奇瑞微型汽车设计（变速器设计）（4+1挡手动变速器）【全套含8张CAD图纸】

喜欢就充值下载吧，，资源目录下展示的全都有，，下载后全都有，dwg格式的为CAD图纸，有疑问咨询QQ：414951605 或1304139763 牵引力和拖拉机性能 Frank M. Zoz，P.E. 已退休，约翰迪尔产品工程中心美国，爱荷华州，滑铁卢 Robert D. Grisso,P.E. 教授，生物系统工程，弗吉尼亚理工大学,美国，弗吉尼亚州，布莱克斯堡 农用拖拉机的主要目的，特别是在中高功率范围内，是执行挂钩工作。一辆拖拉机的价值是由它所完成的工作和它消耗的成本来衡量的。牵引工作是由拉力和行驶速度来定义的。因此，理想的拖拉机将来自燃料的所有能量转换成有用功。在实践中，在化学能转化为机械能的过程中，以及通过传动系，最后通过牵引装置都会失去大多数的势能。研究表明，约20％至55％的可用拖拉机能量是在牵引设备和土界面浪费。这种能量会磨损轮胎并泥土压缩到可能引起有害于作物生产的程度（伯特等人，1982）。 农用拖拉机的高效运行包括：（1）把发动机和动力传动系统的燃料效率最大化；（2）最大化的牵引装置的牵引优势；（3）为一个给定的拖拉机牵引系统选择最佳的行进速度。 经过了几年，实验室的拖拉机牵引性能试验已在坚硬的表面进行并在近几年（30年以上）在混凝土上也进行了试验。虽然这提供了拖拉机之间的有效比较，但数据没有提供有关现实工作条件下的性能的很多信息。实验室试验和现场工作条件之间的主要区别是轮胎或其它牵引装置的性能。 理解和预测拖拉机性能一直是众多研究人员的一个主要目标。牵引原理，土壤条件，实施的类型，和拖拉机的配置都会影响拖拉机的性能（Brixius，1987）。理解牵引性能来预测在现场拖拉机的性能是非常有必要的。结合在实验室拖拉机测试中获得的信息，牵引力公式能够为预测拖拉机性能提供一个很好的基础。 计算机模型可以使研究人员和设计师探讨在大范围的工况下的拖拉机性能，以提高拖拉机设计的诸多问题，以优化拖拉机操作参数，提高拖拉机和实现情况的匹配。这样一来，无需昂贵的现场测试就可以得知影响拖拉机现场性能的一些相关重要因素。对于教师们来说，模型提升了学生的理解和比较影响拖拉机性能的各种参数的能力。这些模型还可以帮助拖拉机运营商提高（微调）和优化其拖拉机的设置，以适应不同的工作条件。 牵引机械 在坚硬地面的硬质轮胎 牵引机械的理解是理解牵引性能和拖拉机性能之间差异的重要因素。实心轮在简单的坚硬地面情况下，驱动轮中涉及的基本的力示于图1。输入扭矩（T）作用在接触表面上产生一个总牵引力（GT）。总牵引力的一部分用来克服运动阻力（MR），包括对车轮内部和外部的阻力。差等于净牵引力（NT），即NT= GT-MR。 在坚硬地面的软质轮胎 在坚硬的表面软质轮胎（图2）是和硬质轮胎大致相同的，不同之处在于垂直反作用力（WD）不是直接通过轴中心线而是有一定距离的偏移。这个偏移对于静态平衡是很有必要的。该偏移量是运动阻力的作用，可以由下式得出： 图1和图2中所示有三个半径:"slr" 是静态负荷半径，其定义为从轴的中心线到硬表面的距离；“rr”为滚动半径，用于速度计算。滚动半径是从滚动圆周衍生出的（通常是通过测量得到，但也可以在轮胎制造商的数据表中得到）。静态负荷半径和滚动半径接近但不相等。要正确地给农用轮胎充气，滚动半径比静态负荷半径大约6％。滚动半径用于速度计算。静态负荷半径更适合于力或力矩计算。两个半径都会受到土壤表面的柔软性的影响，并且通常在坚硬的地面上来确定的。 在图1中所示的第三半径被称为转矩半径（室温）。这是有效半径，其中总牵引力（GT）和运动阻力（MR）的作用。它不能被直接测量，但可以是通过能量计算来确定。详细说明在本文中第2部分“总牵引力比率”。 在柔软表面的变形车轮 在现实世界中，轮子和（土壤）表面都是可变形的，这会导致在图3所示的力和力矩。这样的结果是一个垂直和水平偏移，用“EV”和“EH”分别。偏移的量取决于运动阻力（MR），轮胎负荷半径（SLR）和垂直反作用力（WD）上： 皮带传动 皮带驱动机构的力学（图4）与车轮在许多方面都是相似的;但负载的分布取决于车辆参数。动态负载的位置，“eh”（动态平衡比;科科伦和戈夫，1985），依赖于静态分配，支承在转向架车轮悬架机构的设计，和车辆的重量传递特性。 在一般情况下，最好的牵引性能和最均匀的皮带驱动上可通过让动态平衡比接近50％来获得的。科科伦和戈夫（1985年）定义的动态平衡率的动态负载的垂直分量的位置（外部载荷和拖拉机的重量）从轨道前部由轨道基座长度来划分的。不像轮胎，牵引测试期间必须要考虑总动态重量（WD），对一个轨道机构的动态平衡，无论是在带测试还是完整的车辆测试都必须考虑。得到的动态平衡比不仅取决于拖拉机尺寸参数和位置和气流的角度，也取决于牵引力的大小。 图5所示为出模斜度和车辆牵引比的动态平衡，对拖拉机来说大约为60％一个普通的车轮/皮带拖拉机是很简单的，但对皮带和轮式拖拉机来说重心转移机制是相同的。应该注意，在0.40的典型车辆牵引比中，只需要一个5°拔模斜度就能得到50％的动态平衡比。图5是拉杆上的器具。使用三点悬挂装置的设备可能会导致更高的重量转移，并且会增加前部零件的重量。 牵引参数 描述牵引性能有五个量纲参数： •行驶减少率（TRR），俗称“slip”，并以百分比表示. •净牵引比（NTR），有时也被称为拉重比。 •牵引效率（TE），通常是百分数，但本文中用的是比率。 •总牵引比（GTR）。 •动态阻力比（MRR）。 牵引参数涉及的力通过WD的动力反应的车轮或牵引装置除以来得到归一。WD包括静态车轴重量和任何在测试过程中可能发生的重量转移，即总的反应力。WD允许轮胎的尺寸和重量的其它牵引装置之间的比较有不同，并提供了用于牵引比较的无量纲参数。 需要注意，所有的牵引参数通常表示为比率除了行程减少率和牵引效率，它们通常表示为百分比。如果所有的参数都为比例，有了牵引力的数据，工作是比较容易。之后它会变得更加明显，但请记住，上述参数应用到牵引装置，而不是一定是车辆。 行驶减少率（TRR） 行驶减少通常被称为“滑”或“滑％”，但在技术上，这是不正确。滑移发生在表面之间。行驶减少是发生在行驶距离或速度降低时，这是因为： •牵引装置的挠曲 •表面之间打滑（例如橡胶和混凝土） •土壤发生剪切。 从功率效率的角度来看，行驶减少会引起在行驶速度或行驶距离上功率的损失。滑（行驶减少）发生在任何车轮或牵引设备产生拉力（净牵引力）的时候（Brixius和威斯默，1978年）。 零行驶减少可以使用任何四种方法（ASAE标准，2001b）来定义： 1.不变形表面上的自走式（零净牵引力）的条件（在公布的轮胎数据上选取滚动周长）。 2.对测试表面的自走式（零净牵引力）的条件。 3.行驶在非变形表面上（零毛利牵引，即零转矩）的条件。 4.行驶在（零毛利牵引）上的测试表面条件。 使用任何上述方法得到一个特定牵引试验参数还有争议。在任何情况下，该 方法始终表示用于定义滚动半径为零的条件。最常见的零条件是使用在测试表面（方法2）的自行条件。然而，轮胎数据通常用非变形面（方法1）来给定。一个不变形（硬）表面和一个测试表面之间所测量的滚动半径的差在正常的农业土壤条件下（干土或耕犁土）是很小的，从而使得在最终的结果几乎没有差别。在任何情况下，“零滑移”的错误不会影响最终的牵引效率的结果，因为行驶减少不直接在方程中。它仅影响其中的损失分配，也就是，无论是在行驶减少或运动阻力的结果。这将更加详细在本文的第3节中讨论。 作者的偏好是在坚硬的表面使用一个自推进状态（零净牵引），并使用该方法于整篇。