基于S型加减速的自适应前瞻NURBS曲线插补算法

为实现加工过程中进给速度和加速度的平滑过渡,减小其突变时对机床的冲击,更好地保证加工精度,提出一种基于S型加减速的前瞻自适应非均匀有理B样条曲线插补算法.该算法根据弓高误差的要求,确定出各插补点的自适应进给速度及位置参数,然后找出速度改变点及其等速区间.为避免相邻速度改变点间加减速过程的互相影响,分别在插补前瞻距离和预前瞻距离内,根据设备允许的最大加速度、加加速度以及S型加减速算法对各速度改变点参数进行分析,筛选出决定加减速过程的关键点,再进行S型加减速控制,使进给速度和加速度得以平滑过渡,从而满足机床加减速能力的要求.仿真结果表明,该算法能够满足高速高精度的要求,验证了其可行性.     

一种简化计算的S型加减速NURBS插补算法

针对目前NURBS曲线插补中加减速控制方法不足的问题,实现了加工过程中进给速度的平滑过渡,提出了一种新的NURBS曲线插补方法,包括速度规划和实时插补两个方面。速度规划采用了一种基于曲率自适应的简化计算的S型加减速方法,并结合"双向插补"的思想实时预测减速点,防止产生过大的弓高误差;实时插补则利用Muller插值和Newton迭代法计算了下一周期的插补参数,进而求出了下一时刻到达的空间坐标点。最后与已有插补方法进行了仿真分析比较。研究结果表明,该方法能保证加速度连续和加加速度有界,有效减少弓高误差和进给速度波动,提高机床运行的平稳性。     

参数曲线的自适应实时前瞻插补算法

为实现数控加工中进给速度的平滑过渡,减少速度急剧变化时对机床的冲击,提出了一种参数曲线的实时前瞻插补算法。该算法根据加工弓高误差要求自适应地调整进给速度,同时找出速度敏感点。通过把前瞻距离分成两部分的方法,分析速度敏感点,找出最佳的加减速控制点,避免相邻速度敏感点间加减速过程的互相干涉,提早进行加减速控制,防止速度的急剧变化,从而在满足加工精度的同时也满足了机床的加减速性能。通过RT-Linux软数控下的实例,表明该算法能够适应曲线的各种变化,验证了其可行性。     

Development of a real-time look-ahead interpolation methodology with spline-fitting technique for high-speed machining

Methodologies for converting short line segments into parametric curves were proposed in the past. However, most of the algorithms only consider the position continuity at the junctions of parametric curves. The discontinuity of the slope and curvature at the junctions of the parametric curve might cause feedrate fluctuation and velocity discontinuous. This paper proposes a look-ahead interpolation scheme for short line segments. The proposed interpolation method consists of two modules: spline-fitting and acceleration/deceleration (acc/dec) feedrate-planning modules. The spline-fitting module first looks ahead several short line segments and converts them into parametric curves. The continuities of the slope and curvature at each junctions of the spline curve are ensured. Then the acc/dec feedrate-planning module proposes a new algorithm to determine the feedrate at the junction of the fitting curve and unfitted short segments, and the corner feedrate within the fitting curve. The chord error and acceleration of the trajectory are bounded with the proposed algorithm. Simulations are performed to validate the tracking and contour accuracies of the proposed method. The computational efforts between the proposed algorithm and the non-uniform rational B-spline (NURBS)-fitting technique are compared to demonstrate the efficiency of the proposed method. Finally, experiments on a PC-based control system are conducted to demonstrate that the proposed interpolation method can achieve better accuracy and reduce machining time as compared to the approximation optimal feedrate interpolation algorithm.     

基于曲率特性的柔性加减速NURBS插补器

为降低非均匀有理B样条段间转接时对机床的机械冲击,提出了一种基于曲率特性的柔性加减速控制方法。研究了满足插补误差要求的非均匀有理B样条梯形加减速的算法,推导了满足S型加减速要求的简化算法。用两种算法进行的基于弓高误差的非均匀有理B样条仿真加工实验表明,在曲率突变处加速度和加加速度均出现突变,对机床造成较大冲击。而基于曲率变化进行的柔性加减速的仿真试验表明,相关特性参数符合加减速的规划要求。将算法集成至自行开发的开放式控制器中,加工实验表明,该算法使数控机床的速度变化更加平稳,并具有良好的实时性。     

Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled.In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied.Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation.     

