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五轴联动数控 数控加工中非线性误差 五轴联动数控加工非线性误差 五轴联动数控加工 五轴联动加工 的非线性误差 五轴数控加工 五轴数控加工中非线性误差 中非线性误差 加工中的非线性误差

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用改变加工工具方向的方法来减少五轴联动数控加工中的非线性误差,五轴联动数控,数控加工中非线性误差,五轴联动数控加工非线性误差,五轴联动数控加工,五轴联动加工,的非线性误差,五轴数控加工,五轴数控加工中非线性误差,中非线性误差,加工中的非线性误差

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【中文4260字】用改变加工工具方向的方法来减少五轴联动数控加工中的非线性误差摘要五轴联动数控加工通过改变轴在三维空间位置和方向，从而改变刀具的位置，为加工工件表面提供了一种灵活的方法。五轴联动加工通常运用直线来连接待加工的连贯数据点，通过直线插补来生成从起点到终点的指令代码，由于加工过程中轴的旋转运动和直线进给运动是同时进行的，所以实际的运动轨迹是非线性的。曲线部分偏离线性插补部分使每个加工步骤中存在着非线性加工误差。除了线性加工误差，非线性加工误差同样也会影响到工件加工的高精度。在这篇文章中介绍了一套新的系统的方法来解决五轴联动数控加工中存在的非线性误差问题。这套方法是在特定加工运动和加工轨迹下，在不另增加插补点，通过改变加工工具方向来实现。通过处理一系列的工具在加工表面轮廓偏离加工路径的数据表明上述方法能提高加工精度。关键词非线性误差；机构运动；加工运动轨迹；导论在传统的五轴联动加工中，刀具的路径是由三维空间中切削工具的位置数据（CLDATA）来决定的，而这些位置数据是由轴的方向和工具的位置所组成的。位置数据的生成是依据加工表面和加工工具以及加工表面的几何特性,而这些位置数据在特定加工轮廓下又进一步的处理了成数控代码，然后运用直线插补原理将各个数据点用直线相连并生成所需的位置指令。在五轴联动加工中，所有工具轴的方向的确定至少需要一根轴的运动，那么直线运动和旋转运动是同时进行的。如此，改变工具轴的方向产生的旋转动作和直线动作的合成运动效应同样会影响到工具的位置，合成运动使得切削工具连接点会沿着非直线运动。所以，每个加工动作存在的加工误差包括直线部分的近似误差和额外的加工误差，在图1中，用直线连接二个连贯的加工数据点，不论加工是凹面还是凸面（大部分是轴的加工控制点），直线插补沿着直线生成中间位置点。假设设计所需的曲面（凹面或者凸面）。用直线近似地去逼近所设计的曲面而造成线性误差，t，除了线性误差，非线性工具连接点的轨迹偏离直线部分（加工控制点是沿直线进行插补的，所以工具计量长度是连续的，）造成额外的加工误差，如非线性误差n。在图1a中，所需的曲面是凹面，总的误差等于线性误差减去非线性误差，即: total=t-n。那么，非线性误差缩小了总的误差。相反的在图1b中加工的凸面中，总的加工误差是线性误差与非线性误差的和，就扩大了总的误差，即total=t+n (AIGP Post-processor,1996;Liu,1994).。因此，非线性误差严重地阻碍了对高加工精度的要求，例如，在加工螺旋桨表面的边缘就遇到了麻烦，加工表面曲率变化很大，工具从一个加工位置到另一个位置方向变化频繁，方向的频繁变化就是一个典型的非线性误差问题。为了解决五轴联动数控加工中的误差问题，许多研究人员在对生成数控代码中出现的非线性误差问题付出了诸多的努力。一些研究者和后续工作者采用“线性处理”来达到这一目标，“线性处理”基本的功能就是在总的加工误差超出特定公差范围的数控代码中插入加工数据点Takeuchi et al. (1990)插入点沿空间直线平均分布Cho et al. (1993)用于限制最大加工误差的插入数据点应在公差范围内，并且数据点和插入点的设置能使工具顺利地实现线性方向的改变。在智能自动化后续处理概论中(AIGP)(1996)，“线性处理”计算相邻数控代码之间的中间点，然后在数控代码中插入额外的中间数据点。插入点在连续的数控代码中是有效的，除非各连贯的数据点中所有点超出加工公差或插入点多于63个。当代的后续工作者，如Vanguard Custom Post-processor Generator (1996) , the Ominimill Custom Postprocessor(1992),the AIX Numerical Control Post Generator(1996)，在智能自动化后续处理概论都有类似的“线性处理”。在现在的CAD/CAM软件中，Unigraphics(2001) UG /post postprocessors在相邻的数控代码中插入数据点，用一系列的直线来模拟曲线。插入点是数量是由最大允许偏离量和自身动作的方法来决定的。如果拱形和直线的偏离量在循环20次后仍然超出特定的公差极限，就需要采取新的处理办法。以上所讨论的“线性处理”通过插入额外的加工数据点能熟练的操作数控代码。尽管生成的数控代码能够满足加工的要求，但是它们在连续或改变加工方向中仍存在着大量不平衡的空间数据点。因此，“线性处理”会带来一下问题：在加工具有复杂外部轮廓的表面时，工具位置从一个加工点变化到另一个点时，变化量不宜太小，以避免冲击或随机转动。大量加工叶轮的螺旋桨的过程中，常运用“线性处理”来减少非线性误差。在数控代码中插入许多数据点导致工具方向变化剧烈而位置的变化却接近于0，结果使得旋转运动迅速变化，进给率无限增大，从而损坏工件。插入的加工数据点在沿着曲面加工时也会出现进给不连续是问题。而插入的额外加工数据点，在加速和减速的动作会导致空间部分的不平衡，因此，每个部分的进给率不能达到理想的要求，反而使已加工的表面不平滑，总体加工时间过长。此外，插入的工具方向连续变化使得粗糙度增大。而工具方向的线性变化却能保证良好的表面质量，但是插入的工具方向不精确也会使工具方向变化不呈线性。由于存在非线性误差问题，五轴联动加工动作的轨迹线通常是曲线，多轴之间同时做旋转和转化动作使得合成的轨迹是非线性的，因此，直线插补技术不适用于与曲线和非线性完全重合的路径。一种解决的方案就是设计新的插补方法。Liang et al.(2002)出版的 结合三维直线和圆的插补技术。这种新的三维直线和圆曲线的插补方法能用事先设定的偏离曲线路径来远程操控旋转运动，因此非线性误差是能够计算的，五轴联动加工动作是与加工数据点相关的。换而言之，非线性动作的轨迹取决于生成路线中工具的方向误差和非线性误差。因此，另一种解决非线性误差问题的方法是依据需要生成的工具路径，消除工件与工具之间的干涉，减少加工误差。在工具路径生成的问题上，CAD/CAM有一揽子生产方法用于对不同表面要求的技术。CLDATA,1996;Unigraphics, 1990)和研究者. Huang and Oliver (1992) . Bedi et al.(1997) 出版的五轴联动数控加工中的直线和曲线处理原则Liu (1995)出版的 基于不同的几何特性和分析几何特性下，对侧边铣削路径的生成。Morishge et al.(1999)出版的五轴联动数控加工中工具路径的生成。它运用空间轮廓方法来避免工具位置和方向之间的冲突。他们研究的都是依据加工表面和加工工具的几何特性生成工具路径，而不考虑特定的加工运动。因此，生成的工具路径基本上都会阻碍对加工高精度的要求，尤其是在五轴联动加工中方向的生成上。因此，真正的加工路线实际上是不包括生成的非线性路径。为了保证加工精度，加工工具方向的变化不仅取决于加工表面的几何特性，还取决于特定的加工运动。在这篇文章中介绍了一种能系统的解决五轴联动数控加工中存在的非线性问题的方法，它能优化在特定加工运动和加工运动轨迹的工具位置数据，在工具和工件之间没有干涉的基础上，通过改变工具方向的办法来减少非线性误差。比起现在的智能自动化后续处理的办法，用实例的软件程序来实现上述方法更能提高加工精度。工具路径生成办法在实际中，工具联系点的轨迹决定了加工中的非线性误差，而这些点的轨迹是旋转加工运动的参数，而每个点的轨迹是由旋转加工运动变化的极限公差确定的，以保证工具和工件之间没有干涉。此外，由于旋转加工变化参数取决于工具方向的变化，所以，非线性误差问题是由工具决定的。