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中国地质大学长城学院本科毕业设计外文资料翻译系 别： 工程技术系 专 业： 机械设计制造及其自动化姓 名： 学 号： 2011年 12 月 18 日外文资料翻译译文五轴磨床加工工具运动链的设计和分析E.L.J. Bohez，设计与制造工程部门，亚洲技术研究所摘 要五轴CNC加工中心现在应用得非常广泛。大多数机器的运动学原理都是以直角笛卡儿坐标系统为基础的。这篇文章对有可能的概念上的设计和基于理论上有可能的自由度的结合并且真实存在的器械进行了分类。本文还定义了一些有用的定量参数，例如：工作空间利用因素、机器加工工具的空间利用率、方位空间的指标和方位角。同时还分析了不同概念的优缺点，给出了选择的标准和机器结构的设计。最近在工业中提出的一些基于斯图尔特平台的概念也将在这篇文章中进行简要的论述。关键词：五轴；机器加工工具；运动链；工作空间；CNC；旋转轴1.介绍机器加工工具的主要设计规范应该满足以下法则：1） 运动件在工具和零件的定位和安置上应该 有足够的弹性。2） 以可能的最快的速度进行定位和安置。 3） 以可能的最高的精确度进行定位和安置。 4） 加工工具和工件的快速切换。5） 保护环境。6） 可能的高速材料移动率。 一台机器的加工工具的轴的个数通常是由机器自由度数或者是在机器滑动过程中独立可控的运动数来决定的。随着加工工具轴对应Z坐标轴的产生，ISO轴命名法推荐使用右手坐标法则。一个三轴磨床有三个方向的线性滑动：X、Y和Z，这使得机器能放置在相应轴向滑动范围内的任何一个位置。加工工具轴的方向在加工的时候保持不变。这就限制了与工件连接的加工工具的弹性，并最终导致很多不同的结构。为了增加在可能的加工工具、工件定位中的弹性而不用重新设计结构，我们将要在增加更多的机器的自由度。对于一个传统的三线性轴机器，能通过提供旋转滑动来实现。图1就展示了一个五轴磨床的例子。2.运动链接图制作一个机器的运动链接图对于分析机器是很有用的。从运动链接图中我们可以很快区别两组轴：图2展示了在图1中五轴磨床的运动链接图。从图中我们可以看到，工件由四根轴运载，而加工工具只由一根轴运载。 五轴机器就像两个相互协作的机器人，一个机器人运载工件，另一个机器人则运载加工工具。为了得到工件和工具定位上最大的弹性，机器至少需要5个自由度，这意味着工具和工件能在任何角度下连接起来。从一个刚性的物体运动连接点的观点来说，我们也可以理解对轴的个数的最低要求。为了定位两个在空间上相互连接的刚体，每个刚体（工具和工件）需要6个自由度或者12个自由度。然而，任何不改变两者之间定位的共同的平移和旋转的存在将会使自由度数目减少6个。两个刚体之间的距离是由工具的加工路径来决定的，这个距离也将会允许减少一个多余自由度，这样就使得最小的自由度数为5。3.五轴机器运动结构的分类按照机器的旋转和平移轴分类，我们可以把机器运动结构分为四大类：（1）三个平移轴和两个旋转轴；（2）两个平移轴和三个旋转轴；（3）一个平移轴和四个旋转轴；（4）五个旋转轴。近乎所有存在的五轴机器设备都属于（1）类。很多的定位焊接机器人、圈丝机器和激光加工中心也属于这一类。只有有限的一些用来加工轮船推进器的五轴机器属于（2）类。（3）和（4）类只有在设计需要增加更多自由度的机器人的时候才会用到。五根轴可以分布在工具和工件之间的结合处。第一种分类是根据运载轴的工具和工件的数量和在运动链中各个轴的次序来划分的。另一种分类是根据旋转轴放置的位置（是在工具那边还是在工件那边）来划分的。基于笛卡儿坐标的机器中的五个自由度是：三个平移运动X、Y、Z（一般表示为TTT）和两个旋转运动AB、AC、BC（一般表示为RR）。三个旋转轴（RRR）和两个直线运动轴（TT）的结合是很少见的。如果一根轴承载着工件，习惯上是用一个附加的标记来注释它。图1中的机器能以XYABZ。XYAB轴运载着工件，Z轴运载着工具。图3中展示的是XYZAB，三根直线运动轴运载工具,两根旋转轴运载着工件。3.1基于工件和工具运载轴次序的分类理论上，如果认为在工具和工件运载轴的两个运动链上的轴的次序有不同的结构，可能的结构的数目会非常大。同时只有两根直线运动轴和三根旋转轴结合也包括在内。在一个五轴机器中能以以下方式将一根工具运载轴和四根工件运载轴结合：对于X，Y，Z，A，B，C中任意一个可能作为工具运载的轴，其他工件运载轴可以在剩下的五根轴中选取。所以，对于任意可能的工具运载轴选择（六选一或者有六种可能），在剩下的五根轴中选取四根进行不同结构的排列个数为5*4！=120。所以，理论上只有一根工具运载轴的五轴机器就有6*120=720种可能。其他的结合方式也可以用这种方法分析。假设t代表工具运载轴的数目，w表示工件运载轴的数目（w+t=5），那么全部可能的结合数如下所示：这个方程式的值恒等于6！或者当w+t=5时这个值等于720。在这些720的结合中，有一些只包含两根直线运动轴。如果只考虑有三根直线运动轴的五轴机器，只有3*5！=360的结合也是仍是有可能的。这些结合的预设值Gt主要是由t的预设值决定的。这个预设值和由w的预设值所决定的Gw 的预设值是一致的，其中w=5-t。运用以上的定义，我们可以把五轴机器分为以下小群：（1）G0/G5组；（2）G1/G4组；（3）G2/G3组；（4）G3/G2组；（5）G4/G1组；（6）G5/G0组。3.2基于旋转轴的位置的分类我们能根据旋转轴装配的位置对机器进行分类。只有那些有两根旋转轴和三根线性轴的机器我们才会进一步考虑。可能的结构如下：（a）旋转轴装配在工具杆上；（b）旋转轴装配在机器平台；（c）两者的结合。如果机器的轴的R或者T的类型一样，那么在工具或者工件运载运动链中轴的次序就不重要了。一般来说，如果在工件运载运动链中有根平移轴和根旋转轴，在工具运动链中有根平移轴和根旋转轴，那么结合的个数为11：其中每一组的结合的个数在下面中将会一个个给出。所有组的结合总数为60。从设计的观点来说，这是我们所考虑的选择的数量中较为容易处理的一个。4.五轴机器的工作空间在定义五轴机器设备的工作空间之前，要适当的定义加工工具的工作空间和工件的工作空间。加工工具的工作空间就是通过沿着工具运载轴路线描绘出工具扫过参考点（例如工具尖端）而得到的。工件运载轴的工作空间也是用同样方法定义的（把机器平台的中心选择作为参考点）。这些工作空间能由计算扫过过的体积决定6。基于以上的定义，我们能定义一些对于不同类型机器比较、选择和设计有用的定量参数。4.1.工作空间利用因素 这个因素可以定义为，工件空间和工具空间的交集与工具空间和工件空间的并集的比。公式为4.2.可加工的体积大小一旦工件相对于工件参考点是固定的，并且一个特殊的工具相对于工具参考点也是固定的，那么我们就有可能确定可加工的体积的大小。可加工的体积就是能够在工件上切除的全部体积。机器工具空间和工件的交集给出了可以切除的材料的总量，或者说是可加工的体积（这是对于特殊的工件和工具机构来说的）。4.3.机器工具空间效率机器工具空间效率的定义为：机器工具空间（省略了一部分）和包含着机器的最小凸起体积。4.4.五轴机器的定位空间指数一个我们用来估计定位的最大范围的方法是为了决定能在机器上用两根旋转轴加工的球的最大部分。空间定位指数定义为能够由用所有旋转轴加工的机器来加工的最大的球顶体积除以机器工具空间。如果这个指数趋近于1，这就意味着所有的旋转轴能够在整个机器工具空间中运用。如果这个指数比1小，这就意味着大概百分之的工作空间能运用所有的旋转轴。以上的定义都是理论上的定义。实际上的定位空间指数会因为避免零件和机器、工具和工件之间的碰撞而进一步受到限制。能够加工的球顶变小就说明了这一点。5.五轴机器的选择标准我们的目的不是对五轴机器对于某一项特定的运用的选择或者设计进行一个彻底的研究。