差中的离散问题，这些离散问题使得潜在设备（例如，最终车辆）不同于作为设计目的的设备。由此产生的研究方向需要控制理论与优化设计方面的工具，并结合具体应用领域的知识。这里所提出的结论是基于米兰理工大学与道依茨法尔集团研发部的一项共同的研究项目（SAME, Lamborghini, Deutz-Fahr,Hrlimann, Adim Diesel and Deutz AG）。工作都集中在一个为大功率（200马力）农用拖拉机设计的动力换挡变速器上（见图一）。第一步致力于定义恰当的成本函数已经完成，该成本函数考虑了对换档舒适度与换挡品质的客观评估。然后，对所有相关的换档动力进行准确分析从而设计出一个简单而有效地传动控制策略。最后，为了在每辆生产车上获得尽可能最好的换挡性能，提出自动调整阶段以保证令人满意的和可重复的换挡性能。本文结构如下。第二部分液压与机械的角度介绍动力换挡传动系统。第三部分旨在介绍用来评价换挡质量的性能指标。第四部分介绍所推荐的动力换挡控制策略，无论是对单离合器换档还是对双离合器换档，还有与控制参数相关的性能指标灵敏度分析实验结果。最后，第五部分主要介绍最终自动调整和相关的实验结果。二、 系统介绍图二描述了动力换挡变速器的整个机械布局。如图所示，动力从发动机（图二的左边）依次通过两个不同的齿轮箱（由三个不同齿轮构成的HML组和由三个不同比例大小齿轮构成的123组）流向驱动轮。该变速器还包括其他两部分，即运动逆变器和模式选择器。运动逆变器（见11,16）是由两个离合器构成的电液系统，该系统可执行自动运动逆变，例如，司机仅仅动一下操纵杆就能使车辆从前进速度变成反向速度。模式选择器有三种不同的工作模式，即爬行模式、工作模式和运输模式，这些模式只有当拖拉机静止的时候才能改变。接下来，我们致力于换挡控制并且只考虑两个齿轮箱，同时假设没有进行运动逆变（注意，顺便提一下，在运动逆变时司机不能使用操纵杆）并且一种固定的模式已经投入工作。由于两个齿轮箱是串联的，发动机与驱动轮之间有九种不同的传动比（不考虑比例固定部分的最终差别）。从概念上讲，虽然这两个齿轮箱存在机械上的不同，但对于控制设计目的的作用却是一样的。每个齿轮都与一个湿式离合器相连：要选择一个特定的齿轮，相应的离合器必须完全接合，使得由发动机传出的扭矩完全通过离合器传递。该项目中所使用的都是多盘湿式离合器，为了能够正常工作（以及以后选择相应的齿轮），摩擦盘表面之间必须紧密结合并且相互之间的的正压力要足够大以产生足够的摩擦力来保证摩擦盘之间不会产生相对滑动。 图三是摩擦盘间正压力与离合器油压之间具体关系的示意图。对于变速分析，必须考虑三个不同的区段。第一阶段（即，来自于大气压力），压力的增加对摩擦盘之间的正压力不产生影响。当增加到所谓的转折点压力（见图三），相互之间距离减小为零的摩擦盘开始接合。从此点开始，正压力成比例的增加。在这一阶段，摩擦盘之间的摩擦力能够传递一定的传入扭矩，但是由于摩擦盘间存在一定的相对滑动，没有确定的传动比。一旦达到工作压力（如图三），正压力已经足够大以至于离合器摩擦盘之间不存在相对滑动从而保证了精确的传动比。图四为液压系统示意图，该图解释了离合器中的压力是如何被控制的。一个比例电磁阀控制六个定向启闭阀将每个离合器与掌控液压连接起来。该液压结构产生了如下离合器行为：当定向阀门开启时，离合器上的压力与主压力相等。由于这是一个单向阀，可知压力只能上升，尽管压力压力会降低。相反的，当定向阀关闭，离合器上的压力为零。因此，可用的控制变量如下：(1) 主液压力。注意，由于没有压力传感器，真正的控制变量就是电磁比例阀。这样的一个变量可以通过静态图与输出压力相连。接下来，我们将该压力视为控制变量，并切记上述所提到的电流到压力的转化必须完成；(2) 每个定向阀的启闭状态。为了用动力换挡变速器实现换档，将脱出离合器上的压力必须为零，而传入离合器上的压力必须为最大。注意，非动力换挡变速器是先使将脱出离合器脱出啮合然后再让传入离合器进入啮合，这样一来就存在一个时间间隔，在这一时间间隔内车辆处于中间状态并且发动机传出的扭矩无法传递到驱动轮。在农用车辆中，这种中间状态是必须要避免的，因为超大负荷会导致停车。因此，保证换挡过程中有连续的扭矩传递到驱动轮是极其重要的，这是动力换档变速的一个主要特征。为了对该系统描述进行总结归纳，表一列出了九种可用的齿轮组合以及与之相啮合的离合器。可以看到，通常换档只需要变动一个离合器（例如，齿轮箱HML中的一个）。我们将这种换档称之为单离合换档。然而，当要在三档与四档或者六档与七档时间转换时就必须变动两个离合器（一个属于齿轮箱HML，一个属于齿轮箱123），使得下面将要描述的换挡控制器的设计更加复杂。我们将这种换档称为双离合器换档。三、 换挡质量评估正如第一部分所讨论的那样，定义一个客观地换挡质量评估会产生如下好处：（1） 为换档性能给出了一个特别而客观地指标，有助于比较不同的车辆和（或）不同的控制算法。（2） 依靠适当性能指标的自动优化，最后调整阶段相对容易和更少的资金投入。定义最合适成本函数的关键问题在于决定被测信号与换档舒适度以及换档品质之间有意义的关系。一些在汽车方面进行的研究，在通过加速度测量评估舒适度方面显示出良好的研究结果，例如9，14。对于该项目中所考虑的类型车辆，很明显上述文献中的信号是不合适的，这是因为土壤引起的测量噪声掩盖了换档对车辆加速度的实际作用。此外，加速器并不是农用拖拉机上的车载标准传感器。因此，我们致力于研究换挡品质与车辆速度的关系，车辆速度的测量通常可以通过车轮编码器获得。正如文献16中所讨论的，这种信号可以用来进行符合要求的舒适度评估。为了理解质量指标设计的逻辑依据，图五展示了在三种不同换档情况下车辆速度与时间的关系，三种性能由一名专业司机评断：第一种（图五a）被分为优秀级别，而剩下两种（图五b和c）分别被分为中等级别和较差级别。上述三种换档情况下的速度性能如下：速度总是从一个恒定值增加（所有情况中都必须换高档）到一个较高的最终值，因为在换挡过程中发动机保持恒定且连续的转速，该终值只取决于最终传动比。真正使这几种换档产生不同的是速度提高时的平稳度。注意，事实上，换档品质好的图五a中，速度沿着平滑的斜线上升，而换挡质量中等的情况下速度的提高只是分段线性的（如图五b椭圆框中的部分）并且在速度提高阶段有明显的初始负向脉冲。最后，换挡品质差的情况中速度特性非常不规则并伴随巨大的速度波动（如图五c中椭圆框中的部分）。基于这些考虑，性能指标被定义为：该公式中，表示被测轮速，表示描述最优换当中速度特性的参考信号。被测轮速表示为：式中是通过车轮传感器测得的车轮角速度，是车轮半径。参考信号被设计成有三部分组成（如图六）。第一部分由运动开始时的恒定速度，即式中表示司机换挡的时刻。运动最后的参考速度也是恒定的，表示为：式中是换档开始时的发动机速度（再次强调，换档过程中发动机速度是恒定且连续的），是车轮的平均半径，是输入齿轮的传动比（当换档是由司机完成时，它也是已知的）。在上述两个速度限制之间变化的参考速度被定义为，趋于线性，表示为：式中定义为：即，是被测速度比初始参考速度小的最后时刻，而时刻定义为：因此表示被测速度初次到达参考速度终值的时刻。可以看到，每个换档阶段超出参考信号的部分都暴露了一个与运动品质和舒适度相关的不同问题。尤其是，有三个有待控制系统解决的问题（再看看图六）：（1） 换档开始时速度的负向变化；（2） 加速阶段的速度的波动；（3） 换档后速度稳定阶段速度的继续增大又相继减小。这些问题的解决是通过对不同的控制变量进行适当调整。为进行如此调整，通过基于被测信号的可估客观性能参数来很好的把握这三种现象是很关键的。为此，三个不同的成本函数,和被考虑进来，分别对应于每个运动阶段，定义为：式中固定区间的时间间隔已经被通过专门的灵敏度分析定义了，是在固定区间上算出来的。具体地，式（10）中的表示为：即，使在好坏两种换档情况下的差值最大化时的，该时刻的分类也由专业司机的水平决定。事实上，司机们都是从整体上来评判运动的。于是，在那些被认为低品质的换档中，那些换档情况系超过预定阀值的值被选择用来对进行调整，通过公式（11）。基于所获得的结果，一个1.75秒的间隔被用来计算。为了对换挡质量评估的讨论进行总结，表二列出了图五中的三种换档所对应的值。可以看到，所选的成本函数正确地把握了运动质量，并且与专业四级的估计相符。四、 换挡控制其设计这部分介绍了换挡控制系统的设计。为实现所提出的方法，强调指出第二部分所描述的传动结构具有的一些固有局限性是很有必要，这些局限性必须予以考虑，正如文献1,11,12中所述。具体如下：（1） 由于当启闭阀处于关闭状态时将脱出离合器上的压力为零，调整将脱出离合器上的压力是不可能的。此外，压力消失的具体时刻（即离合器松开的时刻）无法知道，尽管压力力度的变化被认为是非常快的。（2） 由于启闭阀是单向的，离合器上的压力只能升高；（3） 离合器中的油压无法测量。因此，压力值是通过一个将比例阀输入电流和离合器压力联系起来的静态关系来估计的。考虑到这一示意图对所有车辆来说都是独一无二的，以及每个离合器的行为的确都受到一些（数量未知）因素（例如，温度、表面磨损以及摩擦盘圆周速度）的影响，尚无法得到实际驱动扭矩的可靠估计，正如文献11，12中所述。这一事实使得无法设计出一个闭环的压力控制器来解决换挡问题。考虑到上述限制，一个开环控制器将被设计。因此，控制问题的核心就在于定义并优化一条恰当的参考压力曲线来指挥能获得预期换挡性能的比例阀。4.1、单离合器换挡控制回顾表一中的齿轮与离合器组合，单离合器换当中只涉及两个离合器：一个是将脱出离合器，一个是传入离合器。因此，在这种类型的换档中，控制算法在于定义主侧面压力以及恰当地选择将脱出离合器必须断开的时刻。图七展示了一种典型单离合换挡压力曲线。司机执行换档后，主压力（即传入离合器上的压力，该离合器上的启闭阀处于开启状态）逐渐上升至转折点（KP）压力值（如何自动定义这样一个液压阀将在第五部分讨论）。这一初级阶段使用来保证传入离合器已经能够传递扭矩（再看图三可知，当压力值低于转折点压力值时，驱动扭矩无法传递到车轮）。这一充盈期持续一个固定的时间，实验证明为500毫秒。该数值对于传动系中所有离合器达到预想的转折点压力值已经足够了。接下来，动力换挡的核心阶段开始：在Overlap时间段内，传入离合器的压力增大，离合器所能传递的扭矩也随之增大。再往后，当时间到达时，将脱出离合器断开（如图七虚线）。最后，主压力上升到最大值以使传入离合器进入完全工作状态。具体来说，压力沿着斜线增加至一可调最大值，然后跃至最终的最大值。图七所示压力的最后阶段取决于传动系中液压回路的特性。更确切的说，在该压力区间上，调整图七中斜线终点所对应的压力终值实际上是可能的，尽管最后阶段实际上是由液压回路的一个安全控制所引起的（当压力值到达设定值时阀门机械关闭），该安全控制使得压力到达最大值，这样设计是为了保证离合器在任何（一些可能的反常情况）运行状态下都不会断开。至于换挡控制不同部分的压力值，假设整个压力区间分从零到两兆帕；从开始到转折点压力大约占0.4兆帕（假设该数值是不同传动的平均值），调整区间（即斜线部分）上升到1.8兆帕。因此，压力增加但无法调节的最后阶段大约占0.2兆帕，相当于总压力变化的10%。注意到在Overlap区间内，将脱出离合器仍然处于啮合状态，因此给发动机增加了附加扭矩载荷。所以，当Overlap区间太短时，将导致传入离合器无法传递足够的扭矩进而使车辆产生所不希望的突然停车，当Overlap区间太长，拖拉机会由于附加扭矩载荷而减速，这些都将给司机带来不适。另外，离合器表面的过度磨损会增加。对于转折点压力水平，也应做类似的考虑。换句话说，这两个参数值的调整对于获得最优换档起着决定性作用。为控制单离合换档选择最优参数值，选用Eq（8）中的指标。实际上，控制参数与最优参数之间的偏差反映在换档开始时的显著减速，这将导致车辆前进速度的波动（例如，指标所具有的特点，见Eq（8）基于实验性灵敏度分析的最优化调整已经进行。图八显示了获得的结果，即，对于12和23两种换档，图八（上）和图八（下）中的指标的数值分别是充盈压力与转折点压力偏差值和Overlap区间持续时间的函数。使充盈压力与转折点压力产生偏差中的权衡（即获得一个增加的P）显而易见：正如所指，只有转折点压力的精确估计确定后才能获得最优换档。对于Overlap区间的持续时间，这种权衡就没那么明显了：因为实验室在了低负荷条件下进行，那么，在这种情况下最优Overlap区间的持续时间接近于零。反之，在高负荷换档中，为该参数选择一个准确值是重要的：因此，原理上可以考虑一个预定控制器，该控制器根据当时的发动机功率（可以通过发动机控制器知道其值）为Overlap区间持续期选择最恰当的数值。为评估控制器的效果，图九展示了未优化控制参数与已优化控制其参数的单离合换档中时间与被测车速的关系。未优化控制参数与已优化控制参数情况下相应的值分别为12.86和1.48。图九中所显示换档的优化后参数值为兆帕，。图九42、双离合器换档控制在双离合换档中，两个齿轮机构中的离合器都参与进来：理想情况下，双离合换档的控制逻辑可以看做是和单离合换档一样。但实际上变速箱HML中液压回路的动态特性与变速箱123中的不同。具体来说，两个变速箱中离合器脱出所需要的时间是完全不同的，尽管两个变速箱的控制指令是同一时刻发出的。两个变速箱中的不同是因为变速箱中离合器尺寸的不同而使得其中的压力值不同。由于要处理不同的扭矩水平，不同尺寸的离合器是必要的。此外，变速器相对于主液压蓄能器的位置使得压力回路的长度不同，这也影响了变速箱中的压动力。123变速箱中的压力较高。就这点而论，为了准确的实现双离合换档，需要先脱出变速箱123再脱出变速箱HML，以便将两者之间的不同考虑进去。具体地说，在将脱出离合器脱出之前，变速箱123需要更长的时间来补偿所要代替的更高的压力梯度。