高强钢变截面辊弯成形轮廓曲线插补算法与速度规划

针对进给步长为单位短直线逼近实际曲线会引起弓高误差,提出一种限制弓高误差和根据曲率半径变化调整插补步长的轮廓曲线插补算法。鉴于单纯考虑轮廓曲线时,可能会导致单道次的最大速度,最大加速度超出设备极限值,综合分析多道次速度分布规律,找出速度敏感点,分析最佳加减速控制点,并考虑曲线连接点和变速距离等,提出加减速前瞻控制算法。回弹是板材成形内应力的释放结果,为了保证尺寸精度提出回弹补偿算法,试验结果表明,新的算法显著提高了轮廓曲线的插补精度、速度协调性和尺寸精度。     

样条曲线插补速度规划算法的研究

设计了一种适合多种样条曲线（三次样条曲线,Bezier曲线和B样条曲线）插补算法,通过速度控制前瞻缓冲区设置,在保证加工精度的基础上,实现了系统在样条曲线插补过程中加减速处理,改善了插补速度曲线,并满足了机床加减速性能要求。     

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.     

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.     

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.     

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。     

三次参数样条插补精度的主要影响因素分析

分析了采用等弦长方法插补三次参数样条曲线时,进给速度因素和曲率半径因素对插补精度的影响,利用曲线拟合方法分别得出了插补轮廓误差E与进给速度F、曲率半径R之间的函数关系式E—E（F）和E—E（R）。在E（F）中F^2的贡献最大;但当曲率半径较小时,随尺的减小,一次、常数的影响明显增加,在高精度加工中不可忽略;在E（R）中R^-1项贡献最大;曲率半径尺不变时,R叫项的贡献率随进给速度的增加而扩大。采用该算法,根据给定的误差要求,可精确计算出满足精度要求的最大进给速度Fmax和最小曲率半径Rmin。     

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.     

B样条曲线柔性加减速前瞻控制算法的研究

针对B样条曲线插补过程中存在的柔性冲击、过切问题,采用四次多项式加减速与三角函数加减速相结合的方法对B样条曲线进行前瞻速度规划控制。首先,根据曲线曲率的变化情况找出速度规划中的速度敏感点。其次,在对前瞻路径进行四次多项式速度规划时,若遇到曲率频繁变化的曲线段,为了降低柔性冲击,使用三角函数加减速方法进行速度规划控制。最后,为了保证加工精度将弓高误差约束条件引入到速度规划分析中。仿真结果及实例表明,该方法能在保证加工精度的同时降低柔性冲击。     

基于新型柔性加减速控制算法的前瞻插补研究

为解决数控系统处理连续微线段时启停频繁以及插补过程中加速度突变等问题,通过建立圆弧过渡转接模型,根据转折点处的约束条件规划出过渡圆弧处的最优衔接速度,基于新型柔性加减速控制算法对多轨迹段进行速度前瞻规划。经过实验验证,该前瞻插补算法输出的轨迹误差不超过系统给定的最大值,且速度和加速度曲线连续平滑,在满足加工要求的同时能最大限度地提高加工效率,达到了实验最初设计目的。     

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。     

Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties

In precision machining of free-form surfaces at high speed, it is very important to ensure part accuracy and machining properties. To achieve this, this paper develops a guide spline-based feedrate scheduling method for machining along curvilinear paths with simultaneous constraints of chord errors and ac/deceleration. Based on two metrics about feedrate scheduling from the view of geometric and kinematic properties, the nonlinear relationships between the arc-length parameter and path parameter are subsequently established with a parameter correction spline. Then a guide spline associated with the modified curvature radius of paths is constructed to the schedule feedrate. It is shown that determining the largest safe feedrate with constant chord error can be reduced to the issue of changing the feedrate proportionally with the square root of path curvature radii and ensuring the safe feed acceleration can be converted into the issue of presetting the largest slope of guide spline. The simulation results prove that the proposed feedrate scheme has potential applications in the field of finish machining.     

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.     

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.     

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。     

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.     

LOOK-AHEAD ALGORITHM FOR VELOCITY CONTROL BASED ON PARAMETERIZED CURVE INTERPOLATOR

To avoid suffering gouge and transient overshooting in high speed cutting machining, a novel parametefized curve interpolator model with velocity look-ahead algorithm is proposed. Based on a prearrangement step interpolation algorithm for parameterized curves and considering high curvature points, parameterized curve tool path is divided into acceleration segments and deceleration segments by look-ahead algorithm. Under condition of characteristics of acceleration and deceleration stored in control system, deceleration before high curvature points and acceleration after high curvature points are realized in real-time in high speed cutting machining. Based on new parameterized curve interpolator model with velocity look-ahead algorithm, a real cubic spline is machined simulativly. The simulation results show that velocity look-ahead algorithm improves velocity changing more smoothly.     

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。     

参数曲线柔性加减速前瞻控制算法

针对参数曲线插补的特点,使用S形加减速和三角函数加减速相结合的柔性加减速方法对参数曲线的插补路径进行前瞻控制。在规划前瞻速度过程中,首先根据加工曲线的曲率变化自适应地将前瞻距离分为曲率上升段和曲率下降段。在对前瞻路径进行S形加减速规划时,遇到路径上曲率频繁变化段,为了减小计算量,采用三角函数加减速的方法对速度进行重新规划。这样,在满足机床加减速要求的同时降低了系统计算负荷。仿真结果和实例表明,该算法能够适应复杂曲线的变化,满足高速高精度插补的要求。