共轭凸轮的设计制造(CADCAM)及工艺【说明书+CAD】
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共轭凸轮的设计制造(CAD/CAM)及工艺目 录前言-3一、设计任务的基本要求-4二、凸轮机构的应用-4三、凸轮机构的组成-4四、凸轮机构的特点-4五、共轭凸轮机构的选择-5六、从动件的常用运动规律-7七、凸轮机构的分类-9八、共轭凸轮运动规律的选择-10九、共轭凸论的设计-12十、共轭凸轮的工艺方案及相应的工装设计-13十一、共轭凸轮制造与检验-15十二、课题小结-16小结-17参考文献-18前言课题：共轭凸轮的设计制造(CAD/CAM)及工艺目的：根据我们所学的知识设计并制造出织机的凸轮使织机在织造中顺利进行和提高织机的生产率及织物质量课题简介凸轮是常见的机械零件之一，传统的基于人工设计和计算机的凸轮设计方法，依靠模具、夹具等实现制造的工艺远不能达到高精度机械的运行要求，在现代设计理论基础上，利用计算机辅助设计（CAD）和制造（CAM）技术可以使凸轮的设计和制造到很高的精度，提高凸轮机构的运动平稳性。本题目是一种纺机用共轭凸轮为设计制造对象，利用目前先进的设计制造软件Pro/E，根据凸轮设计的原则，将高次方函数的凸轮曲线，用公式方法由软件绘出主动凸轮的轮廓曲线，然后通过数学建模，推导出与其共轭的轮廓曲线，从而建立起凸轮的三维模型，本设计结果还为凸轮的运动分析、仿真奠定了良好的基础。 完成三维造型以后，利用目前通用的MasterCAM软件实现编程，生成数控机床能执行的G代码，通过计算机与数控机床的通讯接口，将加工程序传入机床（或计算机直接控制加工）。从而加工出所需的凸轮廓形整个设计制造过程基本实现无图纸化操作（因图纸不能确切表达凸轮的廓形 ）。一、设计任务的基本要求1 了解凸轮机构的类型及各类凸轮机构的特点和应用场合，能根据工作要求和使用场合选择凸轮机构的类型。2 熟悉该共轭凸轮所应于设备上所起的功能和性能，以及使用工作条件（例载荷性质等）3 熟练掌握凸轮轮廓曲线的设计原理与方法。绘制该共轭凸轮的升程曲线图，并分析其特点。4 了解凸轮机构承载能力计算和结构设计的基本问题，初步具有建立凸轮机构计算机辅助设计和优化设计模型的能力。5 用PRO/E软件，生成该共轭凸轮的技术资料（三维造型及二维技术图纸等）及动力运动分析。6 编制该产品的工艺过程卡片，及相应工装设计。7 数控加工工序的NC程序。8 产品检验方法及误差分析。二、凸轮机构的应用1气阀杆的运动规律规定了凸轮的轮廓外形。当矢径变化的凸轮轮廓与气阀杆的平底接触时，气阀杆产生往复运动；而当以凸轮回转中心为圆心的圆弧段轮廓与气阀杆接触时，气阀杆将静止不动。因此，随着凸轮的连续转动，气阀杆可获得间歇的、按预期规律的运动。2.当圆柱凸轮回转时，凹槽侧面迫使摆动从动件摆动，从而驱使与之相连的刀架运动。至于刀架的运动规律则完全取决于凹槽的形状。三、凸轮机构的组成通过学习我们可以知道，凸轮机构一般由凸轮、从动件和机架三个构件组成。其中凸轮是一个具有曲线轮廓或凹槽的构件，它运动时，通过高副接触可以使从动件获得连续或不连续的任意预期往复运动。四、凸轮机构的特点1、凸轮机构的优点只需设计适当的凸轮轮廓，便可使从动件得到任意的预期运动，而且结构简单、紧凑、设计方便，因此在自动机床、轻工机械、纺织机械、印刷机械、食品机械、包装机械和机电一体化产品中得到广泛应用。2、凸轮机构的缺点1) 凸轮与从动件间为点或线接触，易磨损，只宜用于传力不大的场合；2) 凸轮轮廓精度要求较高，需用数控机床进行加工； 3) 从动件的行程不能过大，否则会使凸轮变得笨重。五、共轭凸轮机构的选择1 消极式开口机构（1）综框联动式凸轮开口机构用这种开口机构织制斜缎纹类织物时，需根据Rw在中心轴与凸轮轴之间选定合适的过桥齿轮，安装凸轮时要注意凸段的轮廓的曲线，以使各页凸轮有相同回转方向。同时要区别凸轮的大小，第一页综框配以大小半径差最小的凸轮，最后一页综框则配以大小半径差最大的凸轮。综框联动式凸轮开口机构简单，安装维修方便，制造精度要求不高，但是吊综皮带在使用过程中会逐渐伸长，故必须周期地检查梭口位置；其次因踏综杆挂综处做圆弧摆动，致使综框在运动中产生前后晃动，增加经纱与综丝摩擦，容易起经纱断头，不适应高速织机。经验表明，这种开口机构的极限转速为230r/min左右；同时，由于凸轮与织机主轴的传动比为1/Rw，当所织品种的Rw比较大（例如Rw=6）凸轮只回转很小的角度（60）便要完成一次开口动作（开口，静止，闭口），势必使凸轮表面的压力角增大，导致其外缘迅速磨损。为了减小压力角，必须放大凸轮的基圆直径（偏心度不变），但由于开口凸轮尺寸受到其它机构的空间限制，因此这种开口机构一般只适合织制Rw5的织物；此外，由于辘轳式吊综装置安装在织机的顶梁上，影响了机台的采光，不利于挡车工检查布面，同时还有可能造成油污疵点。因此，在新型织机中，不采用这种联动式凸轮开口机构。（2）弹簧回综式凸轮开口机构在实际生产中，凸轮灵活应用，如纬重车织引用一般平纹凸轮来织制。用2/2斜纹凸轮，改变穿综方法，可以织破斜纹和山形斜纹，相间采用不同的穿综方法，可织物2/2斜纹和2/2方平组织相间的条子织物，代替多臂开口机构。凸轮开口机构的不足之处，其一是只能生产简单组织的织物，如果织制较为复杂的织物，凸轮外形曲线将变得非常复杂，为减小压力角，又必须将凸轮基圆直径放大，以致开口机构变得过分笨重；其次，一定的凸轮外形只能生产一定开口规律的织物品种，为了适应织物品多变的要求，必须储备大量的各种开口凸轮，这在实际生产中是不经济的。2积极式凸轮开口机构（1）共轭凸轮开口机构在以上消极式凸轮开口机构中，由于回综不是开口凸轮驱动，控制，因此容易造成综框运动的不稳定。积极式凸轮开口机构可克服此缺陷，共轭凸轮开口机构就是随金属加工技术的进展发展起来的积极式开口机构。它的加工精度要求很高。 共轭凸轮开口机构利用双凸轮积极地控制综框的升降运动，不需吊综装置。其传动过程如图。凸轮2从小半径至大半径时（此时凸轮2从大半径经转至小半径）推动综框下降，凸轮2从小半径转至大半径时（此时凸轮2从大半径转至小半径）推动综框上升，两只凸轮依次轮流工作，因此综框的升降运动都是积极的。由于共轭凸轮装于织机外侧，能充分利用空间，可以适当加大凸轮基圆直径和缩小凸轮大小半径之差，达到减小凸轮压力角的目的。此外，共轭凸轮开口机构从摆杆到提综杆都是刚性连接，因此综框运动更为稳定和准确。（2）沟槽凸轮开口机构沟槽凸轮开口机构为另一种积极式凸轮开口机构，其传动过程如图所示，当凸轮从小半径转向大半径时，综框上升，此时沟槽内侧受力；反之，凸轮从大半径转向小半径时，综框下降，此时沟槽外侧受力。在此机构中，综框的升降运动都是积极的。 （3）连杆和开口机构凸轮开口机构能按照优化的综框运动规律进行设计，所以工艺性能好，但凸轮容易磨损，制造成本高，因此，在织制简单的平纹织物时，尚需寻求更为简单的高速开口机构。连杆开口机构就能满足这种需要。如图，综框处于上下位置时没有绝对静止时间，其相对静止时间则由曲柄和连杆的长度，以及各结构点的位置而定，优化结构参数，以求得较长的相对静止时间。与凸轮开口机构相比，连杆开口机构易加工，运动平稳，机构磨损小，适应高速，但只用于平纹织制，因此，这种开口机构用于加工平纹织物的高速喷气织机和喷水织机。共轭凸轮开口机构:1、凸轮轴2、2一共轭凸轮3、3转子 4、摆杆 5、连杆 6、双臂杆 7、7拉杆 8、8传递杆 9、9竖杆 10、综框沟槽凸轮开口机构1凸轮轴2沟槽凸轮3转子4摆杆5支点6连杆77提综杆88传递杆六连杆开口机构1辅助轴22开口曲柄33连杆44摇杆55摇杆轴66提综杆77传递杆88 、综框六、从动件的常用运动规律1. 基本运动规律 基本运动规律系指由单一函数式表达的从动件运动规律。常用的基本规律有以下四种。（1）等速运动规律 从动件运动的速度为常数时的运动规律，称为等速运动规律。 由于材料的弹性变形，加速度和惯性力不会达到无穷大，不过会引起强烈的冲击，这种冲击称为刚性冲击。因此，如果单独采用这种运动规律，只宜用于低速轻载的场合。（2）等加速等减速运动规律方程为：s=1/2at2 =1/2a(2/2)（3）余弦加速度运动规律 质点在圆周上作等速运动时,它在这个圆的直径上的投影所构成的运动称为简谐运动.速度和加速度方程:s=h/2(1-cos/02)v=h/20*sin/02 a=2 h2/200*cos/02由上式可知,加速度按余弦规律变化,故这种规律称为余弦加速度运动规律,也称为简谐运动规律.这种运动规律在始末两点加速度有突变,故也会引起柔性冲击,因此在一般情况下它也只适用于中速凸轮机构.需要指出的是,当从动件作升-降-升循环运动时,若在推程和回程都采用余弦加速度运动规律,则有可能获得包括始末点的全程光滑连续的加速度这种情况下既无刚性冲击也无柔性冲击,故可用于高速凸轮机构中.(4)正弦加速度运动规律方程式为: s=A0B-Rsin=R-Rsin=h(/2-1/2sin)加速度按正余弦规律变化,故这种运动规律称为正余弦加速度运动规律.其速度和加速度曲线都是光滑连续的,因此没有柔性冲击,也没有刚性冲击,故多用于高速凸轮机构.2.组合运动规律简介 上述各种基本运动规律各有一定的优点,对于工作要求比较严格的凸轮机构,为了克服单一的基本运动规律的某些缺陷,可以将几种基本运动规律曲线衔接起来,这种由几种基本运动规律组合的运动规律,称为组合运动规律.曲线衔接时,应遵循以下原则:(1) 对于一般转速,要求位移曲线在衔接点处相切,以保证速度曲线连续,即要求在衔接点处的位移和速度应分别相等,此时加速度可能有突变,但其突变值必为有限值.(2) 对于较高转速,则还要求速度曲线在衔接点处相切,以保证加速度曲线连续,即要求在衔接点处的位移,速度和加速度应分别相等.组合运动规律的设计比较灵活,易于满足特定要求,故应用日益广泛.3. 从动件运动规律的选择在选择从动件运动规律时,需要考虑的问题主要有:（1）应满足机器工作的要求 有的机器工作过程要求从动件按一定的运动规律运动.（2）应使凸轮机构具有良好的工作性能 对凸轮机构工作性能影响较大的因素，除了刚性冲击和柔性冲击外，还有以下几个参数：1） 最大速度v v越大，则从动件系统的最大量mv（m为从动件系统的质量）越大，故在启动，停车或突然制动时，会产生很大冲击。因此，对于质量大的从动件系统，应选择v较小的运动规律。2） 最大加速度a a越大，则惯性力越大。由惯性力引起的动压力，对机构的强度和磨损都有很大影响。a是影响动力学性能的主要因素，因此对高速凸轮机构，要注意a不宜太大。3） 应考虑使凸轮轮廓加工方面 有些从动件只要求当凸轮转过某一角度0时，完成一定的行程h或摆角（对于摆动从动件），而对运动规律没有严格要求。七、凸轮机构的分类1. 按凸轮的形状分:(1) 盘形凸轮: 它是凸轮的最基本型式。这种凸轮是一个绕固定轴线转动并具有变化矢径的盘形构件。(2) 移动凸轮: 当盘形凸轮的回转中心趋于无穷远时，凸轮相对机架作往复移动，这种凸轮称为移动凸轮。(3) 圆柱凸轮: 这种凸轮可认为是将移动凸轮卷成圆柱体而演化成的。比较：盘形凸轮和移动凸轮与从动件之间的相对运动为平面运动；而圆柱凸轮与从动件之间的相对运动为空间运动，所以前两者属于平面凸轮机构，后者属于空间凸轮机构。2. 按从动件的型式分:(1) 尖底从动件: 尖底能与任意复杂的凸轮轮廓保持接触，从而使从动件实现任意运动。但因尖底易于磨损，故只宜用于传力不大的低速凸轮机构中。(2) 滚子从动件: 这种从动件耐磨损，可以承受较大的载荷，故应用最普遍。(3) 平底从动件: 这种从动件的底面与凸轮之间易于形成楔形油膜，故常用于高速凸轮机构之中。比较：以上三种从动件亦可按相对机架的运动形式分为作往复直线运动的直动从动件和作往复摆动的摆动从动件。3. 按凸轮与从动件维持高副接触（锁合）的方式分:（1）力锁合: 利用从动件的重力、弹簧力或其它外力使从动件与凸轮保持接触。（2）几何锁合: 依靠凸轮和从动件的特殊几何形状而始终维持接触。1）凹槽凸轮机构: 其凹槽两侧面间的距离等于滚子的直径，故能保证滚子与凸轮始终接触。显然这种凸轮只能采用滚子从动件。2）共轭凸轮机构: 利用固定在同一轴上但不在同一平面内的主、回两个凸轮来控制一个从动件，主凸轮驱使从动件逆时针方向摆动；而回凸轮驱使从动件顺时针方向返回。3）等径凸轮机构和等宽凸轮机构: 其从动件上分别装有相对位置不变的两个滚子和两个平底，凸轮运动时，其轮廓能始终与两个滚子或平底同时保持接触。显然，这两种凸轮只能在1800范围内自由设计其廓线，而另1800的凸轮廓线必须按照等径或等宽的条件来确定，因而其从动件运动规律的自由选择受到一定限制。比较：几何锁合的凸轮机构可以免除弹簧附加的阻力，从而减小驱动力和提高效率。其缺点是机构外廓尺寸较大，设计也较复杂。八、共轭凸轮运动规律的选择综框运动规律表示综框在运动（闭口、开口）过程中的位移与织机主轴回转角t之间的关系，它对经纱断头和织机振动都有较大的影响。常见的综框运动规律有简谐运动规律和椭圆比运动规律。随着织机速度的提高，多项式运动规律也得到了较多的采用。1.简谐运动规律一个动点在圆周上绕圆心做角速度运动时，此点在直径上的投影点的运动即为简谐运动。取综框在最低处（或最高处）位移S为0，综框开始闭合时织机主轴回转角t为0，并设 k=b,则综框做简谐运动的位移方程：s=sx/2(1-cost/ax)式中： sx-任一页综框动程； -织机主轴角速度； t- 织机主轴回转角； y- 综框运动角，y=b+k=2b对上式求导一次和二次，可得出综框运动速度v和加速度a(公式从略)。现设 ay=ak+ab=(120+120)*/180=4.19rad,Sx=110mm,=200*/30=20.94rad/s.由此可做出综框位移S、速度v、加速度a的曲线，如图7-7中曲线A所示。图7-7 简谐运动规律和椭圆比运动规律比较由图7-7中曲线A 可见在综平前后，综框运动速度快，此时经纱张力小。非但不会造成断头，而且有利于开清梭口；二在闭合开始后的一个时期，综框运动缓慢，对梭子飞出梭口有利。但由于综框从静止到运动和从运动到静止之间过渡时的加速度值不为零，使综框产生振动，不利于做高速运动。因此，简谐运动规律一般用于低速织机（如有梭织机）的开口机构。 图7-7简谐运动规律2. 椭圆比运动规律一个动点在椭圆上绕中心做等角速度转动时，此点在椭圆短轴上的运动即为椭圆比运动规律。当椭圆的长、短半轴之比为1时，既为简皆运动规律。椭圆的长、短半轴之比的大小对综框运动加速度变化幅度影响很大，一般此比值取1.21.3。