变速箱HML延迟的时间已经调整以使变速箱HML脱出时两个变速箱的压力水平大致相同。因此需要引进一个附加控制参数。该新控制变量称为DelayHML,它表示变速箱123脱出时刻（）与变速箱HML脱出时刻（）之间的时间间隔(见图十)。如图十所示，为了将液压设备引起的延时考虑进来，将脱出HML组的脱出只有轻微的延时，等于DelayHML。自从引进新的控制变量后，进行了一个专门的灵敏度分析来对其进行优化调整。在这种情况下，指标和指标都被考虑进来，见Eqs.(8)和Eqs.(9)。事实上，在操纵的一开始就正确地获得了速度脉冲，这主要是KP压力和Overlap持续区间的作用；而描述了加速阶段的振幅，这很大程度上取决于DelayHML的值。最后，值得注意的是，在t大于后压力值最后的斜线阶段上升，此时传入离合器开始进入啮合阶段，但两个传入离合器可能不会同时进入啮合。基于所提到的控制方法，啮合阶段准确开始的途径是通过成本函数估计的，因此目前没有直接的啮合调整方法。图十一描述了所得结果，显示了和的值，和是Overlap和DelayHML的函数。为简明起见，省略了KP压力的值的分析过程，因为所得结果与单离合换档所讨论的相似。通过检验图十一，可以得到一些结论。首先注意到每个控制参数（即，Overlap和DelayHML）对一个单独的指标有显著的影响。即，Overlap主要影响指标，而DelayHML主要影响指标。这一事实可以解耦优化阶段，并考虑两个连续单变量的优化问题，考虑到最后调整阶段这些就更容易解决了。参考文献1 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AMAA 2010, Berlin, Germany, May 2010. p. 1219.14 Scarlett J, Prince JS, Stayner RM. Whole-body vibration: evaluation of emission and exposure levels arising from agricultural tractors. J Terramech 2007;44(1):6573.15 Schwab M. Electronically-controlled transmission systems current position and future developments. Int Cong Transport Electron 1990:33542.16 Tanelli M, Savaresi SM, Manzoni V, Monizza F, Taroni F, Mangili A. Estimating the maneuver quality of an automatic motion inverter for end-of-line tuning in agricultural tractors. In: Proceedings of the 17th IFAC world congress, Seoul, Korea; 2008. p. 1072631. 19 / 19Transmission control for power-shift agricultural tractors: Designand end-of-line automatic tuningMara Tanellia, Giulio Panzania, Sergio M. Savaresia, Carlo PirolabaDipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, ItalybSAME Deutz-Fahr Group, Viale F. Cassani, 15, 24047 Treviglio (Bergamo), Italya r t i c l ei n f oArticle history:Received 24 May 2010Accepted 14 November 2010Available online 8 December 2010Keywords:Power-shift transmissionAgricultural tractorsAutomotive systemsEnd-of-line tuninga b s t r a c tThis paper addresses the analysis and design of the transmission control system for a high-powerpower-shift agricultural tractor. Specifically, all the criticalities involved with the correct managementof both single clutch and double clutch gear shifts are investigated, and a control system capable ofproviding good shifting performance in all operating conditions is proposed. Further, to comply withcomponents tolerances and spreads in the production line, an automatic procedure for the end-of-linetuning of the transmission control system is proposed to objectively classify the quality of the gear shiftand automatically optimize it. The suitability of the proposed approach is thoroughly tested on an instru-mented vehicle.? 2010 Elsevier Ltd. All rights reserved.1. Introduction and motivationAgricultural vehicles have to cope with working conditionswhich are more complex and demanding than those experiencedby other ground vehicles, 10. In fact, agricultural vehicles areessentially designed to work at low speed while providing largetraction forces. Moreover, their ease of moving on uneven soilmakes them suitable also for heavy trailers transportation. To en-sure the maximum flexibility of use at each speed and to exploitthe maximum engine power available in all working conditions,nowadays agricultural vehicles are often equipped with a so-calledpower-shift transmission. This kind of transmission has a largenumber of gears available (typically from 9 to 30) and it allowsto perform a gearshift with no (or at least with a minimum) lossof power from the engine to the driving wheels.Usually, a power-shift transmission is characterized by thepresence of two or more (depending from the number of gearsand the overall mechanical architecture of the gearbox) wetclutches connected to an hydraulic circuit, whose pressure can beregulated by a proportional solenoid valve. Considering the largenumber of gears available and the fact that to achieve an optimalgear shift it is necessary to correctly manage several control vari-ables, this kind of transmission needs to be properly controlled.The design of such a control system is not a trivial task. In thescientific literature, some works dealing with power-shift or dualclutch transmissions control for ground vehicles are available,see e.g., 38,15, but very little has been done on specific solutionsfor agricultural tractors. This is mainly due to the fact that agricul-tural vehicles have very specific performance specifications due tothe very broad range of working conditions and variability of thevehicle load, which make the gear shift optimal performance defi-nition different from that of ground vehicles. As a matter of fact,the main constraints are the repeatability of the manoeuvre andthe comfort of the driver on all working grounds, which vary fromasphalt roads to rough off-road terrains. Also the load distributionin tractors is much different than for other vehicles, due to the factthat it might be due to either front or rear additional loads due tothe various working instruments that need to be employed fordifferen tasks. Finally, note also that the variation of the operatingconditions is most often non measurable via on-board sensors, andthus asks for robust and easily tunable gear shift controllers. Thesefacts make the problem of ensuring an optimal and repeatable gearshift on an agricultural tractor a very challenging task.To design an effective transmission control system, first of allthe most significant variables which influence the gear shift qualitymust be identified, see e.g., 2,16. Further, the gear shift controlsystem has to optimally manage the trade-off among the followingconflicting requirements:(i) yield comfortable gear shifts;(ii) guarantee that no loss of power to the driving wheels occursduring gear shifts;(iii) cause a minimum wear and tear of mechanical componentsover the life of the vehicle transmission.0957-4158/$ - see front matter ? 