我们只是论述能用来判断五轴机器的选择的主要的标准。5.1.五轴机器设备的应用 应用能在布置和造型上进行区分。图12和图13说明了五轴的布置和五轴造型上的区别。5.1.1.五轴布置 如图12所示，一个在不同角度有着很多孔和平面板的零件，仅仅用一台三轴磨床来加工这个零件是不可能的。如果我们在用一台五轴机器，那么工具能在任何方向和工件定位连接起来。一旦达到了正确的位置，在大多数轴固定的情况下，我们就可以对孔和平面板进行加工了。平面板中能包括独立结构的2D平面。如果我们仅仅是要钻孔，那么理论上一轴CNC同步控制就足够了，而加工2D平面时两轴同步控制就够了。然而，三轴同步现在也很普遍了。当我们把工件和工具放置在连接在一起的时候，这就增加了在开始切削前的快进的速度。5.1.2.五轴造型 图13所示为一个五轴造型的例子，为了加工这个形状复杂的表面，我们需要在切削时控制好与零件接触的刀具的位置。刀具工件的位置在每一步工序中都会改变。CNC控制器需要在材料切除过程中同步控制五轴。更多关于造型的细节能在参考文献13中找到。五轴的机器有如下的应用：（1）生产刀刃，如： 压缩机和涡轮的浆；（2）燃料泵的注射器；（3）头饰的外形；（4）医学器官例如人造心脏阀；（5）复杂表面的铸型。5.2.轴结构的选择在设计和选择一个结构时，零件的尺寸和重量是首要的标准。重型工件要求工件运动链短。同时，水平加工平面又是较好的一种设计，这种设计会使定位和处理工件变得很便利。把一个重型工件放在一个单独旋转轴运动链上将会很大程度上增加定位的弹性。从图4中我们可以看出，用一个单独水平旋转轴来运载工件会使得机器更加具有弹性。在很多情况下，我们应该把工具运动链保持得尽量短，因为我们还必须运载工具轴驱动装置。6.结论理论上，五轴机器有很多构成方式。近乎所有经典的笛卡儿坐标五轴机器都属于由三根线性轴和两根旋转轴，或者三根旋转轴和两根线性轴组成的系列。这个系列又可以细分为有着720种情况的六组。就算只考虑三根线性轴的情况，在每个系列中仍然有360种组合。这些不同的组合是根据在工具和工件运载运动链中轴的次序来区分的。如果在对由三根线性轴和两根旋转轴组成的五轴机械进行分组时，只考虑在工具和工件运动链中旋转轴的位置，那么我们能五轴机器分为三组。在第一组中，两根旋转轴安置在工件运动链。在第二组中，两根旋转轴安置在工具运动链。在第三组中，每个运动链都安置一根旋转轴。每一组仍然有20种可能的情况。对于一个特定的应用领域，要从这些组合中选出一组最好的是一项很复杂的工作。为了使这项工作变得容易些，我们定义了一些用于比较的指数，例如：机器刀具空间、空间利用因素、定位空间指数、定位角度指数和机器刀具空间效率。列出了用来计算机器刀具空间和在机器上能加工的最大球顶的直径的算法。详细论述了两个运用这些指数的例子。第一个例子论述的是加工珠宝的五轴机器的设计。第二个例子则阐明了一台机器在线性轴中有着相同范围，在这种情况下，旋转轴选项的选择（略）。运用得最广泛的五轴机器的两根旋转轴安置在运动链末端处的工件一侧。这种结构给出了一种对于机器刀具结构的模块设计。然而，从应用的观点来说，这种模块设计并不总是最理想的。因为理论上存在很多可能的结构，很明显的是，对于一个特殊的工件装置需要一个合适的特定的五轴机器。模块设计应该以在所有的五轴结合中的模块性为基础。当前在设计中的模块性是以三线性轴机器为基础的。五轴磨床使得机器结构的数量变小。这对增加精确度和减小大部分尺寸是有帮助的。然而，它也有一些缺点：（1）五轴机器的高价；（2）增加的旋转轴的同时也增加了定位误差；（3）在同等的进给下，在机器轴上的切削速度更高。在购买五轴机器之前必须要对需要加工的产品的范围进行深入的研究。那些零件也应该分为五轴定位或者是五轴造型，或者两者都是。例如，有着旋转平台的机器对于生产诸如压缩机的旋转工件是很好的。一根旋转轴在刀具侧，一根旋转轴在工件侧，这样的布置将会提供更大的工作空间利用因素。最近所介绍的虚拟轴机器有着一个主要的优点：潜在的更高的动力响应和更高的硬度。然而，它的工作空间利用因素比经典的五轴机器要低。这些机器的更高强度使得他们非常适于高速磨所需要的高速杆19的设计。外文原文Five axis grinding machining tools sports chain design and analysisAbstract: five axis CNC processing center now very widely applied in most machine of the kinematic theory is right Angle Descartes coordinate system is the basis of this article to likely conceptual designs and based on the theory of the combination of may have freedom and real devices are classified this paper also define some useful quantitative parameters, such as: work space use machine tools factors space utilization orientation of the space index and azimuth and analyzes the advantages and disadvantages of different concepts are given, and the standard of the choice and machine structure design in industry recently proposed some based on the concept of Stewart platform will also in this article briefly discussed.Keywords: five axis; Machine tools; Sports chain; Working space; CNC; axis1. Introduction The main machine tool design code should meet the following rules: 1) moving parts in the tool and parts localization and placed it should be Have enough flexibility. 2) may be the fastest speed positioning and placement. 3) the accuracy of the highest possible location and placement. 4) processing tools and workpieces quickly switch. 5) to protect the environment. 