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1、精品学习资源2.5 快速成型一种新的生产产品的概念最近被引进制造过程；在这些观念中，一些是对已经存在的观念的修饰，但是另一些完全是革命性的；在前一类的实例中，我们可以运用数控机床来切割各种各样的材料，使用激光和喷气机可以切割从木头到陶瓷的各种材料；对于后一类，我们可以描述零件的建模和三维快速加工过程；这个概念在内容和工业上很有潜力，因此值得简易争论一下；它在很大程度上是基于运算机才能进展的结果；对于第一组，工作效率的大幅度提高主要是由于运算机的应用，虽然，至少在原就上，这些过程可以以手动方式实现；对于其次组，没有运算机的帮忙是很难执行这些过程的；现在制造依靠于大量的由塑料和金属做成的模具；这些
2、零件有时会有特别复杂的外形和华丽的表面；这些图形是不能在传统机床上处理的，由于仅完成单一部分的加工是特别铺张时间和金钱的；同样，使用模具去生产可能检验后需要转变的个人模式的工件也是特别昂贵的 这种情形发生在非传统工具的生产中，并且这个过程特别昂贵，消耗时间和劳力）；在最近几年中，一个新的解决这种情形的概念被提出；它被称为快速成型，在H. D.Kochan 编写的自由制造一书中描述了立体雕刻，模具快速原型和快速成型 德累斯顿科技高校，德国，科学技术出版社）；我们用图 2.19a 中的模型来说明这种观念下的制造过程；这个模型代表了具有特别齿形的螺旋齿轮，齿是由相互之间具有角度的平面层组成；换句话说
3、，一个具有复杂外形的三维模型是由简洁外形的薄平面层组成的；概念和布局图2.19 a ）快速原型演示工件；留意看齿轮上清楚可见的层；每一个层都按肯定的角度旋转，从而形成了螺旋齿轮的外形 这是依据这种技术生产最终设计完成前的模型Conceptland Ltd., Raanana,Israel的产品）；有好几种不同的技术，利用这种原理并应用运算机帮助加工具有复杂空间的零件；我们将在这里简洁的描述这个概念的本质；电脑的内存用来储备要加工零件的几何图形信息，以至于零件的每个几何薄层通常0.3-0.5mm ）都可以用数值定义；欢迎下载精品学习资源依据这种概念，在制造半层体中一个可能的方案如图2.20 所示
4、；图2.20快速建模布局图 1 ）容器； 2 ）聚合液体； 3 ）金属板； 4）电脑； 5）激光器； 6 ） 旋转镜这样的布局由容器 1布满了一种特别的液体2，这种液体在紫外线的照耀下会变成固体；液体的表面掩盖着板 3，板 3 的垂直位置由电脑系统掌握；紫外线由激光器5 产生并且在镜子 6的帮助作用下聚焦，这也是由电脑系统掌握的，因此，激光可以依据肯定的程序在液体表面移动；这种操作的结果就是，产生了一个事先确定了的薄层；下一步，板3向下移动一个薄层厚度的距离，并且重复上一步的程序；在这个过程中，激光的运行轨迹可以依据新的薄层的外形需要而转变；因此，零件一层一层的被构成所期望的外形；图2.19b
5、 列举了一个用这种方法生产的一个产品的例子；练习题试着设计下面情形的运动布局：1. 缝纫机2. 依据图 2.2 中给出的生产布局来设计如图1 所示的设备生产链条3. 内燃发动机4. 家用面团搅拌器 的进料装置；重物块 M 通过缠绕在滑轮上的线1 作用在滑块 2 上；滑块 2 推动由摩擦面 3 支撑的杆m；因此，推力F= 重物必需克服的摩擦阻力F1 ，F1 可以被表示为：【3.2 】其中 f= 摩擦系数， m 为棒的质量；另外，力 F 使滑轮有了转动惯量 I 因此，方程式以下面的方式达到平稳【3.3 】其中： a 为重力加速度r 为滑轮半径为滑轮的角加速度欢迎下载精品学习资源因此 a=r【3.4
6、 】从方程 3.3, 我们就可以推导出a 的一种表达形式【3.5 】杆运动 L 距离所需时间 t 可以用下面的方程运算出【3.6 】特别明显，由于滑轮的影响可以忽视不计），公式3.6 可以写成下面的形式【3.7 】图 3.2 由重力驱动的运动布局原理在下面的例子中 ,我们分析刚体沿着斜面运动的情形；这种情形发生在例如，零件像图3.3 所示那样随着送料机运动；其中 是送料机的斜度；零件和传送带之间的摩擦力可以由方程来表示； 在这里， f 为抗击零件在传送带上滑动的摩擦系数）；图 3.3 重物在斜坡上的运动力 F 可以从已知公式里得到；欢迎下载精品学习资源【3.8 】方程式仍可以写为：【3.9 】
7、从方程 3.9 中我们得到：【3.10 】运动 L 距离所需时间【3.11 】注：当或者时，刚体将没有运动，时间趋向于无穷长；在这里，我们分析弹性运动；这种运动的原理图如图 3.4a 所示；作为驱动源的弹簧的特性如图 3.5 所示；这个特点说明力 P 的大小由弹簧的变形打算 没有外力作用； b）有外力 F 作用并且【3.13 】作用力 P 总是与 X 方向相反；欢迎下载精品学习资源图 3.5 弹簧的力与变形线性曲线因此，质量块 m 的运动可以由 Dalamber方程式来描述【3.14 】这个微分方程有一个简洁的运算方法【3.15 】肯定要确定未知参数A、B 和；把公式 3.15 带入公式 3.
8、14 ，我们可以得到【3.16 】并且参数为系统的固有频率；我们必需使用系统的原始条件去解决参数A 和 B；假设，在t=0时刻弹簧的变形, 并且；然后我们把这些时刻代入公式3.15就可以直接得到，；因此公式 3.14 的完全解为【3.17 】公式 3.17 说明表达图见图 3.6图 3.6弹簧驱动刚体运动的位移与时间关系欢迎下载精品学习资源为了找到把质量块从3.17 写成一下形式X0 点移动到任何一个距离L 的店 X1 所需时间，我们把公式【3.18 】在实际情形中，我们必需要考虑质量块m 在运动中所受到的阻力，如图3.4b所示；由于自然力可以是多种多样的，例如，假如它是由干摩擦引起的，这个力
9、可以被描述为解读力的形势；【3.19 】方程式 3.19 的图解如图 3.7 所示；图 3.7刚体快速运动中由干摩擦产生的力质量块 m 的运动可以被描述为【3.20 】可以被一系列的方程来代替【3.21 】在公式 3.21 中用 K 来代替, 可以得到【3.22 】方程式两边同时平方，可以得到【3.23 】R 是一个积分常数我们可以用图3.8 来演示质量块在相位面上的运动；欢迎下载精品学习资源图 3.8刚体运动中干摩擦引起的震惊对速度和位移的影响当时，质量块的震荡运动停止在我们的例子中，弹簧使质量块从点运动 L 的距离到点，依据给定的图3.8 ， R 的值等于；这使得我们能够以以下方式重写公式
10、3.23 中的第一个等式【3.24 】并且【3.25 】对 K=0 的情形，依据方程3.25 得到【3.26 】因此，在 K=0 的相怜悯形下，公式 3.26 和公式 3.18 是相等的 在 n=0 的情形下） 现在我们考虑例子中力 F 不变的情形 cutting of a variety of materials, from wood to ceramics, with a laser beam and a water-plus-abrasive jet.With regard to the latter group, we may describe the process of rapid
