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叉车车架辅助设计
Carlos Cosme, Amir Ghasemi and Jimmy Gandevia
Western Star Trucks, Inc.
摘要：
近年来，叉车市场变得非常的注重重量和降低成本。这对设计工程师是重大挑战，因为这些车辆被用在各种各样的公路环境，从高速公路到严重的越野环境。目前的挑战是在不牺牲耐用性和性能降低的前提下满足质量和成本。本文论述了运用计算机集成、计算机辅助设计和工程软件代码（Pro / Engineer，ADAMS软件和ANSYS）来辅助设计更改车架。
特别是，本文集中论述了一个ADAMS多体动力学模型，一个完整的叉车和拖车来模拟车辆的侧翻稳定性，平顺性，和耐久性载荷。该模型包括一个采用灵活的框架模型模态综合模式，探讨了有限元分析程序。之间的多体仿真链接与有限元程序也可以用来传输、加载应力分析有限元模型。所有代码之间紧密连结，确保新的设计并行计算可快速用于设计和分析。一个说明这是如何
已被使用的技术详细的个案研究也包括在内。
简介
最近，重卡行业经历了叉车降低成本和重量的大发展。这一直是叉车制造商的主要挑战，在不牺牲耐用性和性能的前提下，寻找好的方式来优化他们的叉车设计。
由于车架是车辆系统的重要组成部分，它经常被用于完善。本文概述了电脑辅助工程（CAE）分析更改车架以及这些变化会如何影响车辆性能。叉车的车架是该车辆的骨干，上面集成了主要的叉车组成系统，如车轴，悬架，动力总成，驾驶室。典型的结构框架是梯形框架，中间交叉几根横梁。纵梁的断面尺寸变化很大，根据在叉车上的受力而定。而且，需要考虑各种因素：重量，复杂性和成本。这些变化将取决于横梁的作用和位置。请参考图1插图，一辆叉车的车架。然而，横梁布置的变化带来的影响还无法看出来。例如，如果横梁的抗扭刚度降低，对叉车的侧倾稳定性和耐久性的影响是怎么的呢？设计工程师们需要对这些类型的问题给出答案以指导他们的工作。特别是，及时的设计和分析程序是必需的，这样新的设计可以快速评估。
图1载货叉车车架
计算机辅助工程
在过去的二十年中叉车自动化设计工具CAE得到了巨大的发展。这项技术的已被很多叉车制造商采用以改善叉车设计来满足快速增长的市场要求。当今的结构设计通常是使用两个CAE工具：有限元分析（FEA）和多体系统（MSS），结合CAD提高设计和分析。
在过去十五年里，CAD系统已取代绘图板作为首选设计方法。它们使设计师和工程师能够快速画出叉车零部件，叉车真实模型和设计图纸。先进的CAD系统功能丰富，如参数化实体建模和大型装配管理。他们已经发展成为主要的数据库，为工程信息尤其是CAD系统提供下游CAE应用的重要数据。
工程师通常使用有限元分析研究结构构件的强度。典型的有限元分析的重点是结构应力，挠度和自然频率。首先对通常被称为网格的离散结构进行分析。该网格是由节点和元素组成，而且经常从CAD创建几何系统。这些节点代表位移计算的结构。他们定义的局部质量，刚度和阻尼性能结构。有关这些数量方程，可以自动开发节点位移。其他投入，如边界条件，载荷和材料特性，必须是由用户定义。所有这些效果都需要小心的判断和对有意义的结果进行认真的分析。结果后处理包括图像变形负载结构，彩色应力轮廓，振型动画。
MSS多体系统仿真方法研究了运动部件和组件，并经常用来研究车辆暂停或车辆的操作和动态响应。一个典型的完整的车型MSS将刚体组成（车轮，车轴，车架，发动机，驾驶室）模拟成关节连接和理想化力元。 MSS代码自动发展非线性微分方程和代数方程定义模型中的物体运动。该方程在数值上集成刚体位移，速度，加速度和受力。结果以图形和动画显示该系统的运动。至于有限元分析，CAD数据经常使用MSS的发展模式。CAD几何数据是用于建立MSS的布局模式，如接头和力量元素的位置。CAD实体模型数据也可以用来估计每个刚体的位置，质心和惯性特性。作用在刚体上的力可以用作MSS的输入负载，有限元分析确定该刚体的结构应力。CAE技术在本文所讨论的工具包括基与CAD的Pro / Engineer，ANSYS进行有限元分析，以及基于ADAMS的MSS。下面的讨论引用的是某型叉车的车架有限元分析。
CAE叉车建模
如上所述，在目前提供的CAD与CAE工具提供了大量的整合。尽管如此，这些工具是非常粗略的分析，仍然需要努力分析叉车和叉车车架。为了充分了解车架影响叉车操纵的变化，滚动稳定性，平顺性和持久性，需要一个详细的MSS模型，可以模拟所有这些影响。使用ADAMS软件代码，建立了WesterStar叉车的模型。图二展示了在ADAMS环境下的模型。
图2 ADAMS的MSS的模型
该模型包括以下几个特点：
•100刚体
•180力元
•45共同元素
•415度-的自由度
固定的机构包括车架，驾驶室，车桥，车轮，发动机，引擎盖，散热器，钢板弹簧，悬挂臂，传动轴。对于许多质量属性这些机构采用简化的实体模型。
