NURBS曲线插补的运动规划与自适应速度插补

文章整合了以基于曲率速度插补算法与自适应速度插补规划算法,分析了NURBS曲线的特点和NURBS曲线插补的参数值的求取方法;构建了基于曲线几何特性与动力学特征插补器,几何模块提出如何决定NURBS曲线的速度尖点,并根据速度尖点信息将NURBS曲线划分为曲线段,依据弓高误差及曲线曲率规划进给速度;机床动力学模块依据每段曲线长度对加加速度控制,对于每段曲线采取相应的加减速控制规划,实现了基于S形速度曲线的加速度平滑处理,与传统插补方法相比,该插补器能够保持高速度和高精度加工性能,而且能够抑制在插补过程当中产生的轮廓误差和速度波动.     

基于De_Boor递推算法的速度自适应NURBS曲线分段插补算法研究

针对现有大多数NURBS曲线插补算法不能同时满足插补精度和机床加减速性能要求的问题,提出一种基于De_Boor递推算法的速度自适应NURBS分段插补算法。通过前瞻预处理完成插补分段和减速点确定,通过速度修正完成减速段最终插补。MATLAB仿真结果表明,该算法能够同时满足插补精度和机床加减速性能要求。     

基于NURBS曲线插补的五段S曲线加减速控制方法研究

为满足非均匀有理B样条曲线高速高精度插补加工的需要,针对目前参数曲线插补加减速控制方法的不足,常规直线加减速方法存在冲击,七段S曲线加减速方法算法复杂等问题,提出了基于NURBS曲线插补的五段S曲线加减速控制方法.该方法将高速加工中容易超限的弓高误差和机床所能承受的法向加速度等参数均考虑在内,而且合理地解决了插补前加减速控制中的减速点预测困难的问题.仿真结果表明,该方法能够保证加速度的连续,速度的平滑过渡,有效提高了系统的柔性,简化了算法.     

NURBS曲线插补算法及加减速控制研究

针对复杂零件高速高精密加工的需求,提出了一种基于阿当姆斯微分方程的NURBS曲线实时插补算法。通过对算法的合理简化与近似,保证了算法的实时性。此算法基于轮廓误差和法向进给加速度控制,使进给速度能随曲线曲率自适应调整。与之相适应,配合此插补算法,利用NURBS曲线的对称性预测减速点,提出了一种新的插补前抛物线-直线-抛物线S形加减速控制方法。该方法具有位置精度高、速度无突变、过渡平滑、计算简便等优点。通过采用MATLAB对插补轨迹仿真和实例分析,证明了插补算法和加减速控制方法的正确、合理、有效性。     

三次非均匀B样条曲线插补算法研究

插补算法的优劣关系到数控加工的精度和速度。文章提出了一种三次非均匀B样条曲线插补算法。该算法基于已知的型值点反算出曲线的控制点,从而得到曲线方程,然后利用泰勒展开公式预估得到曲线插补下一周期的插补点,并通过弓高误差控制方法对曲线插补精度和进给速度进行控制,最后讨论了利用B样条曲线对称性求减速点的方法。经过Matlab仿真分析,证明该方法的正确性与有效性。     

基于四阶S曲线加减速的NURBS曲线插补算法

为提高NURBS曲线插补的运动平滑性，提出一种基于四阶S曲线加减速的NURBS曲线插补算法。该算法通过使用四阶S曲线加减速求解NURBS曲线节点上的速度，首先分析最大速度、最大加速度和最大加加速度的可达性，同时考虑非对称四阶S曲线加减速模型，并对较短弧长的采用二分法寻找实际最大速度，规划出31种速度曲线类型，然后根据NURBS曲线参数和约束条件生成对应的速度曲线。仿真结果表明，与三阶S曲线加减速控制的NURBS曲线插补算法相比，所提算法的插补精度更高，加速度曲线光滑且加加速度曲线连续无突变，降低其运动过程中的柔性冲击。     

一种改进的NURBS插补算法

提出了一种NURBS曲线快速插补的改进算法.该算法综合考虑了在机床电机的加减速过程速度变化的特殊要求及加工过程中的精度要求和速度波动小等因素,具有计算速度快、精度高的特点.     

