汽车拨杆工艺及夹具设计【两套夹具】.doc

汽车拨杆加工工艺及夹具设计(全套含CAD图纸)

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外文翻译译文题目 一种自动化夹具设计方法 原稿题目 A Clamping Design Approach for Automated Fixture Design原 稿 出 处 Int J Adv Manuf Technol (2001)18:784789一种自动化夹具设计方法塞西尔美国,拉斯克鲁塞斯,新墨西哥州立大学,工业工程系,虚拟企业工程实验室(VEEL)在这片论文里,描述了一种新的计算机辅助夹具设计方法。对于一个给定的工件,这种夹具设计方法包含了识别加紧表面和夹紧位置点。通过使用一种定位设计方法去夹紧和支撑工件,并且当机器正在运行的时候,可以根据刀具来正确定位工件。该论文还给出了自动化夹具设计的详细步骤。几何推理技术被用来确定可行的夹紧面和位置。要识别所完成工件和定位点就还需要一些输入量包括 CAD 模型的技术要求、特征。关键词:夹紧;夹具设计1. 动机和目标夹具设计是连接设计与制造间的一项重要任务。自动化夹具设计和计算机辅助夹具设计开发(夹具CAD)是下一代制造系统成功实现目标的关键。在这片论文里,讨论了一种夹具设计的方法,这种方法有利于在目前环境下夹具设计的自动化。夹具设计方法的研究已成为国内多家科研工作的重点。作者:周在1中对工件的稳定和总需求约束了双重标准,突出重点的工作。在夹具设计中广泛的运用了人工智能(AI)以及专家系统。部分 CAD 模型几何信息也被用于夹具设计。Bidanda 4描述了一个基于规则的专家系统,以确定回转体零件的定位和夹紧。夹紧机制同时用于执行定位和夹紧功能。其他研究者(如 DeVor 等,5,6)分析了切削力钻井机械和建筑模型及其他金属切削加工。康有为等在2中定义了装配约束建模的模块化与夹具元件之间的空间关系。一些研究人员采用模块化夹具设计原则,用以生成2,7-11,另一些夹具设计工作者已经报告了1,3,9,12-23。可以在21,24中找到夹具设计相关的大量的审查工作。在第二节中,对夹具设计任务中各种步骤进行了概述。在第 3 节和第四节中描述了工件的加工过程,要夹紧工件表面,否则将面临工件的全面自动测定。第 5 节讨论了对工件的夹紧点的测定。2. 夹具设计的整体方法在本节中,描述了整体夹紧的设计方法。通常对较理想的位置的那一部分进行夹紧,并减低切削力的影响。夹紧的位置和夹具设计中定位的位置是高度相关的。通常,夹紧和定位可以通过同样的方法来完成。但是,不明白这两个是夹具设计中不同的方面,可能导致夹具设计的失败。多数人的在规划过程中首先解决定位问题,这样可以使开发的定位与设计的定位相契合。不过,整体定位及设计方法不在本文讨论范文内。除了零件的设计(为此夹具设计有待开发),公差规格,过程序列,定位点和设计等因素外,还应投入 CAD 模型到夹具设计方法中。这样的夹具可以夹紧并支撑定位器。指导使用的主要内容应尽量不抵制切割或加工过程和中所涉及的操作。相反,应定位夹具,使切削力在正确的方向,这将有助于保持在一个特定的部分加工操作安全。通过引导对定位器的切割力量,部分(或工件)被固定,固定定位点,因此不能移动的定位器。在这里讨论的夹具的设计方法必须在整体夹具设计方法的范围内。在此之前进行定位器/支撑和夹具设计的初步阶段,涉及到的分析和识别的功能、相关的公差和其他规范是必要的。根据初步的评估和测定,定位/支撑设计与夹具设计结果的在此基础上可以同时进行。本文对所描述夹具设计的方法讨论基于定位器/ 支撑设计与先前已经确定的假设(包括适当的定位和支持测定一个工件的定位,以及识别和夹具,如 V 元素的支持面块,基础板,定位销等)。 (1) 夹具设计的输入输入包括对特定产品的设计翼边模型,公差信息,提取的特征,过程顺序和部分在给定的每一个设计的相关特性的加工方向,面向的位置和定位装置,以及加工过程中的各种工序,须出示每个相应的功能。(2)夹具设计的方法图一是自动化夹具设计主要步骤总结图。对这些步骤概述如下:第 1 步:设置配置清单以及相关的进程_功能条目。第 2 步:确定方向和夹紧力。输入必要的加工方向向量mdv1,mdv2mdvn,面对 nvs 的支持力,并确定法向量。如果加工方向向下(对应的方向向量0,0,-1) ,和面的支持向量平行于加工方向,那么,夹紧力方向平行向下加工方向0,0,-1。如果必需要侧面夹紧并没有可夹紧的地方,那么在其中放置一个夹具夹紧下调,然后边钳方向计算如下。让 sv 和 tv辅助常规的向量代替次要的和三级定位孔。然后,使用夹紧机构夹紧一个方向,例如,av 应平行于这两个法向量,即,正常向量应分别与每块表面的 sv 和 tv向量平行。侧面夹紧面应该是一对分别平行于面 sv 和 tv 的平面孔。第三步:从列表中选出最大有效加工力。这样能够有效的平衡各加工力。第四步:利用计算出的最高有效加工力,才能确定用来支撑工件加工的面积的夹具尺寸(例如,一个带夹子可以作为一个夹紧机构使用)。第五步:确定给定工件的夹紧面。这一步在第 4 步中所述过。第六步:该夹具的夹紧面的实际位置自动在第 5 节中确定。考虑接下来的步骤并返回第一步。3. 判断夹具尺寸在这项工作中所用到的夹具都来自一个系列。夹具的原理与图二相同。在这一节里,描述了一个自动化夹具。锁模力所需的有关螺杆的螺纹装置大小或保存到位钳。夹紧力平衡加工工件使工件保持恰当的位置。让锁模力为 W 和螺杆直径为 D。各种螺丝夹紧力大小,可以按以下方式确定:最初,极限拉伸强度(抗拉强度)和该夹具的材料(供应情况而定)可以从数据检索库检索。各种材料有不同的拉伸强度。该夹具材料的选择,也可直接采用启发式规则进行。例如,如果部分材料是低碳钢,那么钳材料可低碳钢或机器钢。为了确定设计应力,抗拉强度值应除以安全系数(如 4 或 5)。根区的螺丝格 A1(如一个螺丝钳)可以被确定:锁模力/设计应力。随后,螺栓截面全面积可以计算为等于格 A1 /(65),(因为螺丝的地方可能会发生根切面积约为 65螺栓的总面积) 。螺钉的直径 D 可以被确定等同于(D2 的 3.14 / 4)。另一项涉及可用于方程有关的宽度 B,高度 H 和跨度的钳 L 的螺丝直径为 D(B ,H 和 L 可以为不同的值计算 D):d2=4/3 BH2/L.4. 判断夹紧表面确定夹具经常出现的相关参数包括了产品的 CAD 模型,提取的特征信息,特征尺寸,定位面和定位器的选择。考虑所有潜在的加紧面,如图 3。最关键的是夹紧表面不应重叠或与该面相交,如图 4 所示。夹紧面积是与工件表面(或 PCF)接触的是一个二维轮廓线段组成的(见图 6) 。利用线段相交测试,可以测定在给定的光子晶体光纤的任何范围内是否可能有接触面夹紧面重叠。夹紧面的确定可以如下所示:第 1 步:鉴别平行于二级和三级定位面(lf1 和 lf2)是分别到 lf1 和 tcj 最远的距离的面。如下所示:(一)鉴别面 tci,tcj,使面 tci 和 tcj 平行 lf1 和 tcj 平行 lf2。 (二)在 TCF 中列出面对 tci 的面。 (三)通过检查所有 TCF 中面对 tci的面,确定的面对 tci 和 tcj 的面是到 lf1 和 lf2 分别最远的面,并舍弃所有其他TCF 中的面。 第 2 步:鉴别平行面的位置,除了不相邻的附加面。最好是选择一个不与其他定位面垂直相邻的面。这一步如下所示:(a) 考虑 TCF 列表中的 tci 面,获得与每个 tci 面垂直或相邻的面然后,在FCF 列表中插入每个 fci 面。(b) 检查每个 FCI 面,并执行以下测试:如果 FCI 是相邻、垂直于 lf1 或lf2,然后从列表中舍弃它并插入 NTCF 列表中。