实现速度平滑过渡的NURBS实时插补算法

在分析机床最大速度、加速度和速度不连续点对实际加工的影响的基础上,设计了一种能够实现速度平滑过渡的NURBS实时插补算法.算法首先进行一次预插补,求出减速过程中超出机床最大加速度以及速度不连续的点,并采用逆求的方法求出减速点.然后在实时插补时根据求出的减速点进行速度规划.仿真实验结果表明,该插补算法能够在保证加工精度的前提下,以较高效率实现速度的平滑过渡.     

微线段高速加工多线段过渡方法

数控系统的微线段高速加工过程中,为了实现高速加工,常对相邻线段进行直线或曲线过渡,然而现有算法速度变化过大,计算太复杂,影响实时性.在此提出了一种新的处理方法,不仅减小速度变化量,还可以简化计算提高实时计算能力.     

五轴联动数控加工中的微小程序段插补方法

针对五轴联动数控系统在加工微小程序段时频繁启动/停止导致机床产生剧烈振动的问题,提出一种五坐标微小程序段插补方法.该方法能够对多个微小程序段进行统一加减速处理,在保证加工精度的同时,实现对微小程序段的连续加工.五轴联动数控系统上的仿真实验结果表明该方法减少了加工微小程序段时的加减速频率,提高了加工速度.     

基于速度前瞻的数控运动轨迹控制及平滑处理

随着制造技术的不断发展和新材料工艺的应用,制造业数控机床的性能要求越来越高.追求高效率,高精度和高可靠性是数控机床技术发展的一个永恒话题.经前人不懈努力,已取得了一些卓有成效的工作.但在产业化应用方面,需要针对具体的加工需求,尤其是某些特种加工,尚有待于进行深入研究.为此,本文以超快激光加工中的速度规划为研究对象,采用空间圆弧过渡实现程序段间的轨迹转接,保证轨迹的C1连续性,并且算法具有计算简单、技术成熟等特点,使用空间圆可以简洁地描述数控运动轨迹在拐角处的平滑过渡曲线,此外,采用实时前瞻技术,实现平滑且高速的轨迹运动效果.最后,对该算法进行了实际加工的验证,提高了工件的整体加工效率.     

五轴高速高精加工的新型插补算法的研究

传统CNC系统提供的直线和圆弧插补功能不能满足曲线和曲面造型的加工要求.本文针对当前五轴高速高精加工复杂轮廓零件的需求,设计一种新型的四元数-五次样条插补算法.具有该插补功能的CNC系统在进行加工时,不仅缩短了程序处理时间,而且改善了速度、加速度和有限加加速度的平滑程度.将算法在MATLAB中进行仿真实验,实验结果证明了该算法的可行性和可靠性.     

五轴侧铣加工空间刀具半径补偿算法的研究

根据五轴数控侧铣加工主要依靠刀轴矢量姿态变化来完成的特点,对侧铣加工中的刀具半径补偿问题进行研究,提出了一种补偿方法.该方法应用在工件坐标系下,与具体的机床类型无关,充分考虑刀轴矢量可变的各种加工情形.算法包括一个加工块内的半径补偿、拐角类型的判别公式、内拐角和外拐角处的过渡处理方法.文中对补偿方法进行了误差理论分析,并结合加工实例在matlab中进行了仿真实验,实验结果显示补偿算法能够满足系统加工的精度要求.     

微小直线段的动态自整定插补算法

针对目前数控系统中采用微小直线段拟合复杂曲面导致数控机床振动、加工精度低等问题,结合直线 加减速规划方法,提出了一种加工连续微小直线段的新方法．该方法根据用户所需的加工精度、相邻微小直线段间 的拐角角度、各轴的最大加速度等自动调节拐角处的进给速度．在蓝天数控系统上的加工实验结果表明,该方法在 保证加工精度的前提下,能够实现微小直线段的高速加工．     