6) possible high-speed materials mobile rate. A machine processing tools of the number of shaft is usually free degree or by machine is in the machine in the process of independent controllable sliding movement to the number of decision. Along with the machining tools shaft corresponding Z coordinate transformation of produce, ISO shaft nomenclature recommend using the right hand coordinate law. A three axis grinding machine has three of the direction of linear slide: X, Y and Z, which make the machine should be placed in the corresponding axial sliding range of any one place. The direction of the axis machining tools in processing remain unchanged. This limits the workpiece machining tools of connection with the flexibility, and eventually lead to a lot of different structure. In order to increase the processing tools in May, workpiece position of elastic and need not to design structure, we are going to add more machine of freedom. For a traditional three linear axis machine, can provide rotation to realize by sliding. Figure 1 shows a five axis grinding machine example. 2. Sports link figure Make a machine for the movement of the link chart analysis machine is very useful. Links from sports graph, we can quickly difference between two groups of shaft: figure 2 shows in figure 1 5 axis grinding machine movement link figure. We can see from the graph, the four shaft by carrier, and only by machining tools to carry a shaft.Five axis machine like two cooperation robot, a robot carrying workpiece, the other a robot is carrying machining tools. In order to get the workpiece and tools on the elasticity of the largest position, the machine will need at least five degrees of freedom, this means that the tool and workpiece can connect all the way down. From a rigid motion connection point point of view, we can also understand the number of shaft of the minimum requirements. In order to positioning two in space connected rigid body, each rigid body (tool and workpiece) need six degrees of freedom or 12 degrees of freedom. However, any not change the location of the common between translation and rotation of the existence of freedom will make cutting the number six. The distance between the two rigid bodies is the tools to the processing route, this distance will also allow reduce a redundant freedom, this make the smallest degree freedom for five.3、Five axis machine movement structure of the classification According to the rotation of the machine moving axis peace classification, we can get the machine movement structure are divided into four categories: (1) three translation axis and two axis; (2) two translation axis and three axis; (3) a translation axis and four axis; (4) five axis of revolution. Almost all existing five axis machine equipment belong to (1) type. A lot of positioning welding robot, silk machine and laser processing center also belong to this category. Only limited some used to ship propulsion five axis of processing machine belong to (2) class. (3) and (4) class only in design needs to increase more degrees of freedom when the robot will be used. Five shaft can be spread in the tool and workpiece department between. The first kind of classification is carrying the shaft according to the number of tool and workpiece and in sports in the order of the chain of each axis to differentiate. Another classification is placed on the axis of the position (is there or in the workpiece in tool there) to differentiate. Based on Descartes coordinates of machine five of the