受力的元素包括线性和非线性衬套，橡胶隔震支座模型元素，如驾驶室和发动机的座椅。非线性单分力用于模拟空气弹簧和减震器。这些元素的数据来自供应商执行的部件测试。转动关节和球形接头是用来连接点模型，如轮毂轴承和扭矩杆支点。Pro / Engineer的组件是用来确定这些元素的几何位置。
由于重卡行业提供各种各样的车辆布局，为便于进行修改参数，叉车的许多子系统的被分开。例如，前桥组件（车轮，车轴，钢板弹簧和减震器）被链接到一个变量界定前桥纵向位置。使用这种技术，不同的叉车型号，通过改变这个变量前轴位置可快速开发。这一程序是复制以下组件：后悬挂，驾驶室，发动机，引擎盖。轮胎与路面接触处理内置在ADAMS轮胎程序，包括处理模型和轮胎耐用性。在ADAMS路面输入作为一个类似三角形有限元网格。自定义软件程序，然后翻译成两个文件的ADAMS的网格，以确定轮胎/路面相互作用力，图形查看在后面处理成动画。这些文件存储在一个共同的目录，便于检索。自定义控制算法开发，以控制车辆行驶速度，转向，传动扭矩。这些功能可以快速修改，以执行不同的车辆如滚筒稳定，高速行车变化，或耐久性颠簸类似的试验场。模拟运行后，受力和扭矩作用在车架上的数据写入数据文件。一个定制软件程序然后用来提取特定的负载时间步骤，并将其写入一个ANSYS加载文件。该加载文件然后读入ANSYS和应用到有限元模型的车架。然后，车架计算使用惯性释放的解决方案。总之，该模型使用定制软件程序与含代码的CAD和CAE，评定一个定制环境耐用的叉车。但是，模型假设车架是刚性的。在现实中，叉车车架包含了大量的灵活性，会影响车辆性能及稳定。因此，这些影响必须捕获到多体系统仿真。
CAE解决方案的框架灵活性
前人技法 - 在过去，一些技术已经使用捕捉画面灵活性的MSS的模型。流行的三种方法是：轴套无质量的梁单元，超单元和有限元分析。第一种方法车架分为两种更为严格的机构或以刚性元素连接在一起有套管式的车架：刚性和三个阻尼方向。套管性能调整总体车架弯曲和扭转刚度。随着可以预计，这种方法使用起来很麻烦，如果适当调整，这将是唯一的能够捕捉基本弯曲和扭转的框架模式。第二种方法的框车架分为刚体无质量的梁互联元素。这是类似于套管的方法，但许多更为严格的机构通常使用，而且它们的连接用的是无质量的梁单元的方程（Timoshenko梁理论），更适合货车车架纵梁和交叉的横梁。然而，用此方法建立一个车架很费时，详细的梁单元的调整仍需捕获弯曲响应。第三种方法是最准确的，并且是基于有限元的代表性框架。在此方法中的有限元模型，减少到具有代表性的总体刚度超单元和质量属性浓缩到一个主集节点。减少的模型是检查原有限元模型，以确保重要动态参数的捕获。导入MSS的环境下，超单元和主节点转换为等价表示刚性机构和力量的元素。虽然这种方法是在有限元解的基础上，它仍然可以实现难以精确的结果。例如，必须选择主节点，以确保质量和刚度冷凝过程的准确。上述所有方法很难用于创建一个叉车精确灵活的车架。在一般情况下，他们只是捕捉基本响应：最初的几个弯扭、总的框架模式和刚度。在工作中需要很大的努力来调整其属性，配合一些诸如静挠度测试的参考，模态测试，或有限元模拟结果。因此，无论一个方法是同时使用合适的设计和分析环境 ，它只会对模型进行修改，并没有足够的空间分辨捕捉微妙的设计改变。模态综合技术 - 在有限元分析和MSS整合最新进展克服了上述方法的困难。现在可以用有限元模型，直接在多体仿真采用模态叠加，作为模态综合（CMS）的知名技术。利用模态叠加，一个结构变形可以说是由它的每一个贡献模式。通常，一个模式是非常大的数目，需要准确地捕捉点的变形。
约束应用到结构。发达国家解决了这个问题。它结合了正常模式与约束模式。这些约束模式或静态形状，捕捉到关键领域变形而不必维持正常模式结构。因此，他们在计算上更有效率。CMS的程序代码采用的是在ADAMS基于对克雷格-班普顿修改后的版本方法。这种方法的结构被认为是有约束和接口点力量应用，并且每个接口点最多可以有六个自由度：三个平移和三个旋转。该结构的议案，然后用一个两套组合模式：约束接口点的模式和固定接口的正常模式。第一种
约束模式是计算每个自由度的一个接口点，它描述的静态形状是对这种结构的自由度给出一个单位偏斜度，同时保持所有自由度的其他接口点固定。此过程反复
所有的接口模式。由于约束模式是静态的形状，其频率的信息是未知的。固定接口正常模式代表了整个结构的正常模式，对自由度的所有接口点是固定的。在这种形式下，克雷格.班普顿模式不适合集成理想的多体方程。例如，添加刚体约束模式，可在ADAMS非线性刚体上作用。此外，约束模式可能包含高频率，很难解决。Adams可以解决这些在处理克雷格-班普顿模式的问题。它标识刚体模式使它们很容易禁用。它还增加频率信息的约束模式，这是设置的宝贵积分参数。正交化后，修改设置存在的模式：正常模式，无约束结构（如类似的模式在特征值计算的有限元分析运行一个典型）和界面的自由度。所有的模态计算，上述是在ANSYS的环境中进行的。为了计算模式，用户选择的节点代表接口点在受力和限制进入的框架，然后运行宏，执行适当的ANSYS命令。正常模式包括在计算时传递到宏参数。最后一组的方式写入到一个模态中性文件，可读取ADAMS。
