基于3次样条插值的数控机床几何与热复合定位误差建模

通过分析机床整个温升直到热平衡的误差数据,总结误差分布的数学规律,将热误差和几何误差分离,运用基于压紧样条条件下的3次样条插值算法,以线性拟合后的余差为建模数据,建立了数控机床几何与热复合定位误差数学模型.实验结果表明,该数学模型能很好地拟合数控机床定位误差曲线,补偿后数控机床定位精度提高了80%以上.该方法可运用于不同时刻或不同机床温度下的机床定位误差补偿,建模原理明了、过程快速,模型适用性好.

Modeling of Geometric and Thermal Complex Positioning Error of CNC Machine Tools Based on Cubic Spline Interpolation

Abstract： Based on the analysis of the mathematical laws of machine error data up to the thermal equilibrium, the geometric error and thermal error were separated and the mathematical model for geometric and thermal error was established using the cubic spline interpolation algorithm and the residual error of the linear fitting. The experimental results show that the proposed model based on pressing boundary condition can effectively fit the positioning error curve and significantly improve the positioning accuracy of CNC machining by up to 80% at least. The method can be used for positioning error compensation in different processing times or at different temperatures. The modeling process is simple and fast and the result is applicative.