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英文翻译【附】英文原文翻译文献：Five-axis milling machine tool kinematic chain design and analysis作者：E.L.J. Bohez文献出处：International Journal of Machine Tools & Manufacture 42 (2002) 505520翻译页数：Five-axis milling machine tool kinematic chain design and analysis1. IntroductionThe main design specifications of a machine tool can be deduced from the following principles: The kinematics should provide sufficient flexibility inorientation and position of tool and part. Orientation and positioning with the highest possiblespeed. Orientation and positioning with the highest possibleaccuracy. Fast change of tool and workpiece. Save for the environment. Highest possible material removal rate.The number of axes of a machine tool normally refers to the number of degrees of freedom or the number of independent controllable motions on the machine slides.The ISO axes nomenclature recommends the use of a right-handed coordinate system, with the tool axis corresponding to the Z-axis. A three-axis milling machine has three linear slides X, Y and Z which can be positioned everywhere within the travel limit of each slide. The tool axis direction stays fixed during machining. This limits the flexibility of the tool orientation relative to the workpiece and results in a number of different set ups. To increase the flexibility in possible tool workpiece orientations, without need of re-setup, more degrees of freedom must be added. For a conventional three linear axes machine this can be achieved by providing rotational slides. Fig. 1 gives an example of a five-axis milling machine.2. Kinematic chain diagram To analyze the machine it is very useful to make a kinematic diagram of the machine. From this kinematic (chain) diagram two groups of axes can immediately be distinguished: the workpiece carrying axes and the tool carrying axes. Fig. 2 gives the kinematic diagram of the five-axis machine in Fig. 1. As can be seen the workpiece is carried by four axes and the tool only by one axis.The five-axis machine is similar to two cooperating robots, one robot carrying the workpiece and one robot carrying the tool.Five degrees of freedom are the minimum required to obtain maximum flexibility in tool workpiece orientation,this means that the tool and workpiece can be oriented relative to each other under any angle. The minimum required number of axes can also be understood from a rigid body kinematics point of view. To orient two rigid bodies in space relative to each other 6 degrees of freedom are needed for each body (tool and workpiece) or 12 degrees. However any common translation and rotation which does not change the relative orientation is permitted reducing the number of degrees by 6. The distance between the bodies is prescribed by the toolpath and allows elimination of an additional degree of freedom, resulting in a minimum requirement of 5 degrees.3.Literature review One of the earliest (1970) and still very useful introductions to five-axis milling was given by Baughman 1 clearly stating the applications. The APT language was then the only tool to program five-axis contouring applications. The problems in postprocessing were also clearly stated by Sim 2 in those earlier days of numerical control and most issues are still valid. Boyd in Ref. 3 was also one of the early introductions. Beziers book 4 is also still a very useful introduction. Held 5 gives a very brief but enlightening definition of multi-axis machining in his book on pocket milling. A recent paper applicable to the problem of five-axis machine workspace computation is the multiple sweeping using the Denawit-Hartenberg representation method developed by Abdel-Malek and Othman 6. Many types and design concepts of machine tools which can be applied to five-axis machines are discussed in Ref. 7 but not specifically for the five-axis machine. he number of setups and the optimal orientation of the part on the machine table is discussed in Ref. 8. A review about the state of the art and new requirements for tool path generation is given by B.K. Choi et al. 9. Graphic simulation of the interaction of the tool and workpiece is also a very active area of