这种模态叠加方法的优点很多，包括：
•框架是由一个单一的模态中性文件。因此，很容易重复使用其他型号的MSS。这些文件可以存储在共同目下方便以后使用。在MSS的模型中被表示为一个单一灵活的组织，并没有大量的刚体。这使得它更容易操作。
•每个弹性体模式可将一个自由度仿真。使前面的方法添加更多的自由度，因为他们使用了大量的刚性机构和上述每个自由度。
•线性灵活的特点，框架模型更为确切，因为它们是基于一个完整的有限元模型，而不是一个刚体集合和力量的元素。这使得它更容易调整模型与模态试验结果一致。
•阻尼影像于一个模式的基础。因此，阻尼从模态测试的结果可以很容易地添加，从而提高精确度。
•一个模拟模态参与，可跟踪的应变能的贡献为基础。模式不能够作出重大作用，以提高计算效率。
•模拟结果的可视化的改善，因为有限元网格的存在，在环境中的MSS可用于观看画面变形动画。
•对MSS的负荷转移回到原来的有限元分析应力分析模型进行了改进，因为负载与有限元网格节点。
虽然，这种方法具有许多优点，它仍然需要费时实施。例如，并非所有整合和力量的元素都支持直接连接。倒是这些都必须先连接到无质量刚体，然后被锁定在使用固定的网格节点，对自由度添加无质量刚体。由于车架可以有36个或更多的MSS模型的连接点，它非常费时，所以使用灵活的框架。另外，如果现有的灵活的框架，需要取代新的设计更改，更多的建模努力是必要的，潜在的引进建模错误是可能的。为了克服这一困难，自定义程序被集成在开发一个灵活的车架。该过程开始于一个刚性框架。该模型的副本作出了一系列宏程序执行任务的副本：
•阅读柔性体模态中性文件和位置在该车型的弹性体。
•创建并连接每个无质量刚体节点力和约束应用于弹性体。
•修改所有连接到现有的刚体框架，以便它们连接到适当的无质量刚体。
•删除以前的刚体代表框架。
有限元网格建模
为了这些方法有效地开展工作，车架的有限元模型必须易于创建和修改反映由设计师所需的变更。该方法在这里一开始就采用Pro / Engineer的实体模型，如图1所示。每个组件的实体模型建立专门有限元分析网格划分，因此，简化了实际的设计版本。有限元网格是创建一个附加模块为Pro /ENGINEE。它包含的功能有简化有限元网格划分，如自动确定中板地点，壳单元，应用全局和局部网格控制，并确定元素属性。同时建立内部的Pro / ENGINEER环境网格有许多优点。例如，更改实体模型自动反映在网格。因此，改变的轨道几何形状或位置交叉成员可以迅速网状和出口到ANSYS。
验证框架灵活性
为了建立灵活的精度模型，进行模态试验。同一个ANSYS有限元模型，在建成使用过程中，将所述以上特征值和特征向量的计算进行比较。可以看出，在表1中，有限元模型很好地和试验的结果吻合。ADAMS模态频率也符合良好的测试数据，并为确认灵活的框架提供了一个准确的代表性结构。注意只有模式在高达56赫兹时提取模态测试数据。但测试并没有包含足够的测量点、要清楚界定模式形状。该框架模型纳入整车MSS的模型使用上述程序。然后计算和比较以模态的叉车类似的测试数据配置。见表2，一个典型的叉车的动力由模型很好的表示出来。
结论
在这份文件中提出的项目的目的是制定一个过程，设计变更到叉车可快速评估框架，使得并发设计和分析成为可能。如上所述，这个目标已经实现，结合当前
电脑辅助设计及工程代码自定义软件程序。该工艺充分利用了每个代码的优势，创造高逼真度的环境，其中微妙的设计变更影响叉车框架可以衡量车辆性能和耐久性的要求。设计方案可以快速评估并反馈给设计师，虽然仍然有可能做出改变。虽然这个过程能成功使用，在许多地方可以进一步增强提出，将成为未来发展的重点。这些包括：
1、仿真结果验证使用全车试验数据。这将用于了解模拟的弱点，并调整模型的参数。由于模拟精度改善，该模型将提供更好的数据组件优化。
2、柔性使用模态综合技术将被添加到其他结构如驾驶室/卧铺和拖车。这两个灵活性为这些结构在平顺性和耐久性上发挥了重要作用。
3、新的CAE技术，如疲劳分析会被添加。最近几年计算机辅助工程代码显著提高疲劳寿命估算，现在是可能的估计疲劳损伤，该结构在多体仿真中使用全时程负载。疲劳寿命轮廓可以被看作有限元模型，正如现在强调轮廓。这项技术
大大提高了耐久性分析和发展一个虚拟试验场。
致谢
我们要感谢西方星叉车的管理团队，他们为CAE技术的研究提供大力支持。我们还要谢谢肯美利，唐摩尔，鲍勃和马克他们对文件认真审查。
参考文献
1. “Mechanics of Heavy-Duty Trucks and Truck Combinations” ,UMTRI Course Notes, July, 1995.