11、 modeling or three-dimensional processing of parts. This concept is rich in content and industrial potential, and it is therefore worthwhile discussing it in brief. It is based on a principlethat has been possible to formulate largely as a consequence of the power of thecomputer.The productivity of
12、the first group of manufacturing processes mentioned aboveis vastly improved by the application of computers, although, at least in principle, theseprocesses may be carried out in a manual mode. For the second group, it is impossibleto execute the processes without a computer.Modern manufacturing re
13、lies on a large number of molded parts made of plastics and metals. These parts sometimes have very complicated shapes and ornate surfaces.Such shapes cannot be processed on conventional machines, which makes any attemptto produce a single part of this kind very time and money consuming. For the sam
14、ereason, the use of a mold to produce individual patterns, which may require changesafter they are examined, is even more expensive this is the case in whichnonconventionaltools areused and the process is expensive and time and labor consuming.In recent years, a new concept for providing the solutio
15、n to this problem has been proposed.It is known as rapid prototyping, stereolithography, quick prototype tooling, orrapid modeling, andisdescribed in the book Solid Freeform Manufacturing, by H. D.Kochan Technical University Dresden, Germany, Elsevier Scientific Publishers.To explain the idea underl
16、ying this manufacturing process, we use the model shown in Figure 2.19a. The model represents a helical wheel provided with specially formedteeth, consisting of plane layers that are angularly shifted relative to one another. Inother words, a three-dimensional model with a complicated shape is compo
17、sed of anumber of thin, planar, and simply shaped layers.欢迎下载精品学习资源FIGURE 2.19 a Illustration ofa rapidly modeled subject. Pay attention to the clearly visible layers of the material comprising the wheel. Each layer is displaced by a certain angle,thus creating the image of a helical gear here, for
18、purposes of illustration, the thicknessof the layers is exaggerated, b Examples of patterns made by this technique before the final design production of Conceptland Ltd., Raanana, Israel.There are a number of different techniques that exploit this idea for the computeraided processing of spatially c
19、umbersome parts. We will describe here, in brief, theessence of the concept.The memory of the computer is loaded with geometric information about the partto be processed so that the configuration of each thin say, 0.3-0.5 mm slice of thepart can be numerically defined.A possible layout for a process
20、 based on this concept for creating lamellar bodies for an intricate three-dimensional shape is shown in Figure 2.20. This layout consistsof a vessel 1 filled with a special liquid 2, which polymerizes to a solid under ultravioletirradiation.The surface of the liquid covers a plate 3, the vertical l