基于轴加速度限制的NURBS曲线实时自适应插补算法

现有的NURBS曲线插补算法大多只关注合成加速度的平稳过渡,却忽略了各轴加速度是否超出电机的加减速能力.为了把弓高误差、各轴的速度及加速度同时限制在允许范围内,对现有限制合成加速度的自适应插补算法提出改进.算法主要包括两部分:预处理和实时插补.预处理首先对NRUBS曲线进行分段;接着在实时插补中设计了一个前瞻模块,对各分段曲线进行速度规划,使进给速度同时满足弓高误差和各轴加速度限制,并确定减速点.采用高性能处理器,使前瞻处理和插补计算同时进行,实现实时插补.最后通过MATLAB实例仿真,验证了算法的正确性和可行性.     

自由曲线实时插补的减速控制

本文提出了一种自由曲线实时插补过程中的减速控制方法。该方法计算量小,计算效率高,同时该方法减速时的加速度能根据当前插补点离插补终点的距离自动作一些相应的变化,使速度变化更趋平稳,且避免了越程、失步现象的发生,因此非常适合于实时插补的需要。文中给出了该方法的原理,阐明了该控制方法中的相关技术处理。     

基于离线粗插补的数据采样插补法

传统的数据采样插补法受插补周期、位置反馈采样周期的约束,不能充分发挥计算机的性能.针对上述不足,提出将粗插补计算过程放到非实时计算时间,通过通讯接口传送插补数据给精插补控制器,并由精插补控制完成脉冲输出及位置控制任务.以达到合理分配软硬件功能,充分利用CPU资源的目的,以满足高速、高精度插补的要求.     

Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation

To generate continuous velocity, acceleration and jerk curves of parametric interpolation in high-speed and high-accuracy machining, this paper presents a trigonometric velocity scheduling algorithm based on two-time look-ahead interpolation (pre-interpolation and look-ahead interpolation). The algorithm consists of three modules: pre-interpolation, look-ahead interpolation and real-time interpolation. The pre-interpolation module aims to explore and record the information of the path to be machined. The look-ahead interpolation module firstly calculates the velocity scheduling functions according to the data recorded by pre-interpolation, and then tests and adjusts the feedrate scheduling schemes constantly. The real-time interpolation module adapts the method of beforehand deceleration or delaying acceleration according to the signals received from pre-interpolation and look-ahead interpolation to guarantee the processing accuracy. Simulation and experimental tests demonstrate the availability, effectiveness and advantages of the trigonometric velocity scheduling algorithm. And the proposed trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation could realize smooth velocity, acceleration and jerk control with restricted chord error and implement high-quality CNC processing.     

Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics

This paper develops a comprehensive interpolation scheme for non-uniform rational B-spline (NURBS) curves, which does not only simultaneously meet the requirements of both constant feedrate and chord accuracy, but also real-time integrates machining dynamics in the interpolation stage. Although the existing work in this regard has realized the importance to simultaneously consider chord error and machining dynamics, none has really incorporated these in one complete interpolation scheme. In this paper, machining dynamics is considered for three aspects: sharp corners or feedrate sensitive corners on the curves, components with high frequencies or frequencies matching machine natural ones and high jerks. A look-ahead module was developed for detecting and adaptively adjusting the feedrate at the sharp corners. By Fast Fourier Transform (FFT) analysis with a moving window in the interpolation stage identified were some special frequency components such as those containing high frequencies or with frequencies matching machine natural ones. Then, the notch filtering or time spacing method was used to eliminate these components. To more completely reduce feedrate and acceleration fluctuations, the jerk-limited algorithm was also developed. Finally, the interpolated feedrate was further smoothened with B-spline fitting method and the NURBS curves were re-interpolated with the smoothened feedrate. During the interpolation, the chord error was repeatedly checked and confined in the prescribed tolerance. Two NURBS curves were used as examples to test the feasibility of the developed interpolation scheme.     