此方法提供了一种可重复的测试条件，结果与公布轮胎数据大致相符，并且数据可在其它位置和测试条件时被复制。这也很容易想象，在软土的情况下，零状态可能会导致明显的100％转差，即，车辆被卡住，而被人为零行驶减少。 用上述之一方法测定滚动半径（RR）在被用来计算车轮或牵引装置的理论速度（Vt）时： 车辆或车轮的实际前进速度（Va）通常是直接使用第五轮或雷达装置来测量。Vt和Va必须使用相同的度量单位。 净牵引比（NTR） 净牵引比有时被称为拉重比，P / W，动态牵引比，或牵引系数。大部分这些术语实际上指的是完整的车辆，而不是一个简单的牵引装置。动态反作用力或动态重量（WD）包括镇流器的影响，并包括可能会出现在测试过程中的任何重量转移。如果一个整车用于牵引设备测试，重量可以包括从前向后传送由于横拉，并由于执行负载单位拔模斜度的任何传输。净牵引力（N T）必须是在行进方向和垂直于反作用力（WD）上的力分量。 如上所述，上面的方程适用于牵引设备，而不是一个完整的车辆。对于一个完整的车辆（拖拉机），净牵引比（NTR）在车辆牵引比（VTR）中相当于车辆的牵引拉力由总车辆动态重分配。更详细的将在本文第7节叙述。 牵引效率（TE） 牵引“低效率”是由速度造成的损失和拉力损失共同造成的。行程速度的损失通常称为“滑动”，虽然它更准确被翻译为“行驶减少”。行驶减少是理论行进速度（Vt）没有被完全转换成实际前进速度（Va）的结果，这些是由土壤中的损失，土壤表面和牵引装置之间以及在牵引装置（滞后和轮胎卷绕或皮带打滑）之间造成的。行驶减少损耗是可见的，即操作者可以看到它发生。牵引“低效率”，这是不可见，并且经常被忽略的另一个组成部分，是由拉力（净牵引）的损失造成的。行驶减少，但运动阻力在增加。运动阻力损失是和皮带相关的，皮带机构的内部损失比在轮胎内更大。在软土，皮带的内部损耗一般是由比轮胎还低的外部运动阻力来补偿的。 总牵引率（GTR） 总牵引力（GT）有时被称为设计牵引力，或理论拉力。它是由轴扭矩输入转换为拉力。如果没有运动阻力拉力就不会损失。 总牵引比（GTR）是最需要理解的牵引参数。总牵引力（GT）本身不能被直接测量，通常是从车轮或牵引装置的轴扭矩和半径进行计算。问题是半径是没有被明确定义的或可以直接测量的。在牵引力的研究者中没有达成一致计算总牵引比优先使用能量或功率还是考虑另一种方法。 有效转矩半径（rt）可被计算（尽管知道它的值是唯一的学术兴趣在）： 运动阻力比（MRR） 运动阻力比（MRR），有时被称为滚动阻力，包括牵引装置内的内部损耗（例如在一个皮带驱动器或一个轮胎上的损失）和土壤的力量。其它地方的转矩被测量所有的“力”的损失被包括在运动阻力，例如齿轮损失，如果扭矩正在直接在输入到牵引装置则不进行测量。这方面的一个例子是，使用机械前轮驱动机构测试轮胎时，使用的是输入驱动轴的扭矩。皮带驱动机构是另一个例子，和转向架车轮滚动损失一样，需要克服皮带的弯曲所产生的力矩。 牵引数据分析 牵引数据通常是由总的垂直地面反作用力（WD）的数据划分来创建无量纲的比值。除了比较不同大小牵引装置比较容易之外，牵引性能比也可以很容易地得到并和单一的牵引设备比较牵引参数。 拉力滑移和净牵引滑移 最基本的牵引数据是简单地比较拉力和行驶减少。这通常被认为是功率消耗可能不是一个主要的考虑因素或者唯一数据的一个装置。还有一个问题就是其中的自变量，拉力还是滑移？牵引数据历来认为滑移是独立变量，也就是说拉力取决于滑移。然而，这并不一致，并且有理由相信拉力是自变量，即“滑移自己发生”。本文中的大部分数据把NTR（或完整车辆的VTR）视为独立变量。 图6是一个拉力滑移（行驶减少）曲线，显示的是约翰迪尔拖拉机上的皮带。需要注意的是拉力急剧上升，然后行驶减少的增加趋于平稳。它会达到一个最大点，并有可能脱落滑差进一步增加。在本文示出的大多数数据都不超过40％的行驶减少，因为牵引效率的顶点一般发生在拉力较低的时候。此外，考虑到牵引装置的重量也可能会影响拉力，最终重量为11791公斤（26000磅）。 拉力滑移（行驶减少）的另一例子是从内布拉斯加拖拉机测试得到的，如图7所示，为实验室数据（整车）。这也说明了为什么除去牵引装置外的动态重量要创建无量纲的比值，因为这会使比较更有意义。在行驶减少这方面来看，约翰迪尔8400拖拉机是比其他的更优越的，既包括皮带和胶轮拖拉机，也包括有碴和无碴。 然而，拉力的分配是由车辆重量决定的，在此情况下各牵引设备承担的重量也是不同的（图8）。 还有一个问题就是：滑移或者拉力（NTR或VTR）哪个是独立变量？这个问题在这里不能得到解答，因为两个定义委员会分别支持这两种观点，且各有支持的理由。然而，作者的意见是滑移（行驶减少）是因为拉力（NTR或VTR）被应用的结果（图9）。作者的假定将被用于本文的其余部分。 牵引效率 从拖拉机牵引功率的角度来看，牵引效率（TE）是最重要的牵引参数。图10是使用Brixius牵引关系广义曲线图（1987）牵引方程和作为自变量净牵引比（NTR）。对于合适碴和充气的农用轮胎，牵引效率（TE）倾向于0.40的最大净牵引比（NTR）。这也被德威尔（1984）所认可。运动阻力比（MRR）趋向于任一滑动或NTR的线性函数，除非滑移下沉成为一个因素。 行驶和力的损失会使牵引力没有解释的“效率低下”。了解他们最简单的方法是把它们看作为“速度比”和“拉力比”。在方程式的形式为： 在图11中，速度比被表示为净牵引比（NTR）。在零净牵引比的情况下，实际速度（Va）的约等于理论速度（Vt），零滑移的定义某种程度上取决于（ASAE标准，2001年b），和速度比接近统一。随着净牵引力（拉力）的增加，行驶减少（滑移）会增加，速度比会减小。对于一个给定的牵引装置，速度比损耗取决于拉力行驶减少曲线的特征形状。 在图12中，拉力比率显示为NTR的函数。在零值时，净牵引力（拉力），净牵引比（NTR）和总牵引比（GTR）的比值都趋近于零;GTR和NTR之间的差值是运动阻力比（MRR），它是在0.05至0.15的范围内。由于运动阻力，净牵引比决不可能等于总牵引比，拉力比率会趋近但也不会达到。 牵引效率定义为输出功率除以输入功率。它也可以被表达为拉力比和速度比的结果。图13显示了速度比和拉力比是如何结合起来成为整体的牵引效率的。整体牵引效率不能大于拉力比和速度比中的任何一个，因此其达到在NTR介于约0.3和0.4与子午线轮胎的最大值。一个存在于皮带上的类似的范围会在后面说明。 图14所示为拉力比，速度比和牵引效率的实际数据，显示的是在子午线轮胎的牵引条件下的数据。该曲线是在现场测试数据的回归分析的结果。速度（行驶减少）和拉力（运动阻力）的损失有助于整体牵引效率的增加。 相同的功率损耗数据可以根据图15中通过行驶减少（滑移）来进行查看，但涉及行驶减少的损失，它也不是那么容易被直观的得到的。这可能是因为我们观察了一个本身损失的函数发生损失。这再次支持NTR作为独立变量。 