第 3 步:确定加紧面都在有效的加紧面上,如下所述夹紧面:例 1:如果没有条目在列表 NTCF 中,就使用 TCF 中的面并继续执行步骤4。如果任何面发现,垂直于第二,第三位置的面孔 lf1 和 lf2,这将要面临的是下次选择可行的夹具。在这种情况下,唯一剩下的选择是重新审视在列表NTCF 的面。例 2:如果列表中 NTCF 条目数为 1 时,可行夹紧面为 FCI。与 TCI 的法向量垂直相邻的相应轴是夹紧轴。例 3:如果在列表 NTCF 项数大于 1,确定最大的 TCI 加紧面再进行步骤4。例 4::夹紧力的方向可以是1,0,0或0,1,0,可以夹紧 TCI 面的中心位置。在其他几何位置可确定使用零件几何形状和拓扑信息,这在下一节中描述。5. 判断夹紧表面上的夹紧点确定夹紧面后,必须确定实际夹紧位置。输入夹具侧面积,沿着x,Y,Z和潜在的夹紧面 CF 方向。 容下使用 CF 几何获得夹具侧面积:第一步是确定一个箱体的大小,这是用来测试它是否包含在它里面的任何部分。相交测试也可以在前面介绍的方法使用。如果相交测试返回一个负的结果,那么有部分箱体与夹具相交,如图 4 所示。如果相交测试返回一个正的结果,可以执行下列步骤:1 划分成更小的矩形大小条(1 W)夹框轮廓(图 5 和图 6)。2 执行指定与功能配置文件出现在 CF 面的零件设计的相交测试。3 没有功能相交的条形区域,都是可行夹紧区域。如果有一个以上的长方形候选 面,矩形配置文件,向中沿轴夹紧 CF 面点的是夹紧配置文件(夹点)。如果没有发现配置文件,夹具宽度可减少一半,夹具数可以增加两个。使用这些修改过的夹具尺寸,执行前面描述的特征相交测试。如果此测试也失败了,那么可以用相邻的面作为夹紧面用于执行端夹紧。这面可以重复进行 PCF和功能相交测试。:5.1试验曲线的交点输入需要的二维轮廓P1 、 P2,使用下列方法可以自动确定该配置文件的交集。每一个输入的资料组成一个封闭环。此配置文件测试的步骤如下:(T1) 考虑 P1 线段中的 L(i,1)和 P2 线段中的 L(2,j )。(T2) 采用 L(i,1)线段和 L(2,j)线段的相交段。如果边缘相交测试返回一个正值,那么特征面和潜在面相交。如果它返回一个负值,继续执行步骤3。(T3)重复与步骤(T1)相同的部分或者缓慢走过其余 P1 中的(Li,1) 段直到P2 中的 (L2, j1) till j n1段。(T4) 其余部分边和 P1 中的 L12、L13 到 L1n 段重复(T1 )和(T2)步骤。如果特征面与夹紧面重复,线相交测试将决定该事件。相交的边可以进行自动检测两个面是否相互交叉。输入所需的边 L12连接 (x1, y1) 和 (x2, y2)和 L34连接 (x3, y3) 和(x4, y4)。L12 型方程的可表示为:F(x,y) =0 (1)L34型方程的可表示为:H(x,y) =0 (2). 第一步:使用等式(1)计算R3 F(x3, y3),用X 和Y 取代X3和Y3;计算R4 F(x4, y4),用X和Y取代X4和Y4。第二步:如果R3和R4都与0不相等,但R3与R4结果相同(R1与R2在相同的一边),则边L12与L34不相交。如果这样不满足条件,那么进行第三步。第三步:使用等式(2)计算R1 H(x1, y1)。接着,计算 R2 G(x2, y2)再进行第四步。第四步:如果R1与R2 都不等于0,且R1与R2 的结果相同,那么把R1与R2放在相同的一边并输入不相交。如果,这个也不满足条件,那么进行第五步。第五步:给定相交线段。这样就完成了测试。考虑如图 7 所示的一部分样品。将要生产一个盲孔。起初,完成定位设计。定位器的(或主要定位器)是一个基盘(放在 F4 面)和二级和三级定位器面临 F6 和 F5(对应到定位面 lf1和 lf2 在第 4 节中讨论) 。一个辅助定位器也被使用,这是一个 V 型块(对 F3和 F5 面辅助定位),如图 8 所示。在前面讨论的夹具设计方法中所述的步骤的基础上,候选面孔(这是平行的,并在从 lf1 和 lf2 最遥远的距离)是面对 F3和 F5 面。没有面孔,这是平行到定位面,但他们不相邻。在这种情况下使用的优先权规则(如步骤 3 第 4 步讨论),剩余的候选面面对的是 F2 面。夹具方向向下的 V 型块径向定位器和其他与对工件夹紧底面提供所需位置。根据第五步选择夹具的位置。如果没有功能发生在面 F2 上,那么也没有必要进行相交测试确定夹具优美加紧。夹具位置应远离 V 型定位器(这是辅助定位位置)的夹紧面毗邻辅助定位面(这确保了更好的快速夹紧) 。最终位置和夹具的设计如图 8 所示。本文讨论的方法,毫不逊色于其他夹具设计文献中讨论的方法。本文所讨论的方法的独特性是零件的夹紧面的几何形状,拓扑和功能发生了被加工为基础的系统鉴定。其他方法都没有利用了定位器的位置,该方法使用定位器在对持有一级,二级和三级定位器加工的工件。这种方法的另一个好处是在可行的候选面上确定在面上用夹具面交点测试(如前所述),并迅速和有效地确定潜在的下游过程中可能出现问题,夹紧和加工的功能检测。6. 总结在这篇论文中,对在一个夹具设计方法的总体框架内进行了夹具设计方面的讨论。设计定位器,规范零件设计,和其他相关被用来确定夹紧面和夹紧方向。并讨论了各种自动化步骤。Int J Adv Manuf Technol (2001) 18:784789 2001 Springer-Verlag London LimitedA Clamping Design Approach for Automated Fixture DesignJ. CecilVirtual Enterprise Engineering Lab (VEEL), Industrial Engineering Department, New Mexico State University, Las Cruces, USAIn this paper, an innovative clamping design approach isdescribed in the context of computer-aided fixture design activi-ties. The clamping design approach involves identification ofclamping surfaces and clamp points on a given workpiece.This approach can be applied in conjunction with a locatordesign approach to hold and support the workpiece duringmachining and to position the workpiece correctly with respectto the cutting tool. Detailed steps are given for automatedclamp design. Geometric reasoning techniques are used todetermine feasible clamp faces and positions. The requiredinputs include CAD model specifications, features identified onthe finished workpiece, locator points and elements.Keywords: Clamping; Fixture design1. Motivation and ObjectivesFixture design