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黄河科技学院毕业设计(文献综述） 第 7 页 冲压模具的应用及发展趋势摘要：本文基于滑模控制算法和卡尔曼滤波算法的分析,设计了基于卡尔曼滤波的复合滑模控制算法,并将其应用于设计的离合器从动盘测试机的电控系统,以提高测试机的控制性能。经仿真分析验证,复合滑模控制算法比复合PID算法响应速度快,具有较好的稳态精度和跟踪精度,卡尔曼滤波算法能有效消除现场随机干扰和抑制了工频干扰。检测数据表明,测试机的位移和力矩检测精度分别达到了0.005 mm和0.05 N.m 。关键词： 从动盘，滑模控制 ，卡尔曼滤波算法 ，测试机 1 模具的发展及冲压模具的特点 近年来，由于我国国民经济的高速、稳定的增长，促进了我国模具工业的迅速发展壮大，因此，模具设计与制造专业或者相关的材料成型与控制专业已经成为我国国内具有优势的热门专业之一。在日常生活中我们的许多制品都是由模具来生产制造出来的，所以，越来越多的人开始从事模具行业的设计，因此，我国的模具设计水平有了进一步的提高和发展的空间。随着国民经济的高速发展，市场对模具的需求量不断增长，模具工业快速发展，必然会带来模具工业企业的所有制成分也发生了巨大变化，除了国有专业模具厂外，集体、合资、独资和私营也得到了快速发展。随着与国际接轨的脚步不断加快，市场竞争的日益加剧，人们已经越来越认识到产品质量、成本和新产品的开发能力的重要性。而模具制造是整个链条中最基础的要素之一，模具制造技术现在已经逐渐的成为衡量一个国家产品制造水平的重要标志和发展程度的标志之一。目前我国模具年生产总重量虽然已位居世界第三，其中，冲压模占模具总重量的40%以上，但在整个模具设计制造水平和标准化程度上，与德国、美国、日本等发达国家相比还存在相当大的差距。以大型覆盖件冲模为代表，我国已经生产部分轿车覆盖件模具。轿车覆盖件模具设计和制造难度大，质量和精度要求高，代表覆盖件模具的水平。在设计制造方法、手段上已基本达到了国际水平，模具结构功能方面也接近国际水平，在轿车模具国产进程中前进了一大步。但在制造质量、精度、制造周期和成本方面，以国外相比还存在一定的差距。标志模具技术先进水平的多工位级进模和多功能模具，是我国重点发展的精密模具品种，在制造精度、使用寿命、模具结构和功能上，与国外多工位级进模和多功能模相比，存在一定差距。由于冲压模具具有生产效率高、加工成本低、材料利用率高、产品尺寸精度稳定、操作简单容易实现机械化和自动化等一系列优点，特别适合于大批量生产。因而在模具发展过程中，冲压模具又是其重要的组成部分。冲压是在常温下利用冲模在压力机上对材料施加压力，使其产生分离或变形，从而获得一定形状、尺寸和性能的零件加工方法。它是一种压力加工方法，是机械制造中的先进加工方法之一。冲压模具是一个特殊的，一次性的一类精密工具，通过切割与塑形的方式使金属成为一个理想的形状或外形。大多数模具构造有几个基本组成部分，包括模板，防磨装置，模套，导向销，轴衬，垫块，垫板，螺钉，销钉，和螺栓。冲压模具成形作为现代工业中一种十分重要的加工方法，用以生产各种板料零件,具有很多独特的优势，其成形件具有自重轻、刚度大、强度高、互换性好、成本低、生产过程便于实现机械自动化及生产效率高等优点，是一种其它加工方法所不能相比和不可替代的先进制造技术，在制造业中具有很强的竞争力，被广泛应用于汽车、能源、机械、信息、航空航天、国防工业和日常生活的生产之中。 在吸收了力学、数学、金属材料学、机械科学以及控制、计算机技术等方面的知识后，已经形成了冲压学科的成形基本理论。以冲压产品为龙头，以模具为中心，结合现代先进技术的应用，在产品的巨大市场需求刺激和推动下，冲压成形技术在国民经济发展、实现现代化和提高人民生活水平方面发挥着越来越重要的作用。现代冲压模具生产是一种大规模继续作业的制造方式，由于高新技术的参与和介入，冲压生产方式由初期的手工操作逐步进化为集成制造。生产过程逐步实现机械化、自动化、并且正在向智能化、集成化的方向发展。实现自动化冲压作业，体现安全、高效、节材等优点，已经是冲压模具生产的发展方向。 2 冲压模具的进步及新技术的应用近几十年来，冲压技术有了飞速的发展，它不仅表现在许多新工艺与新技术在生产的广泛应用上，如：旋压成形、软模具成形、高能率成形等，更重要的是人们对冲压成形的认识与掌握的程度有了质的飞跃1.现代冲压生产是一种大规模连续作业的制造方式，由于高新技术的参与和介入，冲压生产方式由初期的手工操作逐步进化为集成制造，生产过程逐步实现机械化、自动化、并且正在向智能化、集成化的方向发展。实现自动化冲压作业，体现安全、高效、节材等优点，已经是冲压生产的发展方向。冲压自动化生产的实现使冲压制造的概念有了本质的飞跃，结合现代技术信息系统和现代化管理信息系统的成果，由这三方面组合又形成现代冲压新的生产模式计算机集成制造系统CIMS（Computer Intergrated Manufacturing System）把产品概念形成、设计、开发、生产、销售、售后服务全过程通过计算机等技术融为一体，将会给冲压制造业带来更好的经济效益，使现代冲压技术水平提高到一个新的高度。20世纪60年代初期，国外飞机、汽车制造公司开始研究计算机在模具制造中的应用。通过以计算机为主要手段，以数学模型为中心，采用人机互相结合、各尽所长的方式，把模具的设计、分析、计算、制造、检验、生产过程练成一个有机整体是模具技术进入到综合应用计算机进行设计、制造的新阶段。模具的高精度、高寿命、高效率成为模具技术进步的特征。模具CAD/CAE/CAM是改造传统模具生产方式的关键技术，是一项高科技、高效益的系统工程。它以计算机软件的形式，为企业提供一种有效的辅助工具，使工程技术人员借助于计算机对产品性能、模具结构、成形工艺、数控加工及生产管理进行设计和优化。模具CAD/CAE/CAM技术能显著缩短模具设计与制造周期，降低生产成本和提高产品质量已成为模具界的共识。模具CAD/CAE/CAM在近20年中经历了从简单到复杂，从试点到普及的过程。进入本世纪以来，模具CAD/CAE/CAM技术发展速度更快，应用范围更广。在模具CAD/CAE/CAM发展应用方面，本世纪初，美国UGS公司与我国华中科技大学合作在UG-II软件平台上开发出基于三维几何模型的级进模CAD/CAM软件NX-PDW。该软件包括工程初始化、工艺预定义、毛坯展开、毛坯拍样、废料设计、条料拍样、压力计算和模具结构设计等模块。具有特征识别与重构、全三维结构关联等显著特色，已在2003年作为商品化产品投入市场。于此同时，新加坡、马来西亚、印度及我国台湾、香港有关机构也在开发和试用新一代级进模CAD/CAM系统。我国从上世纪90年代开始，华中科技大学、上海交通大学和北京机电研究院等相继开展了级进模CAD/CAM系统的研究和开发。如华中科技大学模具技术国家重点实验室在AutoCAD软件平台上开发出基于特征的级进模CAD/CAM系统HMJC，包括板金零件特征造型、基于特征的冲压工艺设计、模具结构设计、标准件及典型结构件库工具和线切割自动编程5个模块。上海交通大学为瑞士法因托（Finetool）精密冲裁级进模CAD/CAM系统。西安交大开发出多工位弯曲级进模CAD系统等。近年来，国内一些软件公司也竞相加入了级进模CAD/CAM系统的开发行列，如深圳雅明软件制作室开发的级进模系统CmCAD、富士康公司开发的用于单冲模与复合膜的CAD系统FOX-CAD等。展望国内外模具CAD/CAM技术的发展，本世纪的科学技术正处于日新月异的变革之中，通过与计算机技术的紧密结合，人工智能技术、并行工程、面向装配、参数化特征建模以及关联设计等一系列与模具工业相关的技术发展之快，学科领域交叉之广前所未见。今后10年薪一代模具CAD/CAM系统必然是当今最好的设计理念、最新的成形理论和最高水平的制造方法相结合的产物，其他特点将反映在专业化、网络化、集成化四方面。主要表现为： 1、模具CAD/CAM的专业化程度不断提高； 2、基于网络的CAD/CAE/CAM一体化系统机构初见端倪； 3、模具CAD/CAE/CAM的智能化一人注目； 4、与先进制造技术的结合日益紧密。3 未来冲压模具制造技术的发展趋势1) 全面推广CAD/CAM/CAE技术模具CAD/CAM/CAE技术是模具设计制造的发展方向。随着微机软件的发展和进步，普及CAD/CAM/CAE技术的条件已基本成熟，各企业将加大CAD/CAM技术培训和技术服务的力度；进一步扩大CAE技术的应用范围。计算机和网络的发展正使CAD/CAM/CAE技术跨地区、跨企业、跨院所地在整个行业中推广成为可能，实现技术资源的重新整合，使虚拟制造成为可能。2) 高速铣削加工国外近年来发展的高速铣削加工，大幅度提高了加工效率，并可获得极高的表面光洁度。另外，还可加工高硬度模块，还具有温升低、热变形小等优点。高速铣削加工技术的发展，对汽车、家电行业中大型型腔模具制造注入了新的活力。目前它已向更高的敏捷化、智能化、集成化方向发展。3) 模具扫描及数字化系统高速扫描机和模具扫描系统提供了从模型或实物扫描到加工出期望的模型所需的诸多功能，大大缩短了模具的在研制制造周期。有些快速扫描系统，可快速安装在已有的数控铣床及加工中心上，实现快速数据采集、自动生成各种不同数控系统的加工程序、不同格式的CAD数据，用于模具制造业的“逆向工程”。模具扫描系统已在汽车、摩托车、家电等行业得到成功应用，相信在“十五”期间将发挥更大的作用。