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英文翻譯 【附】英文原文 翻譯文獻(xiàn)：Five-axis milling machine tool kinematic chain design and analysis 作者：E.L.J. Bohez 文獻(xiàn)出處：International Journal of Machine Tools & Manufacture 42 (2002) 505–520 翻譯頁(yè)數(shù)： Five-axis milling machine tool kinematic chain design and analysis 1. Introduction The main design specifications of a machine tool can be deduced from the following principles: ● The kinematics should provide sufficient flexibility in orientation and position of tool and part. ● Orientation and positioning with the highest possible speed. ● Orientation and positioning with the highest possible accuracy. ● 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 axes carry 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 tools The 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 positioning Fig. 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 contouring Fig. 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 selection The 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 jewelry A 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 toolspindle could 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 T
T
T
R
R
kinematic chain shown in Fig. 15. Case two will be a R
R
T
T
T
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 300×250×200 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 (R
R
T
T
T
). 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 selection Two machines with the same kinematic diagram (T
T
R
R
T) 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 T
T
R
R
T 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.Conclusion Theoretically 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. 翻譯題名：Five-axis milling machine tool kinematic chain design and analysis 期刊與作者：E.L.J. Bohez 出版社： International Journal of Machine Tools & Manufacture 42 (2002) 505–520 ● 英文譯文 摘要： 現(xiàn)如今五軸數(shù)控加工中心已經(jīng)非常普及。大部分機(jī)床的運(yùn)動(dòng)學(xué)分析都 基于笛卡爾直角坐標(biāo)系。本文羅列了現(xiàn)有的概念設(shè)計(jì)與實(shí)際應(yīng)用，這些從理論上都基于自由度的綜合。一些有用的參數(shù)都有所規(guī)定，比如工件使用系數(shù)，機(jī)床空間效率，方向空間搜索以及方向角等。每一種概念，它的優(yōu)缺點(diǎn)都有所分析。選擇的標(biāo)準(zhǔn)及機(jī)器參數(shù)設(shè)置的標(biāo)準(zhǔn)都給出來(lái)了。據(jù)于Stewart平臺(tái)的新概念最近行業(yè)內(nèi)已有介紹并作簡(jiǎn)短討論。 1.緒論 設(shè)計(jì)一臺(tái)數(shù)控機(jī)床主要要遵循以下規(guī)則： 1，刀具和工件在空間方向上要有足夠的靈活性。 2，方向和位置的改變要盡可能的快。 3，方向和位置的改變要盡可能的準(zhǔn)確。 4，刀具和工件快速變、換。 5，環(huán)保 6，切削材料速度快 一臺(tái)數(shù)控機(jī)床的軸的數(shù)目通常取決于其自由度數(shù)目或者獨(dú)立控制運(yùn)動(dòng)的導(dǎo)軌數(shù)目。國(guó)際標(biāo)準(zhǔn)委員會(huì)推薦通過(guò)右手笛卡兒坐標(biāo)系來(lái)命名坐標(biāo)軸，刀具相應(yīng)的為Z軸。一個(gè)三軸銑床有三條導(dǎo)軌，X,Y,Z向，它們可用來(lái)在長(zhǎng)度范圍內(nèi)可以在任意位置移動(dòng)。加工過(guò)程中刀具軸的位置始終不變。這就限制了刀具相對(duì)于工件在方向上變化的靈活性，并且導(dǎo)致許多偏差的出現(xiàn)。為了盡可能的提高刀具相對(duì)于工件的靈活性，無(wú)需重啟，必須要加入多個(gè)自由度。對(duì)于傳統(tǒng)三軸機(jī)床來(lái)說(shuō)這可以通過(guò)提供旋轉(zhuǎn)滑臺(tái)來(lái)實(shí)現(xiàn)。圖1給出了一個(gè)五軸銑床的例子。 圖1 五軸數(shù)控機(jī)床 1.運(yùn)動(dòng)鏈圖表 通過(guò)制作機(jī)器的運(yùn)動(dòng)鏈圖表對(duì)于機(jī)器的分析來(lái)說(shuō)十分有用。通過(guò)運(yùn)動(dòng)簡(jiǎn)圖可知兩組軸可以迅速的區(qū)分開(kāi)：工件裝夾軸和刀具軸。圖2給出了圖1.五軸機(jī)床的運(yùn)動(dòng)鏈簡(jiǎn)圖。由圖上可以看出工件由四根軸承載，刀具僅在一根軸上。這個(gè)五軸機(jī)床與兩工位操作機(jī)器人很相似，一個(gè)機(jī)器人夾住工件，另一個(gè)夾住刀具。為了獲得刀具工件方向上的最大自由，五個(gè)自由度已是最低要求，這就意味著工件和刀具可以在任意角度位置相對(duì)定位。最低需求的軸數(shù)也可以通過(guò)剛體運(yùn)動(dòng)學(xué)的方法來(lái)分析。兩個(gè)剛體在空間確定相對(duì)位置，每個(gè)剛體需要6個(gè)到12個(gè)自由度。然而由于任意的移動(dòng)或轉(zhuǎn)動(dòng)并不改變相對(duì)位置就允許將自由度減少到6.兩個(gè)剛體之間的距離通過(guò)刀具軌跡來(lái)描述，并且允許去掉一個(gè)額外的自由度，結(jié)果也就是5個(gè)自由度。 圖2 運(yùn)動(dòng)鏈圖 2.參考文獻(xiàn) 最早（1970年）到目前并且仍就有參考價(jià)值的對(duì)五軸數(shù)控銑床的介紹之一是由 Baughman提出的并清楚的闡述了它的應(yīng)用（附錄1有他的介紹）。APT語(yǔ)言隨后成為唯一的五軸輪廓加工的編程語(yǔ)言之一。后處理階段的問(wèn)題也在數(shù)控發(fā)展的早期由Sim清楚的表述出來(lái)（附錄2有對(duì)他的介紹），并且大部分問(wèn)題到現(xiàn)在仍然有效。Boyd（詳見(jiàn)附錄3）也是最早引進(jìn)數(shù)控機(jī)床的先驅(qū)之一。Beziers的書(shū)（見(jiàn)附錄4）也是非常有用的介紹。Held（見(jiàn)附錄5）在他的小型銑削加工的書(shū)里對(duì)多軸機(jī)床也有非常簡(jiǎn)短但啟發(fā)性的定義。目前一篇適用于解決五軸數(shù)控機(jī)床工作空間計(jì)算的文章，通過(guò)使用Denawit-Hartenberg發(fā)表并由 Abdel-Malek and Othman（見(jiàn)附錄6）改進(jìn)的算法 應(yīng)用于多弧段切削。許多對(duì)機(jī)床的類型和概念設(shè)計(jì)，這些可以被應(yīng)用于五軸機(jī)床，Ref都有討論（見(jiàn)附錄8）.關(guān)于對(duì)刀具路徑生成的技巧和新需求由B.K. Choi et al給出（見(jiàn)附錄9）。工件與刀具的圖像模擬也是研究的熱點(diǎn)并且可以在Ref（見(jiàn)附錄10）的書(shū)是一個(gè)好的入門(mén)讀物。 3.五軸機(jī)床運(yùn)動(dòng)結(jié)構(gòu)的分類 從R軸（旋轉(zhuǎn)軸）和T軸（移動(dòng)軸）劃分大致可以分為四大部分：（i）3個(gè)移動(dòng)軸和2個(gè)轉(zhuǎn)動(dòng)軸；（ii）2個(gè)T軸和3個(gè)R軸；（