research and a good introduction can be found in Ref. 10.4. Classification of five-axis machines kinematic structure Starting from Rotary (R) and Translatory (T) axes four main groups can be distinguished: (i) three T axes and two R axes; (ii) two T axes and three R axes; (iii) one T axis and four R axes and (iv) five R axes. Nearly all existing five-axis machine tools are in group (i). Also a number of welding robots, filament winding machines and laser machining centers fall in this group. Only limited instances of five-axis machine tools in group (ii) exist for the machining of ship propellers. Groups (iii) and (iv) are used in the design of robots usually with more degrees of freedom added. The five axes can be distributed between the workpiece or tool in several combinations. A first classification can be made based on the number of workpiece and tool carrying axes and the sequence of each axis in the kinematic chain. Another classification can be based on where the rotary axes are located, on the workpiece side or tool side. The five degrees of freedom in a Cartesian coordinates based machine are: three translatory movements X,Y,Z (in general represented as TTT) and two rotational movements AB, AC or BC (in general represented as RR).Combinations of three rotary axes (RRR) and two linear axes (TT) are rare. If an axis is bearing the workpiece it is the habit of noting it with an additional accent. The five-axis machine in Fig. 1 can be characterized by XYABZ. The XYAB axes carry the workpiece and the Z-axis carries the tool. Fig. 3 shows a machine of the type XYZAB, the three linear axescarry the tool and the two rotary axes carry the workpiece.5. Workspace of a five-axis machine Before defining the workspace of the five-axis machine tool, it is appropriate to define the workspace of the tool and the workspace of the workpiece. The workspace of the tool is the space obtained by sweeping the tool reference point (e.g. tool tip) along the path of the tool carrying axes. The workspace of the workpiece carrying axes is defined in the same way (the center of the machine table can be chosen as reference point).These workspaces can be determined by computing the swept volume 6.Based on the above-definitions some quantitative parameters can be defined which are useful for comparison, selection and design of different types of machines.6.Selection criteria of a five-axis machine It is not the objective to make a complete study on how to select or design a five-axis machine for a certain application. Only the main criteria which can be used to justify the selection of a five-axis machine are discussed.6.1. Applications of five-axis machine toolsThe applications can be classified in positioning and contouring. Figs. 12 and 13 explain the difference between five-axis positioning and five-axis contouring.6.1.1. Five-axis positioningFig. 12 shows a part with a lot of holes and flat planes under different angles, to make this part with a three axis milling machine it is not possible to process the part in one set up. If a five-axis machine is used the tool can process. More details on countouring can be found in Ref. 13. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v) molds made of complex surfaces.6.1.2. Five-axis contouringFig. 13 shows an example of five-axis contouring, tomachine the complex shape of the surface we need to control the orientation of the tool relative to the part during cutting. The tool workpiece orientation changes in each step. The CNC controller needs to control all the five-axes simultaneously during the material removal process. More details on countouring can be found in Ref. 13. Applications of five-axis contouring are: (i) production of blades, such as compressor and turbine blades; (ii) injectors of fuel pumps; (iii) profiles of tires; (iv) medical prosthesis such as artificial heart valves; (v)molds made of complex surfaces.6.2. Axes configuration selectionThe size and weight of the part is very important as a first criterion to design or select a configuration. Very heavy workpieces require short workpiece kinematic chains. Also there is a preference for horizontal machine tables which makes