基于定向距离理论的五轴加工刀具轨迹规划算法

针对环形刀五轴加工自由曲面的残留误差问题,在传统等残留高度算法的基础上,提出了一种基于定向距离理论的等最大残留高度刀具轨迹规划算法。首先根据微分几何理论计算已知刀触点的初始侧向行距,并在侧向行距方向进行偏置得到相邻刀触点;然后以基于定向距离理论的残高误差计算模型对相邻刀触点间的实际残高值进行计算;最后通过迭代计算规划出等最大残留高度的相邻刀具轨迹。如此循环,从而获得整个曲面的刀具轨迹。实验结果表明,相对于商用软件MasterCAM9.0,该算法在充分保证曲面加工质量的同时最大限度地减小了刀具轨迹的总长度,从而提高了加工效率。     

五轴NC加工干涉检查与避免算法研究

利用刀具刃口回转面在两刀位点间运动形成的包络面方程与CAD模型面求交来实现五轴NC加工中干涉的判断与检验，依据检验结果对干涉进行处理，从而避免实际加工时干涉的发生。该方法考虑了刀具运动路径上全部刀位点的刀具与工件的位置关系，因而能够实现刀位轨迹全过程的干涉检验，避免了加工时对局部型面的破坏，有利于改善加工零件的表面质量。实际计算验证了该方法的可行性和实用性，具有一定的理论和实际意义。     

Geometrical Error Analysis and Control for 5-axis Machining of Large sculptured surfaces

One of the important tasks in five-axis machining of large sculptured surfaces is to control and reduce the machined errors. This paper presents the methods to control geometrical errors based on the establishment of the link between geometrical errors and the parameters of tool path planning. Nonlinear errors, which are the majority of geometrical errors during five-axis machining, are is strictly analysed and formulated. An adaptive step length method is proposed to control effectively the cutter contact path error. The measures to reduce the scallop error in machining of the large sculptured surfaces are discussed also. With the combination of this research with CAM software, both large Kaplan and Francis hydroturbine blades have been successfully machined. It shows that the machined errors can be controlled effectively and the machining efficiency can be improved in the machining of the large sculptured surfaces by the proposed methods.     

A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC Machining

In 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 the 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 proposed 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.     

五轴NC加工中刀具运动包络面的计算

在机械加工过程中,刀具的铣削在加工体表面形成沟槽,对该沟槽型面的数字化描述是精确计算表面加工残差、判断加工干涉的理论基础,进而可实现表面加工精度评估与控制及加工轨迹全过程的精确规划计算。沟槽型面是刀具刃口回转面在空间运动形成的包络面的一部分,因此推导包络面的解析方程成为解决问题的关键。结合五轴加工机床的运动特点,通过建立加工刀具刃口回转面的数学模型,推导出五轴NC加工刀具运动刃口回转面包络的解析方程。数字仿真的结果与实际完全一致,验证了方法的正确性和有效性,具有较强的理论性和实用价值。     

Reduction of geometry-based errors in five-axis machining through enhanced 5D interpolation

Geometry-based errors constitute a special category of CAM-originated machining inaccuracies that significantly influence the precision of five-axis surface machining operations. Geometry-based errors reflect the inability of the cutter to accurately trace a prescribed 3D tool path in five-axis machining. Their magnitude constitutes an overlapped effect of the adopted interpolation scheme, cutter, and surface geometries, as well as kinematics of the five-axis machine tool, assumed free of errors by the CAM software. Although the presence of these errors is inherent in the current configuration of five-axis computer numerically controlled machining systems, little efforts were made so far towards their reduction. In this regard, the present study has investigated the magnitude of geometry-based errors as generated by various 5D interpolation schemes. These enhanced interpolation functions were determined by enforcing better approximations of the ideal machine control coordinate (MCC) trajectory as calculated in five-axis machine tool’s joint space. By comparing the geometry-based errors generated by the enhanced 5D interpolation schemes with linear interpolation baseline, it was found that significant error reductions will be obtained when synchronized 5D quadratic functions are used to approximate the ideal MCC curve in joint space. Moreover, the parametric synchronization between rotational and translational machine tool motions represents an essential requirement for limitation of the amount of geometry-based errors.     

