Feedrate Optimization for Spline Interpolation In High Speed Machine Tools

A feedrate optimization technique has been developed for minimizing the cycle time in machining spline toolpaths. Axis velocity, torque and jerk limits are considered throughout the motion in order to ensure smooth and linear operation of the servo drives with minimal tracking error. Feed modulation is achieved by manipulating segment durations which define the overall minimum jerk feed profile. Long toolpaths are handled by applying a windowing technique. The optimized feed profile allows nonzero acceleration and jerk values at segment connections, resulting in continuous and smooth motion within the velocity, torque, and jerk limits of the drives. The cycle time reduction obtained with the proposed technique is demonstrated in high speed contouring experiments.     

A CNC interpolation algorithm for boundary machining

This paper presents an efficient and accurate algorithm for machining boundaries formed at the intersection of two surfaces, an important manufacturing problem in CNC machining. The algorithm is developed using a locus tracing technique implemented on the basis of Danielson's step selection rules. A vertical ball-end milling cutter moves along the considered boundary, in contact with the two surfaces. The algorithm guides the center of the spherical end of the cutter, to maintain exact contact (within 1 step) along the entire path. A seamless formulation is used, allowing the contact points to move freely from the ball-end to the cutter periphery and vice-versa. The surfaces forming the boundary may be implicitly or parametrically defined. The reliability of the algorithm is demonstrated for both cases, by treating a complex boundary machining example. The boundary considered is formed by the intersecting quadratic surfaces of a sphere and an elliptic hyperboloid.     

Spatial interpolation methods applied in the environmental sciences: A review

Spatially continuous data of environmental variables are often required for environmental sciences and management. However, information for environmental variables is usually collected by point sampling, particularly for the mountainous region and deep ocean area. Thus, methods generating such spatially continuous data by using point samples become essential tools. Spatial interpolation methods (SIMs) are, however, often data-specific or even variable-specific. Many factors affect the predictive performance of the methods and previous studies have shown that their effects are not consistent. Hence it is difficult to select an appropriate method for a given dataset. This review aims to provide guidelines and suggestions regarding application of SIMs to environmental data by comparing the features of the commonly applied methods which fall into three categories, namely: non-geostatistical interpolation methods, geostatistical interpolation methods and combined methods. Factors affecting the performance, including sampling design, sample spatial distribution, data quality, correlation between primary and secondary variables, and interaction among factors, are discussed. A total of 25 commonly applied methods are then classified based on their features to provide an overview of the relationships among them. These features are quantified and then clustered to show similarities among these 25 methods. An easy to use decision tree for selecting an appropriate method from these 25 methods is developed based on data availability, data nature, expected estimation, and features of the method. Finally, a list of software packages for spatial interpolation is provided.     

基于多项式滤波的高性能内插器的ASIC设计

提出了一种设计基于多项式滤波的高性能内插器的有效方法.偏移二进制编码的并串DA算法和折叠技术使滤波和多项式计算仅用一个乘法器完成;存储器资源比同等并行度的DA算法降低50%.在0.13μm工艺下,利用该方法实现了时钟频率为300 MHz,最高插值倍数为256的内插滤波器.总结了该方法与传统多相分解实现相比在资源消耗、灵活性等方面的优势.     

Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path

A novel analytical five-axis path-smoothing algorithm is developed for the high speed machining of a linear five-axis tool path. Segment junctions of the linear tool path in the machine tool coordinate system, which are tangent-discontinuous points, are all blended by two transition cubic Bézier curves. One cubic Bézier curve is used to smooth the segment junction of the translational path, and the other Bézier curve is used to smooth the segment junction of the rotational path. The tangency and curvature continuities are both guaranteed in the new path. The dual-Bézier transition algorithm has three advantages: (1) Compared with the path-smoothing method in the workpiece coordinate system, the new dual-Bézier transition method directly and simultaneously smooths the machine tool axis trajectories of both translational path and rotational path. The feed speed and stability will both be improved because the tool path discontinuities are the most important source of feed fluctuation. (2) The constraints of approximation error and the synchronization of parametrization of two smoothed curves, which are the most challenging problems in the smoothing of 5-axis tool path, are both considered. (3) The transition cubic Bézier curve pair has an analytical solution and can be easily integrated in the real-time interpolator. Computational examples and the cutting experiment of an impeller blade show that the novel path-smoothing method has obvious advantages in both feed smoothness and cutting efficiency over the original linear interpolator.     

三次B样条曲线数据采样插补器的研究

针对复杂轮廓零件数控加工的实际需求，基于数据采样插补原理，提出 了一种改进的三次B样条曲线插补器。利用此B样条曲线插补器进行数控加工，能够保证在整个加工过程中加工效率和加工质量的一致性，三次B样条曲线插补技术的实现将大大提高曲线，曲面零件数控加工的效率和加工质量。     

基于Avalon总线的插补器IP核的设计

针对运动控制器中采用软件实现插补存在实时性问题,设计了一款硬插补器IP核,提高了插补速度从而满足实时性要求.采用了Avalon接口规范对IP核进行紧耦合封装,构成一个模块化的独立构件,以便集成到运动控制系统中.详细介绍了硬插补器的体系结构及其软件实现过程,并进行了功能验证.     

Design and implementation of a real-time NURBS surface interpolator

In recent years, various parametric curve interpolators have been proposed for high-speed and high-accuracy machining. However, these methods are based on a constant cutter location (CL) velocity. Hence, the cutter contact (CC) velocity along the surface tends to vary, resulting in a nonuniform machining performance. Furthermore, machining complex surfaces requires the provision of a large number of tool paths and therefore the associated NC data files are generally very large. To overcome these limitations, the current study presents a novel real-time NURBS surface interpolator which ensures a constant CC velocity along the CC paths and its intervals. A PC-based real-time motion control network utilizing SSCNET is developed to achieve the goal of multi-axis synchronous motion. In this study, both the NURBS surface interpolator algorithms and the SSCNET communication protocols are realized by Embedded XP with the RTX real-time kernel. The experimental results confirm that the proposed real-time NURBS surface interpolator is capable of achieving a satisfactory performance.     

基于最小偏差法的步进电机速度控制方法研究

在最小偏差法直线、圆弧插补算法的基础上,着重论述CNC系统的最小偏差直线、圆弧插补算法的加减速实时控制算法,实现了圆弧插补加减速过程的自动过象限控制。提出了不同于常用的查表法进行加减速控制的方法———加减速控制的直接计算法。并针对直接计算法的缺点提出多种解决方式,最后采用判断步进电机是否失步的经验法,在配以MC68F375数控系统的TDNCX15A型数控铣床与TDNC150型数控车床上验证该算法的可行性。     

Parametric interpolation using sampled data

Trajectory in high-speed precision machining requires very small feed-rate fluctuation and contour error, which can be achieved with parametric interpolation. Since it is impossible to exactly compute the arc-length of a general parametric curve, the conventional parametric interpolation obtains a parameter through a real-time update. Thus it cannot be used with a preplanned feed-rate profile, which restricts its applications. To overcome such a problem, the proposed algorithm estimate parameters using tabulated parameter and length data. The simulations show the proposed method useful with smaller contour error and acceptable feed-rate fluctuation comparable to the second order real-time parametric interpolation.