一种实时轮廓误差估算方法的研究

针对于现有的轮廓误差估算方法通常会将光滑的参考曲线处理成为微小直线段,从而导致估算的轮廓误差值精度较低的问题。采用了一种将参考曲线近似为圆弧,在圆弧上估算轮廓误差的方法。为了证明此方法的有效性,在Simulink环境下对此估算方法进行预补偿仿真。仿真结果显示,此方法可以实时估算并补偿轮廓误差,并且其估算精度高,能够在很大程度上提高数控机床的加工精度。     

五轴数控31/21/2轴倾斜面加工算法

针对五轴机床对带倾斜面类零件加工时编程难度大且精度较低的问题,采用31/21/2轴加工方法,通过定义可以简化加工编程的空间特性坐标系建立了任意结构五轴机床31/21/2轴加工的运动学模型.利用齐次变换矩阵和正向、逆向运动学相结合的方法详细论述了基于特性坐标系的适合三种典型五轴机床的31/21/2轴加工算法.此算法把31/21/2轴加工的空间编程问题转化为倾斜面平面编程问题,不仅简化编程而且可提高机床加工能力和生产效率.通过仿真实验验证了该算法的可靠性和高效性.     

五轴联动数控系统RTCP技术的研究与实现

为了实现高效的五轴加工,本文对五轴RTCP技术进行深入研究,通过对旋转角度的细分及插补点处非线性误差补偿,减小了加工中的非线性误差并满足补偿算法的实时性,通过对各轴速度进行约束的前瞻算法、减小了加工过程中的机床振动,从而提高了工件表面的加工质量.本文提出采用基于参数配置的运动学模型,提高了工件程序的可移植性.最后将该算法添加到GJ-310数控系统中,并进行了试验验证,结果表明该算法可以满足加工要求.     

单圆弧样条保形插值算法

该文以插值具有偶数个点的闭多边形为例提出了一种新的圆弧样条插值算法。这种算法具有以下3个特点：（1）生成的圆弧样条曲线具有保形的特点；（2）圆弧样条中圆弧的段数与型值点个数相同。（3）圆弧段之间的连接点不一定在插值的型值点上，这样就能用更多的自由度来控制拟合曲线的形状。同此文中还提出了一个优化的算法来得到光顺的插值曲线，同时还给出了几个例子加以说明。     

开圆弧样条的保形插值算法

提出一种G1圆弧样条插值算法.该算法选取部分满足条件的型值点构造初始圆,然后过剩下的型值点分别构造相邻初始圆的公切圆.在此过程中,让所有型值点均为相应圆弧的内点,且每段圆弧尽量通过2个型值点.在型值点列满足较弱的条件下,曲线具有在事先给定首末切向的情况下圆弧总段数比型值点个数少且保形的特点.     

基于平面扫描的线状缓冲区生成的改进算法

针对传统双线圆弧算法存在失真现象和效率低下问题,提出了一种改进的基于线段/弧段的平面扫描算法。首先通过在凹点记录线段来避免失真问题;然后利用线段/弧段之间距离远近和相互连接的性质,采用改进的平面扫描算法大幅度地提高求交效率;同时设计一种算法快速剔除非边界点;最后利用线段/弧段具有前进方向的性质,快速构造最终缓冲区边界。该算法能避免失真问题,精确高效,具有较高的空间和时间利用率。     

基于最小均方误差的圆弧分段曲线拟合方法

提出了一种基于最小均方误差准则的圆弧分段拟合方法。该方法采用自适应高斯滤波器对原始曲线进行平滑处理以消除噪声影响,并提出了一种适合于圆弧曲线拟合的分段算法。在该算法的基础上根据最小均方意味着准则,以圆弧作为基元对曲线进行拟合。实验结果表明,该方法能够较好地消除噪声影响并保留曲线的局部特征。     

