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.     

基于UG的NURBS曲线插补技术的应用研究

高速切削加工作为模具制造中重要的一项先进制造技术,NURBS曲线插补技术逐步得到应用。在UG中通过对连结分段、角度公差、拟合公差等参数的设置以及对UGCAM后处理器的修改,生成了NURBS曲线插补指令,从而驱动CNC机床实现了NURBS曲线插补的高速加工。     

一种优化的NURBS曲线插补算法

为弥补目前非均匀有理B样条插补算法的不足,提出一种优化的非均匀有理B样条曲线插补算法。算法采用插补前S曲线加减速方法,不仅优化了前瞻过程,而且在回溯过程中考虑了短样条的情况。算法对长样条和短样条非均匀有理B样条曲线能用统一的方法进行插补,通过引入环形缓冲区和预插补(非离线),提高了加工效率,同时合理地安排插补任务增强了系统的实时性。通过MATLAB仿真,验证了算法的有效性。     

基于干涉预处理的NURBS曲线前瞻插补算法

鉴于直接自适应插补容易在加工过程中引起较大的速度波动,而按曲率极值点对NURBS曲线进行分段插补造成加减速过程中加速度和加加速度超限,提出一种基于干涉预处理的非均匀有理B样条曲线前瞻控制插补算法。首先对曲线进行自适应处理,得到各自适应插补点的运动参数;然后找出其中加速度或加加速度超限的点(即危险点),并对这些点的速度进行前瞻控制,根据前瞻控制信息对相邻危险点进行干涉处理,最终得到用来对曲线分段的危险点信息和相应的控制策略;最后根据各危险点之间的干涉类型对曲线进行实时插补。仿真实验表明,该算法能够在保证加工精度的前提下,实现进给速度的平滑过渡,并且能够保证加速度和加加速度不超限。     

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.     

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.     

一种参数预估-校正的NURBS曲线插补算法研究

提出了Milne-Simpson参数预估-校正的NURBS曲线插补算法.详细阐述了参数插补预估及校正机理.采用最大弓高误差、最大进给速度和最大法向加速度约束,以便实时调整插补进给步长,从而满足了NURBS曲线插补的高速和高精度要求.     

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。     

An accurate NURBS curve interpolation algorithm with short spline interpolation capacity

In this paper, a novel and accurate real-time non-uniform rational B-spline curve interpolation algorithm is proposed. This algorithm not only considers chord errors, feedrate fluctuations, jerk-limited, and acceleration/deceleration (Acc/Dec) capabilities of the machine, but also optimizes the look-ahead process. In the meanwhile, it improves machining efficiency by adding the circular buffer and pre-interpolation (non-off-line) and enhances the real-time performance by removing the time-consuming calculation from the interrupt service routine. Furthermore, the proposed interpolation algorithm can interpolate both the long spline and the short spline with uniform method. The advantages of the proposed method were confirmed by the simulation results.     

NURBS曲线实时插补进给速度控制的研究

数控技术标志着现代制造业的核心,数控插补模块是数控技术中最为重要的模块之一。NURBS曲线是自由曲线的一种,由于其NURBS曲线的诸多优越性,使其能够很好的应用到数控领域中。NURBS曲线插补及加减速控制的精度和速度是CNC系统的重要指标。通过分析NURBS曲线的插补原理,提出了基于Taylor展开公式逼近NURBS样条参数。同时考虑速度波动于曲率的关系,弦误差与插补周期的关系,根据弓高误差调节进给速度,能够将进给速度波动控制在理想水平。     

NURBS interpolation based on exponential smoothing forecasting

To meet the requirement of exploring a new generation of CNC systems based on STEP-NC, NURBS interpolation has been studied. In contrast to existing NURBS interpolation based on the Taylor’s expansion, this paper proposes a new method for NURBS interpolation which is based on exponential smoothing forecasting. The new method is very simple; it decreases the computational load observably, and speed and precision control are also achieved. This paper presents relative formulas and main computational processes, including speed and precision control, computation of real-time mapping, computation of real-time track, etc. The simulation results indicate that the method is feasible and has high-precision and better real-time performance, which is sufficient for the STEP-NC system.     

基于Muller法的NURBS曲线插补算法

在分析NURBS曲线插补原理的基础上,提出了一种基于Muller法的NURBS曲线实时插补算法。该算法首先进行速度控制,由最大进给速度约束、最大弓高误差约束和最大法向加速度约束得到希望进给步长,保证了加工精度。然后利用Muller法迭代计算满足进给步长要求的插补参数,避免了传统方法的复杂求导运算。该算法稳定性好,运算量小,能够对速度波动进行有效控制,并且能够满足实时插补的要求。     

NURBS曲线实时插补算法研究

提出了一种包含插补误差和进给加速度实时监控的NURBS曲线实时插补算法,该算法有效的避免了曲线求导和曲率的复杂计算。运用参数的对分法预估下一插补点,极大限度简化了插补的实时计算,保证了算法的实时性。     

Real-time NURBS curve interpolator based on section

Parameter interpolation is more capable of modern computer numerical control (CNC) than traditional linear/circular interpolation with higher speed and higher precision. Most of non-uniform rational B-spline (NURBS) interpolation algorithms were developed based on the chord error and machines capability, where interpolation points are calculated beforehand to overcome acceleration/deceleration (acc/dec) and jerk problem, which needs large memory. In this paper, a NURBS interpolator based on feedrate section is proposed. Instead of a single interpolation point, this interpolator aims to feedrate section, which makes it possible to run on a digital signal processor or field programmable gate array (FPGA) whose memory is limited. Experiment on FPGA showed the performance of interpolation. A mould experiment verifies the feasibility of application.     