若Sx、和y取值同前，上述比值1.2008时，综框加速度最大值与简皆运动规律相同，但综框从静止到运动和从运动到静止之间过渡时的加速度值比简皆运动规律小；比值大于1.2008时，综框加速度最大值超过简谐运动规律相同，但综框从静止到运动和从运动到静止之间过渡时加速度最大值超过简谐运动规律，而综框从静止到运动和从运动到静止之间过渡时的加速度值变得更小。图7-7中虚线B分别是椭圆比运动规律的位移、速度、加速度的曲线，与简谐运动规律相比，在综平前后经纱张力小时，椭圆比运动规律的综框运动速度更快，更有利于开清梭口；在闭合开始后的一个时期，综框运动更缓慢，更有利于梭子飞出梭口；综框从静止到运动和从运动到静止之间过渡时的加速度值较小，从而综框产生的振动小。3. 多项式运动规律综框的多项式运动规律有多种，其中一种的位移方式为： S=(Sx/2)35(t/y)4-84(t/y)5+70(t/y)6-20(t/t)7 (7-6) 该运动规律可使综框运动开始和运动结束的瞬时加速度都为零，从而避免综框产生运动，适用于织机高速运转。综上所述,为了使设计出来的凸轮能表达到预先的目的,根据纺机的要求及实际中的运动规律,再综合凸轮机构的比较,选用在简谐运动规律前途下的积极式开口机构中的共轭凸轮开口机构.九、共轭凸论的设计Pre/ENGINEER操作软件是美国参数技术公司（Parametric Technology Corpration,简称PTC）的主要产品。Pre/ENGINEER软件能将设计到制造的全过程集成在一起，同时进行同一产品的设计制造工作，即实现所谓的并行工程。Pre/ENGINEER系统可以实现真正的相关性，任何修改都会自动反映到所有相关对象；它具有真正管理并发进程，实现并行工程的能力；具有强大的装配功能，能够始终保持设计者的设计意图，可以极大的提高设计效率。它的系统界面简洁，概念清晰，符合工程人员的设计思想和习惯，整个系统建立在统一的数据库上，具有完整而统一的模型。因此我选用Pre/ENGINEER来完成凸轮的三维造型。MasterCAM是美国CNC Soflware公司研制开发的基于PC平台的CAD/CAM一体化软件在CAD/CAM领域中享有盛名，其装机量居世界第一。它使机械工程的设计和制造发生了革命性的变化。一个工作者在短时间内就能设计出机械工程上各种曲线，如齿轮齿形轮廓用的渐开线、摆线，凸轮设计用的阿基米德曲线，并用各曲线来形成复杂曲面。由于MasterCAM具有良好的性能价格比，操作简单，使用方便，易学易用，可以通过CAD模块绘制几何图形，然后通过CAM模块编制刀具路线（NCI），再通过后处理转换成NC程序，最后通过计算机通讯端口传人数控机床中。所以我选用MasterCAM软件。根据以上选择，现用Pre/ENGINEER三维造型来生成凸轮的三维造型。步骤如下：1 打开Pre/ENGINEER软件2 创建一个新的文件并命名3 在创建新模块下选择曲线命令4 输入由柱坐标表示的凸轮轮廓曲线方程： r1=144+9.5*cos(2.45214*theta)-0.9*1-cos(4.90428*theta) theta=73.405*t 0t1 z=05 由于凸轮最大升程是19，由此推导出公轭凸轮的轮廓曲线方程 设a=r=144+9.5*cos(2.45214*theta)-0.9*1-cos(4.90428*theta) 则b=a2 c=b/38880 d=1.1333-c e=arcos(d) f=90-e g=106.26-f 所以得出r2=sqrt44064-38880*cos(g)/0.9991 theta=73.405*t z=0 0t16 根据凸轮的轮廓曲线方程画出凸轮实体图7 在IGES保存类型下保存图形8 打开MasterCAM软件9 取档，打开保存的图形10 在刀具路径下外形铣削编制出刀具轨迹11 通过后处理转换成NC程序，并保存12通过传输软件由PC机把NC程序传人数控机床中13 用夹具把工件安装好，调出程序，铣出凸轮廓形十、共轭凸轮的工艺方案及相应的工装设计（一）工艺分析拿到这个零件时，我首先想什么样的材料能满足这个凸轮的设计和工作要求。我选择了铝或铸铁，因为我准备用铸造的方法把工件加工出来。进而我又考虑在保证高质量的前提下将工件简单的制造出来。于是初步构思工艺方案如下：铸造出工件毛坯车工件表面（留余量）钻孔铣凸轮外形轮廓铣越程槽钳工去毛刺。经过指导老师的初步指正：铸件的工作性能不够好；两步铣可合并，省工序；直接把外形铣到位是非常困难的，尺寸很难保证，且精度不高。在老师的指点和帮助下，我选择了20CrMnTi低碳合金钢，采用锻模锻出毛坯。构思出另一种较合理的工艺方案：锻毛坯粗、精车工件钻孔铣凸轮外形轮廓及越程槽模工件至尺寸经过老师和我的研究，再次商讨出一套更加合理完善的工艺方案，方案如下：锻毛坯热处理粗、精车工件钻铰孔铣凸轮外形轮廓及越程槽去毛刺渗碳淬火磨端面磨内孔磨凸轮外形检验、作标记入库（注意：每步工序后都要检验）。加入数据和一些加工装夹的细节，便有了详细具体的工艺方案。（二）加工凸轮的工艺流程1 锻：锻出毛坯，外圆直径为229mm，厚度为19mm,中间内孔的直径为40mm，表面无明显凹坑及无其它锻造缺陷检验 2 热：正火（HB197）检验 3 车：（1）用三爪卡盘装夹工件，粗车毛坯各部分。放精车半径余量2mm(内孔表面见光即行)（2）调面装夹，粗、精车端面，车外圆至直径2190.02mm，长6mm，内孔车至54.60.02,孔口倒角（注意尺寸余量）,车直径177mm的台阶圆，长1.345mm,端面标记“A”（3）调面装夹，精车端面，原尺寸14mm至14.60.05mm，车外圆至直径2190.02mm, 外圆接刀. 车177mm的台阶圆，长1.345mm, 台阶外圆长120.1mm,孔口倒角（注意尺寸余量）检验4 钳：A面为基准,采用钻模钻12H7,5-12.5的孔，铰12H7的孔，孔口倒角1.345,去毛刺检验5 铣：A面为基准面，内孔和孔12H7定位,螺钉压紧(1) 粗、精铣凸轮轮廓，凸轮深7.1mm，凸轮深12mm，单边留磨量0.3mm(2)铣越程槽,达图要求检验 6 钳：去毛刺检验7 热：渗碳淬火，有效硬代层深度0.81.1mm硬度5861HRC检验8 钳：喷沙，并清理9 磨：A面为基准装夹，磨端面，原尺寸14mm至14.3mm.调面装夹磨A面，尺寸至140.02mm,其表面粗造度为1.6检验10 磨：装夹工件,找正内孔,磨内孔尺寸直径为550.005mm,粗造度为1.6检验11 磨：粗、精磨凸轮、外形轮廓，达图检验：凸轮共轭误差小于等于0.05mm12 抛光：抛除表面振纹 13 作标：主凸轮 ZXT A4/1 回凸轮 ZXT B4/1 14 清洗、检验、包装、入库 （三）铣床类夹具设计铣床夹具主要用于加工零件上的平面、键槽、缺口及成形表面等。由于铣削时切削力较大，且为断续切削，设计铣床夹具时，应注意工件的装夹刚性和夹具的安装稳定性。由于铣削过程中多数情况是夹具和工作台一起做进给运动，而铣床夹具的整体结构又常常取决于铣削加工的进给方式，因此，按不同的进给方式将铣床夹具分为直线进给式、圆周进给式和仿形进给式三种类型。该凸轮夹具属于仿形进给式。铣床夹具通常通过过定位键与铣床工作台T形槽的配合来确定夹具在机床上的方位。第一套夹具方案：长方体合金钢，中间加块与凸轮内孔直径相配合的圆柱凸台，装夹时用垫块（为了排削），长螺钉、压块压紧。使用长销定位第二套夹具方案：夹具JJ-001，短销定位使用后比较：凸轮使用内孔和定位销孔定位，螺钉夹紧，所以需要内孔和定位销定位很难。如果用长销，每次装夹要么先把销子拔掉再装卸工件（很是麻烦），要么长销和内孔一起（很难装夹）。夹具JJ-001比第一种夹具装夹方便，而且美观。综上，所以选用第二套方案。十一、共轭凸轮制造与检验（一）铣凸轮轮廓 传统的凸轮轮廓形加工方法为使用靠模，效率低，精度差等一些缺点。本课题采用数控铣加工，利用Pro/ENGINEER三维造型和Matercam软件来完成。将凸轮的三维造型文件转换位IGS格式，用Matercam软件打开，由Matercam生成刀轨文件，通过后置处理器处理生成加工中心能接受的加工文件，自动生成程序，将程序通过传输软件由PC机传送至加工中心进行切削加工，加工出一件凸轮实物。（见附表） （二）检验共轭凸轮的共轭误差用检具-00检测共轭凸轮的共轭误差。首先先检测检具的共轭误差值小于0.02mm,再检测凸轮的共轭误差小于0.05mm十二、课题总结本课题采用Pro/E软件进行凸轮设计与制造，比传统的设计制造方法有着极大的优越性。提高了产品的质量和精度。用数控加工中心加工大大提高了零件的精度和效率。通过本课题的训练过程，初步学会了先进的设计方法，制造和加工技术。小结四年的大学学习，让我对机械设计与制造方面的知识有了一个系统而又全新的的认识，也对计算机方面的知识有了深入的了解。毕业设计是我们学习中最后一个重要的实践性环节，是一个综合性较强的设计任务，它为我们以后从事技术工作打下了一个良好的基础，对我们掌握所学知识情况进行了全面而又直观的检测。为了能够较好的完成这次毕业设计，我投入了万分的精力做了充分的准备工作。首先，我先针对毕业课题来考虑，在指导老师的指点和帮助下，对所需的资料进行搜集和整理，根据设计的要求，再对资料做一个简单的归类。其次，依据指导老师给出的设计任务要求，先制定设计的总体方案，按照指导老师要求的设计进度，一步步的完成此次的设计任务。毕业设计虽已结束，但想想我在其中所学到的知识，所遇到的困难，仍记忆犹新。它让我明白了无论是设计新产品，还是改造原先的老产品，都是一个复杂的技术过程，容不得半点含糊。设计人员应先明白设计的目的，了解产品的价值和实用性，其次要对设计的产品进行构思，确定总体方案，查阅资料，最后编写产品的设计说明书，进行绘图。这次的毕业设计培养了我独立设计思考和分析解决问题的能力，拓宽了我的知识面，是一次很好的锻炼机会！感谢指导老师对我此次毕业设计的指导!参考文献1、Mastercan基础与应用技术主编 万世明高等教育出版社2、Pro/ENGINEER2001中文版编者 孙江宏 黄小龙 罗珅清华大学出版社3、机械原理主编 马永林高等教育出版社4、机械设计课程设计手册主编 清华大学 吴宗泽北京科技大学 罗圣国高等教育出版社5、机械制造技术主编 李华高等教育出版社 18GAPP：一个装配工艺生成规划器摘要本文介绍了关于自动化装配规划的深入研究成果。一个装配工艺生成规划器（GAPP）已经开发出来，通过输入要组装的产品的实体模型，然后就可以输出它的可行装配序列。一旦该产品可以用商业建模软件生成实体模型，就可以通过GAPP产生实体模型的边界表示（B-REP）文件，生成一个有装配工艺规划的关系图。此图从几何，稳定性和可访问性的观点展示了一切合理的装配序列。合理的装配序列的共同优点,可以用相关的标准来决定，比如一定数量的再定位或者类似装配序列可以连续的操作。发动机是非常具有柔性的并且可以统一处理不同的装配问题，例如，遇到需要拆卸修复的产品可以不完全拆卸，同时也可以采用预先组件来装配。工业产品实例说明了这种工具的潜力。关键词：组装，拆卸，装配序列，装配规划介绍较短的产品生命周期、小批量、按时制造生产已经大大耗费了组装的时间。这已经呼吁有效的软件工具来协助规划。任务计划执行期间，因为经济的影响，一个适当的装配序列的选择是至关重要的。早期在装配规划侧重于自动生成大量的给定产品的序列，以及调查潜在的紧凑的装配次序表示方案。大部分推论都是凭人们的经验，例如消除不可行的装配序列限制或评估和选择一些基于成本标准的。今天，有许多装配规划人员，可以灵活生成所有可能的装配一个产品的序列，并丢弃所有那些不可行的约束。目前的研究重点在于减少装配顺序因素的制约和相关的成本，这可以从所有可行的那些序列中选择更好的装配准则。 本文详细介绍了综合装配规划的方法，其中关于生成、消除和装配序列的评价都是在每个进程中展现出来的。由此产生的的软件工具，称为生成装配工艺规划师（GAPP），基于C+和OSF/Motif上运行的图形窗口界面软件。图1显示软件的框图。还提出了在本文的结尾图18中是一个窗口界面屏幕转储。本文的下一节描述了产品的图模型，在第三节描述了从产品自动生成的的实体模型用来作为装配顺序引擎的输入。接着概述了一些用于消除不可行的装配约束序列，从而减少搜索空间。该第五部分简要介绍了实际应用中标准成本的作用，最后一个节讨论了该软件的影响成就。图1产品图模型概述装配操作可以被看作是建立零之间的联系和附件，或者是在无冲突路径中组件的使用。因此在装配规划的要素是零件的配对信息。这种信息有助于一个二元关系的一组零件可以更适当地在图模型中表示。其中可以看出零件定点和边缘的配对关系。图2显示了一个简单的四模块产品及其图模型。可以看到三个类型的配对关系是有可能的。他们定义如下:1.如果两个组件在组装产品中一直存在物理接触，他们会有接触约束。2. 如果两个组件在组装产品中不存在恒定的物理接触，或者一个正交方向的线性延长与另外一个产生碰撞，他们会有封闭约束。3. 如果两个组件在组装产品中不存在恒定的物理接触，或者任何一个正交方向的线性延长都不会与另外一个产生冲突，他们就不受约束。图3显示了示例的两个部分自由不受约束的关系。请注意，尽管封闭约束和自由配对关系不涉及接触，但他们意味着无冲突路径的坐标系统的选择可能存在或可能不存在。这些非接触配对关系，从一种几何的干涉角度来看对确定可行装配序列发挥重要作用。显然，上面的定义是这样的，在任何产品的图模型始终是一个完整的图形（即，每一个零件与其他零件至少具有上述中三个配合关系的一个）。生成的图形模型是几何推理的过程，主要包括确定哪些部分有哪些类型的配对关系。N组件产品的配对关系可以表示为n(n-1)/2。从实体模型自动生成图模型一种自动建立了内部的图模型的计算机表示方法已经被研究出来。通过从产品的实体模型生成的B-REP文件的信息自动生成图模型，使用ICEMDD实体建模。该方法主要包括B-REP文件包含的零件的表面信息。特别地，每个涉及在表面上的数学测试，有助于判断这些部位属于表面相互接触，阻止或自由。图4和图5为例“A”和“B”的接触块之间的配合关系，在图2中，从它们的配合的分析在B-REP文件包含曲面定义。在图4中，N1和N2分别是块“A”和“B”表面的单位法向量，两块之间的距离表示为d，PL和P2为表面上的点。假设对块“A”和“B”的限制，与所选择的坐标系统，分别是为识别两个表面之间的配合关系，必须满足三个条件：或者或者或者用于上述所有计算数据，都是从B-REP文件得到。在图5中，N1和N2分别是块“A”和“B”表面的单位法向量，假设圆柱块的约束“a”和“b”相对于所选择的坐标系统，是和这两者之间的接触面的配对关系必须满足三个条件：用于确定表面相同的条件联系也用于阻塞和自由配合关系识别。