is an important task, which is an integration linkbetween design and manufacturing activities. The automation offixture design activities and the development of computer-aidedfixture design (CAFD) methodologies are key objectives to beaddressed for the successful realisation of next generationmanufacturing systems. In this paper, a clamp design approachis discussed, which facilitates automation in the context of anintegrated fixture design methodology.Clamp design approaches have been the focus of severalresearch efforts. The work of Chou 1 focused on the twincriteria of workpiece stability and total restraint requirement.The use of artificial intelligence (AI) approaches as well asexpert system applications in fixture design has been widelyreported 2,3. Part geometry information from a CAD modelhas also been used to drive the fixture design task. Bidanda4 described a rule-based expert system to identify the locatingand clamping faces for rotational parts. The clamping mech-anism is used to perform both the locating and clampingCorrespondence and offprint requests to: Dr J. Cecil, Virtual EnterpriseEngineering Lab (VEEL), Industrial Engineering Department, NewMexico State University, Las Cruces, NM 88003, USA. E-mail:jcecilL50560functions. Other researchers (e.g. DeVor et al. 5,6) haveanalysed the cutting forces and built mechanistic models fordrilling, and other metal cutting processes. Kang et al. 2defined assembly constraints to model spatial relationshipsbetween modular fixture elements. Several researchers haveemployed modular fixturing principles to generate fixturedesigns 2,711. Other fixture design efforts have beenreported in 1,3,9,1223. An extensive review of fixture designrelated work can be found in 21,24.In Section 2, the various steps in the overall approach toautomate the clamping design task are outlined. Section 3describes the determination of the clamp size to hold a work-piece during machining and in Section 4, the automatic determi-nation of the clamping surface or face region on a workpieceis detailed. Section 5 discusses the determination of the clamp-ing points on a workpiece.2. Overall Approach to Clamp DesignIn this section, the overall clamping design approach isdescribed. Clamping is usually carried out to hold the part ina desired position and to resist the effects of cutting forces.Clamping and locating problems in fixture design are highlyrelated. Often, the clamping and locating can be accomplishedby the same mechanism. However, failure to understand thatthese two tasks are separate aspects of fixture design may leadto infeasible fixture designs. Human process planners generallyresolve the locating problem first. The approach developed canwork in conjunction with a locator design strategy. However,the overall locator and support design approach is beyond thescope of this paper.CAD models of the part design (for which the clamp designhas to be developed), the tolerance specifications, processsequence, locator points and design, among other factors, arethe inputs to the clamp design approach. The purpose ofclamping is to hold the parts against locators and supports.The guiding theme used is to try not to resist the cutting ormachining forces involved during a machining operation.Rather, the