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.mechatronics.2010.11.006Corresponding author. Tel.: +39 02 2399 3621; fax: +39 02 2399 3412.E-mail address: tanellielet.polimi.it (M. Tanelli).Mechatronics 21 (2011) 285297Contents lists available at ScienceDirectMechatronicsjournal homepage: /locate/mechatronicsMoreover, in the industrial context, once the control designphase is accomplished and the control system is implemented intofinal products, an end-of-line tuning phase is usually scheduled todeal with constructive tolerances and production spreads whichcause the final system to be different from the prototype one usedfor control validation and testing. Hence, this phase is tailored tooptimize the controller parameters so as to guarantee that theexpected gear shifting performance is achieved on all vehicles.Usually, this phase is carried out by human testers, who tune thecontroller parameters based on personal driving preferences andexperience. Thus, is it clear that end-of-line tuning is a crucialand difficult phase to deal with. As a matter of fact, since no objec-tive indexes to evaluate the gear shift performance and comfort ex-ist, a gear shift can be qualified as comfortable by one operator, butnot by another one: this means that the final tuning can lead tovery different gear shift behaviors on different vehicles of the sametype. Note that, as the vehicle handling qualities, of which the gearshift characteristics are a significant component, is often consid-ered as a trademark of the single manufacturer, the ability of deliv-ering vehicles with identical manoeuvre features can be a key toachieve customers satisfaction and to promote customers loyaltyto the brand. Moreover, another significant advantage of the pro-posed approach is that of reducing the industrial costs associatedwith end-of-line tuning by reducing the number of gear shiftsneeded to tune each vehicle and by making the process automatic,thus not requiring highly experienced operators to perform it.It is worth noting that the approach presented in this work,even though tailored to a specific application, has a validity whichgoes beyond the considered problem, as the aforementioneddesign steps constitute a working paradigm which can be appliedin many different production contexts. As a matter of fact, this pa-per is one of the first contributions which aims at formalizing theend-of-line tuning of industrial applications endowed with controlsystems, proposing a systematic approach to the considered prob-lem. In this respect, the results in 13,16 offer other applications ofthe proposed methodology and address the problem of quantifyingof the driving style and safety via measured data, and of designingand objectively tuning the motion inversion control of an agricul-tural tractor, respectively.Although being different problems with respect to that consid-ered herein, both these works share (all or part of) the systematicapproach presented in this work, which is constituted by the fol-lowing steps:? an evaluation of the characteristic features which define thequality of the considered system;? an experimental sensitivity analysis to single out the relationbetween the features to be optimized and the measurablevariables;? the definition of the cost functions;? the design of the control algorithm and of the procedures for itsend-of-line tuning grounded on the cost functions optimization.This methodology makes the results in the present paper ofgeneral interest for all those applications in which a control systemmust be designed and tuned while dealing with the dispersioncoming from production spreads and tolerances which make theunderlying plant (i.e., the final vehicle) different from that usedfor design purposes. The resulting research area requires tools bothof control theory and optimization, combined with the specificapplication-domain knowledge.The presented results are based on a joint research workbetween the Politecnico di Milano and the R&D Department ofthe SAME Deutz-Fahr Group (SAME, Lamborghini, Deutz-Fahr,Hrlimann, Adim Diesel and Deutz AG). The work has been focusedon a power-shift transmission designed for high-power (200 HP)agricultural tractors (see Fig. 1).The first effort has been devoted to define appropriate costfunctions which allow an objective evaluation of gear shift comfortand quality. Then, an accurate analysis of all relevant gear shiftdynamics has led to design a simple but effective transmissioncontrol strategy. Further, to obtain the best possible gear shift per-formance on every production vehicle, an automatic tuning phaseis proposed which guarantees satisfactory and repeatable gear shiftperformance.The structure of the paper is as follows. Section 2 provides adescription of the power-shift transmission system, both from anhydraulic and a mechanical viewpoint. Section 3 is focused on pre-senting the performance indexes which have been selected tojudge the gear shift quality. In Section 4, the proposed controlstrategy for power-shift gear shifts is described, both for the caseof single clutch and double clutch gearshifts, together with the re-sults of an experimental sensitivity analysis of the performance in-dexes with respect to the controller parameters. Finally, Section 5is devoted to describe the end-of-line self-tuning procedure and topresent related experimental results.2. System descriptionThe overall mechanical layout of the considered power-shifttransmission is depicted in Fig. 2. As can be seen, the power flowsfrom the engine (on the left of Fig. 2) towards the driving wheelsthrough two different gearboxes: the High-Mean-Low (HML)group, composed of three different gears and the 123 group, whichalso comprises three different gear ratios. The transmission is com-pleted with two other components, namely the motion inverterand the mode selector. The motion inverter (see 11,16) is an elec-tro-hydraulic system, constituted by two clutches, which allows toperform an automatic motion inversion, i.e., it takes the vehiclefrom a, say, forward speed to a reverse speed with the driver sim-ply acting on a lever. The mode selector allows to choose amongthree different working modes: creep, work and transport, whichcan be varied only when the tractor is at standstill. In what follows,we concentrate on the control of the gear shift, and consider thetwo gearboxes only, assuming that no motion inversion is occur-ring (note, in passing, that during a motion inversion the drivercannot command a gear shift), and that a fixed mode has beenengaged.As the two gearboxes are in series, nine transmission ratios be-tween the engine and the driving wheels are available (disregard-ing the final differential, whose ratio is fixed). Conceptually,although mechanically different, the two gearboxes can be treatedequally for control design purposes. Each gear is associated with aFig. 1. The tractor employed in this work.286M. Tanelli et al./Mechatronics 21 (2011) 285297wet clutch: to select a particular gear the corresponding clutchmust be completely engaged, so that the torque coming from theengine can be completely transferred via the clutch itself. Thewet clutches handled in this work are multi-plate wet: in orderto be engaged (and hence to select the associated gear) the surfacesof the plates must be in close contact and the normal force they ex-change must be large enough to develop a friction force whichguarantees that no relative slip occurs between them.Fig. 3 shows a schematic view of the physical relationship be-tween normal force and clutch oil pressure. For gear shift analysis,three different zones must be considered. Starting from zero (i.e.,from atmospheric pressure), an increase in the pressure bringsno changes in the normal force between the plates, which remainsnegligible.When the so-called kiss-point pressure is reached (see Fig. 3),this distance that separates the plates has been covered and thesurfaces come into contact. From here over, the normal force in-creases proportionally to the pressure. During this phase, thefriction force between the surfaces allows to transfer a certainamount of incoming torque through the clutch but, as there is anon-zero relative slip between the plates, the gear ratio isindefinite.Once the engage pressure is reached (refer again to Fig. 3), thenormal force is large enough to annihilate any relative slip be-tween the plates of the clutch and a precise gear ratio can bedefined.Fig. 4 shows a schematic view of the hydraulic scheme, whichallows to understand how the pressure in a clutch can be con-trolled. There are six ONOFF directional valves which connecteach clutch to the master hydraulic pressure, regulated by a pro-portional solenoid valve. Such hydraulic architecture yields the fol-lowing clutch pressure behavior: when a directional valve isswitched ON the pressure in the clutch is equal to the master pres-sure. Being this a one-way valve, note that the pressure can onlyincrease, even if the master pressure decreases. Conversely, whenthe directional valve is switched OFF the pressure in the clutch iszero. As such, the available control variables are the following:(1) the master hydraulic pressure. Note that, as no pressure sen-sors are available, the real control variable is the currentdriving the proportional valve. Such a variable can be linkedto the output pressure via a static map. In what follows, wewill regard the pressure as control variable, keeping in mindthat the aforementioned conversion from current to pres-sure has to be performed;(2) the onoff status of each directional valve.To execute a gear shift with a power-shift transmission, theoutgoing clutch must be brought to zero pressure, whereas theincoming clutch must be brought to maximum pressure. Note thata non-power-shift gear shift would disengage the outgoing clutchand then engage the incoming one. In so doing, there is a timeinterval in which the vehicle is in a neutral state, and no enginetorque can reach the driving wheels. In agricultural vehicles theneutral state must be avoided, as the large load forces would causethe vehicle to stop. Thus, it is of utmost importance to ensure acontinuous torque transfer to the driving wheels during the gearshift, which is the main characteristic of a power-shift gear shift.To conclude the system description, Table 1 shows the nineavailable gears together with the associated engaged clutches. Ascan be seen, usually a gear shift requires to change only one clutch(i.e., the one belonging to the HML gearbox). We refer to such gearshifts as single clutch gear shifts. However, when the 34 and 67gear shifts are considered, two clutches must be changed (oneHML gearbox 123 gearboxMotion InverterMode selector Fig. 2. Schematic view of the power-shift transmission.Kiss-pointEngagePressure bar Normal force NFig. 3. Oil pressure in the clutch as a function of the normal force.H M L1 2 3Fig. 4. Simplified hydraulic scheme of the considered transmission.Table 1Available gears and respective engaged clutches.GearLMH1231?2?3?4?5?6?7?8?9?M. Tanelli et al./Mechatronics 21 (2011) 285297287belonging to the HML and one to the 123 gearbox), making the de-sign of the gear shift controller more complex, as will be shownsubsequently. We refer to such gear shifts as double clutch gearshifts.3. Gear shift quality assessmentAs discussed in Section 1, defining an objective gear shift qualityassessment yields the following advantages:? it provides a unique and objective indication of gear shift per-formance, helpful to compare different vehicles and/or differentcontrol algorithms.? it makes the end-of-line tuning phase easier and cheaper byrelying on the automatic optimization of appropriate perfor-mance