degree of freedom is: three translation movement X, Y, Z (usually expressed as TTT) and two rotation movement AB, AC, BC (usually expressed as RR). Three degrees of rotation (RRR) and two linear motion axes (TT) is a rare combination of. If a root bearing carrying workpiece, the custom is with an additional signs to note it. The machine in figure 1 to X Y A B Z. XYAB axis is carrying the Z axis is carrying tools. Figure 3 shows XYZA B, three straight line moving axis vehicles, carrying two of the axis of the workpiece. 3.1 the workpiece and tools based on the classification of the carrier shaft order In theory, if think tool and workpiece axis in carrying the two movement on the order of the chain of shaft have different structure, the number of possible structure will be very big. And only two straight line moving axis and three root the axis of the combination is also included. In A five axis machine in the following way can put A tool carrier axis and the four pillars carry axial workpiece with: for X, Y, Z, A, B, and C at any of the shaft may be as A tool to carry, other workpiece axis can carry in the remaining five selected from the shaft. So, for any possible tool carrier shaft choice (six choose a or are six may), in the rest of the five shaft from the four pillars of different structure arrangement for 5 * number 4! = 120. So, in theory only a piece of the five shaft carrying tool axis machine will have six * 120 = 720 possible. The combination of the other way also can use this method analysis. Assumption t represent tool carrier to the number of the shaft, w said the number of carrying the axis (w + t = 5), so all the possible combination number shown below: The value of this equation in identical 6! Or when w + t = 5 when the value is equal to 720. In the combination of these 720, some contain only two straight line moving axis. If only consider three straight line moving axis five axis machine, only 3 x 5! The combination of = 360 also is still possible. The combination of the default value Gt is mainly composed of t the default value of the decision. The default value and the default value by w determined G w the default value is consistent, including w = 5-t. Using the above definition, we can put the five axis machine divided into the following a small group of: (1) G0 / G 5 groups; (2) the G1 / G 4 groups; (3) the G2 / G 3 groups; (4) G3 / G 2 groups; (5) G4 / G 1 group; (6) G5 / G 0 group.3.2 Based on the classification of the axis of the position We can on the axis of the position of the assembly of the machine are classified. Only those who have the two root and the axis of the three pillars of the linear axis machine we will further consideration. The structure of the may be as follows: (a) the axis of the assembly in the tool pole; (b) the axis of the assembly in machine platform; (c) the combination of both. If the machine of shaft or the type of T R, so in the tool carrier movement or the axis of the order of the chain is not important. Generally speaking, if the carrier movement in the chain with roots translation axis and the axis of the root, the tools of kinematic chains root translation axis and the axis of the root, so the number of combination for 11 :Among them Each of the combination of the number