轮胎建模和分析计算策略—COMPUTATIONAL STRATEGIES FOR TIRE MODELING AND ANALYSIS

1、五座乘用车二轴式六速变速器总成设计外文翻译毕业设计（论文）外文翻译 题 目 五座乘用车二轴式六速变速器总成设计 专 业 城市轨道交通车辆工程 班 级 2011级1班 学 生 何 华 指导教师 杜子学 重庆交通大学 2015年译文轮胎建模和分析计算策略K.T.丹尼尔森,A.K.诺亚 and J.S.格林斯先进的计算技术，弗吉尼亚大学，美国国家航空航天局兰利研究中心，汉普顿，VA 23681，美国研究中心计算机系科学、 摩拉维亚学院伯利恒，PA18018美国(收录于 1995 年 3 月 8 日)摘要计算策略是根据接触路面轮胎的建模和分析，从数字扫描的图像，介绍轮胎截面几何特性简单、准确的测定过程

2、。本文介绍了三个新的为了减少轮胎路面接触的有限元解的计算工作的策略。这些策略利用足迹负载通常不刺激离路面接触地区重大轮胎响应的观察。有限元策略不同于其近似和所需的数量的计算机资源的水平。策略的有效性通过无摩擦和摩擦接触的航天飞机轨道器前起落架轮胎的数值说明。内部研究代码和商业有限元程序进行数值模拟研究，由爱思唯尔科学有限公司出版。1、导言 有限元方法被用于分析充气轮胎已有二十多年的历史，最初由轮胎受到膨胀和载荷而被模型化为旋转的壳体1-4。经典层合板理论来模拟帘线/橡胶复合材料，并用傅立叶级数计算响应量的周向变化。细的三角形板元素也被用于模型的轮胎路面接触 5,6。更详细的轴对称分析涉及的通胀

3、压力，离心力和固化应力，使用早期的有限元代码与恒应变三角形进行（例如参考文献 7 ）。此外，三角形单元，采用平面应变 8 和 9 在圆周方向上的傅立叶级数展开的状态，被用来近似的三维轮胎路面接触。 通用有限元程序的开发提供了手段进行轮胎路面接触的详细分析。早期的简单代码NONSAP 10 ，ADINA 11 和AGGIE 12 被用来模拟三维轮胎的行为，因为他们拥有的能力，如三维实体单元，对帘线/橡胶复合材料和橡胶弹性非保守载荷和现实的本构关系。没有可用的代码，可是，拥有所有必要的功能，一般轮胎的行为建模。因此，轮胎分析师不得不对现有代码进行修改修改（例如，文献13），或者开发专用的代码。此外

4、还有众多由轮胎工业变编制的的内部编码，商业软件比如ABAQUS，MARC，ADINA和MSCNASTRAN已广泛用于轮胎分析。这些专有代码图形预和后处理器以及许多最新的发展在单元技术，本构关系，接触算法和非线性的解决方案。三维有限元分析轮胎路面接触现在是经常使用的轮胎设计过程的一部分（例如，文献14-17）。 尽管在过去的二十年里，有限元技术的发展方面取得了进步，轮胎接触数值模拟仍是一个具有挑战性的和计算量相当庞大的任务。即使在今天的强大的高性能计算机面前，轮胎的结构复杂性和固有的非线性轮胎有限元分析的典型反应仍然需要占用大量的计算机资源。分析人士通常必须做一些简化假设，在合理的时间内得到结果

5、。这包括用更少的元素比不然将被用于更精确的分析模型的使用。目前工业中使用的典型的做法是静态负载轮胎与保守的通胀压力和模拟摩擦或没有轮胎路面和轮胎轮辋之间的滑动接触。通常，一个同质化的技术被用来获取轮胎帘线/橡胶复合材料在不同区域的等效材料性质，和一个单一的元素用于多层钢筋之间。胎面通常被认为是光滑或仅由周向槽。然而，这些分析是计算机密集型的，它们受计算时间的限制。 有几种方法已被用来减少有限元轮胎分析计算机的要求。参考文献 18 运用凭借轮胎厚度来得到一个单一的叠层实体单元。由于联立方程组的数量减少，对计算机的要求明显降低。一个类似的程序已经频繁执行的代码（如ABAQUS）允许钢筋刚度叠加在一