2. Stasa, Frank L., “Applied Finite Element Analysis for Engineers”, CBS College Publishing, 1985.
3. Ottarsson, Gisli, “Modal Flexibility Method in ADAMS/FLEX”, Mechanical Dynamics, Inc., March, 1998.
4. “Using ADAMS/FLEX”, Mechanical Dynamics, Inc.,1997.
5. “ADAMS/Finite Element Analysis Reference Manual”, Mechanical Dynamics, Inc. , November 15,1994.
6. “Pro/MESH and Pro/FEM Post, User’s Guide”, Parametric Technology Corporation, 1997.
7. “ANSYS Structural Analysis Guide”, Analysis, Inc.,1994.
8. Gillespie, Thomas D., “Fundamentals of Vehicle Dynamics”, Society of Automotive Engineers, Inc.,1992.
9. Gobessi, Mark and Arnold, Wes, “The Application of Bonded Aluminum Sandwich Construction Technology to Achieve a Lightweight, Low Cost Automotive Structure”, SAE paper 982279.
1999-01-3760
Application of Computer Aided Engineering in the Design of Heavy-Duty Truck Frames
Carlos Cosme, Amir Ghasemi and Jimmy Gandevia
Western Star Trucks, Inc.
Copyright © 1999 Society of Automotive Engineers, Inc.
ABSTRACT
In recent years the heavy-duty Class 8 truck market has become very focused on weight and cost reduction. This represents a major challenge for design engineers since these vehicles are used in a wide variety of vocations from highway line haul to logging in severe off-road environments.
The challenge is to meet the weight and cost
reduction goals without sacrificing durability and performance. This paper discusses the integration of computer aided design and engineering software codes (Pro/Engineer,
ADAMS, and ANSYS) to simulate the effect of design changes to the truck frame .In particular, this paper discuses the development of an ADAMS multi-body dynamics model of a full truck and trailer to simulate vehicle handling, roll stability, ride performance, and durability loading. The model includes a flexible frame model using a component mode synthesis
approach with modes imported from a finite element analysis program. The link between the multi-body simulation and the finite element code is also used to transfer
loads back to the finite element model for stress analysis. Tight links between all the codes ensures that new design iterations can be quickly evaluated for concurrent
design and analysis. A detailed case study showing how this technology has been used is also included.
INTRODUCTION
Recently the heavy truck industry has experienced a large push to develop vehicles with reduced cost and weight. This has been a major challenge for truck manufacturers
as they look for ways to optimize their vehicle designs without sacrificing durability or performance.
Since the truck frame is a major component in the vehicle system, it is often identified for refinement. This paper outlines a computer aided engineering (CAE) procedure for analyzing changes to the truck frame and how these changes affect vehicle performance .The frame of a heavy truck is the backbone of the vehicle and integrates the main truck component systems such as the axles, suspension, power train, cab, and trailer.
The typical frame is a ladder structure consisting of two C channel rails connected by cross-members. The frame
rails vary greatly in length and cross-sectional dimensions depending on the truck application. Likewise, the
cross-members vary in design, weight, complexity, and cost. These variations will depend upon the cross-member purpose and location. Refer to Figure 1 for an illustration
of a truck frame. However, the effects of changes to the frame and cross-members are not well understood.
For example, if the torsional stiffness of a suspension cross-member is lowered, what is the effect on the vehicle’s
roll stability, handling, ride, and durability? Design engineers require answers to these types of questions to guide them in their work. In particular, a concurrent design and analysis procedure is required so that new
designs can be quickly evaluated.
