基于切比雪夫多项式的数控机床几何误差参数化建模

发布时间：2018-04-15 02:02

本文选题：数控机床 + 几何误差　；参考：《农业机械学报》2015年05期

【摘要】：为了快速精确地建立机床几何误差项数学模型,提出了一种基于切比雪夫多项式的参数化建模方法。首先针对测量得到的机床基本几何项数据,将机床相应运动轴进给量转化为切比雪夫变量。其次将切比雪夫变量代入不同阶次的切比雪夫多项式得到相应的值。然后根据切比雪夫基函数值和切比雪夫变量用多元线性回归方法获得相应的系数,得到关于切比雪夫基函数的数学模型。最后将运动轴进给量与切比雪夫变量之间的转化关系代入得到基本几何误差项的数学模型。建模过程简单且易程序化,切比雪夫多项式的高逼近精度使得建立的模型精度高。将所有几何误差项参数化模型代入机床几何误差模型综合数学模型,从而可得到机床工作空间几何误差场分布。以MV-5A三轴立式加工中心为例,将各个几何误差项参数化模型代入机床几何误差模型中得到该机床综合几何误差数学模型,进而得到该机床工作空间几何误差场分布,为机床设计和误差补偿提供了理论依据。
[Abstract]:A parameterized modeling method based on Chebyshev polynomials is proposed in order to establish the mathematical model of geometric error term of machine tools quickly and accurately.Firstly, according to the measured data of the basic geometric terms of the machine tool, the feed of the machine tool's corresponding moving axis is transformed into the Chebyshev variable.Secondly, the Chebyshev variables are substituted into the Chebyshev polynomials of different order to obtain the corresponding values.Then, according to the value of Chebyshev basis function and Chebyshev variable, the corresponding coefficients are obtained by multivariate linear regression method, and the mathematical model of Chebyshev basis function is obtained.Finally, a mathematical model of the basic geometric error term is obtained by replacing the transformation relationship between the feed of the moving axis and the Chebyshev variable.The modeling process is simple and easy to program, and the high approximation precision of Chebyshev polynomial makes the model more accurate.The geometric error field distribution of machine tool workspace can be obtained by adding all geometric error term parameterized models into the synthetic mathematical model of machine tool geometric error model.Taking the MV-5A three-axis vertical machining center as an example, the parametric models of each geometric error term are substituted into the geometric error model of the machine tool to obtain the comprehensive geometric error mathematical model of the machine tool, and then the geometric error field distribution in the workspace of the machine tool is obtained.It provides theoretical basis for machine tool design and error compensation.
【作者单位】：浙江衢州广播电视大学机械系;浙江大学机械工程学院;
【基金】：国家自然科学基金资助项目(51175461)
【分类号】：TG659

【参考文献】