NC machining of free-form Kriging surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is introduced when the free-form surface is modeled parametrically by free-form surface Kriging. The flexibility of dual Kriging that easily defines the intersection of the surfaces with a set of parallel planes and Cartesian method are combined to generate the tool-paths automatically. The presented algorithm can simultaneously generate the tool path with a predefined machining accuracy and remove gougings along the tool path. The algorithms are validated by three experiments in rough and finish machining and the results prove its reliability. Since Kriging is based on the interpolation of data points, the proposed algorithm can be used for reverse engineering applications. The system was executed on a standard micro-computer and the software was structured to offer a library of machining functions for endusers.     

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.     

A local smoothing interpolation method for short line segments to realize continuous motion of tool axis acceleration

In traditional processing, a large number of G01 blocks are adopted to discretize free surface or curve for NC machining. But, the continuity of G01 line segments is only C⁰, which may lead to discontinuity of axis acceleration, resulting in the frequent fluctuation of tool motion at the junctions in high-speed machining, deteriorating the quality of work piece, and reducing processing efficiency. To solve this problem, a local smoothing interpolation method is proposed in this paper. At first, the analytic relationship between the continuity of the trajectory and the continuity of the axes motion is first systematically described by formula. Based on this relationship, a local smoothing algorithm and a feed-rate scheduling method are proposed to generate a C² continuous tool path motion with axis-acceleration continuity. The local smoothing algorithm smoothes the corners of G01 blocks by the cubic B-spline according to the cornering error tolerance specified by the user. After the feed rate at critical points of smoothed tool path was determined by a modified bidirectional scanning algorithm by considering constrains of chord error and kinematic property, an iterative S-shape feed rate scheduling is employed to minimize residual distance caused by round of time while ensuring the continuity of feed rate and acceleration. Then, a look-ahead interpolation strategy combined with smoothing algorithm and feed-rate scheduling as mentioned is proposed for real-time interpolation of short line segments. At last, simulations are conducted to verify the effectiveness of the proposed methods. Compared with the traditional G01 interpolation, it can significantly improve the processing efficiency and shorten the processing time within error tolerance.     

Precise bi-arc curve fitting algorithm for machining an aspheric surface

With the rapid development of the information/image system and aero-space industries, high quality optic aspheric surface lenses play an increasingly important role for completion of the functionalities. Aspheric lenses are non-spherical surfaces having rotation symmetry about the lens axis. The aspheric lens has various shapes according to its application and often requires tens nanometer order form accuracy since surface roughness and form accuracy play essential roles in the functional performance of the optical products. Interpolation of the aspherical surface path must precisely meet the allowable tolerance. Linear interpolation of the aspheric surface path for CNC machining generates an enormous amount of NC code to satisfy the extremely small tolerance, and produces scallops on the machined surface due to the acceleration and deceleration of the tool during every linear motion. Alternatively, interpolations with bi-arcs are used. In this paper, in order to minimize the error induced by the cutting tool path and to shorten the calculation time of interpolation, a precise -arc interpolation method is proposed. The developed algorithm of bi-arc interpolation meets the given tolerance precisely. This is guaranteed by an analytical proof and error maps. Another advantage is its ability to calculate about five times faster than the existing arc interpolation, since iterative calculations for the maximum error can be omitted. The developed algorithm has been used for the precise aspheric machining.     

Tool path optimization in postprocessor of five-axis machine tools

Generally, tool path is generated in a computer-aided manufacturing software considering only the geometry of machining parts. It is converted into numerical control (NC) codes in the postprocessor based on the particular machine kinematics. For some special types of five-axis machine tools, e.g., non-orthogonal five-axis machine tools, the generated NC codes may produce unqualified parts because of the existence of the non-linear error. Conventional commercialized postprocessors usually do not have the function of non-linear error checking. Observing that the tool path is a non-smooth trajectory full of corners and a series of connected line segments, cubic spline interpolation is applied to smooth the tool path at regular points in this study. The cutter tip center points are computed by the cubic spine interpolation, while the cutter posture vectors are obtained via linear interpolation. At the splines (for regular points) and the line segments (feature points), more points are chosen to be converted into NC codes to reduce the non-linear error, which is called data densification. Using the cubic spline to smooth the tool path and the data densification to reduce the non-linear error, a novel tool path optimization algorithm in postprocessor is proposed. Experiments were carried out on an inclined rotary spindle axis non-orthogonal five-axis machine tool. It shows that the proposed tool path optimization provides improved accuracy and surface quality.     