例如，阻止两个平面之间需要条件(1)及(5)要得到满足，但不满足条件(2)，而同样自由的关系类型的表面只需要条件(1)满足，但不是条件(2)及(5)。构建自由矩阵在3d空间最多六个自由度:三个翻译和三个旋转。在装配规划通过进一步考虑,比实际的方向(+或-)平移或旋转大约一半的自由度是更适当的。这12个自由度分别为 .字母T和R代表分别平移和旋转。一旦两零件之间接触，阻塞，或自由有关系已确定，这种关系提供的自由度隐含在一个适当的3x4的矩阵,称为自由矩阵,在那里矩阵中存在的每个条目和它所代表的自由度之间有对应关系:自由度区间每一个接触表面自动构建自由矩阵。一个自由矩阵函数,包括arg1了arg2配合关系。函数通过一个自由矩阵表示，零件的自由度提供了关系。每个自由度代表的条目可用1或0表示矩阵。这些信息是用来计算几何干涉操作。图6显示了一个简单的例子，用自由矩阵计算了在图4和图5这两种配合关系。自由矩阵表示了与平面接触(图4)所示，与圆柱接触(图5)所示。为了获得在零件表面所产生的最终自由矩阵，所需要的是在先前生成的自由矩阵条目之间做一个 “和”逻辑。该模型的限制就目前而言，该产品的每一个部分进行组装必须使用块，圆柱体，圆锥体进行建模，球体，革命，平板（扫描）和他们的组合。虽然固体建模器用于启用复杂对象建模，例如，使用从空气紧B-样条信封其中可以计算固体这种格式B-REP文件信息很复杂，尚未有明确条件确定其配合关系。另一个限制在于自动计算旋转零件的自由矩阵。现在，从使用B-REP文件分析到目前为止所描述的概念只有平面部分是自动生成的。旋转部分，如有必要，必须手动完成。因此，图模型生成的自动化是限于这种广泛和有代表性的分类产品的零部件。最后，GAPP可以处理的产品其其零件和子组件，在遵守所选择的正交坐标系统是可以组装的。因为B-REP文件明确表示表面法线使用标准4x4齐次矩阵，它是可能的确定装配的方向而不是匹配的坐标系统。扩展的方法这种情况下没有被调查。装配序列的列举来源于实体模型图模型的形式更适合装配序列的表示方案，下一个算法引擎是用来开发和提取模型的装配序列。基本原理枚举德梅洛和桑德森已经开发出一种强大的数学和系统的装配顺序引擎。该过程开始通过把产品的图形模型作为搜索图的根节点。搜索图扩张来完成通过在根节点中的割集的计算（一个割集是图中的一组边，去除其中由onemS增加图形元件的数量）。每一集在下面有对应一个新的节点层。任何新的节点产生的图形表示它的父节点减去边割集。然后在新生成的节点的图形表示的割集计算，得到另一层，等等。这个过程停止，当一个节点已生成的所有边缘已被删除。注意拆卸方法是按照人力来规划的。在GAPP，通过这种方法生成的装配序列是简洁的如（图7）。每个路径从上到下是拆卸序列。要从下到上给出相应的装配序列。更新割集在现实中,一个不能计算一组新的割集，每次在搜索图生成一个新节点，因为底层组合的复杂性,这种计算科学家发明了一种方法,确保只有根节点的装配状态的图形生成。任何其他割集新生成的节点仅是通过更新组割集根节点。图8是用来描述该方法。经过根节点的六个割集已经计算，生成图表的六个新的状态。六个割集根节点的每个新的子节点被继承。继承的割集的一些边缘，这是新的子节点的一部分，必须先删除。例如，从割集获得子集5E1，E3，E5。在此割集的边缘不能是子集5任何割集的一部分。它们，因此，从继承的组中删除，产生新的割集：从这个新的列表，第一和第二，以及第三和第四的组合，因为他们都代表相同的割集。第五，这是从根节点删除的产生子集5，是空集。因此，成为：然后用一种算法来检查边缘的剩余集是割集（即，子的状态产生一个比在父状态更多的组件）。应用该算法对边缘消除了最后一个。然后割集的子集5：1-e2,2-e4.对于每一个新的节点重复这个过程，简单的分析确定其割集。请注意，只有接触式边缘的割集的计算考虑在此阶段，即，包含其他关系类型（如图6在这个例子中）不会有助于识别多个潜在组件,而且减少了计算效率。阻塞和自由的关系只有当几何干扰问题才能得到解决。使用前面描述可行性约束的发动机，没有考虑与每个割集相关联拆卸操作的可行性。三个可行性约束是用来确保生成的装配序列确实是可行的。它们是:1.几何干涉约束2.稳定约束3.可访问性约束扬州大学广陵学院本科生毕业设计（论文）中期自查表（中期教学检查用）学生姓名张 翔学号100007144专业机械设计制造及其自动化班级机械81001班指导教师张帆职 称讲师设计（论文）题目安全带卷加速敏感器组件自动装配机设计个人精力实际投入每天平均工作时间6小时迄今缺席天数出勤率%指导教师每周指导次数每周指导时间（小时）未指导的周次及原因毕业设计（论文）工作进度（完成）内容及比重已完成主要内容（%）待完成主要内容（%）存在问题及解决方案指导教师意见：指导教师签名： 年 月 日扬州大学广陵学院本科生毕业设计（论文）指导教师审阅意见表设计（论文）题目安全带卷加速敏感器组件自动装配机设计学生姓名张 翔专业机械设计制造及其自动化班级机械81001班指导教师姓名张 帆职称讲师得分指导教师审阅意见：指导教师签名：年 月 日14扬州大学广陵学院本科生毕业设计（论文）评阅人意见表设计（论文）题目安全带卷加速敏感器组件自动装配机设计学生姓名张 翔专业机械设计制造及其自动化班级机械81001班评阅人姓名职称得分评阅人意见：评阅人签名：年 月 日扬州大学广陵学院本科生毕业设计（论文）答辩结果表设计（论文）题目安全带卷加速敏感器组件自动装配机设计学生姓名张 翔专业机械设计制造及其自动化班级机械81001班答辩记录：答辩小组意见：得 分组长签名日 期答辩委员会意见：指导教师评分评阅人评分答辩小组得分结构分最终成绩主任签章日 期Journal of Manufacturing Systems Vol. 15/No. 4 1996 GAPP: A Generative Assembly Process Planner Luc Laperrire, Universit6 du Quebec a Trois-Rivieres, Trois-Rivibres, Quebec, Canada Hoda A. EIMaraghy, University of Windsor, Windsor, Ontario, Canada Abstract This paper presents results of exhaustive research in automated assembly planning. A generative assembly process planner (GAPP) has been developed that takes as input a solid model of the product to be assembled and out- puts its feasible assembly sequences. Once the product has been modeled as a solid using a commercial solid modeler, the resulting solid models boundary representation (B-Rep) file is interpreted by the GAPP to generate mating informa- tion among parts in the form of a relational graph. This graph becomes the input of a search graph process whose con- strained expansion reveals all feasible assembly sequences from a geometric, stability, and accessibility point of view. The relative goodness of different feasible assembly sequences can be determined using pertinent criteria such as the number of reorientations involved or the clustering of similar assembly operations into successive ones. The expansion engine is very flexible and enables many different types of assembly problems to be handled uniformly, for example, finding disassembly repair sequences not requir- ing complete product disassembly or generating assembly sequences that force the building of predefined subassem- blies. Examples with real industrial products are provided to illustrate the potential of using this tool. Keywords: Assembly, Disassembly, Assembly Sequence, Assembly Planning Introduction Shorter product lifecycles, smaller batches, and just-in-time production have drastically reduced the time spent for assembly planning activities. This has called for the development of efficient software tools to assist the planner. Among the tasks the planner has to perform, the choice of an appropriate assembly sequence is a cru- cial one because of its economical impact. Earlier research in assembly planning focused on methods for automatically generating the numerous assembly sequences of a given product, as well as investigating potential compact assembly sequence representation schemes./-s Most of the reasoning was left to be done a posteriori by the human planner, for example elim- inating unfeasible assembly sequences with respect to some constraints and/or evaluating and selecting a few good feasible ones based on some cost criteria. Today there are many assembly planners that can automatically generate all possible assembly sequences of a product and discard all those that are unfeasible with respect to some constraints. 6s Current research focuses on the formalization of such constraints used to reduce assembly sequence count and on the formalization of different relevant cost criteria that can be used to select better assem- bly sequences among all feasible ones. 912 This paper describes the developed integrated approach to assembly planning, where generation, elimination, and evaluation of assembly sequences are all performed in a single process. The resulting software tool, called the generative assembly process planner (GAPP) is implemented in C+ and runs the OSF/MOTIF window interface on a Silicon Graphics workstation. Figure 1 shows a block diagram of the software. A screen dump of the window interface is also presented in Figure 18 at the end of the paper. The next section of the paper describes the prod- ucts graph model, which is generated automatically from the products solid model and is used as input to the assembly sequence enumeration engine briefly described in the third section. Next are outlined some constraints used to eliminate unfeasible assembly sequences and, as a result, reduce search space. The fifth section briefly describes the role of cost criteria. Practical applications are presented next, and the last section discusses accomplishments. Product Graph Model General Description Assembly operations can be viewed as establish- ing contacts and attachments among parts or sub- assemblies using collision-free paths. One central element in assembly planning is therefore the knowl- edge of mating information among parts. This kind of information lends itself to a binary relation on the set of parts that can be more appropriately represent- ed in the form of a graph model, where vertices are parts and edges are mating relations among them. 13 282 Journal o/ManuJacturing Systems Vol. l 5/40.4 1996 User input Products solid model I1 Feasibil,ly constraints (on or o I I Eva,oat,on cr,teria,% ofre,at,ve,mpooce, Search method . I . 