Pythagorean-Hodograph曲线插补及其G代码编程的实现

对Pythagorean-Hodograph(PH)曲线与数控加工相关的优点进行了研究,给出了PH曲线的构造方法,分析了PH曲线插补技术和其G代码编程的必要性和可行性,在传统G代码编程的基础上,介绍了一种PH曲线插补G代码编程实现的方法,编写了两个PH曲线插补G代码程序,可以看出该G代码编程可以和直线或圆弧插补G代码混合使用,扩充了传统G代码的使用范围,和通常的直线或圆弧分段逼近插补相比,其在精确性、高效性、传输数据量、灵活性方面具有明显的优势,为开发具有PH样条插补功能的数控系统提供了参考。     

数控加工中非圆曲线轮廓的三圆弧逼近方法

提出了一种以连续相切的圆弧逼近非圆曲线轮廓的方法.方法借鉴曲率圆法中的误差控制原理,通过求取非圆曲线与内、外偏差圆的交点确定圆弧插补节点;在每个插补区间中,曲率圆以及与曲率圆相切的两段圆弧构成连续相切的三圆弧曲线;相邻插补区间的连接点处,三圆弧之间同样连续相切.相比传统的相切圆法及双圆弧样条方法,该方法的误差控制直接,运算简单,具有一定的工程应用价值.     

数控系统中直线与圆弧插补算法的探讨

本文介绍了一种累加极限控制插补算法,用该算法可实现多坐标的空间直线插补与圆弧插补。与逐点比较法和数字积分法(DDI法)相比,该算法具有运算简单、循环次数少、插补速度快等优点,且能获得均匀的输出脉冲分布和稳定的合成进给速度。     

一种高精度插补方案

目前我国使用的数字程序控制线切割机,仅限于进行圆弧和斜线两种类型的控制运算。每一个圆弧段或斜线段,实际上是有X轴向和Y轴向单位长的直线段(目前大多数采用1μ)组成的曲线来逼近。曲线由逐点比较法的加工偏差运算来决定,其精度是较高的,近似曲线与实际轨迹的最大误差值|δ|max<1μ。但是在同样的传动结构条件下,目前的运算控制进给方案是否是最佳的方案呢?本文的结论是否定的,并提出了一种更高精度的插补方案的思想,和实施该方案的简单易行的方法。     

快速数字积分插补算法及其实现

在数字积分（DDA）插补原理的基础上提出了一种可实现多坐标的空间直线插补与圆弧插补的快速数字积分（DDA）插补算法，该算法与普通DDA法相比，具有运算简单，循环次数少，插补速度快等优点，且能获得均匀的输出脉冲分布和稳定的合成进给速度。     

快速数字积分插补算法及其实现

在数字积分(DDA)插补原理的基础上提出了一种可实现多坐标的空间直线插补与圆弧插补的快速数字积分(DDA)插补算法，该算法与普通DDA法相比，具有运算简单、循环次数少，插补速度快等优点，且能获得均匀的输出脉冲分布和稳定的合成进给速度。     

面向开放式数控系统的高性能自适应插补算法的研究

以PC-based开放式数控系统为平台,提出了一种具有数控代码超前解释功能和微小路径自适应前瞻插补的改进型插补算法,以提高刀具插补的速度和精度,同时还可以减少机床加工时的冲击,提高零件的加工质量。以圆弧的三次NURBS插补为例,经前瞻加减速处理后,能够提前预测曲线的变化趋势,并及时的调整插补进给速度,减少了机床加工时的冲击。仿真测试结果表明,插补运算时间很小,插补运算效率大大提高,达到了较好的实时性和平稳性要求。     

数控车床圆弧面螺纹车削研究与程序开发

在车削直螺纹或锥螺纹功能基础上,提出了采用小线段螺纹插补实现圆弧面上螺纹车削的思想。为了求出逼近小线段坐标,采用几何算法对圆弧的圆心进行计算,确定加工圆弧的起始角和终止角,然后通过坐标变换得到逼近小线段点相对工件原点的坐标。最后结合SINUMERIK数控系统的R参数功能,实现了圆弧面螺纹车削的数控程序开发。     

自由曲线轮廓数控刀具路径生成及加工

介绍了一种平面自由曲线轮廓用圆弧和直线拟合生成数控加工刀具路径的方法,该方法依据曲率变化情况,对需加工的截面轮廓曲线进行分段,分别用圆弧和直线线段去拟合,采用控制总体最小误差的方法,计算得到拟合圆弧和直线线段的空间位置参数,借助绘图软件,画出拟合的圆弧和直线线段,通过测量计算得到圆弧和直线的端点坐标,然后用简单插补指令生成数控加工刀具路径程序.以某成型刀具刀盘的加工为例,详细介绍了此方法的应用,实现了具有复杂回转面轮廓曲线零件的手工编程加工,经检验应用此方法加工的刀盘零件完全符合相关要求.     

