PH曲线拟合在数控前瞻中的应用

Application of PH curve in CNC look-ahead function

为解决数控系统进行微小直线段平稳加工的问题,提出了一种拟合方法.综合了误差限制下的微小直线段长度、拐角、直线段相交点单调性等判定条件,将连续的微小直线段分割成若干区域.使用非线性最小二乘法将每一个区域内的点拟合成PH曲线,并通过模拟退火方法调整切矢量来控制拟合误差.根据区域的连接情况,将切矢量分为单向和双向两种调节方法.在模拟退火算法中,将微小直线段的斜率作为切矢量的初始值,利用细分直线的方法逐点计算弓高误差,并将此误差作为目标函数来快速进行切矢量的调整.结果表明,对微小直线段进行区域划分可以提高拟合效率.在控制弓高误差的情况下,此方法可以形成具有良好精度的光滑曲线,可以获得平稳的速度轨迹.

A new method was developed to smooth the micro-line while machining in computer numerical control systems. Four rules including angle between transfer vectors with speed limitation, length and angle between the micro-lines with accuracy limitation and the monotonicity of the point were proposed to divide segments into some areas. Nonlinear least squares method was introduced to fit the lines into PH curves. Simulated annealing algorithm was used to adjust the tangent vector for getting better accuracy. The model of adjustment included both unidirectional and bidirectional adjustments by the situation of the point between the areas. Straight slope was considered as the initial value of the tangent vector in the simulated annealing algorithm. Chord error was computed by segmenting the micro-line, the error was the objective function to determine the adjustment of the vector. The results illustrate the dividing rules improve the fitting efficiency. Smooth curves with high accuracy were obtained to get better velocity profile.