Optimal curvature-smooth transition and efficient feedrate optimization method with axis kinematic limitations for linear toolpath

In industrial areas, the machining performance with linear G01 code is a crucial indicator to evaluate the computer numerical control (CNC) systems and many researchers have presented various methods to deal with the corner tracking issue. However, the axis jerk limitations are not satisfied well and the different axis kinematic limitations are not considered in most researches, which will reduce the machining efficiency and machining quality simultaneously. In this paper, a novel method including trajectory planning, feedrate scheduling, and interpolating is proposed to obtain better machining quality and higher machining efficiency. In trajectory planning, a B-spline curve is utilized to smooth the linear toolpath and obtain a curvature-smooth trajectory, which is third-order geometry continuous. Thereby, a time-optimal method for the geometric continuous trajectory is proposed based on linear programming algorithm in the feedrate scheduling and the bounded multi-constraints, including axis velocity, axis acceleration, axis jerk, and feedrate. Moreover, it can be seen that the proposed method is near Bang-bang control. To reduce the computation time of the optimal numerical method, an efficient method with a look-ahead window around the transition B-spline curve is applied. In the interpolation stage, a novel interpolation method about arc-length is proposed to improve computation efficiency. Finally, simulation and experiment are conducted to show superiorities of the proposed method to the already existing approaches. The results show that the cycling time of the proposed method is reduced by more than 7% than G² method and 20% than G³ method with better contour performance.     

三次均匀B样条曲线高速实时插补研究

为满足复杂曲线高速和高精度的加工要求,研究了具有轨迹预读功能的三次均匀B样条曲线速度规划和插补算法.提出了"重叠拼接法",实现了相邻两条B样条曲线段的光滑连接;推导了插补钳制速度的计算公式,保证了加工精度,满足了系统的动态响应能力.在引入"规划单元"概念的基础上,将速度规划和插补设计成B样条曲线插值、规划单元划分、速度规划、规划单元插补四个并行计算的线程,解决了三次均匀B样条曲线高速加工的插补实时性问题.最后,在GT100数控系统中验证了算法的有效性.     

小线段高速加工的速度模型研究和实现

针对数控插补中离散化进给速度控制的特点，导出了在直线加减速情况下的小线段长度和轨迹形状误差对进给速度的约束条件；完善了小线段高速加工速度衔接数学模型，形成了能实际应用的工程化方法，该方法以给定的最大预处理段数为条件，根据小线段路径的具体形状和长短、速度变化的平滑性和位置误差精度的要求，求解出离散化的进给速度值。同时提出了在指令进给速度实时变化的情况下进给速度的求解方法。仿真结果表明，此数学模型及离散速度的求解方法能实现进给速度的高速衔接，从而大大提高加工效率。     

Real-time NURBS interpolator: application to short linear segments

This study proposes the use of a real-time non-uniform rational B-spline (NURBS) interpolator with a look-ahead function to handle numerous short linear segments. The short linear segments conforming to the continuous short block (CSB) criterion can be fitted into NURBS curves in real time. A modified maximum feedrate equation based on the geometric characteristics of the fitting curves and the dynamics of the servo control system has been derived in this paper. Taking advantage of the multi-thread design and the look-ahead function, the real-time NURBS interpolator can process enough G01 block information and complete feedrate planning before interpolation. In addition, the S-shaped jerk-limited acceleration method is adopted for smoother feedrate profiles. Two part shapes, which possess more than 1,000 short linear segments, are tested on our PC-based real-time control system. Both simulation and experimental results verify the feasibility and precision of the proposed interpolation algorithm.     

Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining

Methodologies for converting short line segments into parametric curves were proposed in the past. However, most of the algorithms only consider the position continuity at the junctions of parametric curves. The discontinuity of the slope and curvature at the junctions of the parametric curve might cause feedrate fluctuation and velocity discontinuous. This paper proposes a look-ahead interpolation scheme for short line segments. The proposed interpolation method consists of two modules: spline-fitting and acceleration/deceleration (acc/dec) feedrate-planning modules. The spline-fitting module first looks ahead several short line segments and converts them into parametric curves. The continuities of the slope and curvature at each junctions of the spline curve are ensured. Then the acc/dec feedrate-planning module proposes a new algorithm to determine the feedrate at the junction of the fitting curve and unfitted short segments, and the corner feedrate within the fitting curve. The chord error and acceleration of the trajectory are bounded with the proposed algorithm. Simulations are performed to validate the tracking and contour accuracies of the proposed method. The computational efforts between the proposed algorithm and the non-uniform rational B-spline (NURBS)-fitting technique are compared to demonstrate the efficiency of the proposed method. Finally, experiments on a PC-based control system are conducted to demonstrate that the proposed interpolation method can achieve better accuracy and reduce machining time as compared to the approximation optimal feedrate interpolation algorithm.     