4) 电火花铣削加工电火花铣削加工技术也称为电火花创成加工技术，这是一种替代传统的用成型电极加工型腔的新技术，它是有高速旋转的简单的管状电极作三维或二维轮廓加工(像数控铣一样)，因此不再需要制造复杂的成型电极，这显然是电火花成形加工领域的重大发展。国外已有使用这种技术的机床在模具加工中应用。预计这一技术将得到发展。5) 提高模具标准化程度我国模具标准化程度正在不断提高，估计目前我国模具标准件使用覆盖率已达到30%左右。国外发达国家一般为80%左右。6) 优质材料及先进表面处理技术选用优质钢材和应用相应的表面处理技术来提高模具的寿命就显得十分必要。模具热处理和表面处理是否能充分发挥模具钢材料性能的关键环节。模具热处理的发展方向是采用真空热处理。模具表面处理除完善应发展工艺先进的气相沉积(TiN、TiC等)、等离子喷涂等技术。7) 模具研磨抛光将自动化、智能化模具表面的质量对模具使用寿命、制件外观质量等方面均有较大的影响，研究自动化、智能化的研磨与抛光方法替代现有手工操作，以提高模具表面质量是重要的发展趋势。8)模具自动加工系统的发展这是我国长远发展的目标。模具自动加工系统应有多台机床合理组合；配有随行定位夹具或定位盘；有完整的机具、刀具数控库；有完整的数控柔性同步系统；有质量监测控制系统。参考文献1 李硕本等编著.冲压工艺理论与新技术M.北京：机械工业出版社，2002.112 中国模具工业协会，模具行业“十一五”规划J.模具工业，2005(7)：3-83 李大鑫，张秀锦.模具技术现状与发展趋势综述J.模具制造，20054 李德群，肖祥芷.模具CAD/CAE/CAM的发展概况及趋势J.模具工业，20055 姜奎华主编。冲压工艺与模具设计M.北京，机械工业出版，1998.56 郑家贤编著。冲压工艺与模具设计实用技术M.北京：机械工业出版，2005.17 模具实用技术丛书编委会编.冲模设计应用实例M.北京：机械工业出版社，1999.68 冲模设计手册编写组编著.冲模设计手册M.北京：机械工业出版社，1999.69 王孝培主编.冲压手册（修订本）M.北京：机械工业出版社，1990 10 Yazheng Liu, Jinghong Sun, et al. Experiment investigation of deep-drawing sheet texture evolution. Journal of Materials processing Technology，140(2003) 11 薛奕翔等编著。冲压模具设计制造难点与窍门M.机械工业出版，2003.712 Yingbin Bao. A comparative study on various ductile crack formation criteria. Journal of engineering materials and technology，2004(7) 毕业设计文献综述 院（系）名称工学院机械系 专业名称材料成型及控制工程 学生姓名高海建 指导教师刘万福 2012年 03 月 10 日窗体顶端9The International Journal of Flexible Manufacturing Systems, 15, 518, 2003c ? 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.Identifying Sources of Variation in SheetMetal StampingKARL D. MAJESKEkdmThe University of Michigan Business School, 701 Tappan Street, Ann Arbor, MI 48109-1234, USAPATRICK C. HAMMETTphammettThe University of Michigan, Transportation Research Institute, 2901 Baxter Road, Ann Arbor,MI 48109-2150, USAAbstract.Manufacturers using traditional process control charts to monitor their sheet metal stamping pro-cesses often encounter out-of-control signals indicating that the process mean has changed. Unfortunately, a sheetmetal stamping process does not have the necessary adjustability in its process variable input settings to alloweasily correcting the mean response in an out-of-control condition. Hence the signals often go ignored. Accord-ingly, manufacturers are unaware of how much these changes in the mean inflate the variance in the processoutput.We suggest using a designed experiment to quantify the variation in stamped panels attributable to changingmeans.Specifically,wesuggestclassifyingstampingvariationintothreecomponents:part-to-part,batch-to-batch,and within batch variation. The part-to-part variation represents the short run variability about a given stable ortrending batch mean. The batch-to-batch variation represents the variability of the individual batch mean betweendiesetups.Thewithinbatchvariationrepresentsanymovementoftheprocessmeanduringagivenbatchrun.Usinga two-factor nested analysis of variance model, a manufacturer may estimate the three components of variation.Afterpartitioningthevariation,themanufacturermayidentifyappropriatecountermeasuresinavariationreductionplan. In addition, identifying the part-to-part or short run variation allows the manufacturer to predict the potentialprocess capability and the inherent variation of the process given a stable mean. We demonstrate the methodologyusing a case study of an automotive body side panel.Key Words:analysis of variance, designed experiment, dynamic batch mean, sheet metal stamping, variationreduction1.IntroductionMost passenger vehicles produced today (automobiles, light trucks, and minivans) havea (structural) body that comprises 100150 stamped metal panels. These panels range insize from small, easy-to-form mounting brackets to large, complex panels such as fenders,hoods, and body sides. The quality characteristics that describe stamped panels are thedimensions of features such as the length of trim edges or the position of a flange usedto assemble multiple panels. The typical approach used to measure a panel feature is todetermine its deviation from the nominal design specification along a specified