上述办法是在旋转加工参数允许的范围下引入加工运动轨迹的模型，通过改变运动工具相关的方向来解决非线性问题。需要强调的是加工运动特性和加工轨迹都是在特定的条件下。因此，工具位置数据点的数据是用一组组的加工参数来转化为改变的方向参数。以上介绍的方法从引入特定机械反向类比运动模型开始，将工具位置点数据转化成数控代码，在一系列的加工参数中，实际的加工轨迹是由采用的特定的加工运动轨迹模型所决定的，所以，加工误差是可以测定的。线性误差是切削表面的局部曲率和加工距离的函数，从加工立方齿形的曲率函数能够确定表面局部的曲率，那么，在每个加工动作中产生的线性误差就能够通过局部曲率和相邻的工具连接点计算出来。我们已知的线性误差，而非线性允许误差的确定是不同于线性误差的，不能用指定的加工公差。用加工轨迹模型和线性方程能够确定最大的偏移量。在工具连接点非线性曲率和直线间取采样点，得到的弦的最大偏移量就是最大的非线性误差，如果非线性误差超出允许范围，前面提到的，可用改变加工方向的参数来实现。改变参数是在工具原来的水平下，在控制矢量上加大或减少一个小角度来增加或减少旋转参数，然后计算新参数所产生的非线性误差，看它是否超出非线性误差范围。因此，在可调范围内，反复调整加工中加工旋转参数使非线性误差达到允许的范围是解决非线性误差和改变非线性误差的一个准则。最后，改变旋转加工的参数，工具方向要与前面步骤中转化的加工运动保持一致。为了避免加工工具与工件之间的干涉，所调整的角度不能大于原来旋转角度的一半，并且加工工具方向的变化也不能大于原方向角度的一半。相比现在的“线性处理”，在不考虑干涉问题的前提下，在工具方向中插入额外的数据点将导致线性变化或旋转平均角度的变化。另外，在原先的方法上改变加工旋转角度产生的误差是角度变化的一半，这样就能使在指定的工具方向范围内保证不会发生干涉。用下列法则能够解决工具位置数据变化的问题。工具路径变化准则1. 用特定的反向加工运动模型将原有是工具位置数据转变成相应的数控加工代码。2. 引入加工运动轨迹模型确定相应的控制连接点。3. 在工具位置数据基础上用立方函数计算所需是工具路径和加工路径中加工点的曲率Kf。4. 用Faux and Pratt(1979)的配方法计算出线性误差：t =1/8 Kf (s)2这里，Kf。表示步骤3得到的曲率，s表示步骤2得到连贯的控制连接点之间的距离。5. 计算出非线性误差允许的变化值：a,n=公差-t.6. 确定点在直线运动和加工轨迹中最大的弦的偏移量；7. 用步骤6中的点计算出最大的非线性误差，max；8. 修正旋转角度的变化：如果maxa,n，增加或减少非线性误差Bm 和Cm以满足(n1-a,n)0;9. 在步骤8的旋转角度修正基础上，计算出加工数控代码的Bm,i+1 和Cm,i+1Bm,i+1= Bm,iBmCm,i+1=Cm,iCm 这里Bm,i, Cm,i是当前旋转修正变量，Bm,i+1 Cm,i+1是下步的旋转修正变量，Bm Cm是旋转角度的修正量，+或是由下步旋转修正变量的增加或减少确定的。10. 在所给定的加工运动模型，修改数控加工代码以优化工具方向。计算机辅助制造系统工具路径的生成是基于加工表面的几何特性预先处理工具方向的改变是基于加工运动和运动轨迹处理通过处理方法将工具位置数据点转化成数控加工代码结论文章介绍用新的路径生成办法来解决五轴联动数控加工中的误差问题，这种方法对于工具偏离线性的修改在工具旋转动作允许的变化范围内，减少非线性误差来保证加工公差。比较现在智能自动化后续处理的”线性处理”, 这种新的方法引入特定加工运动和加工运动轨迹模型，不插入额外的工具位置点下保证了加工精度。利用软件程序能够将这种方法运用到五轴联动铣削中心，以扩大五轴联动加工中心的加工范围。A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC MachiningABSTRACTIn the machining of sculptured surfaces，five-axis CNC machine tools provide more flexibility to realize the cutter position as its axis orientation spatially changes .Conventional five-axis machining uses straight line segments to connect consecutive machining data points ,and uses linear interpolation to generate command signals for positions between end points，Due to five-axis simultaneous and coupled rotary and linear movements, the actual machining motion trajectory is a non-linear path. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in a non-linearity machining error in each machining step. These non-linearity errors, in addition to linearity error, commonly create obstacles to the assurance of high machining precision. In this paper, a novel methodology for solving the non-linearity errors problem in five-axis CNC machining is presented. The propose method is based on the machine type-specific kinematics and the machining motion trajectory. Non-linearity errors are reduced by modifying the cutter orientations without inserting additional machining data points. An off-line processing of a set of tool path data for machining a sculptured surface illustrates that the proposed method increases machining precision. KeywordNon-linear error; Machine kinematics; Machining motion trajectory. INTRODUCTIONIn conventional five-axis machining, a tool path, represented by the cutter locations data (CLDATA), consists of the spatially varying cutter positions and its axis orientations. These CLDATA are generated based solely on the geometrical properties of the machined surfaces and the cutter. These CLDATA are further processed into NC-codes which is specific to a particular machine configuration. Linear interpolation is then used to generate the required commands for positions along line segment connecting the machining data points. The simultaneous linear and rotary movements are involved