1 . 1 . Boundary representation file Products graph model I I Assembly sequences enumeration engine I . I . S,II . Outputs Linear sequence of (optimal) assembly operations I moved subassembly I fixed subassembly directions of insertion L . . . J Figure 1 Block Diagram of the GAPP Figure 2 shows a simple four-blocks product along with its graph model. As can be seen, three types of mating relations are possible. They are defined as follows: 1. Two components have a contact relationship between them if they are in constant physical contact in the assembled product. 2. Two components have a blocking relationship between them if they are not in constant physi- cal contact in the product and if a linear transla- tion of one of them in one of the orthogonal directions results in a collision with the other. 3. Two components have a free relationship between them if they are not in constant physi- cal contact in the product and if a linear transla- tion of one of them in any of the orthogonal directions does not result in a collision with the other. Figure 3 shows an example of two parts having a free relationship between them. Note that although blocking and free mating rela- tions do not involve contact, they imply that colli- sion-free paths with respect to the chosen coordinate system may or may not exist. These noncontact mat- ing relations play an important role in determining feasible assembly sequences from a geometric inter- ference point of view. Clearly, the above definitions are such that the graph model of any product is always a complete graph (that is, every part has at least one of the above three mating relations with every other part). Generating the graph model is therefore a geometric reasoning process that mainly consists of identifying which parts have which types of mating relations with 283 Journal of Manufacturing Systems Vol. 15/No. 4 1996 Z x J- Block a Block b i Block c Contact Blocking - - Block d Figure 2 Four Blocks Product Along with Its Graph Model Block a Z x.L, Plane surface P of block a Plane surface of block b Pz Figure 4 Identification of First Contact Between Surfaces of Two Blocks Z xft , Block b Free . Figure 3 Two Blocks Having a Free Relationship Between Them which other parts. For a product with n components, n (n - 1) / 2 mating relations must be identified. Automatic Generation of Graph Model from Solid Model A method has been developed that builds the inter- nal computer representation of the graph model auto- matically from the information contained in the B-Rep file resulting from the products solid model, using the ICEM/DDN commercial hybrid solid modeler. The method mainly consists of analyzing the parts surface information contained in the B-Rep file. In particular, mathematical tests involving surface pairs each on a different part help determine whether the parts to which these surfaces belong are in contact, blocked, or free. Figures 4 and 5 show an example for the identi- fication of the contact mating relation between blocks a and b in Figure 2, from an analysis of their mat- ing surfaces definition contained in the B-Rep file. In Figure 4, n and n2 are the unit normal vectors of the bold surfaces of blocks a and b, respec- tively. The distance between the two blocks is denot- ed by d. Pl and P2 are points on the surfaces. Assume the limits of the planes of blocks a and b, with respect to the chosen Cartesian system, are (Xmi,1, Xmaxl, Yminl, Ymaxl, Zminl, Zmaxl) and (Xmi.2 , Xmax2 , Ymin2. Ym,x2, Zmin2, Zm2), respectively. For identification of the contact between these two surfaces, three condi- tions must be satisfied: nl n2 = nix * n2 + nly * n2y + nl * n2z .I- Figure 5 Identification of Another Contact Between Surfaces of Two Blocks a_l p2xn l=0 Inl I where P,P2 = (Pz - P,.) i + (Pzy - Ply) j + (P2z - Pu) k and 2 2 In, (2) (3) (4) Xminl Pz Xm,l andyminl P2y Ymaxl or Xmin2 Plx Xmax2 and Ymi.2 Ply Ymax2 (5) All the information required for the above geo- metric reasoning is directly extracted or computed from the B-Rep file. In Figure 5, nl and nz are the unit normal vectors of the bold surfaces of blocks a and b, respec- tively. Assume the limits of the cylinders of blocks a and b, with respect to the chosen Cartesian system, are (Xminl , Xmaxl , Ymlnl, Ym.l, Zmi.l, Zm,x0 and (Xmin2, Xmax2, Ymin2, Y.,.2, Zraln2, Zmax2), respectively. For the identification of the contact between these two surfaces, three other conditions must be satisfied: 284 Journal of Manufacturing Systems Vol. 15/No. 4 1996 , result i ,loo,.,ooo 1=,ooo,ooo 1 FM(el,b)= 1 l oo|n|ooo OlllJ lll 1 011 Figure 6 Freedom Matrices Associated with a Relation Between Two Parts nl nz = 0 (6) Xmin2 Xminl Xmax2 and Xmin2 ( Xmaxl Xmax2 Ymin2 Yminl Ymax2 and Ymin2 Ymaxl Ymax2 Zmi.1 Z ax2 (7) diameter 1 = diameter 2 (8) The same conditions used to determine if surfaces are in contact are also used for blocking and free mating relations identification. For example, a blocking between two planar surfaces requires con- ditions (1) and (5) to be satisfied, but not condition (2), whereas a free relationship between the same type of surfaces only requires condition (1) to be sat- isfied, but not conditions (2) and (5). Building Freedom Matrices A part in 3-D space has a maximum of six degrees of freedom: three