indexes.The crucial issue to deal with in defining the most suitable costfunctions is that of determining meaningful relationships betweenmeasured signals and gear shift comfort and quality. Several stud-ies have been carried out in the Automotive context, showing goodresults in evaluating comfort via acceleration measurements, seee.g., 9,14. For the type of vehicle considered in this work, it is easyto understand that this kind of signal is not suitable, as soil irreg-ularities cause measurement noise which shadows the actual gearshift contributions to vehicle accelerations. Moreover, accelerome-ters are not standard sensors to have on-board of agricultural trac-tors. Thus, we concentrated on investigating the relationshipsbetween gear shift quality and vehicle speed, whose measurementis commonly available via wheel encoders. As discussed in 16,this signal can be exploited to provide satisfactory comfortevaluation.To understand the rationale behind the quality index design,Fig. 5 shows the time histories of the vehicle speed in three differ-ent gear shifts, whose performance was judged by an expert driver:the first one (Fig. 5a) has been classified as good, whereas the lasttwo (Fig. 5b and c) as medium and bad, respectively. The speedbehavior in the three considered gear shifts is as follows: the speedalways starts from a constant value and increases (up-shifts havebeen performed in all cases) until it reaches a higher final value,which depends only on the final gear ratio as the engine speed iskept fixed and constant during the gear shift. What really makesthe gear shifts different is the smoothness with which the speed in-creases. Note, in fact, that while in the good gear shift in Fig. 5a thespeed increases with a smooth ramp, in the medium quality gearshift the speed increase is only piecewise linear (see dotted ovalbox in Fig. 5b) and shows a significant initial undershoot. Finally,the bad gear shift is characterized by a quite irregular speed behav-ior and large oscillations (see dotted oval box in Fig. 5c).Based on these considerations, the performance index has beendefined asJ Varvmt ?vreft?;1wherevm(t) is the measured wheel speed andvref(t) is a referencesignal to be designed, which describes the speed behavior in anoptimal gear shift. The measured vehicle speedvm(t) is computed asvmt 14X4i1xitri;2wherexi(t), i = 1, . , 4 are the wheel rotational speeds measuredvia the wheel encoders and ri, i = 1, . , 4 are the wheel radii.The reference signalvref(t) has been designed as composed ofthree different parts (see Fig. 6). The first is defined by the constantspeed value at the beginning of the manoeuvre, i.e.,vref1vmtreq;3where treqis the time instant at which the gear shift is requested bythe driver. The reference speed in the last part of the manoeuvre isalso constant and computed asvrefendxengtreqrsInc:;4wherexeng(treq) is the engine speed at the beginning of the gearshift (recall that the engine speed is fixed and constant during thegear shift), r is the average wheel radius andsincis the transmissionratio of the incoming gear (also known when the gear shift is issuedby the driver).The reference speed evolution in time between these limitingspeed levels, which definesvref2, is chosen as linear, yieldingvref2t vref1vrefend?vref1t2? t1t ? t1;5where the time instant t1is defined ast1:jvmt1 ?vref1j P 0? fjvmt ?vref1j t1g:6Namely, t1is the last time instant at which the measured speed islower than the initial reference speedvref1, while the time instantt2is defined ast2:jvmt1 ?vrefendj 0;8t tDO,HMLbut the two incoming clutchesmay not engage simultaneously. With the proposed controlapproach, the fact that the engagement phase occurs in a correctway is evaluated by means of the cost functions, therefore withouta direct tuning of the engagement instant.The obtained results are reported in Fig. 11, which shows thevalues of J1and J2, respectively, as functions of Overlap and Delay-HML. For the sake of conciseness, the analysis for the KP pressurevalue is not shown, as the obtained results are similar to those dis-cussed for the single clutch gear shift.By inspecting Fig. 11, some remarks can be made.? First of all note that each controller parameter, i.e., Overlap andDelayHML, has a predominant effect over one single index.Namely, Overlap mostly affects the J1index, whereas DelayHMLthe J2one. This fact allows to decouple the optimization phase,and to consider two successive single variable optimization-1000-50005001000150002468101214P kiss-point pressureJ1 index1-22-3010020030040000.511.522.53Overlap msJ1 index1-22-3mbarFig. 8. Sensitivity analysis on single shifts controller parameters.0123456785.566.577.588.5Time sSpeed km/hNot optimizedOptimizedFig. 9. Time histories of the measured vehicle speed in a single clutch shift: results with non-optimized (dashed line) and with optimized (solid line) controller parameters.ttFig. 10. Double clutch gearshift control: master pressure profile (solid line) andoutgoing clutches disengagement (dashed lines).M. Tanelli et al./Mechatronics 21 (2011) 285297291problems, which can more easily managed in view of the auto-matic end-of-line tuning phase. Specifically, as will be describedin more detail in Section 5, the optimal value for Overlap will befound by minimizing J1, while DelayHML will be tuned accord-ing to J2. Specifically, to assess the correctness of the sequentialminimization of the performance indexes, one has to observethat the function J2(?, DelayHML) has the same shape for all val-ues of Overlap. Therefore, once a value of Overlap has been fixedby optimizing J1, then the optimization of J2done by varying thevalue of DelayHML will lead to a final value for J2which isapproximately always the same (note also that the cost functionalways decreases as the value of DelayHML increases indepen-dently