in five-axis machining since ever new cutter axis orientation requires the motion at least one other axis. There are also coupling effects of the cutter axis will affect the position of the cutter. These simultaneous and coupled movements cause the cutter contract point (CC point) to move in a non-linear manner. As a result, the machining error in each motion step is made up of not only the linear segmentation approximation error but also an additional machining error. As shown in figure 1 for machining is either a concave surface or a convex surface, a line segment is used to connect two consecutive machining data points (the spindle chunk is the machine control point MCP). Linear interpolation generate intermediate positions along the line segment. The desire surface is design curve(either concave or convex). The linear segment approximates to design curve resulting in the linearity error,t. Apart from the linearity error . The non-linear CC point trajectory deviates from the straight line segment (the cutter gage length is constant and MCP is interpolated along the line segment)result in an additional machining error, referred to as the non-linearity error, n. In the case that the desire surface is concave(see figure 1a), the total machining error is difference of the non-linearity error and the linearity error : total=t-n. The non-linearity error, in this case, compensate for the total machining error(AIGP Post-processor,1996;Liu,1994). On the contrary, for the machining of convex surface as shown in figure 1b, the non-linearity error adds onto the linearity error and enlarges the machining error: total=t+n(AIGP Post-processor,1996;Liu,1994). figure1. The multi-axis CNC machining errorConsequently the non-linearity error have caused difficulties for ensuring ultra-precision machining requirements. In the machining of airfoil surface, for example, the machining of the contour surface of airfoil to the edges is problematic. The surface curvature on these area changes abruptly, and thus the cutter orientation varies inconsistently from one cutter to the next. These abrupt cutter orientation variations inconsistently from one cutter location to the next .These abrupt cutter orientation are a typical non-linearity error problem.In order to solve the five-axis CNC machining error problem, efforts have been made to treat non-linearity errors in generate NC codes. Some researchers and postprocessor producers used “linearization processes” for this purpose. The basic function of “linearization processes ” are inserting machining data points between NC codes where the total machining error is out of the specified tolerance range. Takeuchi et al. (1990) inserted points by subdividing the line segment with equally space d interval. Cho et al. (1993) inserted data points by limiting the maximum machining error within the line interval from the start point to the inserted point to be the tolerance. And, both of them set the cutter orientations varying linearly in successive positions. In the Automation Intelligence Generalization Postprocessor (AIGP)(1996), a “linearization processes ” calculates the middle point (MP) between adjacent NC-codes and inserts the MP as an additional data in the NC code. The insertion can be performed further between the consecutive NC-coded until either all points are within the machining tolerance or until a maximum of 63 points are inserted between the consecutive data point. The current post-processors, such as the Vanguard Custom Post-processor Generator (1996) , the Ominimill Custom