translations and three rotations. In assembly planning, it is more appropriate to talk about half degrees of freedom by further considering the actual direction (+ or -) of a translation or rota- tion) 4 This gives a total of 12 half degrees of free- dom for the same part: (Tx, Tx., Ty+, Ty., T+, T., Rx+, Rx., R_, Ry_, R+, R:_). The letters T and R stand for translation and rotation, respectively. Once a contact, blocking, or free relationship has been identified (conditions satisfied) between any pairof surfaces between two parts, the tmderlying half degrees of freedom this relation provides to the parts implied are represented in an appropriate 3 x 4 matrix, called the freedom matrix, where there exists a correspondence between each entry in the matrix and the half degree of freedom it represents: Tx Rx+R- Tz+L-Rz+Rz-J Freedom matrices are built automatically for every contact surface pair. A freedom matrix func- tion, FM (argl, arg2), has been developed where argl is a mating relation and arg2 is a part. The function returns a freedom matrix representing this parts half degrees of freedom provided by that rela- tion. Every half degree of freedom that is available or not is represented by the entry 1 or 0 in the matrix, respectively. Such information is used for computing geometric interference in disassembly operations. Figure 6 shows a simple example or freedom matrix computation, using the two contact relations identified in Figures 4 and 5. The freedom matrices associated with both planar contact (Figure 4) and cylindrical contact (Figure 5) are shown. To obtain the resulting freedom matrix at the part level, all that is required is to perform a positionwise logical and between the entries of each of the surface- level freedom matrices previously generated. Limits of the Model For now, every part of the product to be assem- bled must be modeled using block, cylinder, cone, sphere, revolution, and slab (sweep) primitives and their Boolean combination. Although the solid mod- eler used enables complex objects to be modeled- for example, using air-tight B-spline envelopes from which a solid can be computed-the format of such solids in the B-Rep file is complex and its interpre- tation using some condition(s) to identify mating relations has not been formalized yet. Another limitation lies in the automatic computa- tion of the rotational part of freedom matrices. For now, only the translational part is generated auto- matically from the B-Rep file analysis using the concepts described so far. The rotational part, if nec- essary, must be supplied manually. Complete automation of the graph model generation is there- fore limited to this wide and representative category of products whose parts and subassemblies can be assembled from single translations (this is also a fundamental design-for-assembly rule). Finally, the GAPP can process products whose parts and subassemblies can be assembled in direc- tions complying with those of the chosen orthogonal coordinate system. Because the B-Rep file explicit- ly represents surface normals using standard 4 x 4 homogeneous matrices, it is possible to identify 285 Journal of Manufacturing Systems Vol. 15/No. 4 1996 assembly directions other than those aligned with the coordinate system. Extending the approach for such cases has not been investigated. Assembly Sequences Enumeration After having derived from the solid model a more suitable assembly representation scheme in the form of a graph model, an algorithmic engine is next used to exploit this model and extract assembly sequences out of it. Basic Enumeration Principle Homem de Mello and Sanderson have developed a mathematically robust and systematic assembly sequence enumeration engine? The process starts by putting the products graph model as the root node of a search graph. Search graph expansion is accom- plished through the computation of the cutsets in the root node (a cutset is a set of edges in the graph, the removal of which increases the number of graph components by onemS). To every cutset there corre- sponds a new node in the layer underneath. Any new node has the graph representation of its parent node minus the edges in the cutsets from which it was generated. Then the cutsets in the graph representa- tions of the newly generated nodes are computed, yielding another layer, and so on. This process stops when a node has been generated where all edges have been removed. Note that this disassembly approach is close to that used by the human planner. In the GAPP, assembly sequences generated this way are represented compactly in a graph of assembly states (Figure 7). 2 Every path from top to bottom rep- resents a disassembly sequence. Going from the bot- tom up gives the corresponding assembly sequence. Figure 7 Unconstrained Graph of Assembly States of Four Blocks in Figure 2 of the root node are inherited by each new child node. Some edges of the inherited cutsets, which are not part of the new child node, must first be deleted. For example, child5 was obtained from cutset e, e3, es. The edges in this cutset must not be part of any cutsets of child5. They are, therefore, deleted from the inherited set, yielding the new cutsets: 1 - ea, 2 - e, 3 - e4), 4- e4, 5 - , and 6- e2, e4. Updating the Cutsets In reality, one cannot afford to compute a new set of cutsets every time a new node is generated in the search graph because of the underlying combinator- ial complexity that this computation involvesJ 6 A method has been developed that ensures that only the set of cutsets in the root node of the graph of assembly states is ever generated. Any other cutset in any newly generated node is simply obtained by updating the set of cutsets of the root node. Figure 8 is used to describe the approach. After the six cutsets of the root node have been computed, six new states of the graph are generated. The six cutsets Out of this new list, the first and second, as well as the third and fourth, are combined because they both represent the same cutset. The fifth, which was removed from the root node to generate child5, is eliminated as it became empty. Therefore, the list becomes: 1 - e, 2 - e4, 