6、个实体单元的任意位置。先进的壳单元也被设计用于轮胎19,20的特殊应用。文献 20 的壳单元可以堆叠在彼此的顶部，与固体元素易于连接。而这些元素类型可以准确高效地提供关于轮胎性能的许多重要的细节，用配方中的运动学假设限制了预测的准确性。一个程序，不让这样的运动学假设是减少的基础技术（例如参考文献 21 ）。该技术可以非常有效的，因为原来的轮胎的响应，通过多自由度的描述，可以通过确定一个小数量的基向量的振幅近似。该程序的有效性是非常依赖于基础载体的选择。 轮胎接触分析的一个重要方面是摩擦效应建模。轮胎载荷所经历的最重要的类型是滚动，转弯，刹车和轮胎轮辋的相互作用。充分建立这些模型，对摩擦接触的精

7、确测定是必要的。摩擦会增加相当大的成本和复杂性的有限元分析。一个完整的了解橡胶摩擦也没有实现，在建立弹性力学基本方程建立之前库仑摩擦理论建立已久，；因此，问题已经提出了关于其有效性时，采用逐点的边界值问题 22 。非局部摩擦法 23 已经被提出，以帮助减轻一些与库仑摩擦的问题。此外，更先进的橡胶摩擦模型（例如，文献24-26日）已开发出包括粘附和粘弹性的影响。橡胶摩擦粘弹性性能 27 创建额外的复杂性造成的，由于摩擦系数是依赖于温度，损耗模量，滑动速度和正压力。 利用摩擦接触分析和橡胶摩擦理论的提出在文献日正常的牵引力，摩擦力进行近似为一个机动轮胎 4 。库仑摩擦被纳入一个静态有限元分析 17

8、 接触算法，库仑摩擦也被用于研究模拟轮胎操纵29,30 。文献 23 的非局部摩擦法被纳入tire-3d代码 20 轮胎转向分析。使用损耗模量，正常的压力依赖摩擦法和高度详细的胎面滚动轮胎有限元模型，进行接触分析 31 。由于大量的计算成本或计算结果不确定，这些类型的分析在轮胎行业是不常用的。 更有效的分析程序是建立轮胎接触模型的需要。这将提高轮胎有限元分析的生产力和增加的可行性ofmore精确的分析。可靠的和高效的轮胎摩擦接触过程也是一个重要的研究领域的发展，而不是在讨论。相反，目前的研究主要集中在一般的轮胎模型，有效的计算策略。这将使制定详细的摩擦轮胎接触分析更为可行。 本研究的总体目标是

9、开发高效准确的模拟轮胎路面接触的计算策略。具体来说，本文的目的是：（a）一个简单而有效的轮胎的几何特征的精确测定方法；CAD绘图不可用或当一个描述实际硫化轮胎所需时，这个程序就能发挥它应有的作用；（b）三个全新的计算策略，为降低计算成本在轮胎路面接触的有限元分析；这些策略的有效性是通过数值例子来证明的。1、 根据扫描图像来确定横截面几何图形 轮胎响应的可靠的预测依赖于轮胎断面几何的一个适当的描述。用轮胎断面的扫描图像来准确测定其几何特性是一个半自动化的过程。菜单驱动的软件已经发展到方便的可用程序实现的地步。商业软件PV-WAVE 32 是一款用来显示图像的软件。 鼠标是用来作为用户界 面指定程

10、序选项和识别扫描图像上的项目。 从数字扫描图像的几何细节的测定已被用于各种应用（如空气流动行为 33 ）。作者也意识到其他的图像扫描程序在轮胎行业的应用。这些专用轮胎中的应用尚未有报道，与当前程序方面被认为是原始的。轮胎的截面的周长由一个边缘追踪方案来确定，而结构层的几何特征是由不同颜色的强度来确定位置。边缘和轮廓跟踪技术及其合成的链码被引入参考文献34。自那时以来，许多的变化已被报道。有几个调查文章回顾并分析了这些技术35-37。 本文描述的方法提供了描述轮胎断面周长和股线和线端的位置的准确方法。位置的横截面的周长，正交和曲率都包含在这个描述。如图所示。图1，股线是一个共同的取向对子午线轮胎

11、层线的中心线。两端线在横截面上。该股线的位置来确定层的厚度，相对于一个参考表面的相对位置。该线位置来确定线结束每英寸（例1），这反过来又被用来评估线端刚度或（a）描述的等效层的本构关系（例如，文献 4，19 ）。 在程序开始采集轮胎横断面图像单色与平板扫描仪。图2a显示航天飞机前起落架轮胎这样一个形象。图像是一个网格点（像素），每个都有其自己的灰度值（缩放数值指定的黑色和白色的数值）。几个增强的图像是由软件模块，确定所需的几何特征。稍微增强的图像是用来检查计算几何相对于轮胎图像的精度。一个高度增强的图像也由该算法计算轮胎的几何特性应用。 原始图像通过减去平滑区域平均的副本来使数字化增强，具有图