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.     

复杂曲面五坐标数控加工刀具轨迹的规划算法

提出了复杂曲面五坐标数控加工刀具轨迹的规划算法。该算法在保证刀具不与被加工曲面发生干涉的基础上 ,使得刀具扫描面与被加工曲面在刀触点处切平面上每个方向的曲率相匹配 ,由此规划的等残留高度刀具轨迹能改善曲面加工精度和加工效率     

五轴微段平滑插补算法

在五轴加工编程中,计算机辅助制造系统对曲面加工通常采用以折代曲,采用大量的微小G01直线段来加工曲面,在曲率半径较大的工件表面会出现明显折痕,严重影响工件表面的加工质量。为提高五轴数控加工工件的表面质量,提出一种五轴微段平滑插补算法。该算法考虑五轴加工中刀位数据的量纲差异,根据相邻数据点间的线性轴长度、线性轴的夹角和旋转轴角度变化量识别五轴数控加工程序中非连续微段和连续微段加工区域。对非连续微段加工区域按照原始直线段和旋转轴直接插补,从而保证加工精度。对连续微段加工区域,先通过五维变量获取节点参数,采用最小二乘法对指令点在允许的精度范围内进行修正;对修正后的指令点采用4点构造法计算二阶切矢,根据连续微段的指令点修正值,节点参数值和对应的二阶切矢值获取二阶连续的三次样条曲线;在二阶连续平滑的曲线上进行实时插补计算,控制机床进行五轴加工。试验结果表明:通过提出的五轴微段平滑压缩算法拟合后的路径要更加接近原始的曲面模型,平滑处理过的实际工件加工表面也要优于未进行处理的工件加工表面,提高了五轴自由曲面的表面质量。     

基于等残留高度的自由曲面加工刀具轨迹规划

对于曲面加工来说,效率和精度是相互矛盾的2个方面。加工时,用等残留高度法生成刀具轨迹,选择待加工曲面最长的1条边界线作为第1条加工的轨迹线,通过控制相邻刀具接触点的距离,使刀具轨迹间的残留高度均匀一致,依据刀具半径和允许的残留高度,迭代生成另一条刀具轨迹线。等残留高度法生成的刀具路径间的残留高度均为设定值,所生成的刀位点数最少,刀具路径长度最短。采用牛顿法作为等残留高度法的刀位点搜索方法,得到等残留高度刀具轨迹的生成过程。     

An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.     

五轴加工刀具路径生成的有效加工域规划方法

为复杂曲面五轴数控加工的刀具路径优化生成问题提出一种新的有效加工域规划方法。在对工件被加工表面和刀具的几何特征进行分析的基础上,得到在加工件表面上各处的最优可加工域宽度和刀具切削方向。通过采用离散采样和插值计算生成优化的有效加工域集,得到最优化的初始刀具路径;同时建立一种迭代搜索算法,用于解决最优加工域的选择规划问题。采用此算法生成优化的后续刀具路径,使得有效加工域最终完全覆盖整个被加工表面。给出的示例显示相对于传统的五轴加工刀具路径生成算法,有效加工域规划方法可以减少刀具路径的总长度和加工时间,得到更为优化的刀具路径和更好的工件表面质量,因此有效加工域规划方法可以被用于五轴数控加工实践以降低加工成本和提高产品质量。     

