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CAD模型的发展:在一个汽车应用专题研究的草图中(外文翻译及原文)
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CAD模型的发展:在一个汽车应用专题研究的草图中
R Vignesh,R Suganthan, and K Prakasan*
印度 CoimbatorePeelameduPSG科技学院的制造工程技术部在200646日的原稿于200682日经审核和修正以后的出版物。
DOI (加拿大)工业部:10.1243/09544070JAUTO331
 
摘要:今天产品设计不仅为他们的功能要求,而且还为美学。在汽车制造业,造型风格成为了类表面设计过程的大部分。类表面是自由形态表面以连续的曲度的表面。设计所有组分或系统过程通过引起实际上产品根据它的形式、作用和适合的概念开始。概念图样帮助设计师迅速和容易地到达可以为细节设计指定的一个令人满意的设计阶段。 这些概念图样可以用于对曲线和表面的数字式构思设计和有限元分析的发展。 软件例如别名存在以及可以被用来在电脑屏幕上进行车身概念剪影绘制的合适的硬件支持。在本文一个系统的做法为在图纸上手工绘制的类表面概念剪影准备被讨论。这些图象被放进CATI A V5草图追踪者模块。一个设计师可以用这些图象作为参考使用图象,并且通过用CATIA V5软件追踪图象绘制一个数字式草图而没有增加任何特别硬件。 以后,可以试图用这些表面的审讯来改进美学效果。这个方法为CATIA V5的用户改进他们的设计实践和技能是很有用的。
主题词: 概念剪影,黏土塑造,类表面,反射排行
1导言
产品造型风格被用来创造在众多产品中的视觉吸引力。造型被广泛接受是产品在无需改变它的技术表现下增值的一个重要方式。
当新产品质量等第相差不大时,新兴的外观造型成为吸引消费者的一个关键的因素。新造型款式的创造和令人兴奋震撼的设计理念不仅是一时的兴盛,也是具有定位长远价值的。外观造型在提高车视觉魅力的同时开发了新的设计和为顾客提供了更多的选择余地。 今天,不仅是考虑被设计的产品功能,而且特别考虑能给在人的头脑里能导致一个欲望去拥有那个产品的他们的美学。这是改进类表面的原因和他们的重要性。类表面对我们是可直观看见的,并且具有优选的审美形状和高表面质量的那些审美自由形态表面。
因为工程师通常更喜欢产品的演变进行完全再设计,现有的产品身份证Restyling在汽车制造业频繁地执行了。 用户反映、客户协助建议和市场方针通常影响关于再设计或restyling的决定产品。
一个传统汽车发展过程介入许多手工制造描绘草图的发展为了提供模型的神色的视觉。 从这些草图中,一些通过粘贴一张定格在墙壁上的图画的四个角度看法及 哪些在1:10被做度量下来的黏土模型被开发。 一个打缩小比例的黏土模型被完成,并且模型使用三维扫描器被扫描。 然后被完成的剪影的1:1黏土模型被发展。在这个阶段所有变动都需要很多时间。 概念开发和造型通过常规的方法比较是要建立在计算机辅助的设计 (CAD)可以提供的基础上的。如表 1.
