曲线的通用参数插补算法

一般的ＣＮＣ系统往往只提供直线和圆弧插补功能。尽管一些较新的系统也提供了二次曲线或某些样条曲线的插补程序，但仍然不能满足ＣＡＤ系统的曲线和曲面造型能力对ＣＡＭ系统的要求。本文研究了曲线的参数插补技术，提出了曲线的通用参数插补算法。     

NURBS曲线插补算法的研究

针对目前制造业对数控加工精度要求越来越高的要求,介绍-种改进后的NURBS曲线插补算法,以实例表明其高速、高精度性.     

NURBS曲线修正插补算法的研究

NURBS曲线插补参数递推一阶、两阶求解比较复杂,加工误差较大。本文介绍一种NURBS曲线修正的插补算法,该算法不仅满足加工对精度方面的要求,同时也满足实时性的要求。最后,通过在matlab7.0上验证该算法是正确的,符合NURBS曲线插补的要求。     

CNC系统中任意空间曲线的插补方法

针对机床CNC系统中加工任意空间曲线的实际问题，提出了一种基于泰勒（Taylor)公式的用于实时控制的等速进给插补算法，凡是可以表示为矢量参数方程的正则曲线，都可以用该方法进行插补。     

Bezier曲线参数化高精度插补的研究与实现

给出了Bezier曲线的基本理论,利用差分插补方法来预估参数,结合机床实际加工过程中所必需满足的条件,对进给速度、机床最大加速度、最大弓高误差分别约束的参数进行比较,优化出最小的参数值,进行插补计算,很好地满足现代CNC机床的高精度加工的控制要求.再利用C++ builder开发软件完成了对三次Bezier曲线的插补仿真,给出了插补算法流程图及插补实例,验证了算法的可行性,在CAM中具有很高的使用价值.     

机床CNC系统中任意空间曲线的可控步长插补方法

针对机床CNC系统中加工任意空间曲线的实际问题,提出了一种基于计算机技术的、用于实时控制的、符合机械加工工艺的可控步长插补方法.凡是可表示为矢量参数方程、且Frenet标架存在的正则曲线,都可以用该方法进行插补.     

NURBS曲线插补技术研究

基于一种等弧长插补思想,综合考虑插补精度要求,实现进给速度随曲线曲率变化的调整.     

参数形式空间曲线反馈插补方法探讨

针对参数形式任意空间曲线,提出了一种基于反馈校正思路的插补算法,插补精度较高,同时在实际插补过程中反馈校正的次数非常有限,方法有效且实用。在对数控系统输入编程轨迹的特征点坐标后,数控系统根据这些信息运用一定算法,实时地计算出各个中间点的坐标,从而对各坐标轴进行脉冲分配,完成曲线加工的轨迹控制。插补算法不仅应保证精度要求,更应算法简单,满足控制的实时性要求。     

三次B样条曲线插补技术修正算法

提出一种修正的插补算法,理论上分析了三次B样条曲线递推公式的泰勒展开式一阶、两阶求导在插补周期一定的情况下插补增量只与插补速度有关,通过改变插补增量就可以达到修正三次B样条曲线的目的.经具体实例在MATLAB 7.0上验证该算法是正确的,可以提高插补运算效率,节约计算时间,实现样条曲线的快速插补.     

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.     

Performance Evaluation of a Real-Time Interpolation Algorithm for NURBS Curves

This paper presents a real-time interpolation algorithm for NURBS curves. In contrast to the existing linear and circular interpolators, the proposed interpolator can maintain small contour errors and feedrate fluctuations. Feedrate components, acceleration components and the servomotor driving force for each axis are precalculated from the given curve shape and themachine tool dynamic properties. As a sudden change in the geometrical properties of the tool path can increase contour errors and cause a sudden change of driving force of each servomotor, a new strategy of variable feedrate machining based on the geometrical properties of tool path is suggested. Real-time performance measurement of this interpolator is performed to demonstrate its practical feasibility.     

用短线截交法绘制隐式曲线

本文提出了一种绘制隐式曲线的方法,用一系列短线跟踪隐式曲线,使短线与隐式曲线相交,用二分法求出交点,绘制出隐式曲线。该方法具有简单、可靠、快速等特点,求出的离散点之间间隔比较均匀,对一些后续处理非常有利,此外本方法还能自动地调整步长,适应某些曲线的局部细小特征。     

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。     

参数曲线的恒速通用插补原理与实例分析

阐述了参数曲线恒速插补的通用原理,同时讨论了廓误差近似计算方法。以摆线为例推导了相庆的插补公式和轮廓误差近似计算公式。最后通过VISUAL LISP编程进行插补模拟,表明该插补原理具有无累计误差、恒速进给以及轮廓误差易于控制的特点,而且该算法插补功能的开发和应用前景十分广阔。     

CNC参数曲线实时插补进给速度控制方法

通过分析数控加工中参数曲线的实时插补原理和进给速度控制原理,指出了Taylor展开算法和“参数－弧长”分段拟合算法用于参数曲线的实时插补具有理论上的局限性,并对CNC实时插补进给速度控制问题给出了本质描述,提出了基于牛顿迭代法的解决方案,给出了算法流程。仿真对比实验表明,该算法具有稳定性好、收敛快、运算量小、精度高等特点,满足实时运算要求,能够将进给速度波动率控制在理想水平。     

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.     

CNC系统中三次B-样条曲线的高速插补方法研究

基于参数方程的矢量表示方法,导出CNC系统中三次B－样条曲线的一种高速插补算法。该算法不仅理论上可使所有插补点落在曲线上,而且由于实时插补过程中只有加法运算,因而插补速度极高,基本上适用于任何硬件环境。误差分析表明,只要合理选择参数增量,总能保证插补的弓高误差满足加工精度要求,总能控制机床的实际运动速度满足程编要求。     

High accurate interpolation of NURBS tool path for CNC machine tools

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.     

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。