STATIC ANALYSIS OF SPINDLE SHAFTS ON NONLINEAR ELASTIC SUPPORTS OF INTERRELATED STIFFNESSES

The spindle assembly of a metal cutting machine determines the accuracy and productivity of metalworking. The stiffness of the spindle assembly is estimated by the elastic movements of the spindle shaft under the influence of the working load. Correct modeling of bearing stiffness is necessary for obtaining reliable results during spindle stiffness analysis. An approach is proposed for the static analysis of spindle shafts, in which the elastic behavior of the supports is determined by matrices of interconnected stiffnesses. A stiffness matrix was introduced, which links the radial deformations of the bearing in two mutually perpendicular directions as well as the longitudinal deformation with the corresponding forces. Iterative formation of the coefficients of this matrix is carried out by the Newton-Raphson method based on the values of forces and deformations in the supports. To solve the problem of analysis in matrix form, a system of equations was obtained, the non-linearity of which is formed by the dependence of the stiffness matrices of the bearings on the forces. A universal computer program for the static analysis of spindle shafts, in which the elastic behavior of the supports is specified by matrices of interconnected stiffnesses, has been created using the MatLAB software. The static analysis of a spindle shaft on radial/thrust bearings was considered. A comparison was made with the results for separate bending in two perpendicular planes when calculating the radial stiffness of the bearings according to the Jones-Harris model.