it more convenient to fix and handle the workpiece. Putting a heavy workpiece on a single rotary axis kinematic chain will increase the orientation flexibility very much. It can be observed from Fig. 4that providing a single horizontal rotary axis to carry the workpiece will make the machine more flexible. In most cases the tool carrying kinematic chains will be kept as short as possible because the toolspindle drive must also be carried.6.3.five-axes machining of jewelryA typical workpiece could be a flower shaped part as in Fig. 14. This application is clearly contouring. The part will be relatively small compared to the tool assembly. Also small diameter tools will require a high speed spindle. A horizontal rotary table would be a very good option as the operator will have a good view of the part (with range 360). All axes as workpiece carrying axes would be a good choice because the toolspindlecould be fixed and made very rigid. There are 20 ways in which the axes can be combined in the workpiece kinematic chain (Section 4.2.1). Here only two kinematic chains will be considered. Case one will be a TTTRR kinematic chain shown in Fig. 15. Case two will be a RRTTT kinematic chain shown in Fig. 16.For model I a machine with a range of X=300mmY=250 mm, Z=200 mm, C=n 360 and A=360, and a machine tool table of 100 mm diameter will be considered. For this kinematic chain the tool workspace is a single point. The set of tool reference points which can be selected is also small. With the above machine travel ranges the workpiece workspace will be the space swept by the center of the machine table. If the centerline of the two rotary axes intersect in the reference point, a prismatic workpiece workspace will be obtained with as size XYZ or 300250200 mm3. If the centerlines of the two rotary axes do not intersect in the workpiece reference point then the workpiece workspace will be larger.It will be a prismatic shape with rounded edges. The radius of this rounded edge is the excentricity of the bworkpiece reference point relative to each centerline. Model II in Fig. 15 has the rotary axes at the beginning of the kinematic chain (RRTTT). Here also two different values of the rotary axes excentricity will be considered. The same range of the axes as in model I is considered. The parameters defined in Section 5 are computed for each model and excentricity and summarized in Table 1. It can be seen that with the rotary axes at the end of the kinematic chain (model I), a much smaller machine tool workspace is obtained. There are two main reasons for this. The swept volume of the tool and workpiece WSTOOLWSWORK is much smaller for model I. The second reason is due to the fact that a large part of the machine tool workspace cannot be used in the case of model I, because of interference with the linear axes. The workspace utilization factor however is larger for the model I with no excentricity because the union of the tool workspace and workpiece workspace is relatively smaller compared with model I with excentricity e=50 mm. The orientation space index is the same for both cases if the table diameter is kept the same. Model II can handle much larger workpieces for the same range of linear axes as in model I. The rotary axes are here in the beginning of the kinematic chain, resulting in a much larger machine tool workspace then for model I. Also there is much less interference of the machine tool workspace with the slides. The other 18 possible kinematicchain selections will give index values somewhat in between the above cases.6.4. rotary table selectionTwo machines with the same kinematic diagram (TTRRT) and the same range of travel in the linear axes will be compared (Fig. 17). There are two options for the rotary axes: two-axis table with vertical table (model I), two-axis table with horizontal table (model II). Tables 2 and 3 give the comparison of the important features. It can be observed that reducing the range of the rotary axes increases the machine tool workspace. So model I will be more suited for smaller workpieces with operations which require a large orientation range, typically contouring applications. Model II will be