外文翻译-向5轴计算机数控加工刀具轨迹的实时生成和控制

1、附录A：英文资料Real-time generation and control of cutter pathfor 5-axis CNC machiningAbstract：This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact pat

2、h interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are

3、developed, respectively.Keywords：5-axis machining; Cutter path generation; interpolator; Error compensation; Feedrate adaptation1Introduction5-axis computer numerical controlled () machine tools are widely used in machining dies, molds, turbine blades, and aerospace parts. These parts usually have c

4、omplex geometry and are represented by parametric or free-form surfaces. As compared to 3-axis machining, the 5-axis machining offers many advantages such as higher productivity and better machining quality. In 5-axis machining, the orientation of the tool can be determined by the two additional deg

5、rees of freedom so as to obtain efficient cutter paths. To achieve high efficiency and interference-free cutter path planning, many algorithms for determination of the cutter path direction and interval and detection and avoidance of the cutter interference have been developed. Based on these algori

6、thms that are implemented in a computer-aided manufacturing () system, the cutter paths that comprise cutter location and orientation trajectories are determined and represented by a series of linear or spline motion commands.To conduct on-line 5-axis machining, the motion commands generated by the

7、CAM system are loaded to the machine that adopts a real-time interpolator. The interpolator can convert the cutter path to motion trajectories of the five separate axes in order to coordinate their motion in 5-axis machining. Many interpolators for different types of curves have been developed. Amon

8、g them the linear and the spline interpolators are the most popular in parametric surface machining. It was reported by Yang and Kong that linear interpolator method requires a significantly large file for the linear motion commands and results in federate fluctuation along the cutter path. For this

9、 reason, only the spline interpolator method is considered here. Being accompanied by the coefficients of the spline curve, a preset federate or velocity command is also fed to the machine. Based on the spline coefficients and the federate requirement, the interpolator conducts a real-time interpola

10、tion or generation of the cutter path. In theory, the parametric spline is converted to be a function of time. Notice that in addition to the path interpolator, the 5-axis interpolator must conduct a conversion between the workpiece coordinate basis() and the machine coordinate basis () in which the

11、 cutter path and the practical machine movement are defined, respectively.In the existing approach, the data fed to the interpolator are the path and the velocity for the cutter location (). The cutter location denotes the center of the tool bottom and is usually not the location where the cutting t

12、akes place. In contrast, the cutter contact () location, which denotes the intersection point of the cutter and the sculptured aurface, is our main concern. For this reason, the current approach cannot achieve high efficiency and quality because both the generation and the control of the cutter path

13、 are based on the path, rather than the path. In cutter path generation, a constant velocity is usually assigned along the path. According to the surface curvature, a constant velocity will correspond to a varying velocity. Because the velocity is significantly related to the machining quality, the

14、existing approach may result in low efficiency and/or low quality machining. In real-time cutter path control, the traditional system constructs servo scheme that focuses on eliminating the positioning errors along each driving axes. The servo control scheme can be modified so as to eliminate the pa

15、th error. However, our main concern is the deviation error from the path, which directly relates to the machined error on the sculptured surface. Accordingly, current scheme cannot achieve high efficiency in control of the machining accuracy.In this paper a new method for real-time cutter path gener

16、ation for 5-axis machining is presented. In the proposed method, composite cutter data comprising the cutter orientation, the location, the velocity and the surface normal are fed to the CNC interpolator, which consists of real-time algorithms for path interpolation, the cutter offsetting, and the c

17、oordinate conversion. With the proposed method, the cutter path is generated so as to satisfy the desired velocity along the path on the sculptured surface. In addition to the cutter path generation, the proposed system constructs a global feedback loop to augment the performance in cutter path cont

18、rol. The loop is closed by the interpolator, which can monitor the practical cutter path so as to compensate for the path deviation error or to reduce it through on-line adaptation of the velocity (this means to slow down the machining as the path error is too large).In this paper, we first discuss

19、the existing approach to cutter path generation and control and the corresponding problems. Then, a new approach is proposed. Simulation examples are provided to support the adequacy of the proposed approach. Finally, concluding remarks are given.Tool path description and machine tool motionThe cutt

20、er tools commonly used in 5-axis machining are endmill cutters. The cutters end can be flat, spherical, or filleted. Fig.1 shows a typical filleted endmill cutter with a tool radius of and a corner radius of . Notice that the cutter for =0 refers to a flat endmill and the cutter for = refers to a sp