A look-ahead and adaptive speed control algorithm for parametric interpolation

A novel interpolation algorithm for parametric curves is proposed. The algorithm improves the machining efficiency and precision greatly with full consideration of the geometrical characteristic of the machining curves and the kinematical characteristic of the machine tools. Firstly, a look-ahead process, including a pre-interpolation and a speed adjustment, is sought to achieve an optimal machining speed profile for the whole parametric curve. The pre-interpolation stage with a constant feedrate is performed on the parametric curve. Critical zones are selected according to the chord errors and the changing values of the speed. The criterion for selection is that the chord error or the changing value of the speed exceeds the given threshold values. Then, a speed adjustment is applied to the sampling points of the critical zones. Meanwhile, the speed profile between two adjacent critical zones is developed with an acceleration/deceleration strategy to satisfy the dynamical requirements. After that, some relevant information about critical zones is stored into a dynamic memory buffer for the following fine interpolation process. Secondly, the fine interpolation is adaptively fulfilled with the data stored in the dynamic memory buffer based on the lengths of adjacent critical zones. Finally, a non-uniform rational basis spline curve is selected for simulation and experiment to demonstrate the feasibility of the proposing algorithm. The experimental results show that the algorithm can achieve not only smooth and high-speed transitions but also high accuracy with the minimization of chord errors in critical zones.     

Degree reduction of NURBS curves

Higher degree curves are used in applications because they are easier to manipulate interactively but require heavy computation. Most of the equations for curves used popularly in CAD software are of degree 2 and 3, because two curves of degree 3 can guarantee 2nd derivative continuity at the connection point. This study proposes a different but simpler method than any put forward before to deal with degree reduction of free-form curves. The reduced curves use the simplest knot vector type, i.e., the open uniform knot vector. Unlike other methods, this study does not modify or refine the knot vectors but perturb the control points globally. After obtaining an initial condition, a radiating web-like search algorithm is applied to detect the optimum positions. These NURBS curve formats reach basic industrial standards for CAD/CAM/CNC applications. By defining a global bound error function, this algorithm can achieve an optimum solution not only for NURBS curves but also Bézier/B-spline curves.     

椭圆加工中的圆弧拟合及加减速算法研究

很多数控机床不支持椭圆插补,因此椭圆加工一般采用圆弧拟合的方法转换成圆弧加工.采用椭圆的最优四圆弧逼近拟合算法,用数字积分法(DDA)进行圆弧插补.用小段割线拟合圆弧起点和终点的小段圆弧,将圆弧的加减速控制转换成直线的加减速控制,解决了DDA圆弧插补的加减速控制难题.     

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。     

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。     

鞋楦定制中非均匀有理B样条特征曲线的自适应变形

为实现无实体楦基础的数字化量足制鞋,提出了基于非均匀有理B样条(NURBS)特征曲线自适应变形的个性化鞋楦定制系统,将足部NURBS特征曲线依据一定的舒适度规则变形成相应的鞋楦特征曲线来实现鞋楦定制。该系统采用切平面法获取足部的特征点、特征曲线和特征尺寸,重建出足部NURBS特征曲线。建立了足楦舒适度匹配规则,并根据变形方式及次序不同将特征曲线分为四种类型。以特征点、特征结点和特征尺寸作为约束,结合足楦舒适度规律驱动足部特征曲线自适应变形,生成相应的鞋楦特征曲线。最后,构建出鞋楦特征框架,通过特征曲线增添操作和曲面细分造型完成定制鞋楦的设计。给出了男士皮鞋鞋楦的设计实例和定制结果,定制时间在480 s内,定制的鞋楦美观大方。该系统具有实用性,且定制鞋楦的再设计利用率显著提高。     

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。     

实现高速高精度加工的智能NURBS插补算法研究

为了实现对模具等零件的高速高精度加工,研究了NURBS样条插补的完整算法,同时在此基础上提出了动态调节进给速度的智能NURBS样条插补,并采用模糊判断的方式解决了算法问题.实践表明,智能NURBS样条插补方法可以进一步地提高加工速度和精度.     

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.     

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.