数控系统连续微段重构与插补算法研究

针对目前微段加工研究中采用的非重构微段加工方法存在的加工轨迹与设计曲线轮廓误差较大,轮廓加工精度较低,及微段节点处速度方向不连续,因此加工表面质量不高,加工过程机床振动较大的问题。在计算机数控（Computerized Numerical Control,CNC）中采用实时曲线重构与插补算法进行连续微段加工以实现对曲面的高速高精度加工。微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足加减速要求的可以直接递推的插补样条曲线的重构条件。应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到um级精度的同时,加工速度提高了2~2.4倍。实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内进行整体加减速速度规划,提高加工效率,而且加工轨迹的进给速度的衔接平滑,轨迹光滑,表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了平衡了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度。     

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

A Recursive Subdivision Algorithm for Piecewise Circular Spline

We present an algorithm for generating a piecewise G ¹ circular spline curve from an arbitrary given control polygon. For every corner, a circular biarc is generated with each piece being parameterized by its arc length. This is the first subdivision scheme that produces a piecewise biarc curve that can interpolate an arbitrary set of points. It is easily adopted in a recursive subdivision surface scheme to generate surfaces with circular boundaries with pieces parameterized by arc length, a property not previously available. As an application, a modified version of Doo–Sabin subdivision algorithm is outlined making it possible to blend a subdivision surface with other surfaces having circular boundaries such as cylinders.     

曲线插值的一种保凸细分方法

为了弥补以四点插值细分方法为代表的线性细分方法在形状控制方面的缺陷,提出一种基于几何的插值型保凸细分方法.细分过程每一步中,每条边所对应的新控制顶点由原控制顶点及其切向共同确定;每点处的切向由其邻近的点所确定,并且随细分过程逐步调整.理论分析表明,该方法的极限曲线是G1连续的保凸曲线.如果所有的初始点取自圆弧段,则极限曲线就是该圆弧段.数值实例表明,采用文中方法得到的曲线较为光顺.     

An error-bounded B-spline curve approximation scheme using dominant points for CNC interpolation of micro-line toolpath

This paper presents a unified framework for computing a B-spline curve to approximate the micro-line toolpath within the desired fitting accuracy. First, a bi-chord error test extended from our previous work is proposed to select the dominant points that govern the overall shape of the micro-line toolpath. It fully considers the geometric characteristics of the micro-line toolpath, i.e., the curvature, the curvature variation and the torsion, appropriately determining the distribution of the dominant points. Second, an initial B-spline curve is constructed by the dominant points in the least square sense. The fitting error is unpredictable and uncontrollable. It is classified into two types: (a) the geometric deviations between the vertices of the polygon formed by the data points and the constructed B-spline curve; (b) those between the edges of the polygon and the constructed B-spline curve. Herein, an applicable dominant point insertion is employed to keep the first geometric deviation within the specified tolerance of fitting error. A geometric deviation model extended from our previous work is developed to estimate the second geometric deviation. It can be effectively integrated into global toolpath optimization. Computational results demonstrate that the bi-chord error test applies to both the planar micro-line toolpath and the spatial micro-line toolpath, and it can greatly reduce the number of the control points. Simulation and experimental results demonstrate that the proposed B-spline approximation approach can significantly improve machining efficiency while ensuring the surface quality.     

Effective multiresolution arc segmentation: algorithms and performance evaluation

Arc segmentation plays an important role in the process of graphics recognition from scanned images. The GREC arc segmentation contest shows that there is a lot of room for improvement in this area. This paper proposes a multiresolution arc segmentation method based on our previous seeded circular tracking algorithm which largely depends on the OOPSV model. The newly-introduced multiresolution paradigm can handle arcs/circles with large radii well. We describe new approaches for arc seed detection, arc localization, and arc verification, making the proposed method self-contained and more efficient. Moreover, this paper also brings major improvement to the dynamic adjustment algorithm of circular tracking to make it more robust. A systematic performance evaluation of the proposed method has been conducted using the third-party evaluation tool and test images obtained from the GREC arc segmentation contests. The overall performance over various arc angles, arc lengths, line thickness, noises, arc-arc intersections, and arc-line intersections has been measured. The experimental results and time complexity analyses on real scanned images are also reported and compared with other approaches. The evaluation result demonstrates the stable performance and the significant improvement on processing large arcs/circles of the MAS method.