of the value of Overlap). Of course, the final value of J2will not be rigorously the same irrespectively of the value ofOverlap with which it is evaluated and which is determinedby the minimization of J1, but the small differences in the finalvalue for J2are not practically relevant as they yield no signifi-cant changes in the final gear shift performance.? Note further that the results in Fig. 11b seem to suggest that alarge value of DelayHML would bring good quality gear shifts.Nonetheless, it is worth pointing out that, as DelayHMLincreases, the clutches are left slipping for an increasing amountof time. Thus, this parameter should be kept at the lowest pos-sible value so as to prevent an excessive wear of the clutches.Section 5 will better discuss how to effectively deal with thisissue.? Finally, it is worth comparing the results obtained in the singleand double clutch gear shift controllers as far as the value ofOverlap is concerned. Specifically, at the end of the previous sec-tion we pointed out that in the single clutch gear shift at leastin low load conditions a non-zero Overlap would induce onlythe detrimental effect of yielding a longer manoeuvre, withoutintroducing any potential increment in the performance. Inthe double clutch gear shifts, instead, a trade-off arises, due tothe fact that one needs to manage the two gearboxes differ-ently. Therefore, while on the one hand allowing a non-zeroOverlap time interval has indeed the detrimental effect of yield-ing a longer (hence worse) gear shift, on the other hand it offersthe advantage of taking the pressure level up to a value which isappropriate for the correct disengagement of the two gearboxesthat work at different pressure levels. Finally, note that, as men-tioned in Section 4.1, if a single clutch gear shift performancemust be handled in the face of additional large loads, then anon-zero Overlap might be of help to optimally deal with theincreased inertia of the vehicle, thereby leading to an adapta-tion of the Overlap time duration as a function of the load con-dition. Up to now, however, the tuning of this parameter hasbeen optimized for the end-of-line test conditions, whichinvolve gear shifts carried out at nominal load on asphalt road,and thus led to set it to zero for the single clutch case.To assess the controller effectiveness, Fig. 12 shows the timehistories of the measured vehicle speed in a double clutch shiftwith non-optimized and optimized controller parameters.The corresponding values of the J1and J2indexes are J1= 24 andJ2= 102.98 for the non-optimized manoeuvre and J1= 1.31 andJ2= 35.38 for the optimized one, respectively. The optimized valuesfor the gear shift shown in Fig. 12 are KP = 5.2 bar, Overlap = 390 msand DelayHML = 210 ms.4.3. Analysis of the acceleration phaseThe last issue to be considered for gear shift control, which isshared both by single and double clutch gear shifts, is the possibleovershoot and oscillatory behavior present at the end of themanoeuvre, when the clutch of the incoming gear needs to be fullyengaged and the vehicle must be brought to reach the final, steady-state, speed value.Before discussing this issue and presenting the proposed solu-tion to limit the overshoot, it is worth pointing out that in theFig. 11. J1and J2index values as functions of the controller parameters.234567891011Time sSpeed km/hNon optimizedOptimizedFig. 12. Time histories of the measured vehicle speed in a double clutch shift: results with non-optimized (dashed line) and with optimized (solid line) controller parameters.292M. Tanelli et al./Mechatronics 21 (2011) 285297considered tractor the engine speed is regulated via a dedicatedengine control unit, the internal controller of which is not directlyaccessible. The only interaction with the engine controller can berealized via the specification of the engine speed reference signalwhich should be tracked during the gear shift. The nominal choiceis to have a constant reference engine speed equal to the onemeasured immediately before the gear shift request.Within this setting, if we consider an up-shift, and we letxeng,xoeng,xwandsbe the engine speed, the engine reference speed, thewheel speed and the transmission ratio of the incoming gear,respectively, the evolution in time of these variables during thegear shift can be schematically represented as in Fig. 13.Specifically, immediately before the gear shift the tractor pro-ceeds at substantially constant engine (dotted line in Fig. 13) andvehicle speed (the solid line in Fig. 13 is the scaled wheel speedxw/s, which can be directly compared with the engine speed).Once the gear shift is requested (in correspondence of the leftmostsolid vertical line in Fig. 13), the disengagement of all the clutchesassociated with the incoming gear occurs, and there is a slippingphase during which the system is characterized by two degreesof freedom, as the engine and the tractor can proceed at differentspeeds and they interact via the torque transmitted by the incom-ing clutches, which are slipping.Once the clutches are fully engaged (in correspondence of thesecond solid vertical line in Fig. 13), the engine and the wheelshave the same speed (denoted byxEin Fig. 13), and the systemhas only one degree of freedom. As can be seen from Fig. 13, duringthe slipping phase the engine speed decreases even though the ref-erence engine speedxoeng(horizontal solid line in Fig. 13) is keptconstant at the value at which the gear shift began. This is due tothe fact that the torque at the clutch in this phase is generatedalong the direction of motion of the transmission output shaft, sothat it accelerates the vehicle while it opposes to the rotationof the incoming shaft, thus decelerating the engine. During thetraction phase which follows the clutches engagement, the enginecontroller, in