21、herical endmill. denotes the cutter contact () point that is the intersection of the cutter and the sculptured surface, S.N is the unit normal vector to the surface on and denote the path direction and the path interval (or scallop) direction, respectively. and are the cutter location () point and t

22、he tool orientation vector, respectively. Traditionally, the cutter orientation () is set to a fixed angle off the surface principle normal () during machining. However, the angle formed between and can be altered so as to avoid cutter interference. Geometrically, this angle can be further decompose

23、d into an inclination angle () and a tilt angle () so that the endmill is rotated about with along B and then with along . Based on the surface and cutter path geometry ( and ), the data are defined. Through some mathematical manipulation, we can have the cutter offsetting algorithm as follows. （1）

24、(2 )Based on the above algorithm, the cutter location and orientation trajectories are determined and represented by linear or spline motion commands.Because to utilize linear motion commands requires a significantly large file and results in velocity fluctuation along the cutter path, we utilize pa

25、rametric spline functions to represent the cutter path here. In practice, we need three spline functions for the cutter location () and two spline functions for the tool orientation ().Notice that the three components of can be reduced to two Euler angles. In this paper, the Euler angles, and, are d

26、efined so that the tool axis is originally in the z-direction, then rotates with along x-axis, and finally rotates with along y-axis. Accordingly, we have （3）At the stage, the tool path or is defined in a coordinate frame, , which is fixed to the part or the work table on the machine tool . At the d

27、esired tool path with respect to work table (). Let denote a machine coordinate frame that is attached to a fixed point on the machine tool. Assume that the cutter location is a fixed point in (this means that the 5 degrees of freedom are all applied on the work table). To conduct the 5-axis machini

28、ng, a coordinate conversion algorithm from to must be implemented in the system. This coordinate conversion,usually called an inverse kinematics transformation, obviously depends on the machine tool structure. A typical machine tool structure that is utilized in this paper. In the structure, the too

29、l is fixed and the work table is driven by three sliding and two rotating axes. and are the positions along the three sliding axes. is the rotation angle along x-axis through A( =（),a fixed point on the lower table. is the rotation angle along the y-axis through , a fixed point on the work table. No

30、tice that for simplicity, we let be the origin of the work coordinate frame, . Let (a fixed point with respect to ) and assume that the center of the upper table is right on the top of the lower table, i.e. With the above definitions, we can formulate the kinematics equations that relate the machine

31、 tool motionto the cutter pathas follows. （4a）or (4b) , and (5a)or (5b)Existing approach and problemsAn existing /scheme for 5-axis machining is shown in Fig.1. Through the operation of the system, the data, which include the spline functions for the path and a preset velocity (), are fed to the mac

32、hine that adopts a spline interpolator. On line the 5-axis machining, the interpolator conducts a cutter path interpolation (i.e. finer segmentation at the sampling rate) and an inverse kinematics conversion so as to generate the reference motion commands for the five separate axes. Traditionally, e

33、ach axis forms a control loop to minimize the axial position error. Through the practical machine tool motion and cutting process, the sculptured surface is produced. Notice that the machined surface is produced by the practical path, , and the inclination and tilt angles, and .parametric surface (S

34、)machinedsurface (S*)due topractical CCpath ()inclination angle ()tilt angle ()cutteroffsettingpathschedulinginterpolatoraxialcontrolleraxialcontrolleraxialdriveaxialdrivemachineandprocessdrivesoutput (P)CAMAMCNCdrivesreference (R)path(C,N,T)CL path velocity ()Fig.1. An existing scheme for tool path

35、 generation and controlReal-time tool path generationAs stated above, in order to generate the desired tool path, the interpolator executes algorithms for path interpolation and coordinate conversion. Let the spline functions for the cutter path be expressed by （6）Where is the spatial parameter alon

36、g the spline. Notice that the first three components represent a parametric spline curve for the path and the last two angles represent the tool orientation. The task of interpolation algorithm is to assign a distribution of the sampled tool locations following the parametric curve with the desired

37、velocity, which is usually constant during a recursive approach, which is described by the following equation: (7)Where is the sampling period. and are values of at time and , respectively. and are the first and second derivatives of with respect to at time , i.e. (8)By substituting the spatial para

38、meter into the parametric functions in Eq. (6), the reference position commands at each sampling instant can be calculated, recursively.Instead of the above algorithm, other interpolation algorithms can be utilized. However, the above interpolation algorithm is adopted in the following analysis. In

39、addition to the interpolation algorithm, an inverse kinematics algorithm that refers to Eq.(5a), (5b) and (5c) is needed to implemented in the interpolator. Consequently, we can get the reference commands to the five axial drives as (5c)where the superscript r means that they are reference position.