Figure 1. Class 8 Heavy-Duty Truck Frame
COMPUTER AIDED ENGINEERING
In the last twenty years there has been an enormous growth in the development of CAE tools for automotive design. Much of this technology has been adopted by the truck industry as truck manufacturers look to improve their designs in a rapidly growing market. Today structural design is typically performed using two CAE tools: finite
element analysis (FEA), and multi-body system simulation (MSS). These are combined with computer aided design (CAD) software to improve design and analysis
communication.
CAD – In the last fifteen years CAD systems have replaced drawing boards as the method of choice for design. They enable designers and engineers to quickly
create realistic models of truck components, vehicle assemblies, and design drawings for manufacturing.
Advanced CAD systems are rich in features such as parametric solid model and large assembly management. They have evolved to become major databases for engineering information. In particular , CAD systems provide important data for downstream CAE applications.
FEA – Finite element analysis is usually used by engineers to study the strength of structural components.
Typical FEA activity is focused on analyzing structural stresses, deflections, and natural frequencies. The analysis begins with a discretized representation of a structure
known as a mesh. The mesh is composed of nodes and elements and is often created with geometry from a CAD system. The nodes represent points on the structure where displacements are calculated. The elements are bounded by sets of nodes and enclose areas or volumes. They define the local mass, stiffness, and damping properties of the structure. Equations relating these quantities
to the nodal displacements are automatically developed by the software codes. Other inputs, such as boundary conditions, applied loads, and material properties, must be defined by the user. Each of these quantities requires careful judgement for meaningful results to be achieved. Results post-processing includes images of deformed structures under load, coloured stress contours, and mode shape animations.
MSS – Multi-body system simulation is used to study the motion of components and assemblies and is often used to study a vehicle suspension or a vehicle’s handling and ride response. A typical MSS model of a full vehicle will be composed of rigid bodies (wheels, axles, frame , engine, cab, and trailer) connected by idealized joints and
force elements. The MSS code automatically develops the non-linear differential and algebraic equations that define the motion of the bodies in the model. The equations are numerically integrated to produce time histories of rigid body displacements, velocities, accelerations, and forces. Results are viewed as graphs and animations of
the system motion. As with FEA, CAD data is often used to develop a MSS model. Geometry data from a CAD assembly is used to establish the layout of the MSS model such as the location of joints and force elements. CAD solid model data is also used to estimate the location of the center-of-mass and the inertial properties of each rigid body. Forces acting on a rigid body from a MSS can be used as input loads to a finite element analysis to determine the structural stresses in that rigid body.
The CAE tools discussed in this paper include Pro/Engineer for CAD, ANSYS for FEA, and ADAMS for MSS. The following discussion references the specific capabilities of these codes in developing a customized environment for the engineering analysis of truck frames.
CAE CUSTOMIZATION FOR HEAVY TRUCK
MODELLING
As described above, the current offering of CAD and CAE tools provide a great deal of integration. Nonetheless,
these tools are very general in scope and a significant customization effort is required for the analysis of heavy duty trucks and truck frames. To fully understand how changes to the truck frame impact vehicle handling, roll
stability, ride, and durability requires a detailed MSS model that can simulate all these effects. Using the
ADAMS software code such a model was developed at
Western Star Trucks. Refer to Figure 2 for a view of the model in the ADAMS environment.
Figure 2. ADAMS MSS Model
The model includes the following characteristics:
• 100 rigid bodies
• 180 force elements
• 45 joint elements
• 415 degrees-of-freedom
The rigid bodies include the frame, cab, axles, wheels ,engine, hood, radiator, leaf springs, suspension arms, drive shafts, and the trailer. Mass properties for many of
these bodies were estimated using simplified solid models in Pro/Engineer. The force elements include linear and non-linear bush ielements that model rubber isolators, such as the cab and engine mounts. Non-linear single component forces are used to model air springs and shock absorbers. Property data for these elements are derived from tests performed by component suppliers. Revolute joints and
spherical joints are used to model connection points, such as wheel bearings and torque rod pivots, respectively. Pro/Engineer assemblies are used to determine the geometric location of these elements.
Since the heavy truck industry offers a wide variety of vehicle layouts, the locations of many of the truck’s subsystems were made parametric for easy modification. For example, the front axle subassembly(wheels, axles, leaf springs, and shock absorbers) were linked to a variable defining the longitudinal position of the front axle. Using
this technique, truck models with different front axle positions can be quickly developed by changing the value of this variable. This procedure was duplicated for the following
subassemblies: rear suspension, cab ,engine ,hood, and fifth wheel and trailer .Tire to road contact is handled with the ADAMS built-in tire routines and includes models for tire handling and durability forces. In ADAMS road profiles are represented
as a mesh of triangles similar to a finite element mesh. The geometry and mesh for the road profiles are generated with Pro/Engineer. A custom software program is
then used to translate the mesh into two files for ADAMS :a road file format for the solver to determine the tire/road interaction forces, and a graphics format to view the road
during post-processing animation. These files are stored in a common directory for easy retrieval. Custom control algorithms were developed to control vehicle speed, steering, and drive torque. These functions
can be quickly modified to execute different vehicle maneuvers such as roll stability, a high speed lane change, or durability bumps similar to a proving ground.