clamps should be positioned such that the cuttingforces are in the direction that will assist in holding the partsecurely during a specific machining operation. By directingA Clamping Design Approach 785the cutting forces towards the locators, the part (or workpiece)is forced against solid, fixed locating points and so cannotmove away from the locators.The clamp design approach discussed here must be viewedin the context of the overall fixture design approach. Priorto performing locator/support and clamp design, a prelimi-nary phase involving analysis and identification of features,associated tolerances and other specifications is necessary.Based on the outcome of this preliminary evaluation anddetermination, the locator/support design and clamp design canbe carried out. The clamp design approach described in thispaper is discussed based on the assumption that locator/supportdesign attributes have been determined earlier (this includesdetermination of appropriate locator and support faces on aworkpiece as well as identification of locator and supportfixturing elements such as V-blocks, base plates, locatingpins, etc).2.1 Inputs to Clamp DesignThe inputs include the winged-edge model of the given productdesign, the tolerance information, the extracted features, theprocess sequence and the machining directions for each of theassociated features in the given part design, the location facesand locator devices, and the machining forces for the variousprocesses required to produce each corresponding feature.2.2 Clamp Design StrategyThe main steps in the automation of the clamping design taskare summarised in Fig. 1. An overview of these steps isas follows:Step 1. Consider the set-up SUi in the set-up configuration listalong with the associated process H20841 feature entries.Step 2. Identify the direction and type of clamping. The inputsrequired are the machining direction vectors mdv1,mdv2,.,mdvn and identified normal vectors of support face nvs.Ifthe machining directions are downward (which correspond tothe direction vector 0, 0, 1), and the normal vector of thesupport face is parallel to the machining direction, then thedirection of clamping is parallel to the downward machiningdirection 0, 0, 1. If sideways clamping is required, and ifthere are no feasible regions at which to position a clamp fordownward clamping, then a side-clamp direction is obtainedas follows. Let sv and tv be the normal vectors of the secondary(sv) and tertiary (tv) locating faces. Then, the direction ofclamping used by a side-clamping mechanism such as a v-block should be parallel to both these normal vectors, i.e. thenormal vectors of the each of the v-surfaces in the v-blockwill be parallel to sv and tv, respectively. The side clampingface should be a pair of faces parallel to the faces sv andtv, respectively.Step 3. Determine the highest machining force from the mach-ining forces list (for each feature) MFi (i = 1,.,n). This willbe the effective force FE that must be balanced while designingthe clamp for this set-up SUi.Step 4. Using the value of the calculated highest machiningforce FE, the dimensions of the clamp to be used to hold theFig. 