13 ASAE DISTINGUISHED LECTURE SERIES Tractor Design No. 27 Traction and Tractor Performance Frank M. Zoz and Robert D. Grisso These lectures have been developed to provide in-depth resource information for engineers in the agricultural industry. Copyright 2003 by the American Society of Agricultural Engineers All Rights Reserved Manufactured in the United States of America This lecture may not be reproduced in whole or in part by any means (with the exception of short quotes for the purpose of review) without the permission of the publisher For information, contact: ASAE, 2950 Niles Rd., St. Joseph, MI 49085-9659 USA. Phone: 269 429 0300 Fax: 269 429 3852 www.asae.org ASAE Publication Number 913C0403 The American Society of Agricultural Engineers is not responsible for statements and opinions advanced in its meetings or printed in its publications. They represent the views of the individual to whom they are credited and are not binding on the Society as a whole. Traction and Tractor Performance Frank M. Zoz Retired John Deere Product Engineering Center Waterloo, Iowa, USA Robert D. Grisso Professor Virginia Tech Blacksburg, Virginia, USA For presentation at the 2003 Agricultural Equipment Technology Conference Louisville, Kentucky, USA 9-11 February 2003 Published by ASAE the Society for engineering in agricultural, food, and biological systems 2950 Niles Road, St. Joseph, MI 49085-9659 USA The Lecture Series has been developed by the Power and Machinery Division Tractor Committee (PM-47) of ASAE to provide in-depth design resource information for engineers in the agricultural industry. Topics shall be related to the power plant, power train, hydraulic system, and chassis components such as operator environment, tires, and electrical equipment for agricultural or industrial tractors or self-propelled agricultural equipment. ASAE is grateful to Deere & Co for sponsoring the ASAE Distinguished Lecture Series. Table of Contents INTRODUCTION .5 TRACTION MECHANICS .5 Solid Wheel on a Hard Surface .5 Soft Wheel on a Hard Surface .6 Deformable Wheel on a Soft Surface .7 Belt Drives .8 TRACTION PARAMETERS .9 Travel Reduction Ratio (TRR) .9 Net Traction Ratio (NTR) .10 Tractive Efficiency (TE) .11 Gross Traction Ratio (GTR) .11 Motion Resistance Ratio (MRR) .11 TRACTION DATA ANALYSIS .12 Pull Slip and NTR Slip .12 Tractive Efficiency .14 Regression Analysis .17 TRACTION TESTING .19 Single-Wheel Testing .20 Using Tractors to Test Tires .21 Speed Effects .23 TRACTION PERFORMANCE .24 Effects of Soil .24 Effects of Tire Pressure .25 Effects of Tire Size .25 Effects of Load on Tire .26 Belt and Tire Comparisons .26 SOIL, TIRE, AND TRACTION EQUATIONS .30 TRACTOR PERFORMANCE .33 Tractor Performance Spreadsheet .35 Estimated Drawbar Power .38 OPTIMIZING TRACTOR DRAWBAR PERFORMANCE .39 Tires .39 Ballasting .39 Ballasting Sensitivity .43 Ballasting Limitations .44 Ballast Optimization in the Tractor Performance Spreadsheet .44 CONCLUSIONS .45 ACKNOWLEDGEMENTS .45 REFERENCES .45 5 Traction and Tractor Performance Frank M. Zoz, P.E. Retired, John Deere Product Engineering Center, Waterloo, Iowa Robert D. Grisso, P.E. Professor, Biological Systems Engineering, Virginia Tech, Blacksburg, Virginia The primary purpose of agricultural tractors, especially those in the middle to high power ranges, is to perform drawbar work. The value of a tractor is measured by the amount of work accomplished relative to the cost incurred in getting the work done. Drawbar work is defined by pull