PLC直线插补方法的研究

利用推导出的插补公式,开发了两种具有加减速功能的直线插补方法,分析了两种方法的插补误差.其中频率分解法是直接将合成频率分解为两轴的频率,利用梯形脉冲指令以该频率同时输出,计算量少;时间分割法是每个插补周期都进行插补参数运算,进给步长小,插补精度高.     

粒子群算法在等误差直线逼近节点方法中的应用

自由曲线是数控加工中经常遇到的工件外形轮廓曲线,但一般的数控系统只有直线和圆弧插补功能。对于自由曲线的直接数控加工,只能用直线或圆弧去逼近其节点,并进行逼近的走刀加工。等误差直线逼近节点的方法能够使所有逼近线段误差相等,是自由曲线直线逼近节点的有效方法之一。在对等误差直线逼近节点算法的研究中,基于几何运算,提出一种新的等误差直线逼近节点的计算方法。该方法通过建立自由曲线的数学模型,运用粒子群算法迭代求取自由曲线上的刀位点坐标信息,并通过VC++编程,实现自由曲线等误差直线逼近数控系统的开发,并验证了该算法的有效性。     

NURBS曲线自适应插值拟合算法

针对从DXF文件中构造的NURBS曲线,提出了一种曲线的自适应分解算法.该算法结合了NURBS曲线的形状信息,通过计算比较插补点的曲率半径与给定阈值的大小,以决定当前插补类型为直线段或是圆弧段,在满足加工精度的前提下,采用伸缩步长法使得拟合的区间尽可能大.经实际运行表明,此方法拟合的加工程序段少,能简化数值计算和编程,减少数控机床的预处理时间.该算法具有通用性,为其他曲线的插值拟合也提供了一种有效途径.     

数控机床加工非圆曲线的程序编制方法

对在数控机床上不能直接进行插补加工的非圆曲线、列表函数，提出了用三次样条函数插值、用双圆弧逼近加工轮廓线的方法，并给出了在计算机上予以实现的流程图。     

基于轨迹压缩的机器人轨迹插值与仿真

针对机器人关节空间轨迹插值中插值点选择的复杂性，以Delta机器人动平台门字形轨迹为研究对象，提出一种基于轨迹压缩的轨迹插值方法。采用PH曲线平滑过渡动平台运动轨迹拐角，将任意轨迹点位置以3个主动杆的转动角度表示，形成关节空间轨迹；将遗传算法与改进的TDTR算法结合，对主动杆转动关节的轨迹进行离线压缩，得出特征轨迹点，作为5次NUBRS的插值点进行轨迹插值；与按时间与距离均匀划分所得相同数目的轨迹点作为插值点，进行轨迹插值数据对比，证明基于轨迹压缩的轨迹插值，关节角速度与加速度的最大值降低。仿真对比表明，此方法降低了动平台的最大加速度。测试实验结果验证仿真结论，动平台运动平稳，进行循环拾取操作的速率可达50次/min,证明该方法在提高运动平稳性方面具有优越性。     

A practical evaluation approach towards form deviation for two-dimensional contours based on coordinate measurement data

A precise evaluation of the form deviations of two-dimensional (2D) engineering contours is of essential importance in precision manufacturing. In this paper, we propose a practical approach towards evaluating form deviations of 2D contour profiles based on coordinate measurement data. Using this approach, a 2D contour is divided into straight and curved parts. Each straight part is directly presented by the original definition of the part; and each curved part is further represented by its optimal interpolation circular arc segments whose interpolation accuracy can be specified arbitrarily. The approximate contour curve consisting of the straight and circular arc segments has the fewest interpolation segments under the condition of satisfying the pre-specified interpolation accuracy. The form deviation of a measured point is defined as the distance from the point to its corresponding straight or circular segment. The geometrical form deviation of the contour profile is evaluated using the least square method. It has been demonstrated that the difference between the deviation definitions, relative to the original contour or to the approximate contour, is not larger than the pre-specified accuracy value for circular arc interpolation. Therefore, the evaluation precision of the form deviation can be sufficiently guaranteed. The approach is easy and convenient for engineering applications. The effectiveness and the efficiency of the approach are verified with a practical example of a planar cam contour in the paper.     