基于差分插补原理的数控系统加减速规划

为了实现基于差分插补原理的数控系统加减速控制,以直线与圆锥曲线为研究对象,对差分插补运动进行研究。通过分析差分插补中基准轴与非基准轴的运动特点,制定详细的加减速控制策略。对圆锥曲线进行分区处理后,实现了差分插补加减速控制策略的统一。通过译码获得的速度参数能够应用到多种加减速模型中,实现准确地起停电机,保证插补加工位置的准确性。加工实验结果表明:差分插补加减速控制策略实现了数控系统的加减速功能,为保证数控系统的加工效率与质量、适应现代化生产加工要求奠定了基础。     

Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm

In this paper, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is proposed to generate a smooth and jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules: geometric, dynamics-based, and jerk-limited modules. The geometric module can detect the local maximum/minimum (max/min) curvatures, and divide a NURBS curve into small segments according to the information of sharp corners. The feedrates at the sharp corners are determined based on confined chord errors and curvatures of the curve. The dynamics-based module utilizes a dynamics feedrate modification equation (DFME) to estimate contour errors at the sharp corners and adjusts the feedrates at the locations of the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the segments’ length and the given jerk limit. Simulations are performed to verify real-time performance of the look-ahead algorithm. Experiments using a PC-based motion controller and an X–Y table are conducted to demonstrate that high-accuracy can be achieved with the proposed dynamics-based interpolator as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms.     

基于遗传算法的机器人轨迹插值方法的研究

为了降低工业机器人在运动过程中关节的最大加速度,提升运动的平稳性。通过对机器人运动学分析,求出起始和终止关节角度,分别采用三次多项式和高阶多项式插值算法进行运动插值。分析两种方法的特点,提出一种新型多项式插值方法为三段多项式“414”插值算法。根据运动过程加速度连续且最小原则,采用遗传算法给出最优的两个时间节点。通过MATLAB进行仿真实验证明了“414”多项式插值方法能够使关节加速度变化更加平稳,解决了三次多项式插值算法不能约束加速度和五次多项式插值算法加速度过大的问题,降低了传动机构的冲击。     

High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation

Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely adopted in machining aerospace parts, dies, and molds for this reason; they provide a more continuous feed motion compared to multiple linear or circular segments and result in shorter machining time, as well as better surface geometry. This paper presents a quintic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles. The spline interpolation is realized with a novel approach that eliminates feedrate fluctuations due to parametrization errors. Smooth accelerations and decelerations are obtained by imposing limits on the first and second time derivatives of feedrate, resulting in trapezoidal acceleration profiles along the toolpath. Finally, the reference trajectory generated with varying interpolation period is re-sampled at the servo loop closure period using fifth order polynomials, which enable the original kinematic profiles to be preserved. The proposed trajectory generation algorithm has been tested in machining a wing surface on a three axis milling machine, controlled with an in house developed open architecture CNC.     

基于NURBS曲线自适应实时前瞻插补算法研究

为了提高数控机床的插补精度,在算法中引入轮廓误差和法向加速度作为约束条件,采用ADAMS微分方程迭代计算下一个插补点,通过预估—校正法校正迭代精度。采用前S型加减速控制进行速度规划,利用前瞻模块预测速度敏感点和计算减速点的位置,通过回溯法保证进给速度变化量符合机床加速度的要求。最后利用MATLAB对算法编写相应程序,仿真结果验证了该差补算法的有效性。     

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.     

基于Quasi-Hermite空间曲线的插补优化算法研究

根据参数曲线数控插补原理,针对数控系统中常用的Hermite多项式插补算法递推速度慢、逼近精度较差的缺点以及等参数插补法存在的局限性,提出一种基于代数指数样条基的微段实时插补方法,并采用一阶泰勒拟合实现了插补步长相等条件下的恒速插补,给出算法流程.仿真结果表明,本算法缩短插补时间的同时提高了插补精度,并保持进给速度的稳定.