plane, forexample, fore/aft from front of car, or in/out from the center of car (Roan and Hu, 1995).The first author was supported by NSF grant DDM-9712997 to the University of Michigan.6MAJESKE AND HAMMETTThisresearchprovidesananalysismethodologytoquantifythecomponentsofvariationforthese panel quality features, given the particular characteristics of the sheet metal stampingprocess.For each automotive body panel, the sheet metal stamping process requires two distincttypes of equipment: the stamping press and a set of stamping dies. The set of stamping diesrepresents custom manufacturing equipment used to make specific product geometry. Thestamping press represents flexible manufacturing equipment, capable of producing manydifferentautomotivebodypanels(hood,door,fender,etc.)simplybychangingthestampingdies. Thus, a particular stamping press produces an individual panel in batches, making thesetup of the dies critical to controlling the process mean.To monitor the quality of automotive body panels, most manufacturers apply statisticalanalysis methods (Montgomery, 1996) such as statistical process control (SPC). In SPCterminology, manufacturing processes contain two types of variation: common cause andspecialcause.Commoncausevariationisthenaturalinherentvariationintheprocessoutputwhen all input variables remain stable, that is, independent and identically distributed.Special cause variation represents any increase in product variability above the level ofcommon cause variation. Manufacturers detect special case variation by identifying out-of-control signals on control charts. To correct these out-of-control conditions, and eliminatethe associated special cause variation, the manufacturer must have the ability to adjust theprocess mean.Many North American (NA) automotive stamping facilities lack the attention to de-tail in their die setup procedures to control mean shifts after changing the stamping dies.When beginning a panel batch, the manufacturer measures a sample of panels to createan SPC subgroup. If this subgroup plots out-of-control, the stamping processes have nosimple adjustment mechanisms to change feature dimensions. This inability to adjust theprocess mean has frustrated NA automotive manufacturers applying SPC to their stampingprocesses. Thus, these manufacturers must continually adjust downstream processes (weldfixtures or weld robots) to compensate for changes in the dimensional geometry of stampedpanels. However, many Japanese stamping facilities have eliminated out-of-control con-ditions at die setup by following well-structured die change procedures. By eliminatingthese out-of-control setup conditions, these Japanese manufacturers have also been able toremove traditional control charts.2.Measures of stamped panel quality and quality improvementManufacturers use control charts to assess stability in the process output. The X-bar andR charts are methods recommended by the Automotive Industries Action Group (AIAG,1992) for charting a product described with a continuous, random quality characteristicsuch as panel feature deviation from its nominal measurement. The X-bar chart graphicallytracks the sample averages over time to look for changes in the process mean, while the Rchart tracks the sample range as a measure of process variability.While a majority of statistical techniques assume a stable mean over time, some authorshave addressed the issue of a nonstable process. Woodall and Thomas (1995) suggest anX-bar chart to track the mean of a process that has two sources of common cause variationIDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING7(e.g., within batch variation about the mean and batch-to-batch variability in the mean).They also present a model that captures a third component of variation, measurementerror. Woodall and Thomas caution against using their techniques “. until every realisticeffort is made to remove each of the various sources of what is to be treated as common-cause variability.” Sullo and Vandeven (1999) also have