and travel speed. Therefore, the ideal tractor converts all the energy from the fuel into useful work at the drawbar. In practice, most of the potential energy is lost in the conversion of chemical energy to mechanical energy, along with losses from the engine through the drivetrain and finally through the tractive device. Research shows that about 20% to 55% of the available tractor energy is wasted at the tractive device/soil interface. This energy wears the tires and compacts the soil to a degree that may cause detrimental crop production (Burt et al., 1982). Efficient operation of farm tractors includes: (1) maximizing the fuel efficiency of the engine and drivetrain, (2) maximizing the tractive advantage of the traction devices, and (3) selecting an optimum travel speed for a given tractor-implement system. Throughout the years, official tractor performance drawbar tests have been conducted on hard surfaces and in recent years (30+ years) on concrete. While this provides a valid comparison between tractors, the data does not provide much information about performance under field conditions. The primary difference between official tests and field conditions is the performance of the tires or other tractive devices. The understanding and prediction of tractor performance has been a major goal of many researchers. Tractor performance is influenced by traction elements, soil conditions, implement type, and tractor configuration (Brixius, 1987). It is necessary to understand traction performance to predict tractor performance in the field. Traction equations provide a basis for predicting tractor performance when combined with basic information from official tractor tests. Computer models allow researchers and designers to investigate many problems related to tractor performance under a wide range of conditions with the goal to improve tractor design, to optimize tractor operational parameters, and to improve the tractor/implement match. Relative importance of these factors affecting field performance of a tractor can be achieved without expensive field-testing. For teachers, models enhance the students ability to comprehend and compare various parameters that influence tractor performance. These models can also assist tractor operators to improve (fine-tune) and optimize their tractors setup to match operating conditions. 1. Traction Mechanics Solid Wheel on a Hard Surface An understanding of traction mechanics is fundamental to understanding differences between tractive performance and tractor performance. The basic forces involved in a powered wheel are shown in figure 1 for the simple case of a solid wheel on a hard surface. The torque input (T) develops a gross traction (GT) acting at the contact surface. Part of the gross traction is required to overcome motion resistance (MR), which is the resistance to the motion of the wheel, including internal and external forces. The remainder is equal to the net traction (NT) that the wheel develops, given by NT = GT - MR. 6 GT MR slr rr N T T W Va Wd rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT NT MR GT MR slr rr N T T W Va Wd rt W Wd slr rr rt Vt Va T GT = Gross traction (theoretical pull)NT = Net traction (actual pull) MR = Motion resistance Figure 1. Basic wheel forces for a solid wheel on a hard surface. Soft Wheel on a Hard Surface A soft wheel on a hard surface (fig. 2) is much the same as a solid wheel except that it becomes more obvious that the vertical reaction force (Wd) is not directly under the axle centerline but is offset by a distance designated eh. This offset is necessary for static equilibrium. The amount of the offset is a function of the motion resistance and is given by: ()()WdMRslr eh = (1) Three radii are shown in figures 1 and 2: slr is the static loaded radius, defined as the distance from the axle centerline to a hard surface; rr is the rolling radius, used for speed calculations. Rolling radius is derived from the rolling circumference (usually measured prior to a test but also included in tire manufacturer data tables). Static loaded radius and rolling radius are close but not equal. For a properly inflated agricultural tire, the rolling radius is about 6% greater than the static loaded radius. Rolling radius should be used for speed calculations. Static loaded radius is more appropriate to use for force or moment calculations. Both can be affected by the softness of the soil surface and are usually determined on a hard surface. The third radius shown in figure 1 is called the torque radius (rt). This is the effective radius where the gross traction (GT) and motion resistance (MR) forces act. It cannot be measured directly but can be determined by back calculating using energy calculations. This is explained in detail in section 2 of this paper under Gross Traction Ratio. 7 MR slr rr NT T W Va Wd GT eh rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance MR slr rr NT T W Va Wd GT eh rt W Wd slr rr rt Vt Va T GT NT MR Figure 2. Basic wheel forces for a soft wheel on a hard surface. Deformable Wheel on a Soft Surface In the real world, both the wheel and the (soil) surface are deformable and result in the forces and moments shown in figure 3. The result is both a vertical and a horizontal offset, designated ev and eh, respectively. The amount of the offsets depends on the motion resistance force (MR), the tire loaded radius (slr), and the vertical force resultant (Wd): ()()WdMRev -slr eh = (2) slr rr NT T W Va GT Wd eh MR ev Ground Line Ground Line rt W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radiusrt = Torque radius Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance slr rr NT T W Va GT Wd eh MR ev Ground Line Ground Line rt W Wd slr rr rt Vt Va T GT NT MR Figure 3. Deformable wheel on a soft surface. 8 Belt Drives The mechanics of the belt drive mechanism (fig. 4) is similar to the wheel in many respects; but the distribution of the load is dependent on vehicle parameters. The location of the dynamic load resultant, eh (dynamic balance ratio; Corcoran and Gove, 1985), depends on the static distribution, the design of the suspension mechanism supporting the bogie wheels, and vehicle weight transfer characteristics. MR slr rr NT T W 1 Va Wd GT W 2 W 3 W 4 W 5 Ground Line Dh rt Vt = Velocity, theoretical Va = Velocity, actual T = Axle torque GT = Gross traction (theoretical pull) NT = Net