suited for larger workpieces with less variation in tool orientation or will require two setups. This extra setup requirement could be of less importance then the larger size. The horizontal table can use pallets which transform the internal setup to external setup. The larger angle range in the B-axes 105 to +105, Fig. 17. Model I and model II TTRRT machines. compared to 45 to +20, makes model I more suited for complex sculptured surfaces, also because the much higher angular speed range of the vertical angular table. The option with the highest spindle speed should be selected and it will permit the use of smaller cutter diameters resulting in less undercut and smaller cutting forces. The high spindle speed will make the cutting of copper electrodes for die sinking EDM machines easier. The vertical table is also better for the chip removal. The large range of angular orientation, however, reduces the maximum size of the workpiece to about 300 mm and 100 kg. Model II with the same linear axes range as model I, but much smaller range in the rotation, can easily handle a workpiece of double size and weight. Model II will be good for positioning applications. Model I cannot be provided with automatic workpiece exchange, making it less suitable for mass production. Model II has automatic workpiece exchange and is suitable for mass production of position applications. Model I could, however, be selected for positioning applications for parts such as hydraulic valve housings which are small and would require a large angular range.7.New machine concepts based on the Stewart platform Conventional machine tool structures are based on Carthesian coordinates. Many surface contouring applications can be machined in optimal conditions only with five-axis machines. This five-axis machine structure requires two additional rotary axes. To make accurate machines, with the required stiffness, able to carry large workpieces, very heavy and large machines are required. As can be seen from the kinematic chain diagram of the classical five-axis machine design the first axis in the chain carries all the subsequent axes. So the dynamic responce will be limited by the combined inertia. A mechanism which can move the workpiece without having to carry the other axes would be the ideal. A new design concept is the use of a HEXAPOD. Stewart 16 described the hexapod principle in 1965. It was first constructed by Gough and Whitehall 20 in 1954 and served as tire tester. Many possible uses were proposed but it was only applied to flight simulator platforms. The reason was the complexity of the control of the six actuators. Recently with the amazing increase of speed and reduction in cost of computing, the Stewart platform is used by two American Companies in the design of new machine tools. The first machine is the VARIAX machine from the company Giddings and Lewis, USA. The second machine is the HEXAPOD from the Ingersoll company, USA. The systematic design of Hexapods and other similar systems is discussed in Ref. 17. The problem of defining and determining the workspace of virtual axis machine tools is discussed in Ref. 18. It can be observed from the design of the machine that once the position of the tool carrying plane is determined uniquely by the CL date (point + vector), it is still possible to rotate the tool carrying platform around the tool axis. This results in a large number of possible length combinations of the telescopic actuators for the same CL data.8.ConclusionTheoretically there are large number of ways in which a five-axis machine can be built. Nearly all classical Cartesian five-axis machines belong to the group with three linear and two rotational axes or three rotational axes and two linear axes. This group can be subdivided in six subgroups each with 720 instances.If only the instances with three linear axes are considered there are still 360 instances in each group. The instances are differentiated based on the order of the axes in both tool and workpiece carrying kinematic chain.If only the location of the rotary axes in the tool and workpiece kinematic chain is considered for grouping five-axis machines with three linear