studied processes with run-to-runvariation. They developed an analytic approach for approving a process setup (run) forproduction, assuming a quadratic loss function and a 0-1 loss function.The quality assessment of a panel feature also involves measuring its process capability,the ability to produce products between the upper specification limit (USL) and the lowerspecification limit (LSL), that is, the design tolerance. Breyfogle (1999) discusses CpandPp, two measures of process potentialtheir values are independent of the proportion ofparts within design specificationthat share the theoretical definitionCp= Pp=USL LSL6x.(1)The difference between these two indices lies in the assumption regarding process stabilityand the method(s) used to estimate process standard deviation. The index Cpassumes anin-control process while the measure Ppis considered a “long run” capability index anddoes not require the standard stability assumption. For Cp, the manufacturer can estimatethe process standard deviation with the sample standard deviation as x= S or from therange chart with x=R/d2. To estimate Pp, the manufacturer should take a sample thatcaptures long run process variation and estimate the process standard deviation with thesample standard deviation as x= S.3.Sheet metal stamping process characteristicsSheet metal panels require multiple die operations using either a single press or a series ofpresses in a press line. Stamping dies and presses have numerous input variables (tonnage,shut height, press parallelism, counterbalance pressure, nitrogen pressure in dies, pressspeed, etc.) that can influence stamping panel quality, especially during die setup. Theresultant geometry of the sheet metal panels depends, in part, on these settings.Using the same press settings each time a particular die is set would help reduce longrun variation in the associated panels. Unfortunately, the relationship of the numerouspress settings and other process input factors (incoming material, blank size, etc.) on panelgeometry is not well documented or understood by manufacturers. For example, many oftheinputvariablesettingsuseasinglevaluefortheentirepanel.Individualpanels,however,havemultiplefeaturesindifferentareasthatarenotnecessarilycontrolledbythesamesetofinputvariablesettings.Thissituationlimitstheabilitytobringtheprocessbacktothetargetvalue when SPC charts exhibit out-of-control conditions for certain features, especially ifotherfeaturesdonotchange.Inaddition,noneoftheprocessinputvariablespossessadirectcause-and-effect relationship with a panel feature. For example, increasing the tonnage bysome amount will not cause a predictable change in a panel feature, as it does in machiningwhere adjusting the position of a cutting tool has a predictable impact on the process mean.8MAJESKE AND HAMMETTHammett, Wahl, and Baron (1999) show how the difficulties resulting from a lack ofsimple, process input variable adjustments to shift the process mean have led many auto-motive body manufacturers to apply functional build concepts. Functional build (MajeskeandHammett,2000)involvesdelayingthedecisiontomodifyastampingdieuntilassessingthe impact of the variation on the downstream assembly process.Thelackofeasilyadjustableinputsettingsiscomplicatedbythelargenumberofpotentialsignificant variables. Numerous case studies describe the complex relationship betweensheet metal stampings and their process input variables. Siekirk (1986) suggests “The sheetmetalprocessforhighvolumeproductionisbestdescribedasanart.”Usingtwodesignedexperiments to study the relationship between stamping process output quality and processinputs, Siekirk found significance in all five of the process variables studied: blank size,blank location, lubrication, binder force (outer tonnage), and metal thickness.Zhou and Cao (1994) examined the process of stamping a door inner, and identified twotypes of variation found in metal stamping: within run and run-to-run. They studied theimpactofthreeprocessvariables(outertonnage,innertonnage,andpunchspeed)onwithinrun