这工作宗旨是为了实现一种为开发CAD模型和表面审讯将手工准备的用于CATIA V5软件跟踪影曲线概念性草图的图象的方案。也有一种将未做曲度连续性审核的表面和做过曲度连续性审核的表面进行美学和外观造型比较的想法。这里用的方法透露出在很难注意其他方面时表面可能显露间断性,虽然两个在这里同是由CATIA V5软件创造的。这里引用的这一程序可以被CATIA V5的用户实践操作来进行革新。 一个由术家画在纸上的图案被用于这一工序。这看来是一种新方法。 从当前作者的经验它被发现用户在领悟IA V5表面审核的功能是有限的。
 
2文学效果的检验
为了进行造型表面的审核来决定工业生产实践,一个符合人文气息的检验被执行并且在这里提出相关的观察。
Tovey [1]谈论了草图和它的在汽车构思设计中的角色。 汽车设计师使用草图通过它的二个阶段构思设计支持造型创造的活动和在移交到顺流之前设计发展过程。 计算机造型辅助设计(CAD)的重要性被突出
Tovey [2]描述了在草图的工作映射作为一个有用的工具并且和那些更加方便直接而看起来有局限性的塑造方法进行了对比。 他也给了一个在工作进展中直接地从草图获得简要说明的形式。 构思设计方法学也被讨论了。
Sunner [3]等谈论了对于用镜子反射线聚焦的用途为汽车身体表面质量进行检测管理。 一个高度反射性表面原型被建立了并且在一间立方的屋子里观看到有许多平行的被安排的光。 用光的反射原理来检验表面质量是一项好措施即: 为检测表面曲度间断性和探讨形状的特征。
哈根[4]等提出了一个表面审核方法的细部鉴定。 Orthotomics用于凸形测试。 焦曲面,一套自由形态曲线和表面分析新工具是用于在向CNC机器寄发数据之前分析表面质量的一致特别线。
Hahmann [5]给了一个一般方法为包括反射线、isophotes、曲率测算、聚焦线和isolines的表面校核。 这些工具主要用在计算机图型计算和建立用CAD分析自由形态表面的申请。
Theisel [6]显示isophotes和反射线是为不同的表面审核,Isophotes的工具是使用辨认曲度间断性在表面之间,并且反射线用于测量表面质量的。
Monacelli [7]谈论了对减少在车开发过程和费用的虚拟现实(VR)申请介入的时间。 VR可能帮助从一个手工方法改变最初的概念草图到一个数字式的开发环境。 VR有应用在造型,并且设计师能用一个更好的方式形象化数字式模型。
Barone [8]解释了将传统制图过程更新到一个基于CAD的制图过程的需要并阐释了传统制图的过程期间面对的困难。
车身造型风格
 关于汽车外部造型图样的一项研究被执行,因为顾客对一辆车的第一印象是车身造型设计。在市场竞争,不仅需要一个好的设计,而且关键是在制造汽车时外观造型师能准确实施。
传统汽车发展过程缺点是当需要做出做变动时才更改,且黏土模型是不能够开发创造新产品种类的。而概念模型仅能够在设计过程的最后阶段看出是否需要变动,在最后阶段做对概念模型的变动是困难的。
这种方法学被采取是基于CAD的逐步发展过程的和为使用CATIA V5进行车身设计见图(2)解释。
3.1 概念图样的重要性
概念开发的输入是图样。概念图样帮助设计师迅速和容易地到达可以为细节设计指定的一个令人满意的设计阶段。 图样被输入CATIA V5剪影追踪者模块。 他们被这样排列:汽车的正面图置靠在前平面上。 同样汽车的所有视图都被排列在对应的平面上。 那些图案将形成一个边界框,并且模型将放置在边界框里面。 图3展示了手工准备的概念速写被输入CATIA V5 (被扫描)时所排列的概念草图。
3.2追踪和翻译曲线
两张被描述为最好的生成的曲面图将被选择以及曲线在图样之上被追踪。 两曲线都置于草图相对应的平面上。要在曲线追踪模块中生成一单一的曲面,需要用交叉点技术; 被追踪的曲线被挤压并且相交,以便生成的曲线将是必需的最后成型曲线。
 如果全部三个视图都来描述曲线,则点密排在一个视图上且当涉及到那些点被翻译时那两个视图也有点的密排。这样那些点将密排在所有的三个视图上。
生成的视图将误认为如图4显示的生成的一组适合于那些补丁的曲线。
3.3 曲面校核
好曲线导致好表面。 所以,在生成曲线表面之前它们的质量应首先得到分析。用CATIA V5检查整个曲线的光滑度来分析它的曲率度。 如果曲线导致光滑的表面。 如果它不是光滑的,则代表曲线的控制点被翻译,以便获得在曲度上光滑度的变化。 图5代表在曲度上的不规则的变化,并且Gig.6显示了曲度光滑的变异。 曲度的疏密绘制将显示在曲率半径的巨大变异。 当补钉的面积是小的时,这在曲线表明是一个平的区域。补丁面积必须顺利地或者也有变化地用在分析连续性的曲线之间。 为曲度连续性它是必要在没有曲度疏密的跳跃的前提下。
3.4引起表面及其变形
表面从曲线引起作为补丁。 7展示了用CATIA V5.生成的概念模型。表面描述了汽车的一个特殊组分(即 敞篷和上面是分开的组分)安置是分开的,因为能够是身体舒适的休息空间。 图89显示在本研究期间引起的某些变形。
3.5表面审核  
表面为类质量被检查。 Isophotes和反射线是表面审讯的通常使用的工具。 Isophotes用于辨认间断性在表面之间。 当光从表面时,反射他们突出形式的表面的行为或形状。用户根据这光的反射给理解关于曲度间断性。 这反射应该具有自然流线型,并且应该均一。 它被用于辨认曲度间断性和找出凹痕表面。 曲度间断性由不连续的聚焦光线排列而成。 图10显示isophote组分中其中一个模型。凹痕由强光聚焦排列于凹痕点的光程测算来描述。 Figure11显示了在用Isophotes在测算表面凹痕。 反射线用来测量表面质量。反射光线是一组汽车表面的光平面上的平行光线。图12显示了用反射光线来检测汽车表面。
3.6模型的翻译
模型翻译是对模型的形象化方面进行改进。 真实生活的翻译主要执行使顾客赞赏最后的模型的神色。A VR环境用于形象化和真实翻译。 Figure13展示在CATIA V5软件上翻译过来的模型。
 结论   本文在开发的造型设计方法提供一种系统的方法,从艺术家做的手工准备的概念草图的图象以及到使用CATIA V5软件援助。它具体地也阐述了二表面显露满意的间断性。当常规地设计表面,表面也许有间断性时,并且将必须美学改进。这种方法为需要类表面化的所有产品开发是有用的。 CATIA V5的用户在他们的实践实施同一个技术时并没有增加任何昂贵的硬件。