axes and two rotational axes, three groups can be distinguished. In the first group the two rotary axes are implemented in the workpiece kinematic chain. In the second group the two rotary axes are implemented in the tool kinematic chain. In the third group there is one rotary axis in each kinematic chain. Each group still has twenty possible instances. To determine the best instance for a specific application area is a complex issue. To facilitate this some indexes for comparison have been defined such as the machine tool workspace, workspace utilization factor, orientation space index, orientation angle index and machine tool space efficiency. An algorithm to compute the machine tool workspace and the diameter of the largest spherical dome which can be machined on the machine was outlined. The use of these indexes for two examples was discussed in detail. The first example considers the design of a five-axis machine for jewelry machining. The second example illustrates the selection of the rotary axes options in the case of a machine with the same range in linear axes.翻译题名：Five-axis milling machine tool kinematic chain design and analysis期刊与作者：E.L.J. Bohez 出版社： International Journal of Machine Tools & Manufacture 42 (2002) 505520 英文译文 摘要： 现如今五轴数控加工中心已经非常普及。大部分机床的运动学分析都 基于笛卡尔直角坐标系。本文罗列了现有的概念设计与实际应用，这些从理论上都基于自由度的综合。一些有用的参数都有所规定，比如工件使用系数，机床空间效率，方向空间搜索以及方向角等。每一种概念，它的优缺点都有所分析。选择的标准及机器参数设置的标准都给出来了。据于Stewart平台的新概念最近行业内已有介绍并作简短讨论。1.绪论设计一台数控机床主要要遵循以下规则：1，刀具和工件在空间方向上要有足够的灵活性。2，方向和位置的改变要尽可能的快。3，方向和位置的改变要尽可能的准确。4，刀具和工件快速变、换。5，环保6，切削材料速度快 一台数控机床的轴的数目通常取决于其自由度数目或者独立控制运动的导轨数目。国际标准委员会推荐通过右手笛卡儿坐标系来命名坐标轴，刀具相应的为Z轴。一个三轴铣床有三条导轨，X,Y,Z向，它们可用来在长度范围内可以在任意位置移动。加工过程中刀具轴的位置始终不变。这就限制了刀具相对于工件在方向上变化的灵活性，并且导致许多偏差的出现。为了尽可能的提高刀具相对于工件的灵活性，无需重启，必须要加入多个自由度。对于传统三轴机床来说这可以通过提供旋转滑台来实现。图1给出了一个五轴铣床的例子。图1 五轴数控机床1.运动链图表 通过制作机器的运动链图表对于机器的分析来说十分有用。通过运动简图可知两组轴可以迅速的区分开：工件装夹轴和刀具轴。图2给出了图1.五轴机床的运动链简图。由图上可以看出工件由四根轴承载，刀具仅在一根轴上。这个五轴机床与两工位操作机器人很相似，一个机器人夹住工件，另一个夹住刀具。为了获得刀具工件方向上的最大自由，五个自由度已是最低要求，这就意味着工件和刀具可以在任意角度位置相对定位。最低需求的轴数也可以通过刚体运动学的方法来分析。两个刚体在空间确定相对位置，每个刚体需要6个到12个自由度。然而由于任意的移动或转动并不改变相对位置就允许将自由度减少到6.两个刚体之间的距离通过刀具轨迹来描述，并且允许去掉一个额外的自由度，结果也就是5个自由度。图2 运动链图2.参考文献 最早（1970年）到目前并且仍就有参考价值的对五轴数控铣床的介绍之一是由 Baughman提出的并清楚的阐述了它的应用（附录1有他的介绍）。APT语言随后成为唯一的五轴轮廓加工的编程语言之一。后处理阶段的问题也在数控发展的早期由Sim清楚的表述出来（附录2有对他的介绍），并且大部分问题到现在仍然有效。Boyd（详见附录3）也是最早引进数控机床的先驱之一。Beziers的书（见附录4）也是非常有用的介绍。Held（见附录5）在他的小型铣削加工的书里对多轴机床也有非常简短但启发性的定义。目前一篇适用于解决五轴数控机床工作空间计算的文章，通过使用Denawit-Hartenberg发表并由 Abdel-Malek and Othman（见附录6）改进的算法 应用于多弧段切削。许多对机床的类型和概念设计，这些可以被应用于五轴机床，Ref都有讨论（见附录8）.关于对刀具路径生成的技巧和新需求由B.K. Choi et al给出（见附录9）。工件与刀具的图像模拟也是研究的热点并且可以在Ref（见附录10）的书是一个好的入门读物。3.五轴机床运动结构的分类 从R轴（旋转轴）和T轴（移动轴）划分大致可以分为四大部分：（i）3个移动轴和2个转动轴；（ii）2个T轴和3个R轴；（iii）1个移动轴和4个转动轴以及（iv）5个转动轴；几乎所有五轴机床都是第一组。也有一些焊接机器人，弯折机器以及激光机器也属于这一类。只有限距五轴机床属于第二组，用以制造船舶螺旋桨用。第三组和第四组用于制造机器人，常常另加三个自由度。在不同的制品中，五根轴可以在工件或刀具之间分配。第一分类可以由工件和刀具所承载的轴数以及每根轴在运动链中的功能来划分。另一种分法是据于旋转轴的位置，在工件一边还是在刀具一边。五自由度基于笛卡尔坐标系的机床是：3个移动轴X,Y,Z(通常表述为TTT)和2个旋转运动AB,AC,BC（通常称作RR）。拥有3个旋转轴和2个移动轴的制品并不多见。如果一个轴装夹工件，习惯上不另加东西在这根轴上。由图1五轴机床可记为 X Y A B Z. XYAB轴装夹工件，Z轴装刀具。图3展示的是XYZAB型机床，3个移动轴装夹刀具，2个旋转轴装工件。图3 XYZA B 型机床5.五轴机床工作空间 在定义五轴机床工作空间之前，有必要说明一下刀具工作空间和工件工作空间。刀具工作空间就是通过刀具参考点沿着刀具轨迹生成轴（详见刀具帮助说明）来获得。工件空间也是同样定义的（工作台中心可以被选择为工件参考原点）。这些工作空间可以通过计算切削量来定义。 基于上述定义一些参数量可以定下来，这些参数对比较，选择以及设计不同类型机床都是十分有用的。 图11 G2/G3组中的 R R机床6.选择五轴机床的标准 完全学习好如何为专用机床选择或设计一个五轴机床是不现实的。只有主要标准，这些标准可以用来核实五轴机床的我们加以讨论。6.1 五轴机床的应用应用可以分为位置和轮廓。图12和图13展示了五轴位置机床和用于轮廓机床。6.1.1图12展示了一个多孔以及不同角度有平台的工件。要用一个三轴磨床加工这个工件，一步也无法完成。如果用五轴机床则可以加工。轮廓更多的参数等信息可以在参考文献13中去查看。五轴机床用于加工轮廓的有：（i）叶片类产品，例如空气压缩机的叶片和涡轮机的叶片；（ii）燃料泵的喷嘴；（iii）轮胎的轮廓；（iv）医学假肢，例如人工心脏瓣膜；（v）复杂表面的模具。图12 五轴加工多孔复杂方位角零件 图13 五轴加工复杂轮廓零件6.1.2五轴轮廓图13显示了一个轮廓的例子，5轴，机器的表面形状复杂的，我们需要控制的工具，相对的部分切割过程中的方向。该工具工件每一步方向的改变。数控控制器需要控制，同时在材料去除过程中所有的5轴。关于countouring更多详情，可发现号。 13。轮廓应用五轴是：（一）生产刀片，如压缩机，涡轮机;（2）泵喷嘴燃油;（三）轮胎剖面的;（四）心脏瓣膜的医学假体，如人工;（五）模具制成复杂曲面。6.2轴配置选择轴配置选择的大小和重量的部分是非常重要的配置作为第一标准，设计或选择一个。工件的要求非常沉重的运动链短的工件。也有一个工件偏爱横机表内，使之更方便修复和处理。把灵活性非常沉重的工件在一台旋转轴运动链将增加的方向。可以观察到图。 4，提供一个单一的横向旋转轴进行工件，机器会更加灵活。在大多数情况下，工具进行运动链将保持尽可能短，因为toolspindle驱动器必须同时进行。6.3轴加工的首饰轴首饰加工工件的一个典型的可能是花形图的一部分作为研究。此应用程序是清楚轮廓。该器件将相对比较小的工具集。小直径工具也将需要一个高速主轴。一个水平旋转表将作为经营者很好的选择将有一个良好的部分看法范围（360 ）。所有工件轴载轴作为将是一个很好的选择，因为toolspindle可能是固定的，并提出非常严格的。有20个）方法，使轴可以合并起来，工件运动链（第4.2.1。这里只有两个运