Postprocessor(1992),the AIX Numerical Control Post Generator(1996) , are all having the similar “linearization processes ” as in the AIGP. In the current CAD/CAM software. Unigraphics(2001), the UG /post postprocessors inserts data points between adjacent NC-codes, thereby simulating a straight line with series of small curves. The number of the inserted points is determined based on the maximum allowable deviation and an iteration method is used to segment the move. In the extreme case, namely after looping 20 times, if the deviation between the segmented arcs and the line are still out of the specified tolerance limit, the process is aborted. “linearization processes ” discussed above manipulate NC-codes by inserting extra machining data points. Although the produced NC-codes satisfy the machining requirement, they may contain dense sets of non-equally spaced data with constant or linearly varying cutter orientation. Consequently, the linearization process has raised the following problems. In the machining of complex contour surface, the cutter orientation varies from one cutter location to the next. The cutter position changes in this case can not be too small since the machine will produce either jerk motion or random rotary movements. As in an industrial procedure of machining airfoil surface of an impeller, a linearization process was used to reduce the non-linearity errors. Many data points were inserted between a pair of NC-codes. The insertion of many data points caused the cutter position change to be nearly equal to zero while the cutter orientation changed abruptly. As a consequence, the machine rotary movements were rapid with infinite feedrate. Random rotary movements resulted and the workpiece was damaged. The insertion of machining data points can also cause non-constant federate along the cutting curve. The insertion of additional data results in non-equally spaced segment, while acceleration and deceleration steps are required for each segment. Thus, the feederate varies in each segment and may never reach the desired value. The result of varying feederate causes a nonsmooth surface finish and the unreachable feedrate increases overall machining time. In addition, the insertion of constant cutter orientation variation also causes severe roughness around the end points along the surface. Linearly inaccurately since the change in cutter orientation is not necessarily linear. The non-linearity error problem arises from the fact that five-axis machining motion trajectories are non-linear curve segments. The simultaneous and coupled rotary and translation movements generate the non-linearity motion trajectory, and the linear interpolation technique is not capable to curve fit the nonlinear path. One solution to is to design new interpolation methods. Liang et al.(2002)presented a combine 3D linear and circular (3D L&C) interpolation technique. The new 3D L&C interpolation can on-line drive the rotation movement pivot along a pre-designed 3D curve path, so that the CC point motion trajectory is a via a straight line connecting machining data points, thus, the non-linearity error can be eliminated. Five-axis machining movements are kinematically related to the cutter location data. In other word, the non-linear motion trajectory depends on the cutter orientation changes and non-linearity errors are related to the tool path generation. Thus, another solution to the non-linearity error problem can be approached from tool path(CLDATA)generation with the requirements that the machining errors are minimized and there is no interference between the workpiece and the cutter. In tool path generation, various techniques for different surface representations have been used by the CAD/CAM package producers (CLDATA,1996;Unigraphics, 1990)and researchers. Huang and Oliver (1992) . Bedi et al.