variation. Using a designed experiment, they identified levels for these three variables,suggesting better control could reduce within run variation by 54%.Wang and Hancock (1997) also studied a door inner stamping process. They investigatedthe impact of 15 process variables on formability (split/no split) of the stamped panels.Using logistic regression, they concluded that three variables influenced the ability to forma panel without splits: surface roughness of the steel, outer tonnage of the press, and theamount of lubricant.Berry (1996) discussed the relationship between the composition of sheet steel (theraw material) and stamped panel quality. Berry suggests that, in general, Japanese man-ufacturers run their stamping processes in statistical control while their US counterpartsdo not. Noting that these manufacturers purchase steel from the same sources, he main-tains that US manufacturers should focus quality improvement efforts on nonsteel relatedvariables.A general conclusion across these various case studies is the existence of a large poten-tial number of significant input variables that are not well understood and hard to control.For example, the true cause-and-effect relationship of the various inputs often is unknown.Rather than exploring the relationship between stamping press parameters and panel geom-etry, this research develops a method for quantifying the variance in product output basedon typical variations observed in the input variable settings. This provides an analytic toolfor determining whether a variation reduction plan is necessary.4.Model developmentManufacturers produce many different panels in the same stamping press by removingone set of stamping dies and inserting another. Placing a die in a stamping press is oftenreferred to as die setup. Die setup involves setting the stamping process variables such asshut height and binder force (tonnage). Thus, die setup signifies a reconfiguration of thestamping process. The quantity of parts produced following a die setup is referred to as abatch.IDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING9-0.500.5ProductionMean Bias-111.5NominalLowerSpecification.UpperSpecificationBatch 1MeanLong RunProductionMean-0.500.5ProductionMean Bias-111.5NominalLowerSpecification.UpperSpecificationBatch 1MeanLong RunProductionMeanFigure 1.Stamping process data (note: horizontal lines represent batch means).Figure 1 conceptually shows data from a batch production process. While each batch hasits own mean, in the long run, the batch means vary randomly about some overall processmean. The difference between the overall process mean and the design nominal or targetvaluerepresentsthemeanbiasinthemanufacturingprocess.Wedefinethevariabilityaboutthe current or instantaneous process mean as the natural inherent variability (part-to-part)in the process.4.1.Total process: TPTP represents the long run output as seen by the customer. This variable captures all thesources of variation for the quality characteristic X. While not an assumption of this work,historical data shows that for many stamped panels, TP follows a normal distribution. Theexpected value of TP represents the long run process average for the quality characteristic,ETP = TP= x. The variability of TP, VarTP = 2TP= 2x, represents the variationdeliveredtodownstreamprocessesandcustomers.Thetotalprocessvariationrepresentsthevariability one should use when assessing the capability of the stamping process to achieveengineering specifications or tolerances.4.2.Batch mean: BA large number of stamping process variables affect the mean of a single batch. Pressoperators and die setup personnel often do not consistently replicate stamping processsettingseachtimetheysetupthesamepanel.Severaldifficulttocontrolinputvariables,suchas steel properties or lubrication levels, could also affect the mean of a batch. Therefore, we10MAJESKE AND HAMMETTmodel process mean as a random variable where each batch mean, Bi, represents the