traction (actual pull) MR = Motion resistance W = Weight, static Wd = Weight, dynamic slr = Loaded radius, static rr = Rolling radius rt = Torque radius Vt Va T GT NT MR W Wd slr rr rt eh Figure 4. Belt drive. In general, the best tractive performance and the most uniform ground pressure on a belt drive can be obtained with a dynamic balance ratio of near 50%. Corcoran and Gove (1985) defined dynamic balance ratio as the ratio of the location of the vertical component of the dynamic load (external loads and tractor weight) from the front of the track divided by the track base length. Unlike a tire, where only the total dynamic weight (Wd) must be considered during a traction test, the dynamic balance of a track mechanism must be considered either in a belt test or a full vehicle test. The dynamic balance ratio obtained depends not only on tractor dimensional parameters and the location and angle of the line of draft but also on the magnitude of the drawbar pull. Figure 5 shows the effect of draft angle and vehicle traction ratio on the dynamic balance for a tractor with 60% of the static weight at the front. A generic wheel/belt tractor is shown for simplicity, but the weight transfer mechanics are the same for belted and wheel tractors. Note that it only takes a 5 draft angle to give a 50% dynamic balance ratio at a typical vehicle traction ratio of 0.40. Figure 5 is for implements hitched to the drawbar. Even higher weight transfer, and hence higher front weight requirements, may result from the use of three-point hitch equipment. 9 5 0 10 20 40 42 44 46 48 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 0.6 Vehicle Traction Ratio Dynamic Balance (% Front) Draft Angle With Dh/ Wb = 0.20 Dl/ Wb = 0.30 Wb Dl Draft Angle Dh 0.60 0.58 0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 Dynamic Balance Ratio 5 0 10 20 40 42 44 46 48 50 52 54 56 58 60 0 0.1 0.2 0.3 0.4 0.5 0.6 With Dh/ Wb = 0.20 Dl/ Wb = 0.30 Wb Dl Draft Angle Dh 0.60 0.58 0.56 0.54 0.52 0.50 0.48 0.46 0.44 0.42 0.40 Figure 5. Tractor/belt drive dynamic weight distribution (when starting with 60% static front weight). 2. Traction Parameters Five dimensionless parameters are used to describe tractive performance: Travel reduction ratio (TRR), commonly called slip and expressed in percent. Net traction ratio (NTR), sometimes called pull/weight ratio. Tractive efficiency (TE), usually thought of as percent but used as a ratio in this paper. Gross traction ratio (GTR). Motion resistance ratio (MRR). The traction parameters involving forces are all normalized by dividing by Wd, the dynamic force reaction supporting the wheel or traction device. Wd includes static axle weight and any weight transfer that might take place during the testing process, i.e., the total reaction force. Dividing by Wd allows comparisons between tires and other tractive devices of different sizes and weights, and provides a dimensionless parameter for traction comparisons. Note that all the traction parameters are normally presented as ratios except travel reduction and tractive efficiency, which are commonly expressed as percentages. Working with traction data is easier if all parameters are presented as ratios. It