below will give one. All set for the total number of combinations of the 60. From a design point of view, this is what we consider the number of choice in to deal with a relatively easy. 4. Five axis machine work space Five axis machine equipment in the definition of the work before space, to the proper definition machining tools work space and the work space. Machining tools work space is along the tool carrier axis line through paint tools swept reference points (such as tool tips) and get. The carrier of shaft space also is working with the same methods defined (the center of the machine platform choice as a reference point). These work space can have the volume by calculating and decision 6. Based on the above definition, we can define some for different types of machine more, selection and design of useful quantitative parameters. 4.1. Work space using factorThis factor can be defined as the work space and tools of the space with tools with space and the space and set than. Formula for 4.2. Can be processed to the volume of the size Once the relative to the workpiece reference point is fixed, and a special tool relative to tool reference point is fixed, so we probably can determine the size of the processing. But the volume of processing is to the all the volume resection. The machine tool and workpiece with space of given the amount of material can be removed, or is it can be processed to volume (this is the special workpiece and tools for institutions). 4.3. Machine tools space efficiency The machine tool is the definition of efficiency of space for: machine tools space (omitted part) and contains the minimum volume machine raised4.4. Five axis machine positioning space index A we used to estimate the positioning of the maximum range of method is to determine in the machine with two of the processing of the axis of the ball the most. Space positioning index is defined as can use all of the processing by axis machine to the biggest ball processing top volume divided by machine tools space. If the index is approaching to 1, this means that all the axis in the whole machine tool can be used in space. If the index greater than 1 small, that means about of working space can use all the axis of revolution. The above definition is theoretical definition. In fact the positioning of the space index will avoid components and machine, because the collision between tool and workpiece and further limited. Can the header smaller processing is showed this point.5. Five axis machine selection criteria Our purpose is not to the five axis machine to one a specific use of choice or design for a thorough research. We just discussed five axis machine can be used to judge the choice of the main criteria. 5.1. Five axis machine equipment used Application in decorate on modelling and can distinguish. Figure 12 and figure 13 shows the five axis decorate and five axis modelling difference. 