1ToveyM.I.、纽曼、R.M.和搬运工, SSkeching、概念开发和汽车设计。Des. 螺柱。, 2003,24,135-153
2 ToveyM.I.,构思设计CAD为汽车制造业。.J.Engng Des。, 2002,13,5-13
3 SunnerG.GreinerG.AugustiniackS。 表面质量的交互式考试在cau身体。 计算机辅助的Des。, 2004,36,425-436
4哈根, H.HahmannS.SchreiberT.NakajimaY.Wordenweber B.Hollemann-Grundstedt P 表面审核algorithma IEEE计算机图表Applic。, 1992,12 (5) 53-60
5 Hahmann S 表面分析的形象化技术。 在先进的形象化技术(EDC Bajaj) 1999年, pp.1-26 (约翰威里,纽约)
  6   Theisel H isophotes和反射线同样。 计算机辅助的几何学Des。, 2001,18,711-722 7  MonacellliG。 对减少veicle developmet过程的时期和费用的VR申请。 在第八次国际会议ATA的记录关于车建筑学的: 产品、过程和未来发展,佛罗伦萨,意大利,瑞士52003(Eurographics Assoceation)
 
制动力测算器显示制动力矩的变化取决于制动盘的厚度
Jaeyoung Kang and Sungjin Choi 
美国西部拉斐特Purdue大学的机械工程;
韩国 Chungnam  Chonan  韩国汽车技术学院,身体和底盘工程学中心,
原稿在2005511日在200665日被审核和在修正以后的出版物。
DOI (加拿大)工业部: 10.1243/09544070JAUT091
摘要: 在这项研究中,功率计的一个制动系统数学模型被提议用来辨认闸扭矩的变化(BTV),以及发电机功率测试和模拟之间的交互作用是确定了的。在时间界域里,当点联结元素和瞬时响应分析时,在触头补丁金属片上垫和圆盘之间的互作用被简单地塑造。 模型表明相当数量的BTV与硬垫、摩擦系数、圆盘厚度偏差和制动块的有效的半径成线性比例关系。使用闸功率计和别的物质性的测试被执行核实分析模型。 发电机试验证明建议的模型在准确性的预测制动系统的BTV是有理由的。
1 介绍
制动圆盘厚度偏差(DTV)和热量畸变(BTV)导致的制动器扭矩变化和制动器震动的励磁来源一样知名。既然取决于摩擦力的定量热量作用很难被预测,那么热能畸变在这里就不会被发现。反而,本文考虑制动器功率计的在相对地低温试验条件减少热量作用。功率计被用来减少热量作用的。制动器工作的动力特性在制动器功率计操作期间被观察记录,并且所有振动分析被省去,因为制动器组分和制动器功率计的方式是太高以至于不能由制动圆盘的自转激发。时域分析本身能有效地揭露制动咬合的低频率励磁的机制。 动态模型包括正常负载变异[1]在制动垫和圆盘之间的联结并且允许BTV分析形式被表达。 一些资料[2]通过实验表示, BTV取决于几个因素例如温度、改变的数量和DTV。 在本文, DTV假设是时间不变式,并且摩擦系数被简化,当圆盘的仅有角速度的一个特定作用。 制动试验在制动功率计和一些机械测试进行核实的动态模型。
2 制动力的陈述
制动功率计对制动模型的测试被用来衡量制动系统BTV的水平,这被称为BTV测试。制动模型功率测试是由等效惯性与车和制动系统的四分之一重量组成的。当惯量达到一定的角速度,驱动力被阻止,而制动力被增强。在制动系被约束的过程中,一些动力性参数被测量用一种分析的方法来描述BTV测验,见下面的例子。
2.1 没有BTV的制动模型。
制动系的一般运动方程是:f=2µN
Iθ=-2µNReff
Development of CAD models from sketches: a case study for automotive applications
R Vignesh,R Suganthan, and K Prakasan*
Department of Production Engineering, PSG College of Technology ,Peelamedu,Coimbatore,India
The manuscript was received on 6 April 2006 and was accepted after revision for publication on 2 August 2006.
DOI:10.1243/09544070JAUTO331
Abstract: Today products are designed not only for their functional requirements but also for aesthetics. In the automotive industries, styling has become a major part of the design process with class-A surfaces Class-A surfaces are freeform surfaces with a continuous curvatureThe process of engineering any component or system begins by generating a concept that actually describes the product in terms of its form, function, and fit. Concept sketches help the designers to arrive quickly and easily at a stage where a satisfactory design can be specified for detailed design. These concept sketches can be used for development of the digital concept design and analysis of the curves and surfaces. Software such as Alias exists and thus