will become more obvious later, but remember that the above parameters apply to a traction device and not necessarily to a vehicle. Travel Reduction Ratio (TRR) VtVa1Velocity lTheoreticaVelocity Actual1TRR= (3) Travel reduction has traditionally been called slip or % slip, but technically this is incorrect. Slip occurs between surfaces. Travel reduction is a reduction in distance traveled and/or speed that occurs because of: Flexing of the tractive device 10 Slip between the surfaces (rubber and concrete, for example) Shear within the soil. From a power efficiency standpoint, travel reduction is a power loss caused by a loss in travel speed or distance traveled. Slip (travel reduction) occurs any time a wheel or traction device develops pull (net traction) (Brixius and Wismer, 1978). Zero travel reduction can be defined using any of four methods (ASAE Standards, 2001b): 1. A self-propelled (zero net traction) condition on a non-deforming surface (recommended for rolling circumference data, as in published tire data). 2. A self-propelled (zero net traction) condition on the test surface. 3. A towed (zero gross traction, i.e., zero torque) condition on a non-deforming surface. 4. A towed (zero gross traction) condition on the test surface. There are arguments for using any of the above methods for a particular traction test. In any case, the zero condition used to define the rolling radius should always be stated. The most common zero condition is use of the self-propelled condition on the test surface (method 2). However, tire data are usually given for a non-deforming surface (method 1). The difference in measured rolling radii between a non-deforming (hard) surface and a test surface is small under normal agricultural soil conditions (dry and/or untilled soil) and thus makes little difference in the final results. In any case, errors of defining zero slip do not affect the final tractive efficiency results, as travel reduction does not enter directly into the equation. It only affects the results where the losses are assigned, that is, either to travel reduction or motion resistance. This will be discussed in more detail in section 3 of this paper. The authors preference is to use a self-propelled condition (zero net traction) on a hard surface, and this method is used throughout this paper. This method provides a repeatable test condition, results that should agree closely to published tire data, and data that can be replicated at other locations and test conditions. It is also easy to imagine a case of very soft soil where the zero condition may result in an apparent 100% slip, i.e., the vehicle gets stuck, while being assigned zero travel reduction. The rolling radius (rr) measured under one of the above methods is used to calculate the theoretical speed (Vt) of the wheel or tractive device: Vt (m/s) = (rpm) rr 2/60 (4) The actual forward velocity (Va) of the vehicle or wheel is usually measured directly using a fifth wheel or radar device. Both Vt and Va must use the same units of measurement. Net Traction Ratio (NTR) WdNTForceReaction DynamicTractionNet NTR= (5) The net traction ratio is sometimes referred to as pull/weight, P/W, dynamic traction