batchaverage for the ith batch. Assuming equal batch sizes, the expected value of B, the batchmean, is equal to the long run process average EB = ETP. The variance of B, thebatch mean variation, represents the panel variability associated with batch-to-batch meanshifts or VarB = 2BB.4.3.Within batch mean: WBAlthough Birepresents the average or mean of panels stamped in the ith batch, this modelallows for instability of the mean within a batch. In other words, this model allows for anonconstant or dynamic batch mean. These changes within a batch are believed to be theresult of changes in input and process parameters such as differences in steel propertiesbetween incoming material lots, or changes in die pressures due to a nitrogen cylinder leak.We let WB represent the instantaneous average or mean of panels stamped in a batch as adeviation from the overall batch average Bi, that is, EWB = 0. The WB variable capturesthe changes in batch mean, Bi, during a batch. Therefore, the within batch mean variance,VarWB = VarBi = 2WB, represents the variability of the process mean within a batch.4.4.Part-to-part: PPPP represents the inherent process variation about a given mean value. We assume thestamping process follows a conditional normal distribution, that is, for a given value of thecurrent batch mean, the process produces a normally distributed output. This part-to-partvariable is intended to capture any noise variable that would be expected as part of normalprocess operations. The part-to-part variable has an expected value of zero EPP = 0 witha variance of VarPP = 2PP. The part-to-part variation represents the potential for totalprocessvariationortheleveloftotalprocessvariationthatcouldbeachievedbyeliminatingwithin batch and batch-to-batch variation.4.5.Sources of variation modelThis model assumes that the variables are additive or that TP = B +WB+PP. We furtherassume that the components are independent and derive the model by taking the variance2TP= 2BB+ 2WB+ 2PP. The part-to-part variation in this variation model represents theshortrunprocessvariationaboutthemean.Ifthemanufacturerweretocontrolthestampingprocessmean,thenpart-to-partvariationwouldequalthetotalprocessvariation.Wesuggestusing a statisticCPP=USL LSL6PP(2)in consort with Ppto assess stamping process capability. Cpprepresents the potential capa-bility or the level of Cpthe manufacturer would obtain by controlling the process mean.IDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING115.Estimating the model parametersWe suggest estimating the components of variation using a designed experiment or DOE(Box, Hunter, and Hunter, 1978). However, given the nature of the model, the samplingplan cannot be purely random in a statistical sense. The sampling plan should more closelyrepresent the rational sampling used in control charts, that is, taking consecutive parts fromtheprocess.Whilethemodeldoesnotrequireobservationswithinasampletobeconsecutivepieces, they should be obtained from a relatively short window of parts, for example, everyother or every third piece. When conducting the designed experiment, one should allow theprocess to run the way it normally runs in production. A manufacturer should not attemptto influence any process or steel property variables differently from regular production.To estimate the parameters of the model we suggest taking observations from b batchesor die sets. Taking samples from multiple batches will allow estimating the batch-to-batchvariation.Withineachbatchordieset,amanufacturershouldsampletheprocesss differenttimestoestimatethewithinbatchvariationinthemean.Finally,amanufacturershouldtakea sample of size n each time the process is sampled. Taking replications per samplingallows estimating the part-to-part or pure error in the process. This approach results in atotal sample of size N, where N = bsn. Using the response variable X, this approach willgenerate data of the form:Xijk,i = 1,.,b (batch),j = 1,.,s (sample within batch), andk = 1,.,n (observation in sample).Fitting