NURBS曲线高速高精度插补及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,提出了一种新的控制方法.该方法考虑了高速高精度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因素,使进给速度既符合加减速的要求,又能随曲线曲率自适应调整,因而可在提高轮廓加工精度同时,显著地减小加工过程对机床的冲击.同时,采取了改进、简化算法,实现了快速、实时自适应的非均匀有理B样条曲线插补的加减速控制.实例表明,该方法在实时插补过程中,满足了速度和加减速的要求,保证了插补加工的高速与高精度,且实现了速度的平滑过渡.     

腰轮转子建模与高速高精度加工研究与分析

建立了腰轮转子数字化实体模型;提出了在腰轮转子加工制造过程中,采用三次NURBS样条曲线插补替代通常的微直线拟合插补;研究了腰轮转子摆线段三次NURBS曲线插补算法;为了解决NURBS曲线自适应速度控制存在的速度冲击问题,采用S曲线加减速控制策略重新规划进给速度;应用MATLAB软件模拟摆线段三次NURBS样条曲线插补算法并与微直线拟合插补算法进行了比较;最后在数控机床上对三次NURBS样条曲线插补算法进行了数控加工验证并与微直线拟合插补算法进行了比较,结果证明NURBS样条曲线插补算法具有更快的速度和更高的精度。     

五轴NURBS插补中的速度前瞻控制方法

为提高五轴非均匀有理B样条的插补精度,减轻段间转接时对机床的机械冲击,提出了一种速度前瞻控制处理方法.采用曲率圆逼近的方法建立了插补误差计算模型,并推导出满足插补误差要求的最小曲率半径与进给速度间的关系.采用数值分析方法预先计算出减速点的参数值,对样条插补进行了加减速前瞻规划处理.实时插补时对样条曲线上曲率半径较小的地方进行减速处理,以提高插补曲线的逼近精度.实例证明,该方法能有效降低插补误差和段间转接时的加速度,具有良好的实时性,可以应用到实际的数控系统中.     

数控系统高性能微段插补技术研究与应用

针对在复杂曲线曲面加工时,由CAM产生的连续微段在加工中由于频繁加减速所带来的加工精度和速度的矛盾问题.在CNC中采用微段插补技术对连续微段进行实时样条重构及递推插补以实现对曲面的高速高精度加工.给出的微段插补技术包括新设计的代数指数样条函数,结合速度规划给出的样条重构及样条曲线的递推插补算法.应用微段插补技术进行的样件数控加工实验中,在保证原曲线加工轮廓误差的同时,加工轨迹以μm级精度逼近原曲线,并且加工速度提高了5～5.4倍.实验结果表明,算法在加工轨迹的整体上实现了进给速度的平滑衔接,在加工过程中避免了频繁的加减速,机床运行平稳,加工精度高,表面质量好的同时提高了加工效率.     

一种自适应B样条插补算法研究

针对复杂轮廓零件数控加工的实际要求,设计了一种在可控弦高误差插补算法基础上加入前瞻功能的自适应非均匀B样条插补算法.该方法能够根据曲线的形状,自适应地调整进给速度,保持速度平稳,并通过前瞻模块在速度变化敏感区域对加减速进行处理,满足机床加减速要求.     

基于曲线长度自调整速度方程的非均匀有理B样条插补算法

针对非均匀有理B样条(NURBS)曲线加工过程中速度规划复杂、效率低以及机床震颤剧烈的问题,提出一种高效规划进给速度的NURBS插补算法。预处理过程计算出待加工NURBS曲线插补参数及误差速度,根据误差速度曲线分析加工路径的加减速情况,并基于加/减速区间长度自动调整三次多项式速度方程,实现平滑的速度与加速度曲线;实时插补过程采用基于Adams-Moulton方法计算初始参数,然后采用二分法对参数进行寻优,将插补过程中速度波动控制到加工要求精度范围内,从而降低机床的振动。通过MATLAB仿真,验证了所提算法加减速规划的高效性和参数计算的精确性,表明该算法在复杂曲线曲面加工领域可以提高机床加工效率与精度。     

NURBS曲线S形加减速双向寻优插补算法研究

由于非均匀有理B样条(Non-uniform rational B-splines,NURBS)曲线的弧长与参数之间无精确解析关系,并且进给速度总是受到非线性变化的曲线曲率的约束,因此基于S形加减速进行NURBS曲线插补时,减速点难以准确预测。传统算法通常是沿曲线单方向插补,不仅未考虑曲率对进给速度的持续限制,而且加减速分类与计算公式复杂。为此,提出运动路程未知情况下不依赖于弧长精确计算的正向和反向同步加速的插补新算法,实时动态地求解曲线段内最大进给速度和正反向插补会合点,从而实现处处满足全部速度约束条件的最优插补。该算法无需求解高次方程与繁琐的加减速模式分类,并可保证以确定的速度通过曲率极值点和曲线终点。通过两个插补实例证明算法简明高效,适应性好,能够满足高速高精度数控要求。     

连续微段样条曲线重构加工算法

针对复杂曲面在采用连续微段模式加工的过程中合成速度波动大导致加工效率降低的问题,提出了适用于微段加工的样条曲线重构新算法,该方法包含建立一种具有快速递推性质的样条曲线,及基于该曲线的速度规划和快速递推插补加工的方法。实验表明,算法在保证加速度连续的条件下,通过样条重构及速度规划减少了频繁加减速,提高了加工效率;快速递推则提高了插补计算的速度,插补点精确通过微段节点,保证了加工精度,提升了数控系统的性能。     

面向高速加工的样条曲线实时插补算法

数控加工追求更高的加工效率和光洁的加工表面,但大多数样条曲线插补算法是根据进给速度、最大合加/减速度和合加加速度来设计的,并没有考虑如何充分利用单轴的最大加减速能力。提出一种时间近似最优的样条曲线实时插补算法,它面向数控系统对高速加工的需求,在考虑机床动态性能的基础上,充分利用单轴的最大加减速能力,以达到理论上近似最优的加工效率。同时该算法通过预处理求速度限制曲线、速度曲线反向链接和平滑处理三个步骤求出满足加工精度以及机床单轴的最大加速度、加加速度等约束条件的加工速度曲线,能有效提高加工表面的粗糙度。仿真结果表明,该算法在有效提高加工效率的同时,能实现对减速点的精确定位,得到光滑的加工速度曲线。     

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。     

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。     

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.     

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.     

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de Boor算法的NURBS曲线插补和自适应速度控制研究

以NURBS曲线deBoor递推插补算法为基础，针对NURBS曲线速度处理的特殊性，建立了一种NURBS曲线自适应速度控制模型，该模型分为速度自适应控制和插补前加减速处理两部分。以deBoor算法为基础对整个插补周期的弓高误差以及切向和法向加速度进行实时监控，分析了误差产生的原因并进行了相应的速度控制；以插补前直线加减速为例引入NURBS反向插补的概念，解决了NURBS曲线减速区长度计算问题。实验结果表明，该模型满足实际的NURBS曲线插补的需要。     

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.     

5轴联动数控系统速度控制方法

高速加工过程中,在刀具路径上容易产生过冲,影响加工精度,因此必须提前对加工速度进行优化处理.基于数据采样法,利用当量位移和坐标轴方向系数实现了5轴联动线性插补;利用直线加减速原理进行插补前加减速控制;对速度前瞻控制方法进行了深入探讨,实现了相邻程序段转接处速度优化、连续微小程序段速度计算、减速点提前预测及前瞻程序段数动态选择等.仿真结果表明,速度平滑连续,有效地解决了5轴联动线性插补中的速度控制问题,提高了加工精度和加工效率.