After the simulations are run, the forces and torques acting on the frame are written to data files. A custom software program is then used to extract the loads at specific
time steps and write them to an ANSYS load file. The load file is then read into ANSYS and applied to a finite element model of the frame. The frame stresses are then calculated using an inertial relief solution.
In summary, the model uses custom software routines and the existing links between the CAD and CAE codes to create a custom environment for evaluating the performance and durability of a heavy-duty truck. However, the model assumes that the truck frame is a rigid, under formable body. In reality, the truck frame contains a great deal
of flexibility which can impact vehicle performance and stability. As a result, these effects must be captured in the multi-body system simulation.
CAE SOLUTION FOR FRAME FLEXIBILITY
PREVIOUS TECHNIQUES – In the past, several techniques have been employed to capture frame flexibility in a MSS model. Three popular methods are: bushings,
mass beam elements, and FEA super element reduction. In the first method the frame is divided into two or more rigid bodies connected together with force elements having bushing-like properties: stiffness and damping in three translational directions and three rotational directions. The bushing properties are adjusted to give the overall frame bending and torsional stiffness.
As can be expected, this method is cumbersome to use, and if properly tuned, it will be capable of capturing only the fundamental bending and torsional modes of the frame. In the second method the frame is divided into a large number of rigid bodies interconnected by massless beam elements. This is similar to the bushing method but many more rigid bodies are usually used, and they are connected with massless beam elements whose equations (Timoshenko beam theory) are better suited to modelling
truck frame rails and cross-members. Nonetheless, it istime consuming to build a frame with this method and careful tuning of the beam elements is still required to capture the frame’s flexural response. The third method is the most accurate of the three methods and is based on a finite element representation of the frame. In this method the finite element model is reduced
to a super element representation with the overall stiffness and mass properties condensed to a set of master nodes. The reduced model is checked against the original finite element model to ensure that the important frame dynamics are still captured. It is then imported into the MSS environment where the super elements and
master nodes are converted to an equivalent representation of rigid bodies and force elements. Although this method is based on a finite element solution, it can still be difficult to achieve accurate results. For example, care must be taken in selecting the master nodes to ensure that the mass and stiffness condensation process is accurate.
All the methods described above are difficult to use for creating an accurate flexible model of a truck frame. In general, they are only capable of capturing the basic frame response: the first few bending and torsional
modes and the gross frame stiffness. If each method is to work, a significant effort is required to tune its properties to match some reference, such as static deflection testing,
modal testing, or finite element simulation results. Consequently, neither method is suitable for use in a concurrent design and analysis environment - it would simply take too long to make changes to the model, and it would not have adequate spatial resolution to capture subtle design changes to the frame.
COMPONENT MODE SYNTHESIS TECHNIQUE –
Recent advances in the integration of FEA and MSS have overcome the difficulties in the methods described above .It is now possible to use a finite element model directly in a multi-body simulation using a modal superposition technique known as component mode synthesis (CMS).Using modal superposition, the deformation of a structure can be described by the contribution of each of its modes. Normally, a very large number of modes are required to accurately capture the deformations at points where constraints are applied to the structure. CMS was developed to alleviate this problem. It combines normal modes with constraint modes. These constraint modes,
or static shapes, capture the deformation of key areas of the structure without having to maintain an excessive number of normal modes. As a result, they are computationally more efficient. The CMS procedure adopted in the ADAMS code is based on a modified version of the Craig-Bampton approach. In this method the structure is considered to
have interface points where constraints and forces are applied, and each interface point can have up to six degrees-of-freedom: three translations and three rotations. The motion of the structure is then described by a combination of two sets of modes: constraint modes for
the interface points, and fixed interface normal modes. A constraint mode is calculated for each degree-of-freedom
of an interface point, and it describes the static shape of the structure when that degree-of-freedom is given a unit deflection while keeping the degrees-of-freedom of all the other interface points fixed. This procedure is repeated to develop a family of constraint modes for all the interface points. Since the constraint modes are static shapes, their frequency information is unknown. The fixed interface normal modes represent the normal modes of the entire structure when all the degrees-of-freedom of all the interface points are held fixed.
In this form, the Craig-Bampton modes are not ideally suited for integration with the multi-body equations of motion. For example, the constraint modes add rigid body modes which conflict with the ADAMS non-linear rigid body motions. Also, the constraint modes may contain high frequencies that are difficult to solve. In the ADAMS implementation these problems are handled by orthogonalizing the Craig-Bampton modes. This identifies the rigid body modes making them easy to disable. It also
adds frequency information to the constraint modes which is valuable for setting integration parameters during the multi-body simulation. After orthogonalization, a modified set of modes exist: normal modes for the unconstrained structure (free-free like modes similar to those calculated in a typical FEA eigenvalue run), and the interface degrees-of-freedom. See Ottarsson [3] for a complete description of this method.