1. The clamp design activities.workpiece can be determined (for example, a strap clamp canbe used as a clamping mechanism). The approach for this taskis explained in Section 3.Step 5. Determine the clamping face on a given workpiece.This step can be automated as described in Section 4.Step 6. The actual position of the clamp on the clampingface is determined in an automated manner as explained inSection 5.Consider next set-up SU(i + 1) and proceed to step 1.3. Determination of the Clamp SizeIn this work, the clamps used belong to the family of clampsreferred to as strap clamps. A strap clamp is based on thesame principle as that of the lever (see Fig. 2). In this section,the automated design of a strap clamp is described. Theclamping force required is related to the size of the screw ora threaded device that holds the clamp in place. The clampingforce should balance the machining force to hold the workpiecein position. Let the clamping force be W and the screwdiameter be d. The dimensions of the various screw sizes forvarious clamping forces can be determined in the followingmanner. Initially, the ultimate tensile strength (UTS) of thematerial of the clamp (depending on availability) can beretrieved from a data library. Various materials have differenttensile strengths. The selection of the clamp material can alsobe performed directly using heuristic rules. For example, if thepart material is mild steel, then the clamp material can be low786 J. CecilFig. 2. The strap clamp.carbon steel or machine steel. To determine the design stress,the UTS value can be divided by a safety factor (such as 4or 5). The root area A1 of the screw (for a clamp such asa screw clamp) can then be determined: Clamping forcerequired/Design Stress DS. Subsequently, the full area FA ofthe bolt cross-section can be computed as equal to A1/(65%)(since the root area of the screw where shearing can occur isapproximately 65% of the total area of the bolt). The diameterof the screw d can then be determined by equating FA to(3.14 d2/4). Another equation which can be used involvesrelating the width B, height H and span L of the clamp to thescrew diameter d (B, H, and L can be computed for variousvalues of d): d2= 4/3 BH2/L.4. The Determination of the ClampingFaceThe required inputs to determine the clamping region includethe CAD model of the product, the extracted features infor-mation, the feature dimensions and faces on which they occur,the locating faces and locators selected. Consider a potentialclamping face PCF as shown in Fig. 3. The crucial criterionto be satisfied is that the clamping surface should not overlapor intersect with the features on that face, as shown in Fig. 4.The clamping surface area, which is in contact with theworkpiece surface (or PCF) is a 2D profile consisting of linesegments (see Fig. 6). By using line segment intersection tests,it can be determined whether the potential clamping area ofcontact overlaps any of the features on the given PCF.The determination of clamping faces can be automated as fol-lows:Fig. 3. Potential clamping face and feature profiles.Fig. 4. Potential clamping face and clamp box profile.Step 1. Identify faces that are parallel to the secondary andtertiary locator faces (lf1 and lf2) and at the farthest distancefrom lf1 and tcj, respectively. This is performed as shownbelow:(a) Identify faces tci, tcj such that tci is parallel to lf1 andtcj is parallel to lf2.