机器人砂带磨削路径优化插补算法

为解决经典泰勒插补算法生成的加工轨迹在加工中产生的过切问题,在机器人打磨离线编程系统上进行了机器人打磨路径插补算法的研究。通过对比各种路径刀位点生成方法,提出一种改进的泰勒插补算法。该算法在加工路径曲率变化较大的区域刀位点自适应地致密,避免了弓高误差超差引起的过切;当加工路径较为平滑时,刀位点稀疏,保证加工效率。通过设计优化算法与经典算法的对比磨削试验,验证了该插补算法的有效性。     

Optimal Archimedes’ spiral interpolation for cutter path generation in NC machining of noncircular contours

In NC machining of noncircular contours with a rotation table, the cutter is fed along a straight line intersecting perpendicularly the rotation axis of the work piece. In this situation, the cutter path usually consists of a series of Archimedes’ spiral segments. This paper proposes an optimal interpolation approach of Archimedes’ spiral segments to generate the cutter path for machining noncircular contours. The number of segments for the cutter path resulted from the approach is the fewest under the condition that the interpolation accuracy completely satisfies the specified limit value. It has been also evidenced that the profile error of the machined contours corresponding to the cutter path is perfectly controlled within the specified interpolation accuracy limit. The effectiveness of the proposed approach has been sufficiently confirmed by applying it to machining a disc cam and an algebraic spiral type of scroll wrap.     

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。     

NC Machining of Freeform Pockets with Arbitrary Wall Geometry Using a Grid-Based Navigation Approach

A tool path must be determined in an efficient manner to generate NC (numerical control) code for machining. This is particularly important when machining freeform pockets with arbitrary wall geometry on a three-axis CNC machine. In this paper, a grid-based 3D navigation algorithm for generating NC tool-path data for both linear interpolation and a combination of linear and circular interpolation is presented for three-axis CNC milling of general pockets with sculptured bottom surfaces. The pocket surface is discretised by defining a grid and the navigation algorithm plans the tool motion. The grid size and the cutter diameter are chosen so that a predefined tolerance for surface roughness is satisfied. The grid-based navigation algorithm is simulated graphically and verified experimentally.     

A study on motion of machine tools’ hexapod table on freeform surfaces with circular interpolation

Accuracy is greatly affected by nonlinear motion of hexapods. This need is more obvious when these mechanisms are used in machining environments where precision and surface qualities are of critical importance. In this paper, comprehensive algorithm for hexapod tool path programming is developed. Using C#.Net, this algorithm is developed based on circular motion and rotation of the table which has the capability of checking nonlinear error and keeping it in a controlled limit as well. Improved Tustin algorithm is used for interpolating circular path. To evaluate the accuracy of the developed algorithm on a freeform surface, a turbine blade is scanned, and its CAD model is developed. Taking zigzag strategies, movement on turbine blade surface is approximated with smaller circles using the algorithm presented in this paper. The output accuracy resulted from interpolation algorithm for passing on turbine blade surface is studied in SimMechanics of MATLAB software. Using Total Station camera, motion path of two turbine blades with different radius curves on the hexapod table is experimentally obtained. Finally, it can be stated that the developed algorithm based on circular interpolation has the capabilities of motion on freeform curves.     

数控加工中基于自由曲面表面特性的刀具路径安排

目前CNC上的轨迹控制功能仍主要是直线和圆弧插补,因此当加工自由曲面时,大多只能采用直线或圆弧逼近算法来对曲线进行逼近处理。针对数控加工的实际需求,现在数控系统技术人员对数控机床插补器进行研究并开发出了许多曲线和曲面插补功能。基于曲线插补,在保持进给速度尽可能恒定的条件下,对刀位路径和刀位速度进行离线的曲线拟合,以便于得到用于数控加工的刀位文件。这种方法能有效解决进给速度的波动问题,并能有效压缩刀位文件。为此,提出几种算法来拟合刀位路径和刀位速度轮廓曲线。曲线和曲面插补在数控代码数据量和逼近误差方面都有较大的改善。     

Correcting and compressing interpolation algorithm for free-form surface machining

The existing interpolation algorithm cannot meet the need of high-speed and high-accuracy machining of a free-form surface. So this paper proposed a correcting and compressing interpolation algorithm. Depending on the distance and angle evaluated from the adjacent command points, the machining path of free form can be divided into two machining types. For those regions where the accurate figure is critical such as corners, the convention linear interpolation is performed exactly between the adjacent command points. For those regions having a large radius of curvature where the smooth figure is critical, firstly, the interior point selection method based on circle transition is derived to reduce the tolerance between the machining path and the original surface; secondly, the interior point correction method based on the least-square method is proposed to reduce the calculation error and round-off error in the interior point and estimate the first- and second-order derivative vectors of the interior point; thirdly, the shape-defining point is selected by the bend direction of the machining path and fitted to a quintic spline curve which has the C2 continuity; fourthly, the fitting accuracy controlling method is proposed to ensure the machining accuracy; lastly, the curve interpolation is performed on the fitted smooth curve. Machining tests carried out on a vertical machining center show that the proposed algorithm can improve the machining efficiency and machining quality of a free-form surface.     