12、像的低频成分为主，从原来的平滑的或平均的图像增强的高频分量减，尤其是轮胎帘线端的图像。其增强程度是由平均面积大小的确定的。一个高度增强的图像，对应于在图2a，如图2b所示。 由于几何变化一般与颜色的变化有关，采用灰度值确定几何细节。 通过边缘跟踪程序34-37确定内、外表面的位置。这是通过检查时，像素的灰度值从白到黑的实现。同样，通过灰度累加表明图像中的一簇白色确定在橡胶轮胎帘线的位置。这些程序是通过一个高度增强的图像如图2b中的一行。 在边缘跟踪完成后，B样条曲线拟合的内表面和外表面。样条曲线的拟合到航天飞机的前起落架轮胎的一个例子是在图3所示。曲线是用来计算不同点的坐标和法线在点的表面曲率

13、。在一个理想的点上的外表面的鼠标点击然后做出的图像，和外表面的法线的点确定。在正常的内表面的距离的计算，并对每层的中心线的距离由一个像素的灰度值求和确定。由于正常一般不跨所有线末端（图2），像素灰度值是由到每一面的固定距离确定。当绘制沿正交方向（图3b），这些数字显示的峰白，峰作为厚度中心线的位置然后绘制在横断面图像检测。不准确的股线现在可以通过简单的鼠标点击来进行删除或添加新的期望图像。这一过程的例子如图3所示。计算位置位置相对的外侧表面上的某一点，由如图3b的主要峰来确定，以跨越扫描图像上的图3c。图3b由于受到干扰产生了两个小峰的高度增强的图像。 对股线位置的最准确的检测，灰度值的总和应

14、沿厚度方向。由于股线位置不被先验已知的，一个方向必须选择灰度累加。该代码提供了一个简单而有效的方式指定和方向。期权给出了利用外表面，内表面或两个表面之间的平滑过渡。在这些方向是不充分的情况下，该股线的位置，还可以通过添加或删除由鼠标点击图像精确地指定选项。 线端间距也可以用类似的方法确定。由于线的角度取向的横截面，计算了实际线间距的预测。在每层的中心线，该像素的灰度值被绘制为固定距离对正常的两侧。峰作为线末端和绘制图像。不准确的线端又可以用鼠标点击图像来删除或添加新的。由于线的两端计算，一条给定的线，然后提供一个选项，选线。另外的内表面，外表面或两个表面之间的平滑过渡，一条直线，也可以指定为通

15、过对正常图像上显示的每一侧制作鼠标点击的铺层方向。线端间距确定为之间的平均距离的两端线。一股线如图3c所示，计算线条末端位置的一个例子是由图3d显示的交叉。 本程序是沿子午线轮胎的其他点的重复，直到一个可接受的轮胎断面的描述已经定义。软件生成的几何特征是写的一个简单的数据库，可以用来与CAD系统连接，创造出各种不同类型的有限元模型，或执行其他操作。 虽然大多数精确的几何细节是自动生成的，而全自动化的功能又可能不完全可靠。故而该程序需要用户参与，每一个细节可以交互查看和更改。此外，用户已经连续访问和控制上述的自动化算法的详细参数。原文：COMPUTATIONAL STRATEGIES FOR T

16、IRE MODELING AND ANALYSISK.T.Danielson,A.K.Noor and J.S.GreensCenter for Advanced Computational Technology, University of Virginia, NASA Langley Research Center, Hampton, VA 23681, U.S.A.Department of Computer Science, Moravian College, Bethlehem, PA 18018, U.S.A.(Received 8 March 1995)Abstract-Comp

17、utational strategies are presented for the modeling and analysis of tires in contact with pavement, A procedure is introduced for the simple and accurate determination of tire cross-sectional geometric characteristics from a digitally scanned image. Three new strategies for reducing the computationa

18、l effort in the finite element solution of tire-pavement contact are also presented. These strategies take advantage of the observation that footprint loads do not usually stimulate a significant tire response away from the pavement contact region. The finite element strategies differ in their level

19、 of approximation and required amount of computer resources. The effectiveness of the strategies is demonstrated by numerical examples of frictionless and frictional contact of the Space Shuttle orbiter nose-gear tire. Both an in-house research code and a commercial finite element code are used in t

20、he numerical studies. Published by Elsevier Science Ltd.1. INTRODUCTION The finite element method has been used to analyze pneumatic tires for more than two decades. Tires subjected to inflation and footprint loadings were first modeled using shell of revolution codes 1-4. Classical lamination theor

