基于勒让德多项式的加工中心几何误差参数化建模

Legendre polynomials based parametric modeling of geometric errors for machining center

为快速准确地对加工中心的几何误差进行预测,提出一种基于勒让德多项式的几何误差参数化建模方法。基于多体系统理论对加工中心的误差进行建模,构建勒让德多项式基函数,将误差数据以勒让德多项式基函数展开,通过线性最小二乘法拟合求得线性回归系数,得到误差关于勒让德多项式基函数的拟合多项式,根据变量关系得到误差项关于运动轴位移的多项式模型,应用雷尼绍XL-80激光干涉仪测量加工中心直线轴的定位误差,以Y轴为例进行参数化建模。通过勒让德多项式得到的机床误差参数化模型能够很好地拟合误差数据,其残差较小,精度较高;五阶模型拟合的精度更高,拟合效果较好,可用于误差补偿。

To predict the geometric error of machining center quickly and accurately,aparametric modeling method was proposed based on Legendre polynomials.The error of machining center was modeled with the multi-body system theory.The Legendre polynomials basis functions were constructed to expand the error data.The linear regression coefficients were obtained with least square method to get the fitting polynomial of error.The polynomial model of error term on displacement of moving axis was obtained from the relationship of variables.The XL-80 Renishaw laser interferometer was used to measure the positioning error of machining center＇s linear axis and the Y axis was taken as an example for parametric modeling.The parametric model of machine tool obtained by Legendre polynomials could fit the error data very well,which had smaller residual error and higher accuracy.The fifth-order model had higher fitting accuracy and could be applied to error compensation.