基于Adams-Bashforth-Moulton预估校正法的NURBS插补算法研究

Research on NURBS Interpolation Algorithm Based on Adams-Bashforth-Moulton Predictive Correction

针对传统的基于连续微小线段的插补方法在复杂零件型面加工中具有插补误差大和速度波动大等不足,对NURBS曲线的插补原理、插补参数计算、速度波动等方面进行了研究,结合加工弓高误差、法向加速度、法向加加速度等约束条件进行了速度规划,提出了一种基于Adams-Bashforth-Moulton(ABM)预估校正法的NURBS曲线插补算法,阐述了基于Adams-Bashforth-Moulton法的参数预估原理,对基于速度波动控制的Newton-Rapson迭代插补参数校正原理进行说明。最后在Matlab平台上仿真验证了该算法在插补速度波动控制方面的优越性。

Aiming at the shortcomings of the traditional interpolation method based on continuous micro-segments in the processing of complex part profiles,such as large interpolation error and large speed fluctuation,the interpolation principle of NURBS curve,calculation of interpolation parameters,and speed fluctuation are studied. Based on the constraints of machining bow height error,normal acceleration,normal jerk and other constraints,a speed planning is proposed,and a NURBS curve interpolation algorithm based on Adams-Bashforth-Moulton(ABM)prediction and emendation method is proposed. The principle of parameter estimation based on Adams-Bashforth-Moulton method is introduced. The principle of Newton-Rapson iterative interpolation parameter correction based on speed fluctuation control is explained. Finally,simulation on Matlab platform verifies the superiority of this algorithm in interpolation speed fluctuation control.