(1997) presented a principle curvature alignment technique for five-axis machining using a toroidal shaped tool. Liu (1995)presented the single point offset and the double point offset algorithms for five-axis flank milling tool path generation based on differential geometry and analytical geometry. Morishge et al.(1999)presented a tool path generation method for five-axis CNC machining, which applies the C-space(a 3D configuration space)to determine collision-free cutter positions and its orientation. These research work on tool path generation are all based exclusively on the geometric of the machined surfaces and the cutter, without considering the machining-specific machining kinematics. As a result, the generated tool paths(the machining NC-codes transformed from these CLDATA)commonly cause obstacles for meeting the ultra-precision machining requirements, particularly for the cutter orientation generation in five-axis machining. Thus, the problem with present off-line tool path generation approaches is that the real machining kinematics is not directly incorporated. To ensure machining precision, cutter orientation generation should be based not only on the geometry of the machined surfaces but also on the machine type-specific kinematics. In this paper, a novel methodology for solving the non-linearity error problem in five-axis machining is presented. The method optimizes the CLDATA based on machine-specific kinematics and machining motion trajectory, whereby the cutter orientations are modified to reduce the non-linearity errors provided that there is no interference between the cutter and the workpiece. A software program for implementing the proposed method is presented. As an application of proposed method, a case study is presented, which shows an increase in machining precision as compared with those processed by the existing AIGPs method.PROPOSED TOOL PATH GENERATION METHODThe machining non-linearity errors depend upon the actual CC point trajectory, since a CC point trajectory is a function of the machine rotary variables, each actual CC point trajectory can be manipulated within the tolerance limit by changing the machine rotary variables, provided that there is no interference between the workpiece and the cutter. Further more, because of the machine rotary variables are kinematically related to the cutter orientation changes, the non-linearity error problem can be approached by manipulating cutter orientations. To proposed method reduces the non-linearity errors by determining the acceptable machine rotary variables employing the machine motion trajectory model, and by modifying the cutter orientation through the machine kinematic relations. It must be emphasized that the machine kinematic properties and motion trajectory are machine type-specific. Hence, the modification of CLDATA has to be carried out in teams of machine variables and subsequent use of the kinematic transformation to determine the modified CLDATA.The procedure of the proposed method starts with the transformation of the CLDATA to machining NC-codes by employing the machine-type specific inverse kinematic model. In teams of machine variables, the actual machining motion trajectory is determined by using the specific machine motion trajectory model. Then, the