the model outlined in this article requires three sample size decisions: the numberof batches, the samples per batch, and the replicates or the size of each individual sample.Sample size planning prior to conducting the experiment can assist the manufacturer withobtaininginformativeresultsatthelowestcost.Todeterminethethreecomponentsofsamplesize planning, the manufacturer can use a statistical power approach (see Montgomery,1991). For a random effects model, this requires specifying the magnitude of the variancecomponents the manufacturer would like to detect and the probability (statistical power)that they will detect this condition.Again,whenconductingthedesignedexperiment,oneshouldallowtheprocesstoruntheway it normally does during normal production. To estimate the components of variationfrom the experiment, one needs the mean squares batch (MSB), mean squares within batch(MSWB), and mean squares error (MSE). This can be accomplished with a statisticalsoftware package by having three variables: the values of the response Xijk, batch (thevalue of the subscript i), and sample number within the batch (the value of the subscript j).We recommend fitting a nested two-factor random effects analysis of variance (ANOVA)model to the data. One should not include an interaction term, but must nest the samplefactorunderthebatchfactor.Thesoftwareshouldprovidetheestimatesofthemeansquares.Next, we may estimate part-to-part variation with the mean squared error 2PP= MSE(3)12MAJESKE AND HAMMETTand within batch variation, if it is significant, using 2WB=MSWB MSEn.(4)If within batch variation is significant, estimate batch-to-batch variation as 2BB=MSB MSWBsn.(5)However, if within batch variation is not significant, estimate batch-to-batch variation as 2BB=MSB MSEsn.(6)Factors that are not statistically significant may be removed from the model and the modelrefit prior to estimating variance components.6.Case study: Automotive body side panelTo demonstrate the technique, we utilize data obtained from an automotive body stampingfacility. These data represent measurements taken from a body side panel as shown inFigure2.Thisparticularpanelhas16outputfeatures,withthequalityofindividualfeaturesaffected by different operations and input variables in the die/press lineup. Thus, althoughthe features may not be truly independent, stamping manufacturers treat these features asindependentcharacteristics.Insomecases,manufacturerseliminatesignificantlycorrelatedfeatures during manufacturing validation prior to the start of regular production. Thus, wefirst identify the sources of variation for an individual feature.To study the body side panel stamping process we designed the following sampling plan.To capture batch-to-batch shifts in the mean, we sampled b = 6 nonconsecutive batchesduring a period of two months of production. The manufacturer also felt that this processFigure 2.Automobile body side panel.IDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING13Table 1.Body side panel data.BatchWithin batch groupSample 1Sample 2Sample 3110.620.330.51120.400.180.367220.260.280.45310.490.450.40320.540.640.22410.190.300.24420.050.150.04510.130.320.56520.460.480.48610.270.020.20620.310.230.13mighthaveshiftsinthemeanwithinabatchduetodifferencesinmaterialpropertiesresultingfrom changing coils of steel. Since the length of the individual runs is approximately4 hours, we had a limited time window to detect these within batch shifts. Therefore, weselected s = 2 samples per batch taken at the beginning and at the end of the batch tomaximize the probability of trapping a mean shift between samples. The last component ofsample size planning was to determine the number of replicates. The manufacturer alreadytook samples of size n = 3 at the beginning of the batch for SPC. For cost reasons, wechoosetoaugmentthesesampleswithanadditionalsampleofn = 3attheendofthebatch,rather than generate entirely incremental data for the study.Table 1 contains the dimensional data, in millimeters, for measurement