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.     

Guide curve based interpolation scheme of parametric curves for precision CNC machining

Real-time parametric interpolation has played a key role in the computer control of machine tools. To achieve highest quality parts, generated trajectories not only describe the desired toolpath accurately, but also have smooth dynamics profiles. This paper presents a novel parametric interpolator based on guide curve. The relationships between geometric properties and kinematic properties are firstly discussed. Then, with a consideration of the important effect of the curvature of curvilinear path on the machining dynamics, a corresponding formula, which describes the relation of the maximum allowed feed acceleration/deceleration and the maximum allowed rate of change of curvature radius of paths, is built. Thus, based on a near arc parameterization and through modifying the curvature radius curve to deal with corners, key regions and other cases, adaptive feedrate schedule is completed according to the reconstructed smooth curvature radius curve. Consequently, confined chord errors, corners on the path and the acceleration/deceleration capabilities of the machine tool are simultaneously considered and incorporated into the guide curve based parametric interpolation system without using look-ahead scheme. Simulation results indicate the feasibility and precision of the proposed interpolation method.     

A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints

Feedrate scheduling is crucial for CNC systems to generate a smooth movement which is able to satisfy increasing requirements on machining quality and efficiency. In this paper, a novel adaptive feedrate interpolation method is proposed for NURBS tool path with drive constraints. The tool path is first expressed in NURBS form, and then the satisfaction conditions of drive constraints are derived according to the kinematic and geometric characteristics of the NURBS tool path. On this base, a proportional adjustment algorithm, which can quantitatively reduce the accelerations and jerks of drive axes at the sensitive regions of feed profile, is proposed to achieve the new positions of violated sampling points. After each adjustment, a curve evolution strategy is used to ensure the feed profile is locally or globally deformed to the target positions with a good smoothness of path curve and the avoidance of re-interpolation. Through the iterative adjustment, a smooth feed profile with limited velocities, accelerations and jerks of drive axes is thus yielded along the entire tool path. Finally, performances of the proposed method are validated by performing both simulations and experiments on two freeform NURBS curves. The results show the effectiveness and reliability of the proposed feedrate interpolation method.     

Augmented Taylor's expansion method for B-spline curve interpolation for CNC machine tools

In computer numerical control (CNC) systems, parametric curves can be used instead of a large amount of linear blocks to describe tool paths for freeform surface or curve machining. However, existing parametric curve interpolation methods may cause large feed fluctuations or even a failure of the machining process near the sharp corners of a parametric curve. Therefore, a parametric curve interpolation method with an error correction and failure prevention scheme is required. In this paper, the augmented Taylor's expansion (ATE) method for computing B-spline curve parameters is proposed. A group of calibrators consisting of the knots and the arc lengths between adjacent knots are pre-computed before the interpolation starts. The parameter is computed based on Heun's method in a prediction–correction manner, and the accumulated errors caused by the cut-off errors of Taylor's expansion are eliminated by the calibrators at the knots. To cope with the extreme cases that usually occur near the sharp corners of a curve, a linear parametric interpolation between the previous parameter and its next calibrator is carried out when Heun's method fails to obtain a parameter in the domain. Simulation and experimental results show that, when the arc length increments are kept small enough near the sharp corners, the ATE method attains high accuracy and robust computation. The proposed method is also applicable to the NURBS curves.     

时间分割圆弧插补新算法

圆弧插补是现代数控系统最重要最基本的插补方法，而现有文献时间分割圆弧插补算法存在的缺点有两个方面，一是进给速度计算是近似的，从而造成了速度之波动；二是计算进给坐标增量要进行反复迭代．浪费了机时。文章提出了一个计算简单的递推公式，由此可方便地从当前插补点出发算出下一插补点的坐标，从而求出两个坐标方向的进给增量。此方法加快了计算速度，也保证了插补精度。