(b) Insert candidate faces tci in list TCF.(c) By examining all faces tci listed in TCF, determine facestci and tcj that are farthest from face lf1 and lf2, respect-ively, and discard all other faces from list TCF.Step 2. Identify the face that is parallel to the location facesbut not adjacent to the additional locator faces. It is preferableto select a clamp face that does not have to share the adjacentperpendicular face with a locator. This step can be automatedas shown below:(a) Consider each face tci in list TCF and obtain correspond-ing faces fci that are adjacent and perpendicular to eachtci. Then, insert each face fci in list FCF.(b) Examine each fci and perform the following test:If fci is adjacent, perpendicular to lf1orlf2,then discard it from list FCF and insert it in list NTCF.Step 3. Determine the clamping faces, based on the availabilityof potential clamping faces, as described below.Case (a). If there are no entries in list NTCF, then use thefaces in list TCF and proceed to step 4. If any faces werefound that were perpendicular to the secondary and tertiarylocation faces lf1 and lf2, such faces are the next feasiblechoices to be used for clamping.In this case, the only remaining choice is to re-examine thefaces in list NTCF.Case (b). If the number of entries in list NTCF is 1, thefeasible clamping face is fci. The normal vector of thecorresponding adjacent, perpendicular face tci is the axis ofclamping.Case (c). If number of entries in list NTCF is greater than 1,determine the face tci with larger area and proceed to step 4.Step 4. Depending on the direction of clamping which is either(+ or )1, 0, 0 or (+ or ) 0, 1, 0, the clamp can bepositioned along the centre of the face tci. The candidategeometrical positions of the clamp can be determined usingpart geometry and topological information, which is describedin the next section.A Clamping Design Approach 787Fig. 5. Determination of the clamp profile dimensions.5. Determination of the Clamping Pointson a Clamping FaceAfter the clamp face has been determined, the actual clampingpositions on that face must be determined. The inputs are theclamp profile dimensions, clamp directions x,y, z, and poten-tial clamping face CF. The clamp profile dimensions areobtained (as in case (g) using CF geometry as follows.The first step is to determine a box size, which is tested todetermine whether it contains any features inside it. Profileintersection tests can also be performed using the methoddescribed earlier. If the intersection test returns a negativeresult, then no feature intersects with the clamp box profile,as shown in Fig. 4. If the intersection test returns a positiveresult, the following steps can be performed:1. Divide the clamp box profile into smaller rectangular stripsof size (1 w) (Figs 5 and 6).2. Perform the intersection tests with the feature profiles offeatures that occur on the face CF for the given part design.Fig. 6. Profiles intersection test of feature and clamp regions.3. The rectangular strips, where no feature intersection occurs,are feasible clamping regions. If there is more than onecandidate rectangle for clamping, the rectangle profile thatis toward the mid-point of the CF face along the