view of the engine speed error, tries to compensatefor it by increasing the engine torque. Due to large vehicle inertia,this acceleration phase has a long settling time, and the enginecontroller dynamics (most probably endowed with an integralaction) is such that the transient is characterized by an overshootand subsequent oscillations, which cause discomfort to the driver.To counteract this phenomenon, which is more critical in thedouble clutch up-shifts, the idea is to appropriately modify the en-gine reference speed (of course, an alternative may be to directlyact on the engine controller; in our case, this is not possible asthe engine control algorithm cannot be accessed or modified).To this end, consider the modified engine speed referenceshown in Fig. 14: as can be seen in the slipping phase the enginereference speed is decreased along a ramp up to the point at whichthe incoming clutches are fully engaged, while, during the tractionphase, the reference is increased along a second ramp which takesthe engine speed back to the final value which coincides with thatat the beginning of the gear shift.The motivation for this choice is as follows: in the slippingphase the engine is forced to decelerate in view of the torque gen-eration mechanics. Hence, in order to limit the magnitude of thetracking error and the resulting detrimental effect of the relatedintegral action of the controller, it is convenient to let the referencespeed decrease accordingly. This has also the additional beneficialeffect of shortening the slipping phase, as the engine does not try33.544.555.566.577.581250130013501400145015001550160016501700Time sEngine speed rpmtraction phaseslipping phaseengEw/oengFig. 14. Schematic view of the time histories of engine speed, wheel speed in a gear shift with modified engine speed reference.33.544.555.566.577.581250130013501400145015001550160016501700Time sEngine speed rpmtraction phaseslipping phaseoengEw/engFig. 13. Schematic view of the time histories of engine and wheel speed in a gear shift with constant engine speed reference.M. Tanelli et al./Mechatronics 21 (2011) 285297293to accelerate opposing to the clutch engagement, thus limiting theclutch wear and tear.Then, once the clutch engagement is detected the engine mustbe accelerated as quickly as possible while avoiding the overshoot.To achieve this, a ramp set-point has proved appropriate, and anappropriate (fixed) value of the slope has been tuned for each gearshift. The same tuning has been performed to define the ramp dur-ing the slipping phase, with the only difference that the point atwhich the clutch is engaged is not known a priori, and thus needsto be estimated. Specifically, the clutch is defined to be engagedwhen the engine speedxengequals the scaled wheel speedxw/s.To correctly compare the two speed values, however, one mustconsider that, even during constant motion, these are not perfectlyequal due to the geometry of the transmission.Based on a large set of gear shifts data, the residuals of theequation:xeng?xw=s 012have been studied, so that it was possible to verify that they arenormally distributed and that the confidence interval at 99% wasgiven by a spread of 30 rpm. Thus, the clutch is considered to befully engaged when the relationjxeng?xw=sj 6 30 rpm13holds over a time window ofDt = 250 ms. This last condition isneeded to average out the measurement noise and avoid outliers.To appreciate the effectiveness of the proposed approach Fig. 15compares the time histories of the engine speed, of the engine tor-que and of wheel speed measured in a double clutch gear shift withconstant (dashed line) and modified (solid line) engine speed refer-ence. As can be seen, with constant engine speed reference the en-gine controller makes the engine torque saturate to its maximumvalue, and this causes of course a delay in the settling time and sig-nificant oscillations at the end of he transient. This clearly reflectson the vehicle speed, the transient of which significantly benefitsfrom the engine reference modification, yielding a much morecomfortable gear shift. The positive effect can be objectively quan-tified by means of the quality index J3(see Eq. (10): the gear shiftwith constant engine speed reference yielded J3= 720.4, while thatwith the modified reference scored J3= 73.4.05101512501300135014001450150015501600Time sEngine speed rpmwith modified engine reference speedwith constant engine reference speedEngine reference speed(a) 051015102030405060708090100Time sEngine torque % maximum torquewith modified engine reference speedwith constant engine reference speed(b) 0510152324252627282930Time sSpeed km/hwith modified engine reference speedwith constant engine reference speed(c) Fig. 15. Time histories of engine speed (a), engine torque (b) and wheel speed (c) in a double clutch gear shift: results obtained with constant (dashed line) and modified(solid line) engine speed reference.294M. Tanelli et al./Mechatronics 21 (2011) 2852975. End-of-line automatic gear shift tuningWe now present the automatic end-of-line tuning algorithm de-signed to optimize the gear shift controller parameter values whichis needed to ensure satisfactory and repeatable performance ondifferent production vehicles. The parameters that have to be cor-rectly tuned are:(1) the KP pressure for each clutch;(2) the Overlap and DelayHML time intervals duration for doubleclutch shifts.Note that the profile chosen for modifying the engine referencespeed is not object of end-of-line tuning, as the fact that a closed-loop controller is present to regulate the engine speed, combinedwith the chosen reference signal adaptation strategy, yielded a ro-bust solution not needing additional tuning.As the kiss-point pressure has a clear physical meaning, a modelbased procedure will be followed to identify its value.For