An algorithm for generating spiral tool path of shoe last with varying pitch

In shoe-last high-speed numerical machining, the key step is to generate CNC machining tool path by data sampled from the shoe last rapidly and accurately. By analyzing the characteristics of helical line and the model of the shoe last expressed in cylindrical-polar coordination system, an algorithm for generating spiral tool path of shoe last with varying pitch was presented. By sample data interpolation, mathematic models with different pitch of helical line were built, and the tool paths with different machining parameters were determined. The effectiveness is verified by the emulation and experimental results represented in the paper.     

Self-adjustment computing method for time-partition interpolation in motion trajectory control of CNC machine tools

For time-partition interpolation in computer numerical control of the motion trajectory of a machine tool, the trajectory in a sampling cycle is approximated by a line segment from the current position of the tool to another on the expected trajectory; and locating the terminal of the line is the goal of the interpolation. In this paper, a self-adjustment computing method applicable to any explicit curve type is proposed. With the method, the terminal of the linear moving path in a cycle is first estimated by the motion information in the previous cycle, then adjusted according to the ratio of the desired moving distance to the computed linear path length. The result of the computation is fairly accurate, and it can be further enhanced with more adjustments performed in a sampling cycle, which is demonstrated in the simulation results. Furthermore, an adaptive feedrate adjustment algorithm is also introduced to enable the proposed method to control the trajectory contour errors.     

Curve interpolation with variable feedrate for surface requirement

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This function, called a NURBS interpolation, adopts a feedrate optimizing strategy based on both the geometrical information of the curved path and dynamic properties such as the curvature of the curve, the allowable acceleration and the time constant. However, in the case of a finish cut using a ball-end mill, the curve interpolator needs to take the machining process into account for improved surface roughness, while reducing the polishing time. This surface roughness on high-speed machining is theoretically defined by the feed per tooth and the pickfeed at the given radius of the tool. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A curve interpolation algorithm is proposed for generating particular feedrate commands that are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented. A feedrate scheme that depends on the inclination angle has important potential application in part finishes consistent with prescribed surface roughness. The results show that the proposed algorithm is potentially useful for roughness-controlled machining of curved surface products.     

Three-Dimensional Implicit Curve Interpolation

An approach to 3D implicit curve interpolation in computer numerical systems (CNC) is presented. A 3D implicit curve is the intersection of two implicit surfaces. Geometric entities of 3D implicit curves are related to motion entities along the curve. The results are then used to develop real-time 3D implicit curve interpolation. An improved interpolation scheme has been proposed to augment the initial interpolation scheme to eliminate the cumulative point deviations. Simulations of implicit curve interpolation have been carried out to verify the effectiveness of the proposed algorithm. They also demonstrate that under typical machining conditions, the interpolation error for the improved scheme is well within the accuracy requirements of typical machines. The example has an application potential for tool-path interpolation when tool paths are obtained by intersecting an implicit design surface by drive cylinders. These show that the proposed algorithm is potentially useful for the machining of implicit surfaces.     

螺旋曲面加工刀位轨迹数值算法研究与应用

为了提高复杂螺旋面的加工精度,对其刀位轨迹算法进行研究,提出了基于最小有向距离的刀位轨迹数值计算方法。建立了刀具与工件曲面的三维数值几何模型,并通过坐标变换矩阵来建立与实际加工情况一致的数值计算模型。采用空间离散化思想将刀具与工件两空间曲面的最小有向距离的求解问题简化为一个二维求解问题,保证了求解效率和精度。根据阿基米德插补曲线原理,建立了刀位轨迹的数值计算方法。实例加工结果证明,基于该方法得到的刀位轨迹编制的数控加工程序能够加工出满足精度要求的螺旋面。     

基于数控高次曲线插补的研究与应用

数控机床加工的零件轮廓一般由直线、圆弧组成,也有一些非圆曲线轮廓例如高次曲线、列表曲线、列表曲面等,但都可以用直线或圆弧去逼近。本文主要论述了插补算法对数控系统的影响和插补算法的工作流程,并对高次曲线的插补原理进行分析与研究,最后推导出高次曲线插补的递推公式,绘制插补逻辑图,其递推公式和插补逻辑图同样适用于其它高次曲线。     

一种适应插补离散化特性的微线段直接插补算法

由于插补的离散化特性,微线段内很难实现梯形速度控制,并存在最后一个插补点与线段终点不重合问题。提出一种新的算法,以连续微线段为研究对象,从两端向中间进行线段端点速度前瞻,然后在预定点进行速度衔接处理。速度前瞻通过正向规划和反向验证使拐点速度达到最大,从而规划出微线段端点速度。根据微线段的端点速度和长度调用基于变插补周期的线段内速度规划,完成整个速度处理。仿真结果表明:该算法能够实现离散插补过程的梯形加减速并消除了插补残余长度。     

隐曲线的线性和旋转插补

基于数控五轴刀具运动分析,提出了旋转插补的概念,给出了旋转插补的相关定义,在此基础上提出了隐曲线的线性和旋转插补原理和方法,并进一步提出了改进的插补方法。