clampingaxis is the clamp profile (and clamp points).If no profile Pi can be found that does not intersect with thefeature profiles, clamp width can be reduced by half and thenumber of clamps increased to two on that face. Using thesemodified clamp dimensions, perform the feature intersectiontest described earlier. If this test also fails, then the side faceadjacent to the PCF can be used as the clamping surface toperform side clamping. The side face then becomes the PCFand the feature intersection test can be repeated.5.1 The Intersection of Profiles TestThe required inputs include the 2D profile P1 another 2Dprofile P2. The intersection of profiles can be determined inan automated manner using the following approach. Each inputprofile Pi consists of a closed loop of line segments Lij. Thesteps in this profile test are as follows:(T1) Consider a line segment L(i,1) in P1 and another linesegment L(2, j)inP2.(T2) For inputs L(i,1) and L(2, j), the intersection of edgescan be employed. If the edge intersection test returns a positivevalue, then the feature profile intersects with the candidate orpotential clamp profile under evaluation. If it returns a negativevalue, proceed to step 3.(T3) Repeat step (T1) for the same segment or edge (Li,1) inP1 with all remaining segments (L2, j+1) till j = n1 in P2.(T4) Repeat steps (T1) and (T2) for the remaining edges orsegments L12, L13,. . .,L1n in profile P1.If the feature profiles overlap the clamping profiles, the lineintersection tests will determine that occurrence. The inter-section of edges test can be performed automatically to detectwhether two edges intersect with each other. The inputsrequired for this test are the line segments L12 connecting(x1, y1) and (x2, y2) and L34 connecting (x3, y3) and(x4, y4).Let the equation of L12 be represented by:F(x,y) = 0 (1)and that of L34 by:H(x,y) = 0 (2)Step 1. Using Eq. (1) compute r3 = F(x3, y3) by substitutingx3 and y3 for x and y and compute r4 = F(x4, y4) by substitut-ing x4 and y4 for x and y.Step 2. If r3 is not equal to 0, r4 is not equal to 0, and thesigns of r3 and r4 are the same, (which indicate r1 and r2lie on same side), then the edges L12 and L34 do not intersect.If this is not satisfied, then step (3) is performed.Step 3. Using Eq. (2), compute r1 = H(x1, y1). Then, computer2 = G(x2, y2) and proceed to step 4.Step 4. If r1 is not equal to zero, r2 is not equal to zero, andthe signs of both r1 and r2 are the same , then r1, r2 lie on788 J. CecilFig. 7. Sample part to illustrate the clamping design approach.the same side and the input line segments do not intersect.Else, if this condition is not satisfied, proceed to step 5.Step 5. The given line segments do intersect. This completesthe test.Consider the same sample part shown in Fig. 7. The featuresto be produced are a step and hole. Initially, the locator designis completed. The support locator (or primary locator) is abase plate (placed against face f4) and the secondary andtertiary locators are placed against faces f6 and f5 (whichcorrespond to the locator faces lf1 and lf2 discussed in Section4). An ancillary locator is also used, which is a v-block(positioned against the ancillary faces f3 and f5), shown inFig. 8.
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