汽车玻璃钢化风栅成形器五轴加工刀轴矢量插值

为了解决汽车玻璃钢化风栅成形器五轴加工时刀轴矢量频繁变换造成冲击或发生干涉等问题，提出一种刀轴矢量插值方法。根据被加工曲面的几何形状和误差要求确定刀触点，根据被加工曲面的微分几何性质确定刀轴矢量的后跟角和摆转角。在已确定刀触点处的刀轴矢量的基础上，采用空间矢量光滑插值方法获得一系列中间位置刀轴矢量使刀轴变化较均匀。以货车前挡风玻璃钢化风栅成形器的一个拼镶块工作表面和风栅孔五轴NC加工为例进行仿真。结果表明，该刀轴矢量光顺方法可以避免刀轴方向频繁变换，同时也可有效地提高加工精度。     

NURBS曲面的参数化离散及其在数控加工干涉避免中的应用

复杂曲面加工中，如何快速、有效地筛选出特殊曲面点以进行刀具干涉判断是实现无干涉刀具路径生成的关键。通过推导有理Bezier曲面的参数离散算法并结合NURBS曲面可转化为有理Bezier曲面的性质，实现了NURBS曲面基于参数的离散。该离散结果保留了离散曲面点与曲面参数域的一一对应关系，通过切削点的参数信息可快速筛选出少量需进行干涉校验的离散曲面点，从而有效简化了刀具干涉检测计算。实例分析表明，该算法能在保证曲面离散精度的前提下提高无干涉刀具路径规划的效率。     

五轴数控加工中旋转轴运动引起的非线性误差分析及控制

五轴数控(Computer numerical control,CNC)加工中,刀具路径规划阶段与实际加工阶段对旋转轴运动采用的插补方式存在差异,其中刀具路径规划阶段是根据零件的几何信息进行插补,而实际加工中则根据机床信息进行插补,这种差异将引起原理性加工误差。针对五轴数控加工中旋转轴的运动,分析采用线性插补方式控制两个旋转轴进行加工时刀具姿态变化引起的原理性误差,进一步研究不同加工情况下由此产生的在垂直于走刀方向的平面内的非线性误差。通过分析旋转轴运动过程中线性插补引起的刀轴偏差角,证明刀具在相邻两刀位点运动过程的中间时刻处刀轴偏差角取得最大值,并得到由该最大值的显式表达式,在此基础上分析最大偏差角的影响因素。提出通过限制相邻两刀位点间刀轴夹角来控制此非线性误差的方法,并给出实例验证。     

Effects of inclination angles on geometrical features of machined surface in five-axis milling

With the development of manufacturing technology, five-axis milling has been one of the most important solution strategies in machining field. To deepen the understanding of multi-axis processing and improve the application level of the technology, the current work was carried out. This paper investigated the effects of tilt and lead angle on the scallop height, surface roughness, surface topography, and surface damages in five-axis ball-end milling process. Both geometrical analysis and experiment research are conducted to investigate the scallop height after five-axis milling, and variation of the surface roughness and surface topography with tool inclination angle obtained from the experiments was analyzed. Surface damages under the different inclination angles were also observed and analyzed with optical profiler. Several conclusions are made as follows. The inclination angles of the ball-end mill have no effect on the scallop height when only the spherical part of the cutter participates in the cutting process according to the geometrical analysis. Surface roughness with regard to tilt angles presents symmetrical characteristic around 0°. Surface texture feature, especially the texture direction, is closely related with the tool posture. The surface concave pits, convex marks, microscopic cracks, and spot corrosions are mainly the damage forms of the machined surface. More surface blemishes appeared when small inclination angles are adopted in cutting. As a result, the recommendatory inclination angle values for inclination angle are proposed. A better understanding of the five-axis machining process would be given by the detailed analysis of generation reason of the machined surface features, and the results could provide support for process parameter optimization.     