5.1.1. Five axis layout As shown in figure 12 shows, a different Angle in a very porous peace panel parts, with only a three axis grinding machine to processing the parts is impossible. If we use a five axis machine, so tools can in any direction and workpiece positioning joined up. Once reached the correct position, In the most fixed a number line, we can carry on the processing of hole peace panel. Graphic board can include independence structure of 2 D plane. If we merely to drilling, so in theory a axis CNC synchronous control is enough, and processing 2 D plane two-axle synchronous control is enough. However, three axis synchronous now also very popular. When we put the workpiece and tools placed in together, this increases the start before cutting in the speed of fast forward.5.1.2. Five axis modelling Figure 13 shows is a 5 axis of modelling example, in order to processing the complex shape of the surface, we need to be in control when the cutting tool parts contact with good position. The position of the tool workpiece in every step process will change. CNC controller needs in the material removal process of synchronous control five axis. More about the details of the modelling in reference 13 find. Five axis machine has the following: (1) the application of blade production, such as: the compressor and turbine blades; (2) the fuel pump injector; (3) tire appearance; (4) medical organs such as artificial heart valve; (5) complex surface of the casting. 5.2. The choice of shaft structure In the design and choose a structure, part size and weight is the first standard. Heavy workpiece requirements workpiece sports chain short. At the same time, the plane is a good level processing a design, the design can make positioning and processing workpiece become very convenient. Put a heavy work in a single axis motion chain will greatly increase the elasticity of the positioning. In figure 4 we can see that, with a single level to carry workpiece axis will make the machine more flexible. In many cases, we should put the tool to keep sports chain short, because we must also the vehicle shaft drive device. 6. Conclusion In theory, the five axis machine has many structure mode. Almost all the classic Descartes coordinates five axis machines are belong to by three root linear axis and the axis of the two root, and two or three root the axis of the root of linear axis of the series. This series can be divided into 720 and has a sort of six group. Even if only consider three pillars of linear axis, and in every series 360 is still kind of combination. These different combinations is according to the tool and workpiece axis of the chain carrying movement order distinguish. If in the three pillars of linear axis and the two root of the axis of the five shaft machinery group, considering only in the tool and workpiece movement in the position of the axis of the chain, then we can five axis machine into three groups. In one group, the two root placed on the axis of the workpiece sports chain. In the second group, the two root placed in tool axis motion chain. In the third group, each movement chains find a place for the root the axis of revolution. Each group still have 20 May. For a particular application fields, from the combination of the best choose a group is a very complicated work. In order to make the work become easier, we define some used to compare the index, for example: the machine tool space, space using factor, positioning space index, orientation Angle index and machine tool space efficiency. Lists the machine tool is used
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