All the modal calculations described above take place in the ANSYS environment and are performed on a finite element model of the frame. To compute the modes, the
user selects the nodes representing the interface points where forces and constraints enter the frame, and then runs a macro that executes the appropriate ANSYS commands. The number of normal modes to include in the calculations are passed as a parameter to the macro. The final set of modes are written to a modal neutral file
MNF) that can be read by ADAMS.
The advantage of this modal superposition method are many and include:
• The frame is represented by a single modal neutralfile. As a result, it is very easy to reuse the frame in other MSS models. The files can be stored in common
directory for archiving and future use.
• In the MSS model the frame is represented as a single flexible body and not a large number of rigid bodies. bodies. This makes it much easier to manipulate the
frame in the model.
• Every flexible body mode adds only one degree-of freedom to the simulation. Previous methods added many more degrees of freedom since they used a
large number of rigid bodies and each of these added six degrees-of-freedom.
• The linear, flexible characteristics of frame model are more accurate since they are based on a full finite element model and not a collection of rigid bodies and force elements. This makes it much easier to
tune the model to agree with modal test results.
• Damping is added on a modal basis. Thus, damping results from modal testing can be easily added for increased accuracy.
• Modal participation during a simulation can be tracked based on the strain energy contribution. Modes that do not contribute significantly can be deactivated for improved computational efficiency.
• Visualization of simulation results is improved since the FEA mesh exists in the MSS environment and it can be used for viewing frame deformations during
animation.
• The transfer of MSS loads back to the original FEA model for stress analysis is improved since loads are associated with nodes in the finite element mesh. Although, this method has many advantages, it can still be time consuming to implement. For example, not all joint and force elements are supported for direct connection to the frame mesh when it is the MSS environment. These must first be connected to massless rigid bodies that are then locked to nodes of the mesh using fixed joints which remove the degrees-of-freedom added by the massless rigid bodies. Since a truck frame can have
36 or more connection points in a MSS model, it can be very time consuming to connect a flexible frame. Also, if an existing flexible frame needs to be replaced with a
new one to evaluate a design change, more modeling effort is required and the potential to introduce modeling errors is great.
To overcome this difficulty custom programs were developed to integrate a flexible frame in a vehicle model. The process begins with a full vehicle model with a rigid frame. A copy of the model is made and then a series of macro programs are executed that perform the following tasks on the copy:
• Read the flexible body modal neutral file and position the flexible body in the vehicle model.
• Create and connect massless rigid bodies at each node where forces and constraints are applied to the
flexible body.
• Modify all connections to the existing rigid body of the frame so that they connect to the appropriate massless rigid bodies.
• Delete the rigid body that previously represented the frame. In a typical analysis, a simulation will be run with the rigid frame as a baseline, and then after importing the flexible frame, it is repeated. The results of both are studied to understand the influence of the frame’s flexibility. Then another copy of the model with the rigid frame is made
and it is converted to have a different flexible body (a different modal neutral file is read into the modelling database). This new flexible body will have some design change that needs to be evaluated such as a new crossmember .The same simulations are repeated and all the results are compared.
With this process the burden of adding a flexible frame to a model is greatly reduced. For example, it takes less than one minute to convert a model with a rigid frame to have a flexible frame. As a result, this procedure works very well for concurrent design and analysis.
FINITE ELEMENT MESH MODELLING – In order for these methods to work effectively, the frame’s finite element model must be easily created and modified to reflect changes required by designers. The approach adopted here begins with a Pro/Engineer solid model assembly of the frame rails and cross-members similar to
the one shown in Figure 1.The solid models for each component are created specifically
for finite element analysis meshing, and as a result, are simplified versions of the actual designs. The finite element mesh is created with an add-on module for Pro/ENGINEER called Pro/MESH. It contains features to simplifyfinite element meshing such as automatically determining midplane locations for shell elements, applying
global and local mesh controls, and defining element properties. When requested, a mesh of shell, beam, and mass elements is created that reflects the current CAD
Creating the mesh while inside the Pro/ENGINEER environment has many advantages. For example, changes to
the solid models are automatically reflected in the mesh.
Thus changes to the frame rail geometry or the position of cross-members can be quickly meshed and exported to ANSYS. Likewise, beam elements that represent bolt
connections follow components as they are moved to new positions. Subassemblies, such as cross-members, can also be suppressed so that they are not included in
the mesh. This makes it very easy to turn on and off different cross-member designs and develop meshes of each configuration.
After the mesh is created, it is read into ANSYS, and a custom macro is run that renumbers the nodes where forces and constraints will eventually be applied in
ADAMS. This ensures that the same node numbers are always used. Nodes for constraint mode calculation are then selected and the modal neutral file for ADAMS is created. The file is then ready for input to the ADAMS model.