can be used with writable hardware for sketching the concept of the car body on a computer screen. In this paper a systematic procedure is discussed for generating class-A surfaces from the images of concept sketches which are manually prepared on paper. These images are imported into the sketch tracer module of CATIA V5.A designer can use the image as the reference and produce a digital sketch by tracing the image using CATIA V5 software without adding any special hardware. Laterinterrogation of these surfaces for improved aesthetics can be attemptedThis method will be useful for the users of CATIA V5 to improve their design practices and skills.
Keywords: concept sketchesclay modelingclass-A surface, reflection lines,
1 INTRODUCTION
Product styling is carried out to create visual attractiveness in products. Styling is widely accepted as an important way to add value to a product without changing its technical performance.
  As new product quality rankings convergestyling is emerging as a key differentiator for consumersThe role of styling is to create fresh and exciting design concepts that are not just contemporary but trend setting as well. Styling enhances the visual appeal of the vehicles and at the same time develops innovative designs and components for customers. Today, not only are products designed considering the functionality but also special considerations are given to their aesthetics which can produce a desire in a person’s mind to own that productThis is the reason for the evolution of class-A surfaces and their importanceClass-A surfaces are those aesthetic freeform surfaces that are visible to us and that have an optimal aesthetic shape and high surface quality .
Restyling of existing products ids frequently performed in the automotive industries, since engineers usually prefer the evolution of product to a complete redesign. Customer feedback, client assistance suggestions, and market directives usually influence the decision on redesign or restyling of a product.
  A traditional car development process involves the development of many handmade rendering sketches in order to offer a vision of the model’s look. From these sketches, a few are selected andby pasting the four views of a constrained drawing on the wall. Which are made on a 1:10 scale-down clay model is developed. One scaled-down clay model is finalized and the model is scanned using three-dimensional scanners. Then a 1:1clay model of the finalized sketch is developed. In this phase all the changes require much time. A comparison between concept development and styling by the conventional method and the approach based on computer aided design (CAD) is provided in Fig. 1.