3 - ea, e4. An algorithm is then used to check if the remain- ing sets of edges are indeed cutsets (that is, yielding 286 Journal Of 44anujbcturing Systems Vol. 15ANo. 4 1996 Child 1 Child 2 Child 3 Child 4 Child 5 Child 6 Cutsets of root node J e, e, e, e3, , , e, e, e, es, e, e, e, e, e, es Inherited by child 5 e, ez, e2, e3, es, e3, e, e, e, eE, e, e3, eE, e2, e, es Remove edges not in child 5 ez, eTJ, e, e, , e2, e, I Combine similar, remove empty , e, e2, 04 ( Eliminate non-cutset 1 , e,) Figure 8 Determination of Cutsets of New Child Node by Analyzing Ones Inherited from Its Parent exactly one more subassembly in the child state than in the parent state). Applying this algorithm for the above sets of edges eliminates the last one. The cut- sets of child5 are then: 1 - e, 2 - e4. This process is repeated for every new child node to determine their cutsets by means of a simple analysis of the ones inherited from their parent. Note that only contact-type edges are considered at this stage in the cutsets computations; that is, inclusion of other relation types (like e6 in this example) would not help identify more potential subassemblies and would simply decrease the computational efficiency. Blocking and free relations are considered only when geometric interference issues are addressed. .L x 1 Blocka Cutset Block c Blockd FM(e, b) FM(e, b) FM(e2, b) Result ollo V l Fl 000 0=0 /oooo/q,oo/n/,o ooo / LOl 111 LlOllj LlOll OOllj Figure 9 Cutset in Graph Model of Four Blocks and Corresponding Freedom Matrices Using Feasibility Constraints The engine described earlier does not consider the physical feasibility of the disassembly operations associated with each cutset. Three feasibility con- straints are used to ensure that the generated assem- bly sequences are indeed feasible. They are: 1. Geometric interference constraints, 2. Stability constraints, and 3. Accessibility constraints These can be turned on or off by the user for com- parison purposes (see Figure 18). Geometric Interference Figure 9 illustrates how freedom matrices are used to compute automatically the geometric feasi- bility of separating two subassemblies in a disas- sembly operation. It is desired to determine if an operation that splits the four blocks into the two sub- assemblies b and a, c, d is geometrically feasi- ble. The cutset e, ez, e6 is associated with this operation (note that all types of relations must be considered here in the cutsets). The freedom matri- ces of block b relative to the relations in this cut- set, also shown in Figure 9, are used to compute the geometric feasibility of this operation. In particular, by performing a positionwise logical and between the binary entries of the freedom matrices, the resulting matrix contains all zeros in the first two columns associated with translations. The interpretation is that this operation is not geometrical- ly feasible because there does not exist a disassembly direction along which part b can be removed. 287 Journal of Manufacturing Systems gol. 15/No. 4 1996 Stability Another important constraint during assembly execution is stability. Among all possible assembly sequences, many must be discarded due to stability problems. Because the four blocks in Figure 2 are not very interesting from a stability point of view, consider instead the flashlight in Figure 10. Note that although the represented disassembly operation is geometrically feasible, it clearly results in a high- ly unstable configuration. Following is a brief description of the stability model used by the GAPP. Stability is computed by first finding a subgraph of the graph model called the stability-directed subgraph. It is build by a progressive graph-grow- ing procedure using an algorithm. The basic con- struction principle is to find, for every component in the original graph model, which other component stabilizes (or secures) it, using which relations. The first step is to identify a part considered fixed (or grounded) in the complete product (usually the one with the lower z-coordinate assuming the z-axis is pointing upward). This part is put in the set P of processed components. Then the algorithm starts and picks another part not yet in P. It checks if this component is secured by any relation with the parts in P. If so, the relation(s) is (are) added to the set A of arcs. The arc(s) point(s) from the secured component to the securing component. As an example, in Figure 11 the component head was chosen as the initially fixed (or ground- ed) component and put in set P. Assume the part reflector was then chosen by the algorithm. Because this part is implicitly attached to the head by a snap fit, this part is in turn added to P and the relation between the reflector and head becomes an arc in the stability subgraph. This arc points from the Cap =- Spring Body Flashlights graph model I _ battery2 battery1 Reflector J- H Bulb r., . _- Lens Head Figure 10 Geometrically Feasible Disassembly Operation that Can Be Applied to Completely Assembled Flashlight reflector to the head and is added to the set A. Assume the cap is chosen next. This part is not secured by any of the parts in P at this stage. Another part is then chosen, say, the bulb. This part is secured by an implicit screwing to the reflector, already in P. The bulb is then added in turn to P and the arc pointing from the bulb to the reflector is added to A. The process continues until all parts have been successfully processed. A much more detailed description of the stability subgraph and the algorithm used to build it can be found in Lavoie and Laperri6re. v Once the stability subgraph D = P, A has been constructed, stability can be computed by the fol- lowing simple rule: if a cutset breaks at least one outgoing edge of the fixed subassembly or more than one outgoing edge of the moved subassembly, Cutset associated with Figure 10 X Cutset Moved subassembly fixed Flashlights stability subgraph Fixed subassembly Figure 11 Using Stability Subgraph to Estimate Disassembly Operations Stability 288 Journal qf Manufacturing Systems Vol. 15/No. 4 1996 then the corresponding disassembly operation is considered unfeasibleJ 7 Going back