machining errors are determined. The linearity error is a function of surface local curvature on the cutting curve and the step-forward distance. From the cubic spline cutting curve function, the surface local curvature can be determined. The linearity error for each move then can be computed from the adjacent CC point data and the surface local curvature. By knowing the linearity error, the allowable non-linearity error can be determined as the difference of the linearity error from the specified machining tolerance. Using the machine trajectory model and the line segment equation, the maximum deviation can be determined. By taking sample points on both of the CC non-linear curve and the line segments, the maximum chord deviation is the maximum non-linearity error. In the steps where the maximum non-linearity error exceeds the allowable non-linearity error, the proposed method modifies the machine rotary variable changes. The modification is carried out by increasing/decreasing a machine rotary variable variation a small angle in the plane containing the two original cutter vectors, and by adding/subtracting the angle to the original machine rotary variables. The new rotary variables are then used to calculate the resultant non-linearity error, which in turn is compared again with the allowable non-linearity error. Thus, by using the difference between the allowable non-linearity error and modified non-linearity error as the criterion, the acceptable machine rotary variables can be determined iteratively. Finally, from the modified machine rotary variables, the corresponding cutter orientations can be determined by performing the forward kinematic transformation. In order to avoid interference between the workpiece and the cutter, the rotary angles were adjusted such that the angle changes are less than half of the orientation angle changes are less than one half of the original cutter orientation changes. Comparing to the existing “linearization processes ”, the additional data points are inserted with cutter orientations either varying linearly or as the average variation(i.e., the one half)of the rotary angle change, and the interference problem is not considered. Alternatively, the modified machine rotary variables angle change from the proposed method are smaller than one half of angel change, which thus ensures the corresponding cutter orientation are within the range such that no interference occurs. For a set of CLDATA, the modification procedure can be performed by using the following algorithm.TOOL PATH MODIFICATION ALGORITHM1. Transform the initial CLDATA, into its corresponding machining NC-codes by using the specific machine inverse kinematic model;2. Determine the CC point coordinates by employing the machine motion trajectory model;3. Compute the desire tool path by using cubic spline function based on the CLDATA and calculate the local surface curvatures Kf of the tool path at the machining points;4. Computer the linearity error by using the formula given by Faux and Pratt(1979):t =1/8 Kf (s)2where, Kf-the surface local curvature determined from step(3); s-the segment length between consecutive CC points from step(2).5. Compute the allowable value of the non-linearity error: a,n=tolerance-t.6. Determined the points on the straight line segment and on the machine motion trajectory segment that correspond to the maximum chordal deviation.7. Compute the maximum non-linearity error , max, using the points from step(6);8. Modify the machine rotary angle change ifmaxa,n ,that is, increase or decr