21、ocation of which iscontrolled by the systems computer 4. The ultraviolet beam generated by means of laser 5 is focussed with the aid of a mirror 6, which is also controlled by a computer, so that the beam moves on the surface of the liquid according to a given program. As欢迎下载精品学习资源a result of this o
22、peration, a thin plane layer is created with a predetermined shape. In the next step, the plate 3 moves down for a distance corresponding to the thickness of one layer, and the procedure is repeated. At this point in the process, the trajectory of the beam may be changed according to the configurati
23、on of the new layer. Thus, the body grows, layer by layer, to form a model of the desired shape. Figure 2.19b shows examples of possible units produced in this wayExercisesTry to design the kinematic layout of a:1. Sewing machine.2. Machine for producing the chain shown in Figure 2.1 in accordance w
24、ith theproduction layout given in Figure 2.2.3. Internal combustion engine.4. Domestic dough mixer dough kneader.5. Typewriter.6. Mechanical toy, spring or electrically driven.7. Machine gun.8. Automatic record player.9. Photocopying machine.3Dynamic Analysis of DrivesIn this chapter we shall discus
25、s examples illustrating the operation time computation techniques for drives of different physical natures. We begin with the simplest a purely mechanical drive.3.1 Mechanically Driven BodiesThe first case we shall consider in this section may be classified as a free-fall phenomenon. This is the sit
26、uation which occurs, for instance, when a stack of parts movesvertically downwards in a magazine-type hopper or dispenser. The simplest exampleis presented in Figure 3.1, which shows a body falling from level I to level II through adistance L Assuming that there is no resistance of any kind, we can
27、write thefollowing expression for the time t required for this process:【3.1 】Figure3.2showsamechanismusedinautomaticmachineslathesfor feedingrod-like material during processing. The weight M acts on the slider 2 via a cableIwhich欢迎下载精品学习资源passesovera rollerwith momentof inertia/. The slider2 pushest
28、he rod mwhichis supported by frictional guide 3. Thus, the acting force F=Mg must overcomethe friction F1in the guides； Flmay be expressed as:【3.2 】where/= the dry friction coefficient and m is the mass of the rod.Inaddition,theforceF rotatestherollerwith momentof inertia/. Therefore, theequilibrium
29、 equation of forces takes the form【3.3 】where a = the linear acceleration of the weight or rod, r = the radius of the roller, anda = the angular acceleration of the roller.Sincea=r【3.4 】from Equation 3.3 we can derive an expression for a in the form【3.5 】The time t needed to displace the rod through
30、 distance L can be calculated from theFormula【3.6 】Obviously,forI /. M+mi.e.,the influenceof therolleris negligibleincomparison with that of the moving masses, Equation 3.6 can be rewritten in the form【 3.7 】In this case we analyze movement along an inclined plane. This is the case thatoccurs when,