40、 Notice that when referring to the practical output positions, the superscript r is replaced by p.With the above interpolator method, the cutter location will follow the path at assigned velocity. However, those that should of concern are the path and the velocity (that is denoted by in the followin

41、g). There is a schematic description for the path and the path. As can be seen, the location where the cutting takes place is along the path, rather than the path. According to the path curvature as well as the tool geometry, the relationship between the velocity and thevelocity is nonlinear. Becaus

42、e it is the velocity that is related to the machining quality, we cannot achieve a high efficiency and uniform quality machining with the existing approach. In practice, the machining may be low quality and/or low efficient .5-axis motion controlAccording to software and hardware deficiencies, the p

43、ractical machine tool motion is always not perfect, i.e. . The traditional control scheme constructs five separate control loops to eliminate the axial position errors,In practice, decoupled controls of the five axial error components does necessarily correspond to an efficient control of the path e

44、rror along the cutter path. This is because the control effort is conduction in , not in that the concerned tool path (with respect to the table) is defined. In order words, to minimize does not mean to minimize In our previous research, a servo control scheme was proposed so as to achieve a direct

45、and efficient reduction of the path error,.It should be emphasized that in real machining, the practical path, rather than the path, is our main concern, because it results directly in the machined surface. It shows two cases of practical 5-axis motion results. denote the desired point, tool orienta

46、tion and point, while and denote the practical ones for Case 1 and 2,respectively. Let the two cases have the same tool orientation but different and points ( and ). Although the first case results in a smaller error than the second case , it causes a larger error .This means that reduction of the p

47、ath error does not correspond to reduction of the path error. Consequently, the existing 5-axis machine tool control scheme cannot achieve highly efficient control of the path error that is directly related to machined errors. Notice that in addition to the path error, the errors for inclination and

48、 tilt angles may also cause machined errors. However, their effects are not important, unless a tool orientation near to the gouging condition is assigned.附录B：英文资料翻译面向5轴计算机数控加工刀具轨迹的实时生成和控制摘要：本篇论文描述了一种关于面向5轴计算机数控加工刀具轨迹的实时生成和控制应用软件的新的方法。刀具轨迹的生成方法包含了面向刀具间轨迹插补、刀具偏置以及坐标变换的实时运算法则。另外，一个球形的反馈链被计算机数控插补器封闭使得实

49、际刀具轨迹生成的控制精确度增加。一个面向控制链的误差补偿运算法则和进给率适应运算法则分别得到了提高。关键词：5轴加工；刀具轨迹生成；计算机数控插补器；误差补偿；进给率适应介绍5轴计算机控制系统工具被广泛用于加工冲模、模子、涡轮叶片和航空宇宙的部件。这些部件通常有着复杂的几何结构，并且用参变量或是自由形式曲面描述出来。相比3轴加工，5轴加工有很多的优势，比如：较高效的生产力和较好的加工品质。在5轴加工中，刀具的方向可以由两个附加级别的自由度改变，以获得高效的刀具轨迹。为了达到高效和自由互相作用的刀具轨迹的目标，很多关于刀具轨迹方向、时间间隔、探测和刀具间冲突的避让的运算法则都作了改进。基于这些用

50、计算机辅助制造系统实现的运算法则，包含了刀具位置和方向轨迹的刀具路径通过一连串的直线或齿条运行指令确定和描述出来。为了指导在线5轴加工，由计算机辅助制造系统生成的运行命令采用了实时插补器装载在计算机数控机器上。计算机数控插补器为了调整它们在5轴加工中的运作可以将刀具轨迹转换成5个独立轴的运行轨道。很多用于不同类型曲线的插补器都得到了提高。在它们当中直线或齿条运行指令是在参变量曲面加工中最流行的。据杨和孔报道直线插补器方法需要一个明显的大的直线运行指令文档，从而导致沿着刀具轨迹的频繁进给。由于这个原因，只有齿条插补器方法被考虑在内。跟随曲线图表系数，一个事先调整的进给或速度指令也用来实现计算机数

51、控加工。基于曲线系数和进给需要，插补器指导着一个刀具轨迹实时的插补或生成。理论上，变化的曲线被转换成一个时间的功能。考虑到附加的轨迹插补器，5轴插补器必须在工件调整原理和机器调整原理之间指导一个转换来分别定义刀具轨迹和实际机器运作。在现有的方法中，计算机数控插补器的数据是靠刀具位置的轨迹和速率给出的。刀具定位在刀具底部的中心而通常不是刀具切入的位置。相比之下，刀具触点位置是道具和零件表面的交叉点，这是需要我们注意的。鉴于这个原因，通用的方法不能达到高效和高品质的标准，因为刀具轨迹的生成和控制是建立在刀具的定位而不是在刀具的触点。在刀具轨迹生成过程中，通常沿着刀具定位路线赋给它一个恒定不变的刀具