A cutter orientation modification method for five-axis ball-end machining with kinematic constraints

Cutter orientation modification with kinematic constraints is very necessary and effective for five-axis machining especially machining at high speed. It is very helpful for achieving a smooth cutter motion and keeping the process steady. Therefore, a cutter orientation adjustment method is proposed to obtain an optimized tool path which makes best use of the kinematic characteristics of angular feed for five-axis machining. For the given five-axis cutter location path and the feed profile of cutter tip point both expressed by b-spline formats with the same parameterization, the analytic relations of angular feed, angular feed acceleration, and jerk with respect to the geometric and tangential feed parameters of the cutter tip trajectory are first derived. Then, the conditional inequalities of these kinematic constraints used for orientation adjustment are built. Subsequently, the determination method of feasible cutter orientation and detailed algorithm of orientation adjustment are given. Finally, illustrated examples are conducted to validate the proposed orientation adjustment method. The results show that the developed method is effective and can be applied to optimize geometrically complex five-axis tool path by taking the angular feed, angular feed acceleration, and jerk into account.     

A CL surface deformation approach for constant scallop height tool path generation from triangular mesh

In this paper, we present a cutter location (CL) surface deformation approach for constant scallop height tool path generation from triangular mesh. The triangular mesh model of the stereo lithography (STL) format is offset to the CL surface and then deformed in accordance with the deformation vectors, which are computed by the slope and the curvature of the CL surface. In addition, the tool path, which is computed by slicing the deformed CL surface, is inversely deformed by those same deformation vectors to a tool path with a constant scallop height. The proposed method is implemented, and a tool path is generated and tested by simulation and by numerical control (NC) machining. The scallop height was found to be constant over the entire machined surface, demonstrating much better quality than that of mesh slicing, under the same constraints for machining time.     

An improved calculation method for cutting contact point and tool orientation analysis according to the CC points

Tool path generation is an important step of five-axis NC milling which plays an important role in parametric surfaces and free-form surfaces manufacturing. Cutter contacting (CC) point calculation is considered as a basic procedure of tool path generation. The step lengths formed by cutter contacting points have an effect on the chord error along feed direction. In traditional calculation method for CC point discretization, the segments connected by adjacent CC points distribute on both sides of the theoretical tool path curve. This situation magnifies the cutting error to some extent and enlarges the expected margin if the surface demands polishing or grinding. Aiming at this issue, this paper proposes an improved constant chord error method for CC point calculation. In the proposed method, the CC points lay on the theoretical tool path curve when the tool path curve is concave and lay on the chord error offset curve when is convex, which ensures the segments connected by the adjacent CC points distribute on one side of design surface, the side of the scallop height between tool paths. Therefore, the actual margin of polishing or grinding can be reduced. The influence of inflection points is also considered in this method to avoid accuracy deterioration caused by the long steps occurring near the inflection points. In part processing, local gouging and global collision must be avoided in tool orientation determination. This paper analyzes tool orientations with no rear gouging and no collision based on the calculated CC points. The novel discretization method for CC points is calculated on a single blade model, and the tool orientations are generated on an open integral impeller. A DMG DMU50 machine tool and a Hexagon three coordinates measuring machine are applied for experiments and measurements. The results show that, the CC point discretization method proposed in this paper offers many advantages over the traditional constant chord error method and commercial software, such as quantity of points, curve fitting, no overcut, and residual margin distributing. At last, blade and tunnel of the open integral impeller with safety tool orientation is machined and verified on the DMG DMU50 machine tool.     

曲面笔式加工刀位点曲线的实时拟合

针对曲面高速高精度加工问题,给出一种刀位点轨迹实时生成算法。该方法的实现包括曲面上离散刀触点的生成和基于三次非均匀B样条曲线的刀位点轨迹实时高精度拟合两部分。第一部分,由导动曲线和刀触点轨迹的运动学关系,通过计算导动曲线参数,间接得到投影在曲面上的离散刀触点;第二部分,通过合理参数化、构建模长因子等实现刀位点参数曲线的分段实时拟合。仿真实例表明该算法简单易于编程,曲线拟合精度高,适用于自由曲面笔式加工中刀具路径计算与生成,从而满足复杂曲面高性能数控加工需求。