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。     

Variable Feedrate CNC Interpolation for Planar Implicit Curves

The machining of planar implicit curves is common in computer numerical control (CNC) machining. It is usually carried out through approximating these curves as segments of straight line/circular arc for CNC interpolation. This paper considers real-time variable feedrate interpolation of planar implicit curves. Geometric entities of planar implicit curves were related to motion entities along the curve. The results were then used to develop real-time variable feedrate schemes for geometry-dependent feedrate and time-varying feedrate interp-olation in general. Detailed schemes have been worked out for the cases of varying the feedrate for constant contour error and for initial acceleration/final deceleration. Examples have been provided to demonstrate how these schemes can be used in combination to enhance the efficiency of machining. They demonstrate how the feedrate for curve interpolation can be varied according to feedrate and feed-acceleration constraintson the machine tool and contour error constraint on the machined product.     

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.     

样条曲线插补速度规划算法的研究

设计了一种适合多种样条曲线（三次样条曲线,Bezier曲线和B样条曲线）插补算法,通过速度控制前瞻缓冲区设置,在保证加工精度的基础上,实现了系统在样条曲线插补过程中加减速处理,改善了插补速度曲线,并满足了机床加减速性能要求。     

Real-time P-H curve CNC interpolators for high speed cornering

In this paper, real-time Pythagorean hodograph (P-H) curve CNC interpolators are used for high speed corner machining. There are large contouring errors around sharp corners when low-bandwidth servo controllers (such as P-PI control) are used. In order to decrease the amount of the cornering errors, an improved interpolation method is proposed. The first deceleration phase of motion and the over-corner P-H curve constructed for regions with sharp corners are devised by quadratic and constant velocity interpolation algorithms, respectively. The geometric parameters of the over-corner P-H curve and the feed rate along the modified tool path are computed by pattern search algorithm in order to reduce the maximum cornering error. The proposed interpolation algorithm is implemented for symmetrical and unsymmetrical corners. The results of simulation, such as the cornering error and the total cornering time, are compared with previously published methods. It has been observed that the developed over-corner P-H approach can substantially reduce the amount of cornering error.     

新型并联机床数控系统插补算法的研究

提出一种用于新型并联机床的粗、精插补策略和算法 ,粗插补采用直接对加工曲面进行插补的方法。以NURBS曲线为例 ,运用合理计算方法推导出粗插补计算公式 ,并对粗、精插补进行了误差分析。插补实例结果表明 ,该插补算法具有恒速进给、加工表面轮廓误差易于控制等特点     

Simultaneous 3D machining with real-time NURBS interpolation

Increasing demand on precision machining using computerized numerical control (CNC) machines have necessitated that the tool move not only with the smallest possible position error but also with smoothly varying feedrates in 3-dimensional (3D) space. This paper presents the simultaneous 3D machining process investigated using a retrofitted PC-NC milling machine. To achieve the simultaneous 3-axis motions, a new precision interpolation algorithm for 3D Non-Uniform Rational B-Spline (NURBS) curve is proposed. With this accurate and efficient algorithm for the generation of complex 3D shapes, a real-time NURBS interpolator was developed using a PC and the simultaneous 3D machining was accomplished satisfactorily.     

曲线的三参数路径规划车削插补算法研究

为了保证数控加工中复杂曲线零件的车削加工精度,在普通二参数车削加工的基础上,提出了一种三参数路径规划车削插补算法。该算法将复杂曲面数控加工插补过程的路径规划分解为若干插补点之间的最优路径搜索和选取问题,根据不同加工要求设置决策变量,并进行取值判别,通过3个参数联动对曲线进行插补运算,优化加工过程中刀具的路径,并应用于相关的实例分析。研究结果表明,该优化算法能保证加工曲线的光滑性,有利于提高曲线的加工质量,并且该算法还具有计算规模小、求解迅速、数控加工插补误差小等优点。     

A novel machining of multi irregular surface using improved noncircular turning method

The backplane processing is an important part of the manufacture of electronic communication equipment; the current processing of backplane surface, especially the rough machining, is still using milling; and the production efficiency is quite low. This paper presents a new method to turn with a cylinder for the rough machining of multi backplane surfaces, which is based on a conventional horizontal lathe and uses the improved method of noncircular machining. The performance requirements of fast tool servo (FTS) device and control model for the machining of noncircular surface are analyzed firstly; the position following control strategy is used instead of traditional position interpolation, according to the multi backplane surfaces machining technology and control strategy; and a novel algorithm, which is combined UG (Unigraphics NX) software surface fitting with cubic spline curve fitting of multi backplanes’ space, is proposed for computer-aided manufacturing (CAM) software design. Finally, the proposed processing method and CAM model algorithm are proved to be effective through the simulation and actual verifications, the products meet the processing requirements and the processing time of each piece is reduced from 8 to 2 min, and they also greatly improve the production automation and achieve energy saving and emission reduction.     

Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining

Parametric interpolation has many advantages over the traditional linear or circular interpolation in computer numerical control (CNC) machining. The existing work in this regard is reported to have achieved constant feedrate, confined chord error and limited acceleration/deceleration in one interpolator. However, the excessive jerk still exists due to abrupt change in acceleration profile, which will cause shock to the machine as well as deteriorate the surface accuracy. In this paper, an adaptive interpolation scheme incorporating machine’s dynamics capability consideration is proposed and illustrated in details. In the proposed algorithm, the commanded feedrate is maintained at most of the time and adaptively reduced in large curvature areas to meet the demand of the machining accuracy requirement, while at the same time, the acceleration and jerk values are limited within the machine’s capabilities during the whole interpolation process. It ensures a high machining accuracy, eliminates the phenomenon of overshoot/undershoot and reduces mechanical shock to the machine tools. The real-time performance of this interpolator is also measured to demonstrate its practical application. Two non-uniform rational B-spline (NURBS) curve interpolation experiments are provided to verify the feasibility and advantages of the proposed scheme.     

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.     

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.     

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 interpolation method for the open CNC system based on EPM

A typical open computer numerical control (CNC) system should own the capability of being redeveloped easily and effectively, and any improvements of interpolation algorithm or machining technique could be put into practice by users conveniently. However, this is not always available in the current open CNC systems. To solve this problem, an interpolation method based on external profile mode (EPM) is introduced to improve the universality and the performance of an open CNC system in this paper. The method is realized with a rough interpolation in the PC host and a fine interpolation in the slave motion controller. With this method, various interpolation algorithms can be easily realized in the rough interpolation when machining complex contours. Meanwhile, the machining parameters during each interpolation cycle can be wholly determined by the host, so a real-time adjustment of machining parameters can be accomplished during the interpolation. The working principal of EPM is presented in this paper, and the realization of interpolation algorithms with the proposed method is described. A look-ahead algorithm for determining the machining parameters of each segment is implemented based on the length of segments in the rough interpolation. An acceleration/deceleration strategy with confined jounce is proposed in the look-ahead algorithm. The experimental results of specific profile interpolation show that the interpolation method based on EPM can make the open CNC system more universality and high performance.     

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.     

新型5轴混联加工单元的后置处理算法

5轴混联加工单元因其高刚性、快速响应及灵活调姿等优点,已被视为复杂铝合金结构件高效加工的一种替代方案。后置处理是改善此类装备加工能力的重要环节。以一种新型5轴混联加工单元为研究对象,提出一种可提高其加工件表面质量的后置处理算法。首先,基于B样条曲线构造一种双参数曲线插补算法,进行刀尖和刀轴轨迹的光顺处理,并采用参数同步化保证刀尖点与刀轴点的同步插补。其次,通过推导混联加工单元的速度映射模型,构造驱动轴的速度分配算法以确保刀尖进给速度的稳定性;接着,运用混联加工单元的位置逆解与速度分配策略,将其末端的进给速度、光顺处理后的刀尖插补点及刀轴插补点转换成驱动轴的位置与速度运动控制点集,实现混联加工单元刀具轨迹的后置处理;最后,基于前期开发的实验样机开展一组S形试件的切削实验,验证所提后置处理算法的有效性。     

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.     

基于径向基函数和自适应单元分解的大规模散乱点云快速重构

径向基函数用于散乱数据的插值和拟合具有精确和稳定的优点,但是它不适合大规模点集的曲面重构。把径向基函数和单元分解原理综合起来,提出一种大规模散乱点云的隐式曲面快速重构算法。把整体定义域自适应细分成一系列稍微重叠的子域,基于径向基函数在各子域上计算局部表面,最后采用单元分解函数对局部表面进行加权混合得到全局的重构表面。方法适于处理数量较大和分布密度变化较大的点云数据重构。     

用工业控制机实现的空间任意圆弧的扩展DDA插补算法

提出一种用工业控制机的汇编语言实现的空间任意圆弧的ＮＣ插补算法。该算法利用ＤＤＡ算法的原理，并在此基础上予以扩展，能实现三轴联动加工，它的运算速度快，精度高，用该算法加工空间曲面取得了满意的效果。     

基于空间填充法的刀具路径生成算法及其仿真

针对空间填充曲线法的网格只具有正则矩形,生成的刀具路径存在频繁转向、长度冗长、生成时间长等缺点,提出一种基于空间填充法的刀具路径生成算法。选用T样条曲面为造型曲面,生成具有非正则矩形的网格并进行回路的规划;用改进的Hamiltonian算法初步生成刀具路径;用改进的倒圆角算法进行拐角优化,获得最终的刀具路径。开发出了基于该算法的仿真系统,对算法进行了仿真验证和实际的加工实验,结果表明所提出算法有效可行,生成的刀具路径长度及生成时间都得到缩短。