ratio, or coefficient of traction. Most of these terms actually refer to a complete vehicle rather than to a simple traction device. The dynamic reaction force or dynamic weight (Wd) includes the effects of ballast and any weight transfer that may occur in the testing process. If a complete vehicle is used for the traction device testing, the weight may include front to rear transfer due to horizontal pull, and any transfer due to implement or load unit draft angle. The net traction force (NT) must be the force component in the direction of travel and perpendicular to the reaction force (Wd). As stated, the above equation applies to a tractive device and not to a complete vehicle. For a total vehicle (tractor), the equivalent to net traction ratio (NTR) is vehicle traction ratio (VTR), which is the vehicles drawbar pull divided by the total vehicle dynamic weight. This will be covered in more detail in section 7 of this paper. 11 Tractive Efficiency (TE) =VtVaGTRNTRVtVaWdGTWdNTVtVaGTNT Power AxleVa NTPowerInput PowerOutput (ratio) TE (6) Tractive inefficiency is caused by both velocity losses and pull losses. The loss in travel speed is commonly referred to as slip, although it is more accurately refered to as travel reduction. Travel reduction is the result of the theoretical travel speed (Vt) not being entirely converted to forward progress (Va) due to losses within the soil, between the soil surface and the traction device, and within the traction device (hysteresis, and tire windup or belt slippage). Travel reduction losses are visible, that is, the operator can see it happening. The other component of tractive inefficiency, which is less visible and often overlooked, is a loss of pull (net traction) when motion resistance reduces the amount of gross traction that is converted to useful output (net traction). This is part of what happens when a tractor is overballasted. Travel reduction is reduced, but motion resistance is increased. Motion resistance losses are especially relevant to belts, as internal losses within the belt drive mechanism, rollers, and bending of the belt are normally greater than those within a tire. On soft soils, the internal losses of belts are generally compensated for by lower external motion resistance than that of tires. Gross Traction Ratio (GTR) Wdrt T WdGT GTR = (7) Gross traction (GT) is sometimes referred to as rim pull, design drawbar pull, or theoretical pull. It is the axle torque input converted to a pull force. It is the pull you would develop if there were no motion resistance loss. The gross traction ratio (GTR) is the least understood of the traction parameters. Gross traction (GT) itself cannot be measured directly and is usually calculated from the axle torque and radius of the wheel or tractive device. The problem is that the correct radius to use is not well defined or directly measurable. There is no general agreement among traction researchers as to what radius to use, and an alternate method of calculating gross traction ratio is preferred using energy or power considerations. From equations 6 and 3: ()TRR1TENTRVtVaTENTRGTR= (8) Having thus determined the gross traction ratio (GTR), since Wdrt T W