基于进给速度引导曲线的参数曲线实时插补器

设计了一种基于进给速度引导曲线的参数曲线实时插补器,给出了进给速度引导曲线的B-样条曲线生成方法。该方法在数控加工之前,通过建立进给速度引导曲线,来取代参数曲线实时插补进给速度规划的前瞻处理。实验表明,采用这种基于速度引导曲线的参数曲线实时插补器后,实时计算任务少,可以获得良好的伺服轴进给速度平滑效果和实时插补性能。     

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.     

基于自适应前瞻和预测校正的实时柔性加减速控制算法

为了提高离散小线段的加工效率和质量,提出一种实时柔性加减速控制算法。该算法由三部分组成：前瞻处理部分利用加减速可行性判断条件,保证加减速可达和实时前瞻;速度规划部分在保证速度和加速度连续变化的条件下,实时计算下一插补周期的进给速度;动态修调部分对当前速度规划结果进行调整,及时响应加工中机床参数的改变。实验结果表明,该算法能够实现数控系统的实时柔性加减速控制,支持动态修调,满足实际加工的要求。     

An accurate adaptive parametric curve interpolator for NURBS curve interpolation

In this paper, an adaptive parametric curve interpolator with a real-time look-ahead function is developed for non-uniform rational B-spline curves (NURBS) interpolation, which considers the maximum acceleration/deceleration of the machine tool. In the proposed interpolator, both constant feedrate and high accuracy are achieved while the inconsistency of feedrate is reduced dramatically as well. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, a look-ahead function is introduced to detect and adjust the feedrate adaptively. Two cases were respectively studied to evaluate the feasibility of the developed interpolator: one is for feedrate sensitive arc corner; the other is for feedrate sensitive sharp corner.     

5轴联动数控系统速度控制方法

高速加工过程中,在刀具路径上容易产生过冲,影响加工精度,因此必须提前对加工速度进行优化处理.基于数据采样法,利用当量位移和坐标轴方向系数实现了5轴联动线性插补;利用直线加减速原理进行插补前加减速控制;对速度前瞻控制方法进行了深入探讨,实现了相邻程序段转接处速度优化、连续微小程序段速度计算、减速点提前预测及前瞻程序段数动态选择等.仿真结果表明,速度平滑连续,有效地解决了5轴联动线性插补中的速度控制问题,提高了加工精度和加工效率.     

Design of a real-time adaptive interpolator with parameter compensation

The interpolator is the key part of a CNC system, which has strong effect on machining accuracy, tool motion smoothness, and machining efficiency. In this paper, a real-time adaptive interpolator is developed for non-uniform rational B-spline curves (NURBS) interpolation while considering the maximum acceleration/deceleration of the machine tool. In this proposed interpolator, both constant feedrate and high accuracy are achieved while the inconsistency of feedrate is dramatically reduced as well. In order to deal with the acceleration/deceleration around the feedrate-sensitive sharp corners, a look-ahead function is introduced to detect and adjust the feedrate adaptively. Furthermore, a parameter compensation scheme is proposed to eliminate the parametric truncation error which has been analyzed by several researchers but still not incorporated into any real-time interpolator so far. A case study was conducted to evaluate the feasibility of the developed interpolator.     

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.     

高速装备前瞻自适应速度优化算法

为了实现高速加工中进给速度的高速衔接,避免因加速度突变导致对数控设备的冲击,提出了一种基于插补前S曲线加减速的前瞻自适应速度优化算法。该算法能够根据加工段的过渡情况自动调节预读段数。以进给速度最大化为目标,在预读段衔接进给速度限制和加工过程平滑减速的约束条件下,根据离散化S曲线加减速规律求解最优衔接进给速度。将求得的最优衔接进给速度作为相应加工段的实际末速度,来实现加工段的速度控制。给出了该算法在高速数控系统中的实现方法,并在管切割数控系统中得到了应用。实验结果表明,该算法能够实现进给速度的高速、平滑衔接,满足高速加工的要求。     