to Figure 11, it can be seen that the cutset under investigation breaks the flashlight into the following two subassemblies: cap spring body and head lens reflector bulb batteryl battery2. The former is the moved subassembly (grasped), and the latter is the fixed subassembly (because it contains the head initially chosen as grounded). This cutset breaks one outgoing edge of the moved sub- assembly: body head. Thus the rule above is not violated so far. But it is also seen from the figure that two outgoing edges of the fixed subassembly are broken by the cutset: batteryl body and bat- tery2 body. Thus by taking away the body, the bat- teries become unsecured and fall instantaneously (unless special fixtures are supplied, which is not considered for now). Experiments with this stability model have shown surprising results on how stringent the stability con- straint can sometimes be. For the flashlight product in Figure 1 O, by turning on only the geometric inter- ference constraint, there were 331 nodes expanded in the graph of assembly states, giving 12 896 paths (assembly sequences). By adding the stability con- straint in the expansion process, 17 nodes with 14 paths were generated (Figure 12). This drastic reduction is explained by the fact that for this prod- uct the stability constraint leads to the elimination of many nodes in the higher levels of the search graph, close to the root node. Accessibility Consider the removal of part a in Figure 13. The restricted access of a tool to hold and remove it makes the corresponding disassembly operation very difficult or impossible to execute. Such a constraint is used during graph of assembly states expansion to eliminate those state transitions that imply unfeasible operations with respect to accessibility. The notion of accessibility is implemented using models and con- cepts whose preliminary description can be found in Sere, Laperrire, and MascleJ 8 Search for Optimal Solutions In spite of considering all the above constraints, the graph of assembly states usually contains more than one feasible solution. To make a choice, one must then reason on pertinent criteria to determine the relative goodness of the feasible alternatives. Up to now, four such criteria have been used in the GAPP. They are: 1. Reorientations 2. Parallelism 3. Stability 4. Clustering Note that stability appears at two levels: as a con- straint to eliminate unstable states during graph expansion, and as a criterion to evaluate the relative stability of those states that have successfully passed the stability constraint test (using the stability sub- graph described earlier). ltiiiiiiiii iiiiiii l - ,.:. . b L% %. % % %.%,%,%.% Figure 12 Graph of Assembly States of Flashlight Considering Both Geometric Interference and Stability Figure 13 Typical Example of Inaccessible Component (in this case, a) in a Geometrically Feasible and Stable Disassembly Operation 289 Journal of Manufacturing Systems Vol. 15/No. 4 1996 By triggering one criterion on and leaving all three others off prior to search graph expansion, one can generate the optimal assembly sequence with respect to this criterion. By further providing relative importance (in terms of a percentage) to each criteri- on, optimal solutions with respect to all four criteria and their relative importance can also be obtained (see the window interface in Figure 18, where each criterions weight is represented as a slider from 0 to 100). Typically, this is useful for comparing different solutions in concurrent engineering. 13 Practical Examples Generation of Repair Disassembly Sequences of an Electrical Switch Some components within a product may be expected to fail during service and be replaced peri- odically. The disassembly sequences allowing access to these components generally do not require total product disassembly. Consider, for example, the insulators of the elec- trical switch in Figure 14, shown along with its graph model in Figure 15. The goal is to partly dis- assemble this product to get to the insulators and replace them. To generate a repair plan, all that is required is the identification of the contact relations of the graph model that should not be broken in the repair disassembly plan. In this particular example, these relations could be: ( central_body, switchcase ) ( terminal_blocks, switch_case ) ( spark_covers, switch_case ) ( sparkcovers, terminal_blocks ) ( actuator, central_body ) These relations are not part of any cutset used in the search process. This ensures that the generated disas- sembly plan will preserve the above relations and avoid total disassembly. A first disassembly sequence generated for this example is presented below: 1. remove (screws)from (switch_case central_body spark covers insulators terminal_blocks actua- tor switch cover) along z+ 2. remove (switchcover) from (switch_case cen- tral_body spark_covers insulators terminal_blocks actuator) along z+ switch_cover screws (4) insulators (3) terminalblocks I actuator spark_covers (3) centralbody switch_case Figure 14 Exploded View of Simplified Electrical Switch Assembly 1 - switch_case 2 - central_body 3 - spark_covers 4 - insulators 5 - terminal blocks 6 - actuator 7 - switch cover 8 - screws- Figure 15 Graph Model of Electrical Switch in Figure 14 3. remove (insulators)from (switch_case cen- tral_body sparkcovers terminal_blocks actua- to O along z+ It has been generated using only the geometric interference constraint turned on. Breadth-first was the chosen search mode. All cost criteria were turned off (sliders to zero). Note that the spark_covers were left in place, as required by the specification of the above relations to be preserved. Another test was performed with the same para- meters, except that the accessibility constraint was 290 Journal qf Manufacturing Systems Vol. 15/No. 4 1996 also turned on. No solution was returned by the GAPP. The reason is that the spark_covers were rec- ognized to interfere with the final removal of the insulators. Because the spark_covers were at the same time specified not to be disassembled in the preserved relation list above, no solution could be found. A more appropriate