52、定位速率。根据表面曲率，一个恒定不变的刀具定位速率将相应于一个变动的刀具触点速率。因为刀具触点速率很明显地与加工质量相关联，现有的方法可能导致低效率或低品质的加工。在实时刀具轨迹控制中，传统的计算机数控系统专注于消除沿着各个驱动轴的定位误差建立了伺服方案。伺服控制方案可以被更改用来消除刀具定位轨迹误差。然而，我们的主要注意力放在来自刀具触点轨迹的背离误差上，它与零件表面的机器误差直接相关。总的来说，通用的计算机数控方案在加工精确度的控制方面不能达到高效的要求。此篇论文我们提出了一种新的用于实现面向5轴加工刀具轨迹生成的方法。在这个合理的方法中，包含了刀具方向、刀具触点位置、刀具触点速率和表面的

53、复合刀具数据一般用于进给计算机数控插补器，它包括了面向刀具触点轨迹的实时运算法则，刀具偏置和坐标变换。有了合理的方法，刀具路径生成满足了在零件表面沿着刀具触点轨迹的期望速率。除了刀具路径的生成，被提议的计算机数控系统构造了一个球形的反馈链来讨论关于刀具路径控制的运作。这个链是由插补器封闭，可以监控实际的刀具轨迹使得补偿背离误差或是通过在线更改减少刀具触点速率的误差（也就是当刀具触点误差太大的时候减慢加工的进程）。在这篇论文中，我们首先要讨论的是现有的关于刀具轨迹生成、控制以及相应问题的解决方法。之后，找出一个较为合理的方案。我们用相似的例子来证明这个方案的合理性。最后，得出结论。2. 刀具轨迹

54、的描述和机器刀具的运作 通常被用来做5轴加工的刀具是磨刀。刀的末端是平的，球形的，内圆的。典型的工件半径为和角半径为的内圆磨刀。注意到=0的刀具末端是平的，=所指的末端是球形的。C表示的是刀具和工件表面交叉点的刀具触点。分别表示了在表面上的单位矢量,表示了刀具触点轨迹方向和轨迹间隔(或扇贝)的方向。和分别指的是刀具定位点和轨迹方向矢量。传统上，刀具方向在加工过程中被设置在表面法线的一个定角上。然而，这个在和之间形成的角为了避免刀具间相互作用可以被更改。几何学上，这个角可以被延伸分解成一个倾角和一个倾角使得刀具末端沿着B后带着沿着绕着C旋转角度。在表面和刀具轨迹几何学的基础上，定义了刀具的定位数

55、据。通过一些数学变换，我们可以得到以下的刀具偏置的运算法则。 （1） (2 )在以上运算法则的基础上，刀具定位和方向轨道用直线和曲线运行指令定义和描述。由于利用直线运行指令需要一个显著的大的刀具定位文件，将导致沿着刀具轨迹的速度变化，在这里我们利用参变量直线功能描述刀具轨迹。在目前，我们需要三种面向刀具定位的直线功能和两种面向工具方向的直线功能。注意到的三个成分可以被分解为两个欧拉角。在这篇论文中，欧拉角被定义为和，工件轴起初是在Z轴方向，然后沿着X轴旋转角度，最后沿着Y轴旋转角度。从而，我们得到： （3） 在计算机辅助制造阶段，工件轨迹是定义在一同等的结构中，在工作母机上是固定到那部分或工作桌的。在计算机数控加工阶段，工作台由三个变化的和两个旋转的轴驱动着，跟随工作台的运作得到期望的工件轨迹。表示放在机器工具一个固定点的一台机器的并列结构。假定刀具位置是上的一个固定的点（这表示着5个自由度在工作台上被应用了）。为了指导5轴加工，一个从 到的坐标变换运算法则必须在计算机数控系统中被实现。这个坐标变换经常被称作旋转运动学转换，很明显的依赖于机器工具的结构。有一种是一个本轮文中用到的典型的机器工具结构。在这个结构中，刀具被固定并且工作台被三个变化的和两个旋转的轴驱动着。和是三个可变化的轴。是通过工作台较低的A点沿着x轴的旋转角。是通过工作台的B点沿着y