location #3 onFigure 2 generated from the N = 36 body side panels. The manufacturer measures thelocations on the body side panel as deviations from the design nominal or the center of thedesign specification. For example, the first panel in the first subgroup selected from batch 1deviated0.62mmfromitstargetvalue,thatis,thecenterofthedesignspecification.Weusethis raw data to construct control charts to assess the stability of the stamping process. Wealso fit the ANOVA model described in Section 5 to this data to estimate the componentsof variation.To assess long run process stability of this body side feature, we constructed controlcharts for individuals (moving range and individuals charts) as shown in Figure 3. Toprepare the charts in Figure 3, we used only the first observation from each sample of threeconsecutive parts. Here, both charts exhibit statistical control, suggesting that the processhas a stable mean and variance. In the context of the components of variation model, themoving range chart estimates the total process variation. Therefore, the individual chartsuggests process stability over the long run, rather than a constant mean from batch tobatch.Toassessthebatchtobatchstabilityofthisbodysidefeature,weplacedthedataonX-barand R charts as shown in Figure 4. Looking first at the R chart, we see that the variance is14MAJESKE AND HAMMETTFigure 3.Individual and moving range control charts for body side panel.Figure 4.X-bar and R charts for body side panel data.in statistical control. For the stamping process, this suggests that the part-to-part variationremains stable. Next, we look at the X-bar chart and see that the process mean runs out ofcontrol. The special cause variation on this control chart indicates a potential opportunityfor improvement.To quantify the contribution of the variation sources, we recommend fitting the nestedtwo-factorANOVAmodelpresentedearlier.FittingtheANOVAmodel(usingaTypeIerrorof = .05) to these data allows estimating the mean squares for the batch and within batchfactors. Using equations (3) through (6), we estimate the components of variation as shownin Table 2. Note that the body side panel has an insignificant within batch effect, implyingTable 2.Components of variation for quality characteristic.ComponentVariancePercentage of total variancePart-Part0.03021Within-Batch0.0000Batch-Batch0.11679Total process0.146100IDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING15that the mean remains stable within a batch (die set). For the batch factor, changes in themean between die setups account for 79% of the total process variation. This represents anopportunity to reduce variation and to benefit downstream processes.Finally,weusethesedatatoassessprocesscapability.Usingtraditionalprocesscapabilityindices with these data appears to violate the “stable process” assumption. However, givensome inherent variability in batch setup, we argue that a manufacturer may predict a certainlevel of mean shifts over the long run.Using the data from Table 1, we estimated the process mean as x=X = 0.055 andthe sample standard deviation as x= S = 0.3540. We then used equation (1) to calculateCp= 0.942. This value suggests that the width of the process output distribution is greaterthan the width of the design specification. In other words, no matter where the processis centered, it will produce panels outside of the design specification. In the automotiveindustry, a process with a Cp 1.67Pass Cpp 1.6711.712.64YesYes21.793.85YesYes31.485.80NoYes41.953.33YesYes52.112.11YesYes62.134.67YesYes71.515.76NoYes82.132.56YesYes92.276.19YesYes101.461.96NoYes110.701.22NoNo120.991.76NoYes130.981.86NoYes140.802.03NoYes150.871.92NoYes161.321.86NoYesIDENTIFYING SOURCES OF VARIATION IN SHEET METAL STAMPING17variationmodel,wewereabletoquantifythemagnitudeofthevariousvariancecomponentsand assess the need for improvement during the setup operation.While multivariate process capability indices seem appropriate to assess a sheet metalstampingprocess,autom