 The objective of this work is to present a case in which the images of manually prepared conceptual sketches are used in CATIA V5softwareto trace the curves for developing CAD models and surface interrogation. An attempt is also made to compare a surface that is not checked for curvature continuity for their aesthetics and appearance. The approach used here can reveal the discontinuity in the surface which is difficult to notice otherwise although both are created in the same software The procedure adopted here can be practiced by the users of CATIA V5 to improve their innovations. A sketch on paper by an artist is made use of in this procedure. This appears to be a novel approach. From the experience of the present authors it was found that awareness of the capability of CATIA V5 for surface interrogation is limited among users. 
 
LITERATURE REVIEW
To determine the industry practices and surface interrogation techniques for styling, a literature review was carried out and relevant observations are presented here.
Tovey [1] discussed sketching and its role in the concept design of automotives. automotive designers use sketches to support the styling activity through its two phases of concept design and design development before handing over to the downstream development processes. The importance of computer aided styling’ over CAD is highlighted.
  Tovey [2] described the work on sketch mapping as a usable tool and contrasted it with the more conventional direct modeling approach which is seen to have limitations. He also gave a brief description of work in progress on deriving forms directly from sketches. The concept design methodology was also discussed.
  Sunner et al.[3] discussed the use of reflection lines and specular highlights for the quality control of car body surfaces. A prototype with a highly reflective surface was built and viewed in a cubing room, which has many parallel arranged lights. The reflections of the lights are a good measure for surface quality, i.e. for detecting surface curvature discontinuities and for discussing the character of the shape.
   Hagen et al.[4]presented a detailed survey of surface interrogation methods. Orthotomics are used for convexity tests. Focal surfaces, a new tool for analyzing freeform curves and surface, are special line congruences that are used to analyse the quality of the surface before sending the data to CNC machines.
  Hahmann [5] gave a  general method for surface interrogation which includes reflection lines, isophotes, curvature plots, highlight lines, and isolines. These tools are mainly used in computer graphics and found application in analyzing freeform surfaces in CAD.
   Theisel [6] showed that isophotes and reflection lines are different tools for surface interrogation Isophotes were used to identify curvature discontinuities between surfaces, and reflection lines were used to measure the quality of the surface.
Monacelli[7] discussed the virtual reality (VR) applications for reducing the time and cost involved in the vehicle development process. VR can help to change the initial concept sketching from a manual method to a digital environment. VR has applications in styling and the designer can visualize the digital model in a better way.
  Barone [8]explained the need for renovating the traditional styling process to a CAD-based styling process and addressed the difficulties faced during the traditional styling process.
STYLING OF A CAR BODY
 A study was carried out on the styling of automotive exteriors because the first impression that a customer has of a car is the design of the car body. To be competitive in the market, not only is it necessary to have a  good design but also it is crucial that the stylists guidelines will be accurately implemented when building the car.
 The disadvantages with the traditional car development process are the time taken to make changes and the inability of the clay model to create variants of the new productAs the concept model can be seen only at the final stage of the design process, making changes to the concept model in the final stages is difficult.
The methodology adopted and the step-by-step procedures of the CAD-based development process for the car body using CATIA V5 are explained in Fig.2.
3.1 Importing concept sketches
The input for concept development is sketches. Concept sketches help the designers to arrive quickly and easily at a stage where a satisfactory design can be specified for development of detailed design. The sketches are imported into the sketch tracer module of CATIA V5. They are aligned such that the front view of the car will lie on the front plane. Similarly all the views of the car are aligned to lie on the corresponding plane. The sketches will form a bounding box and the model will form a bounding box. Figure 3 show the aligned concept sketches imported into CATIA V5 using the images (scanned) of manually prepared concept sketches.
3.2 Tracing and translating curves
 Two sketches that will best represent the curve to be generated are selected and curves are traced above the sketch. Both curves will lie on the corresponding plane of sketch.To generate a single curve from the curves traced, an intersection technique is used; the curves traced are extruded and intersected so that the resulting curve will be the required curve  for surface generation.