An iterative feedrate optimization method for real-time NURBS interpolator

Non-uniform rational B-spline (NURBS) interpolator has been widely used in modern manufacturing systems to machine arbitrary geometries with great relief of the data flow bottleneck and feedrate fluctuation. However, in practice, real-time feedrate does not always meet the computer numerical control (CNC) command exactly subject to the system dynamics. To solve this problem, we present a real-time NURBS interpolator with feedrate optimization for CNC machining tools in this work. The parametric curve is first approximated with the Adams–Bashforth method which provides uniform feedrate in each sampling period in the interpolation process. And then, a feedback scheme is introduced to adjust the feedrate in real time so as to guarantee a specified deviation between the measured and the desired feedrate. The convergence condition for this closed-loop algorithm is presented and analyzed. Simulation and real experiments on an X–Y table are employed to verify its feasibility. And the comparisons with traditional interpolators based on Taylor's expansion are also provided to demonstrate its improvement in accuracy.     

Real-time PH-based interpolation algorithm for high speed CNC machining

Various methods for parametric interpolation of non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a feedrate planning module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X?CY table confirm that the developed method improves tracking and contour accuracies significantly compared to previously proposed algorithms.     

A look-ahead and adaptive speed control algorithm for high-speed CNC equipment

A novel look-ahead and adaptive speed control algorithm is proposed. The algorithm improves the efficiency of rapid linking of feedrate for high-speed machining and avoids impact caused by acceleration gust. Firstly, discrete S-curve speed control algorithm is presented according to the principle of S-curve acceleration and deceleration. Secondly, constraints of linked feedrates are derived from several limits, including the axis feedrate and feed acceleration limits, the circular arc radius error limit, and the machining segment length limit. With these constraints, the optimal linked feedrate is sought to achieve the maximum feedrate by using look-ahead method. Since the actual ending velocity of machining segment equals to the corresponding optimal linked feedrate, speed control of each segment can be executed. Finally, the proposed algorithm is implemented in a pipe cutting CNC system, and experimental results show that the proposed algorithm achieves a high-speed and smooth linking feedrate and improvements in productivity and stationarity.     

Research on ECM process of micro holes with internal features

Micro holes with internal features are widely used as spray holes and cooling holes nowadays, which are usually required to be with high aspect ratio and shape accuracy, as well as good surface quality. An electrochemical machining (ECM) process is presented to machine these micro holes with diameter <200 μm. A quantitative relation between micro-hole diameter and machining parameters including voltage, duty ratio and feedrate is obtained through orthogonal experiments. According to the designed shape of internal features, change rules of machining parameters for varied diameters in different depth are obtained, and then micro holes with internal features are shaped precisely. Taking reverse tapered hole as an example, ECM experiments by varying parameters of voltage, duty ratio and feedrate (called varying voltage machining, varying duty ratio machining and varying feedrate machining, respectively) are carried out. Micro holes with inlet diameter of 178 μm and taper angle of 1.05° are shaped on a 1.0 mm-thick workpiece of 18CrNi8. The deviation of inlet is <3 μm and the taper-angle error is <0.1° in varying voltage machining. The corresponding dimensional accuracy of taper angle is improved by 51% than that of varying duty ratio machining under the same efficiency. The machining efficiency of varying voltage machining is increased by 36% compared to the efficiency in varying feedrate machining. In addition, the micro holes with complex features of funnel shape and bamboo shape are machined.     

一种简化计算的S型加减速NURBS插补算法

针对目前NURBS曲线插补中加减速控制方法不足的问题,实现了加工过程中进给速度的平滑过渡,提出了一种新的NURBS曲线插补方法,包括速度规划和实时插补两个方面。速度规划采用了一种基于曲率自适应的简化计算的S型加减速方法,并结合"双向插补"的思想实时预测减速点,防止产生过大的弓高误差;实时插补则利用Muller插值和Newton迭代法计算了下一周期的插补参数,进而求出了下一时刻到达的空间坐标点。最后与已有插补方法进行了仿真分析比较。研究结果表明,该方法能保证加速度连续和加加速度有界,有效减少弓高误差和进给速度波动,提高机床运行的平稳性。     

提高数控加工速度和精度的几种方法

介绍了高速加工的数控编程策略,论述了高速高精度加工的几种方法,如待加工轨迹监控法、专家系统法、曲线插补法及试切法等,其中待加工轨迹监控法和专家系统法能够动态调节机床的进给速度,曲线插补法能够提高机床的平均进给速度,试切法则可以为任意半径的圆弧段设一个最允许进给速度。