31、for instance, parts slide along a tray from a feeder, as is shown in Figure3.3. Here is the inclination angle of the tray. The friction between the parts andthetray is described by the force Fl =frng cos 0 here again, /= the dry friction coefficientwhich欢迎下载精品学习资源resists the movement along the tray.
32、 The driving force F in this case can befound from the known formula【 3.8 】The equilibrium equation thus has the form【3.9 】From Equation 3.9 we obtain【3.10 】The time t required to displace a part through a distance L equals【3.11 】Note:Whensin=/cos0 or/=tan0,no movementwilloccur.Thetimetendsto infini
33、tely long values.Hereweanalyzethemovementofa massdrivenbya previouslydeformed spring.The layout of such a mechanism is shown in Figure 3.4a. A spring as a drivingsourceisdescribedby its characteristicshownin Figure3.5. Thischaracteristicshows thedependence of the force P developed by the spring on t
34、he values of the deformationjcinboththestretchedandcompressedmodes.Whenthisdependenceislinear, asshown in Figure 3.5, parameter c, which is the stiffness of the spring, is constant forthiscase.Inotherwords,stiffnessofthespringisa proportionalitycoefficienttyingthe deformation of the spring to the fo
35、rce P it develops. It also defines the value of theslopeof the characteristic and can be described as【3.12 】And欢迎下载精品学习资源【3.13 】The force P always acts in the direction opposite to x.Thus,themovementofthemassmisdescribedbythefollowingequation basedon the Dalamber principle:【3.14 】This differential h
36、omogeneous equation has a simple solution:【3.15 】wheretheunknownparametersA,B,andcomustbedetermined.Substituting Expression 3.15 into Equation 3.14, we obtain【 3.16 】And【3.17 】Theparametercoisknownasthenaturalfrequencyofthesystem.Tofindthe unknownparameters A and B, we have to use the initial condit
37、ions of the system. Say, at themomentt = 0 the deformationof the springx = x0 and x = 0. Wethensubstitute thesedata into expression 3.15 and obtain directly A = x0 and B = 0. Thus the completesolution of Equation 3.14 is【3.18 】欢迎下载精品学习资源Expression 3.17 is interpreted graphically in Figure 3.6.To fin
38、d the time needed to move the mass from the point JCQ to any other point xllocated at a distance L from JCG, we rewrite Expression 3.17 in the following way:【3.18 】In a more realistic approach, we must consider a resisting force acting on the massm during its motion, as shown in Figure 3.4b. Since t
39、he nature of the force can vary,so can its analytic description. For example, if it is caused by dry friction, the forcemaybe described analytically in the form【3.19 】Thisgraphicinterpretationof Equation3.19is givenin Figure3.7.Themovement ofmass m can be described by【3.20 】which can be replaced by a system of equations in the form【3.21 】Substituting k =, in Equations 3.21, we obtain【3.22 】It is convenient to transform these equations multiplying them by 2 x and integratingthem into the following form:【3.23 】The value