If all three sketches represent a curve, then points are plotted in one view and with the other two sketches as references the points are translated such that the points will appear to lie on all three sketches.
 The generated sketches are mirrored to generate a grout of curves as shown in Fig.4, which are suitable for generating patches.
3.3 Curve interrogation
 Good curves will result in good surfaces. Therefore, before generating surfaces the curves are analysedfor their quality. Porcupine curvature analysis in CATIA V5 checks for a smooth variation in curvature (plots) throughout the curve. If the curves will result in smooth surfaces. If it is not smooth, then the control points representing the curves are translated so that a smooth variation in curvature is obtained. Figure 5 represents an irregular variation in curvature and Gig.6 shows a smooth variation in curvature. The curvature comb plot will show variation in the magnitude of the radius of curvature. When the magnitude of the spikes is small, this indicates a flat region on the curve. The magnitude must vary smoothly, or also useful in analyzing the continuity between the curves. For curvature continuity it is necessary that there is no step in the curvature comb.
3.4 Generating surfaces and variants
 Surfaces are generated from the curves as patches. Figure 7 show s the concept model generated in CATIA V5.The surfaces representing a particular component in a car (e.g. the hood and the top are separate components )are placed in separate open bodies because of the ease in restyling. Figures 8 and 9 show some of the variants generated during the present study.
3.5 Surface  interrogation
 Surfaces are interrogated for class-A quality. Isophotes and reflection lines are the most commonly used tools for surface interrogation. Isophotes are used to identify the discontinuity between surfaces. They highlight the behaviour of the form or shape of a surface when light reflects from the surface. This reflection of light gives the user an understanding about the curvature discontinuity. This reflection should be natural and streamlined and should have uniformity. It is used to identify curvature discontinuities and to locate the dents in surfaces. Curvature discontinuities are represented by discontinuous highlight plots. Figure 10 shows the isophote plot of one of the models.Dents are represented by convergence of the highlight plot at the point of dent. Figure11 shows the isophote plot at on a dent on the surface. Reflection lines are used to a family of parallel lines on the light plane on the surface. Figure 12 shows the reflection line plot on the car surface.
3.6 Rendering
Rendering of the models is carred out to improve the visualization aspects of the model. Real-life rendering is mainly performed to make the customers appreciate the look of the final models. A VR environment is used for visualization and real-life rendering. Figure13 shows the rendered model generated in CATIA V5.
CONCLUSIONS
 This paper tries to provide a systematic approach in developing styles from the images of the manually prepared concept sketches made by an artist with the aid of CATIA V5 software .It also interrogated two surfaces specifically to reveal the discontinuities that satisfied while designing a surface conventionally,the surface may have discontinuities and aesthetics will have to be improved.This approach is useful for any product development that needs class-A surfacing . The users of CATIA V5 can implement the same technique in their practice without adding any costly hardware.
REFERENCES
1 Tovey, M.I., Newman, R.M., and Porter, S. Skeching, concept development and automotive design Des. Stud.,2003,24,135-153.
2  Tovey,M.I., Concept design CAD for the automotive Industry.J.Engng Des.,2002,13,5-13
3  Sunner, G., Greiner, G., and  Augustiniack,  S. Interactive examination of surface quality on cau bodies. Computer Aided Des., 2004,36,425-436
4 Hagen,H., Hahmann, S., Schreiber, T., Nakajima, Y., Wordenweber,, B., and Hollemann-Grundstedt, P. Surface interrogation algorithma. IEEE Computer Graphics Applic.,1992,12(5),53-60
5  Hahmann, S. Visualization techniques for surface analysis. In Advanced visualization techniques (EDC. Bajaj), 1999,pp.1-26(John Wiley, New York).
6   Theisel, H. Are isophotes and reflection lines the same? Computer Aided Geometric Des., 2001,18,711-722
7   Monacellli, G. VR applications for reducing time and cost of veicle developmet process. In Proceedings of the Eighth International Conference ATA on Vehicle Architectures: Products, Processes and Future Developments, Florence, Italy, May 2003(Eurographics Assoceation, Switzerland).
