直线滚动导轨非赫兹接触静刚度模型

Non Hertz contact static stiffness model of linear rolling ruide

为建立导轨非赫兹接触静刚度模型,首先给出并求解了一般性点接触问题的基本方程,将其应用到单滚动体和滚道的非赫兹接触问题中进行非赫兹接触分析;其次用拟合精度较高的四阶线性方程拟合出了单滚动体和滚道的静刚度模型;再次基于齐次坐标矩阵法与单滚动体和滚道非赫兹接触静刚度模型建立了滚动导轨非赫兹接触静刚度模型;最后以某一滚动导轨为例求解并分析了非赫兹接触下的五自由度静刚度,结果表明用赫兹接触理论求解非赫兹接触下的导轨静刚度误差最大可达33%。

The accuracy of the static stiffness model based on Hertz contact theory is not high when the compactness of the rolling body and the raceway is high.In order to establish the non Hertz contact static stiffness model of the guide rail,the basic equation of the general point contact problem is given and applied to the non Hertz contact problem of single rolling body and raceway,and the non Hertz contact analysis of single rolling body and raceway is carried out.Secondly,the fourth-order linear equation with high fitting accuracy is used to fit the static stiffness model of single rolling body and raceway.Based on the homogeneous coordinate matrix method and the non Hertz contact static stiffness model of single rolling body and raceway,the non Hertz contact static stiffness model of rolling guideway is established.Finally,a rolling guide is taken as an example to solve and analyze the static stiffness of five degrees of freedom under non Hertzian contact.The analysis shows that the maximum error of Hertz contact theory is 33%.