采用NURBS插补的G代码解释器设计

国产数控机床常利用小段直线插补逼近曲线模型,造成G代码冗长、对机械设备损伤大等问题,严重制约着数控技术的长远发展.非均匀有理B样条(NURBS)是一种优秀的插补技术,是计算机数控的一项支撑性技术.通过在实时Linux操作环境下对开放操作平台EMC2的G代码解释器重新编译,使其集成NURBS插补功能.实验证明:此解释器能直接构造曲线模型,具有良好的稳定性能.     

基于Hamming法的新型NURBS曲线插补算法研究

针对零件曲线曲面加工过程中,传统插补方法逼近误差大和速度进给波动大等众多缺点,对NURBS曲线的插补原理、速度规划、插补参数计算等方面进行了研究,对弓高误差、法向加速度、进给加速度过大的情况进行了考虑,提出了一种基于Hamming法的新型NURBS曲线插补算法,对基于Hamming法线性递推得到的参数预估公式进行了具体说明,对基于Lagrange的参数校正机理进行了详细阐述,最后使用Matlab软件对此插补算法进行了实例仿真。研究结果表明,该算法简化了参数插补的计算,保证了插补的实时性;同时提高了插补精度,在限制加速度及速度波动方面具有很好的效果。     

Internal energy minimization in biarc interpolation

The problem of scheduling n multioperation jobs on a single machine such as the flexible manufacturing system is considered. Each job comprises up to F operations, which belong to several distinct families, and a sequence-independent setup time is incurred whenever an operation is to be processed following an operation of a different family. A job completes when all of its operations have been processed. Two variants with maximum lateness and total completion time as optimality criterion are considered. The problems are denoted as $1\left| {s_f ,{\text{assembly}},GT} \right|L_{\max } $ and $1\left| {s_f = 1,{\text{assembly}},GT,p_{ij} = 0\,{\text{or}}\,1} \right|\sum {C_j } $ . The decision is to sequence all the families in order to minimize the predefined criterion. This environment has a variety of real world applications such as flexible manufacturing systems scheduling and food industry scheduling. A heuristic is presented and a branch and bound is developed for benchmarking. Experimental results show that the heuristic provides good results and the branch and bound procedure is efficient. These results may narrow down the gap between easy and hard cases of the general problem.     

基于FIR滤波的NURBS插补算法研究

在考虑数控加工精度和加工效率的基础上,针对传统加减速控制中减速点预测不准的缺陷,提出了一种基于级联滤波器的NURBS插补算法。该插补算法根据速度敏感点将要加工的曲线进行分段处理,避免了插补过程中的爬行与过冲,提高了加工质量。基于弓高误差的速度自适应调整使得加工精度一直在允许的范围之内,基于滤波器的进给速度控制方案使速度过渡平稳,提高了插补的效率。最后对提出的NURBS插补算法进行了实验仿真,结果证明该算法的可行性。     

改进的NURBS曲面片拼接算法

研究了已网格化的曲面片之间的拼接技术并对现有的拼接算法进行了改进。首先,根据哈特利-贾德的弦长参数化算法求取非均匀有理B样条（NURBS）曲线上的节点向量,利用节点向量和曲线反求出控制顶点,并采用投影变换的方法求出权因子。其次,根据要求调整曲面片上的控制顶点,使曲面片之间达到G1连续。最后,再对已拼接好的曲面片上的控制顶点进行整体修改,重新排列整张曲面片上的控制顶点,从而实现曲面片的无缝拼接。用专业的三维造型软件对拼接后合并的曲面片进行了测试,结果表明,该方法在保证曲面片之间G1连续的情况下可使多块曲面片实现无缝拼接,无缝拼接试验中的平均误差为0.0049°。     

同周期控制NURBS曲线高速高精度插补算法研究

为实现对NURBS曲线的高速高精度加工,基于同周期控制思想,提出了一种同周期控制NURBS曲线插补算法(即数控系统的插补周期与伺服系统的控制周期同步).通过软件系统的模块化设计,将费时、复杂的运算经过合理设计安排到预处理模块;同时,为进一步提高算法运算速度和指令高速传输,在算法处理方面采用计算简单并能确保速度曲线平滑的移动平均加减速控制算法对曲线进行加减速处理;在硬件通讯方面采用双端口RAM作为传输接口.最后搭建系统实验平台并对同周期控制NURBS曲线高速高精度插补算法进行实验研究.实验结果表明同周期控制NURBS曲线插补算法可以实现高速高精度加工的插补控制.