1. Brake dynamometer model predicting brake torque variation due to disc thickness variation
Jaeyoung Kang and Sungjin Choi 
Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA
Body and Chassis Engineering Centre, Korea Automotive Technology Institute, Chonan, Chungnam, Republic of Korea
The manuscript was received on 11 May 2005 and was accepted after revision for publication on 5 June 2006.
DOI: 10.1243/09544070JAUT091
 
Abstract: In this study, the mathematical model for a brake system in a dynamometer is proposed to identify brake torque variation (BTV), and correlations between the dynamo test and simulation are determined. The interaction between the pads and the disc on the contact patch is simply modeled as a point-contact element and the transient response analysis in the time domain is introduced. The model indicates that the amount of BTV is linearly proportional to the pad stiffness, the friction coefficient, the disc thickness variation, and the effective radius of the brake pads. To verify the analytical model. A brake dynamometer is used and additional material tests are carried out. The dynamo test shows that the suggested model has reasonable accuracy in predicting the BTV of a brake system.
Keywords: brake dynamometer model, brake torque variation, disc thickness variation
1INTRODUCTION
The brake torque variation (BTV) induced by the disc thickness variation (DTV) and thermal distortion is well known as the excitation source of brake judder. Since it is hard to predict the quantitative thermal effect due to frictional forces(摩擦力), thermal distortion will not be covered here. Instead , this paper considers the relatively low-temperature test condition of a brake dynamometer to reduce the thermal effect. The dynamometer is to reduce the thermal effect. The dynamic characteristics of brake motion during brake dynamometer operation are sought and any vibration analysis is omitted because the modes of the brake component and the brake dynamometer are too high to be excited by rotation of the brake disc. Time-domain analysis itself can effectively uncover the mechanism of the low-frequency excitation induced by brake engagement. The dynamic model includes the normal load variation [1] on the contact between the pads and the disc and allows the BTV to be expressed in an analytical form. Some papers [2] have shown through experiment that the BTV depends on several factors such as the temperature, the number of revolutions, and the DTV. In this paper, the DTV is assumed to be time invariant and the friction coefficient is simplified as a given function of only the angular velocity of the disc. The braking test in the brake dynamometer and some mechanical tests are conducted to verify the dynamic model.
2 BRAKE DYNAMIC FORMULATION
The braking-mode test of the brake dynamometer is used to measure the BTV level of the brake system; this is called the BTV test. The braking-mode dynamo test consists of the inertia equivalent to the quarter weight of the vehicle and brake system. When the inertia reaches a certain angular velocity, the driving force is stopped and then the brake system is engaged. During engagement(约束)of the brake system, several dynamic parameters are measured. To describe the BTV test in an analytical way, the following model is suggested.
2.1Brake model without BTV
The general equation of motion for the brake system is
f=2µN
Iθ=-2µNReff
The normal load is generated by the brake fluid pressure Pn acting on the brake cylinder cylingder with a  section area Acylinder and is expressed as
          N=PnAcylinder
The brake rorque (BT) is equivalent to  Iθ and can be measured in the brake dynamo test . In reality, μ varies with the angular velocity, temperature, etc., but it is often regarded as a constant design parameter. Gigure 1 shows the result of dynamic simulation
2.2 Modified brake dynamic model
To account for the brake torque, the normal load variation should be included in the brake dynamic model.
 2.2.1 Normal load variation
The normal load at the contact between the pad and the disc can be modeled by contact stiffness [3,4]. The pad lining is composed of soft non-metallic materials such as fibre or rubber, and the contact stiffness has a non-linear function of the normal load.
The disc profile has thickness variation in the circumferential direction, namely the DTV, which is defined as the difference between the maximum thickness and the minimum thickness of the disc. Since the peak value of the DTV has a key role in the brake dynamic model, the disc thickness can be simplified as a sinusoidal function (Fig.2) with first-order rotation
  tv=tmax-tmin=tmean=DTV
Also the run-out value of the brake disc does not produce the net normal load on the contact patch between the pads and the disc because the outward normal load on one side of the disc cancels out the inward normal load on the other side. Therefore, the normal perturbation function u on the contact can be simply expressed as the complex exponential function according to
 U=
For viscous elastic pads, the function of the normal load variation becomes (Fig.3)
Nvariation=Kpadu+Csystemu
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