21、y was used to model cord-rubber composites, and Fourier series were used to account for circumferential variations of the response quantities. Thin triangular plate elements were also used to model tire-pavement contact 5,6. More detailed axisymmetric analyses involving inflation pressure, centrifug

22、al forces and curing stresses, were performed using early tinite element codes with constant strain triangles (e.g. Ref. 7). In addition, triangular elements, using a state of plane strain 8 or a Fourier series expansion in the circumferential direction 9, were used to approximate three-dimensional

23、tire-pavement contact. The development of general-purpose finite element codes provided the means to perform detailed analyses of tire-pavement contact. The early codes NONSAP 10, ADINA 11 and AGGIE 12 were used to simulate three-dimensional tire behavior,since they possessed capabilities such as th

24、ree-dimensional solid elements, nonconservative loadings and realistic constitutive laws for cord-rubber composites and rubber elasticity. None of the available codes, however, possessed all the necessary capabilities for modeling general tire behavior. Therefore, tire analysts had to make modificat

25、ions to existing codes (e.g. Refs 13-15), or develop special-purpose codes. In addition to the many in-house coding efforts made by the tire industry, commercial programs such as ABAQUS, MARC, ADINA and MSC/NASTRAN have been widely used for tire analysis. These proprietary codes have graphical pre-

26、and post-processors as well as many of the latest developments in element technologies, constitutive laws, contact algorithms and nonlinear solution schemes. Three-dimensional finite element analyses of tire-pavement contact are now routinely used as part of the tire design process (e.g. Refs 14-17)

27、. Despite the strides made in the development of finite element technology over the last two decades, the numerical simulation of tire contact remains a challenging, approximate and computationally expensive task. The complex nature of the tire structure and the inherent nonlinear tire response requ

28、ire a large amount of computer resources for typical tinite element analysis, even on todays powerful high-performance computers. Analysts must generally make several simplifying assumptions to obtain results in a reasonable amount of time. This includes the use of models with fewer elements than wo

29、uld otherwise be used for more accurate analyses. The typical practice currently used by industry is to statically load the tire with nonconservative inflation pressure and simulate frictionless or no-slip contact between the tire-pavement and the tire-rim. Usually, a homogenization technique is use

30、d to obtain equivalent material properties for cord-rubber composites in different regions of the tire, and a single element is used between layers of reinforcement. The tread is usually assumed to be smooth or to only consist of circumferential grooves. Whereas these analyses are computer intensive

31、, they are within the practical limits of computer time. Several approaches have been used to reduce computer requirements for finite element tire analysis. A single laminated solid element through the tire thickness was used in Ref. 18. The computer requirements were significantly decreased as a re

32、sult of the reduced number of simultaneous equations. A similar procedure has been frequently performed with codes (e.g. ABAQUS) that allow the superposition of rebar stiffness at an arbitrary location within a solid element. Advanced shell elements have also been devised for special application to

33、tires 19,20. The shell elements of Ref. 20 can be stacked on top of each other and can easily interface with solid elements. Whereas these types of elements can accurately and efficiently provide many important details about tire behavior, the kinematic assumptions used in their formulations limit t

34、he accuracy of the predictions. A procedure that does not make such kinematic assumptions is the reduced basis technique (e.g. Ref. 21). The technique can be very efficient, since the original tire response, described by many degrees of freedom, can be approximated by determining the amplitudes of a

35、 small number of basis vectors. The effectiveness of the procedure is critically dependent on the selection of the basis vectors. An important aspect of tire contact analysis is the modeling of frictional effects. The most significant types of loadings experienced by tires are rolling, cornering, br

36、aking and tire-rim interaction. To adequately model each of these, an accurate determination of frictional contact is needed. Friction can add considerable cost and complexity to finite element analysis. A complete understanding of rubber friction has also not been achieved. The Coulomb friction the

37、ory was developed long before the fundamental equations of elasticity were formulated; therefore questions have been raised about its validity when applied pointwise in boundry value problems 22. Nonlocal friction laws 23 have been proposed to help alleviate some of the difficulties associated with

38、Coulomb friction. In addition, more sophisticated rubber friction models (e.g. Refs 24-26) have been developed that include adhesion and viscoelastic effects. Rubber friction resulting from viscoelastic properties 27 creates additional complexities, since the coefficient of friction is dependent on

39、the loss modulus, the temperature, the sliding speed and the normal pressure. Using normal tractions from a frictionless contact analysis and a rubber friction theory proposed in Refs 24,28, frictional forces were approximated for a maneuvering tire 4. Coulomb friction was incorporated into the cont