As described earlier, the ADAMS simulation loads are transferred to ANSYS and the stresses acting on a finite element model of the frame are calculated. This can be the same finite element model that was used to develop the modal neutral file for ADAMS or it can be a different model with a finer mesh. For a different finite element model to work, its mesh must have the same node numbers
at the connection points as the original model used for ADAMS. This is easily achieved by executing the node renumbering macro as used earlier. Consequently, a model with a refined mesh can be used for stress calculations, while a model with a coarse mesh can be used to
calculate the modal properties for ADAMS.
A sub modelling approach was also developed so that cross-member stresses could be computed more accurately.
First a finite element analysis is performed on the same coarse finite element model as used for ADAMS.
Custom macros in ANSYS are then used to read the results and extract the forces and torques from beam elements that represent the bolt connections between the frame rails and the cross-members. These are then applied to a detailed finite element model of the cross member alone. The bolt forces are applied using ANSYS RBE3 elements that are configured to distribute the bolt loads to nodes that would be under the bolt head of the two mating components. Again, this is achieved with custom macros and is completed in a matter of minutes. Mesh controls in Pro/MESH are used to ensure that an annular ring of nodes and elements exist to represent the bolt hole and the area under the bolt head. This technique
can be applied to finite element models with shell or solid elements.
VALIDATION OF FRAME FLEXIBILITY
In order to establish the accuracy of the flexible frame model, a modal test was conducted on a bare truck frame. An ANSYS finite element model of the same frame was then built using the procedures described
above and the eigenvalues and eigenvectors were computed for comparison. As can be seen in Table 1, the finite element model agrees very well with the test results. A modal neutral file was then produced for
ADAMS and the modes were recomputed using the ADAMS/Linear option. The ADAMS modal frequencies also agree well with the test data and confirm that the
flexible frame provides an accurate representation of the real structure. Note, only modes up to 56 Hz were extracted from the modal test data. Higher modes exist,
but the test did not contain enough measurement points to clearly define the mode shapes. The frame model was then incorporated into the full vehicle
MSS model using the procedures described above.
The modes for the vehicle were then computed and compared to modal test data for a linehaul truck with a similar configuration. See Table 2. Again the agreement is good and indicates that the dynamics of a typical linehaul truck
are well represented by the model.
CONCLUSION
The aim of the project outlined in this paper was to develop a process by which design changes to a truck frame could be quickly evaluated such that concurrent design and analysis would be possible. As described
above, this goal has been achieved by combining current computer aided design and engineering codes with custom
software routines. The process takes advantage of the strengths of each code to create a high fidelity environment where the impact of subtle design changes to the truck frame can be measured against vehicle performance and durability requirements. Design alternatives can be quickly evaluated and fed back to the designer while it is still possible to make changes. Although this process is being used successfully, there
are many areas where further enhancements can be made and will be the focus of future development. These include:
1. Validation of simulation results using time history data from full vehicle tests. This will be used to understand the simulation weaknesses and tune model parameters. As the simulation accuracy improves, the models will provide better data for componentoptimization.
2. Flexibility using the component mode synthesis technique will be added to other structures such as the cab/sleeper and the trailer. The flexibility of both these structures is believed to play an important role
in ride and durability.
3. New CAE technologies such as fatigue analysis will be added. Computer aided engineering codes for fatigue life estimation have improved dramatically in recent years, and it is now possible to estimate the fatigue damage to a structure using the full time history loads from a multi-body simulation. Fatigue life contours can then be viewed on finite element models just as stress contours are today. This technology greatly enhances durability analysis and the development
of a virtual proving ground.
ACKNOWLEDGMENTS
We would like to thank the management team at Western Star Trucks for having the vision to support the development of an integrated CAE process. We would also like to thank Ken Murray, Don Moore, Bob Perra, and Mark Gobessi for their careful review of the paper.
REFERENCES
1. “Mechanics of Heavy-Duty Trucks and Truck Combinations”, UMTRI Course Notes, July, 1995.
2. Stasa, Frank L., “Applied Finite Element Analysis for Engineers”, CBS College Publishing, 1985.
3. Ottarsson, Gisli, “Modal Flexibility Method in ADAMS/FLEX”, Mechanical Dynamics, Inc., March, 1998.
4. “Using ADAMS/FLEX”, Mechanical Dynamics, Inc.,1997.
5. “ADAMS/Finite Element Analysis Reference Manual”, Mechanical Dynamics, Inc., November 15,1994.
6. “Pro/MESH and Pro/FEM Post, User’s Guide”, Parametric Technology Corporation, 1997.
7. “ANSYS Structural Analysis Guide”, Analysis, Inc.,1994.
8. Gillespie, Thomas D., “Fundamentals of Vehicle Dynamics”, Society of Automotive Engineers, Inc.,1992.
9. Gobessi, Mark and Arnold, Wes, “The Application of Bonded Aluminum Sandwich Construction Technology to Achieve a Lightweight, Low Cost Automotive Structure”, SAE paper 982279.