the double shift parameters, instead, an optimizationprocedure is proposed, based on the quality indexes described inSection 3.5.1. Kiss-point pressure identificationWe have previously discussed that, if a clutch is completely en-gaged, the overlap of another clutch is seen by the engine as anadditional load torque. As the engine is itself controlled so as tokeep its speed constant (at a set-point imposed by the driver),when this additional load torque acts on it more power is neededto keep the engine speed constant. From this basic idea, the algo-rithm to identify the kiss-point is as follows. While a clutch is en-gaged, the clutch pressure whose kiss-point value is to beidentified is slowly increased. The engine power (available asoutput by the engine control unit) is monitored: when its value in-creases meaning that the overlapping clutch is actually transfer-ring torque the corresponding pressure value is identified as thekiss-point one.As the sensitivity analysis showed (see Fig. 8), a precision of atleast 500 mbar is needed in the KP pressure identification to guar-antee optimal gear shift performance.Fig. 16 reports the KP pressure identification results obtained byapplying the above identification procedure for four times on threedifferent vehicles (each colored1bar refers to a single vehicle and itis divided into four smaller bars that represent different executionsof the automatic procedure proposed). The maximum standarddeviation of the identified KP values is of 90 mbar, which, com-pared to the measured KP values, shows that the proposed algo-rithm is strongly repeatable. It is also worth underlining that theprocedure can be carried out in a fully automatic way, as it doesnot require the vehicle to move. In fact the tuning involves onlythe HML and 123 clutches, and the procedure can be executedwhile opening the final clutch between the transmission and driv-ing wheels, thus without transferring torque to the ground andwith the vehicle at standstill.5.2. Automatic tuning of the double clutch gear shift controllerparametersUnlike the kiss-point pressure, the two parameters involved in adouble clutch gear shift do not have a precise physical meaning.Therefore, their optimal values will be found by experimental opti-mization of the introduced cost functions. Namely, the Overlaptime interval will be tuned so as to minimize the cost function J1.Notice, in fact, that for double clutch gear shifts this parametercannot be easily set to a fixed value for all vehicles (as for singleclutch ones) as it changes significantly from a vehicle to another.As for DelayHML, recalling the discussion at the end of Section 4,its tuning phase is performed by minimizing the following costfunction:JHMLJ2;DelayHML c1J2 c2DelayHML14where c1and c2are constant scaling factors. The cost function JHMLtakes into account both J2and the value of DelayHML itself in orderto prevent excessive wear of the clutch surfaces. Specifically, theconstant parameters c1and c2in (14) are selected so that the twoterms on the right-hand size of (14) have the same size. The neces-sity of an equal weighting of the two components is motivated bythe following fact: as mentioned in Section 4.2 the optimal valueof J2occurs for large values of DelayHML, which are not appropriatein general, as they induce wear and tear of the HML clutches thatare left slipping for long times. Thus, one needs to weight DelayHMLso that its final value is not too large. On the other hand, however,DelayHML must not be too low either so not to lose the advantage ofdifferent disengagement times for the two gearboxes involved in adouble clutch gear shift.As all indexes can be computed in real time, the tuning proce-dure is as follows:1. define a maximum number of gear shifts NMaxand a lower-bound JiMinon the performance index JiHLM123050001000015000ClutchPressure mbarVehicle 1Vehicle 2Vehicle 3Fig. 16. Kiss-point pressure identification results obtained on three different vehicles.1For interpretation of color in Figs. 118, the reader is referred to the web versionof this article.M. Tanelli et al./Mechatronics 21 (2011) 2852972952. while N 6 NMaxi. perform a gear shift and compute the performance index Jiii. if Ji6 JiMinin the last three gear shifts go to Step 3iii. else update the value of the parameter pkto be optimized viaa gradient-based optimization algorithm, i.e.,pk1 pk?arJipk;wherearJi(pk) is the step size which depends on the experimen-tally computed gradient of the cost function (ais a positive real-val-ued parameter used to scale the gradient);3. save and store the current value of pkNote that, to terminate the auto-tuning procedure, it is requiredthat the termination condition on the cost function value is met inthree successive manoeuvres, so as to account for possible varia-tions in the working condition which can affect the single gearshift. Furthermore, the tuning cycle is repeated while the numberof performed gear shifts is lower than the upper-bound NMax= 35.This additional condition has been added to the tuning logic forsafety reasons, so as to ensure that the automatic procedure termi-nates even in case of faults or unexpected system behavior. In allthe experimental campaign conducted up to now this limit hasnever been hit and the procedure has always terminated in viewof condition 2.ii.This procedure is applied for DelayHML and subsequently forthe Overlap time duration. The self-tuning procedure has been re-peated four times on the same vehicle (whose controller parame-ters have been manually de-tuned after each run) in order toverify that the proposed algorithm allows to obtain repeatable gearshift performances at the end of the tuning phase.Fig. 17 reports the time histories of the two performanceindexes J1and J2and of the two parameters DelayHML and theOverlap time duration obtained in