40、act algorithm of a static finite element analysis 17. Coulomb friction was also used in studies simulating tire maneuvering 29,30. The nonlocal friction law of Ref. 23 was incorporated into the TIRE-3D code 20 for tire steering analyses. Using a loss modulus, normal pressure-dependent friction law a

41、nd a highly detailed finite element model of the tread, a rolling tire contact analysis was performed 31. Because of the large computational cost or the lack of confidence in the results, these types of analyses are not frequently performed in the tire industry. More efficient analysis procedures ar

42、e needed for simulating tire contact. This would improve the productivity of tire finite element analysts and increase the feasibility ofmore accurate analyses. The development of reliable and efficient frictional contact procedures for tires is also an important area of research, but is not address

43、ed in this paper. Instead, the present study focuses on efficient computational strategies for general tire modeling. This should help make detailed frictional tire contact analyses more viable. The overall objective of the present study is to develop accurate and efficient computational strategies

44、for simulating tire-pavement contact. Specifically, the objectives of this paper are to present: (a) a simple and effective procedure for the accurate determination of geometric characteristics of a tire; the procedure can be useful for cases when CAD drawings are not available or when a description

45、 of the actual cured tire is desired; and (b) three new computational strategies for reducing the computational cost in the finite analysis of tire-pavement contact; the effectivness of these strategies is demonstrated by means of numerical examples. 2.DETERMINATION OF CROSS-SECMONAL GEOMETRY FROM A

46、 SCANNED IMAGE The reliable prediction of tire response is dependent on an adequate description of the tire crosssectional geometry. A semi-automated procedure is described for the accurate determination of geometric characteristics using a scanned image of the tire cross-section. Menu driven softwa

47、re has been developed to facilitate the implementation of the procedure. The commercial software PV-Wave 32 is used to display the images. A mouse is used as the user interface to specify program options and to identify items on the scanned image. The determination of geometric details from digitall

48、y scanned images has been used for various applications (e.g. air flow behavior 33). The authors are also aware that other scanned image procedures have been used by the tire industry. These proprietary tire applications have not been reported, and aspects of the current procedures are believed to b

49、e original. The perimeter of the tire cross-section is determined by an edge tracing scheme, and geometric characteristics of the structural layers are determined by the locations of different color intensities. Edge and contour tracing techniques and their resultant chain codes were introduced in R

50、ef. 34. Since then, numerous variations have been reported. Several survey articles have reviewed and analyzed these techniques 35-37. The procedure described herein provides an accurate description of the perimeter of the tire crosssection and the locations of plylines and cord-ends. The position,

51、normals and curvatures of the crosssectional perimeter are included in this description. As shown in. Fig. 1, the plylines are the centerlines of layers of cords with a common orientation to the tire meridian. The cord-ends are the cord cross-sections. Locations of the plylines are used to determine

52、 the ply thicknesses and their relative positions with respect to a reference surface. Locations of the cords are used to determine the cord-ends per inch (ep1), which in turn are used to evaluate cord stiffnesses or (a) describe equivalent ply constitutive relationships (e.g. Refs 4, 19). The proce

53、dure begins by capturing the tire crosssectional image in monochrome with a flat bed scanner. Figure 2a shows such an image for the Space Shuttle nose-gear tire. The image is a grid of points (pixels), each with its own grayscale value (a scaled numerical value specifying the amount of black and whi

54、te). Several enhanced images are needed by the software modules that determine the geometrical characteristics. Slightly enhanced images are used to inspect the accuracy of the calculated geometry with respect to the tire image. A highly enhanced image is also used by the algorithms that calculate t

55、he geometric characteristics of the tire. The raw image is digitally enhanced by subtracting a smooth area-averaged copy, which has a predominance of low frequency components of the image, from the original. Subtraction of a smoothed or averaged image enhances the high frequency components, especial

56、ly the tire cord-end images. The degree of enhancement is determined by the size of the averaged area. A highly enhanced image, corresponding to that in Fig. 2a, is shown in Fig. 2b. Since geometry changes are generally associated with changes in color, the grayscale values are usedto determine geom

57、etrical details. The locations of the inner and outer surfaces are determined by an edge tracing procedure 34-37. This is achieved by examining when pixel grayscale values go from white to black. Similarly, the tire cord locations within the rubber are determined by grayscale summations that indicat

58、e a cluster of white in the image. These procedures are performed using a highly enhanced image like the one in Fig. 2b. After the edge trace is completed, B-splines are fit to the inside and outside surfaces. An example of the splines fit to the Space Shuttle nose gear tire is shown in Fig. 3a. The curves are used to calculate coordinates of different points as wel