solution is shown below: 1. remove (screws)from (switch_case central_body spark_covers insulators terminalblocks actua- tor switch_cover) along z+ 2. remove (switch_cover)from (switch_case cen- tral_body spark_covers insulators terminal_blocks actuator) along z+ 3. remove (spark_covers)from (switch_case cen- tral_body insulators terminalblocks actuator) along z+ 4. remove (insulators)from (switch_case cen- tral_body terminal_blocks actuator) along z+ Note that the sparkcovers have been removed to provide better access to the tool before removing the insulators. This new solution required the relation (spark_covers, switch_case) to be removed from the list of relations not to be broken during the expansion process. Depth-first search was used in this case. Another approach where only the part or sub- assembly to be replaced is specified instead of the relations not to be broken is being implemented. Generation of Assembly Sequences that Build Predefined Subassemblies Consider the air cylinder in Figure 16. A first assem- bly sequence generated by the GAPP is shown below: 1. fit (bearing_oring) (bearing) along z- 2. fit (bearing_oring bearing) (body) along z- 3.fit (piston_rod) (bearing_oring bearing body) along z- 4. fit (piston_oring) (piston) along z- 5. fit (piston_oring piston) (bearing_oring bearing body piston_rod) along z- 6. screw (pistonscrew) (bearing_oring bearing body piston_rod piston_oring piston) along z- 7. against (cover_oring cover) along z- 8. reorient (cover_oring cover) 180 degrees 9. against (cover._oring cover) (bearing_oring bearing body piston_rod piston_oring p i s - ton pistonscrew) along z- / beadng_oring bearing body IF piston_ring piston pistonscrew piston oring cover oring cover ,- cover screws (2) Figure 16 Exploded View of Air Cylinder 10. screw (cover_screws) (bearing_oring bearing body piston_rod piston_oring piston piston_screw cover_oring cover) along z- This solution was obtained using clustering as the only criterion turned on. This has led to the genera- tion of an assembly sequence where, as much as pos- sible, consecutive operations are of the same type (as determined by the operation name, such as fit, against, and so on, and neglecting reorientation operations, which are not considered during cluster- ing). However, in trying to do so, it can be seen that this solution does not build one inherent subassem- bly of that product, that is, the piston, piston_rod, piston_oring, piston_screw. Another solution is shown below where the input graph model was that of Figure 17: 1. against (piston) (piston_rod) along z- 2. against (cover_oring body) along z- 291 Journal of Manufacturing Systems Vol. 15/No. 4 1996 3. screw (piston_screw) (piston piston_rod) along z- 4. fit (piston_oring) (piston piston_rod piston_screw) along z- 5. fit (bearing_oring) (bearing) along z- 6. fit (bearing_oring bearing) (cover_oring body) along z- 7. fit (piston piston_rod piston_screw piston_oring) (cover_oring body bearing_oring bearing) along z- 8. against (cover) (cover_oring body bearing_ oring bearing piston piston_rod piston_screw piston_oring) along z- 9. screw (cover_screws) (cover_oring body bear- ing_oring bearing piston piston_rod piston_ screw piston_oring cover) along z- Note that this unconnected graph model encom- passes the inherent subassembly (one component of the graph) along with the subassembly bearing_oring bearing body cover_oring, for demonstration purposes. As a result, the solution returned builds the required subassemblies. On the other hand, assuming that each operation name requires a different tool, then this new solution requires one more tool change than the previous one. Conclusions This paper presented an approach for integrating assembly sequence generation, elimination, and evaluation. Compared to other works reported in the literature, the developed GAPP presents: an efficient method for computing the cutsets, a rather straight- forward method for computing geometric interfer- ence based on freedom matrices, and a new stability model for computing stability constraints, all embedded in a functional computer software that can be easily used to tackle different kinds of assem- bly problems. 2 - bearing 3 - body 4 - piston_ring 5 - piston 6 - piston_screw 7 - piston_oring 8 - cover_oring 9 - cover /r 1 n 10 - cover_screws kS) Figure 17 Unconnected Graph Model of Air Cylinder The product to be assembled is first described in a relational graph model. The data structures underly- ing this model are built from the products B-Rep file resulting from solid modeling. An important piece of information resulting from the B-Rep file analysis is the freedom matrix. The freedom matrix approach is explicit because it directly specifies which assembly directions are available. On the other hand, this approach is limited to assembly directions aligned with the chosen coordinate system. Although the approach works for a vast variety of mechanical products compatible with this limitation, it would be desirable to investigate how the generalization of the model to arbitrary directions could be implemented using the same basic approach. Once the graph model has been generated, Homem De Mello and Sandersons engine is used to find a sequence of mutually exclusive cutsets in the prod- ucts graph model and its subgraphs. From a purely mathematical point of view, the combinatorial com- plexity behind this computation when used with the expansion of graph of assembly states is nontrivial. 1 However, the computation of feasibility constraints, including geometric interference, stability, and acces- Figure 18 Screen Dump of GAPPs Window Interface 292 Journal of Manufacturing Systems Vol. 15/No. 4 1996 sibility, as the search graph is expanded greatly reduces this combinatorial complexity. Experience with the system has shown that search space reduc- tion is not always the same using the same constraint for different products. For example, the electrical switch in Figure 14 is highly geometrically con- strained by nature. Thus the geometric interference constraint leads to the most significant reduction for th
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