Stiffness model of machine tool supports using contact stiffness

Abstract

The stiffness of machine tool supports should be properly designed for reducing both the ground disturbance vibration and the drive disturbance vibration. However, the stiffness cannot be easily calculated from the geometry and material properties of the support. In this paper, a 3D stiffness model of a machine tool support is proposed using contact stiffness. The stiffness in each direction is assumed to be determined by the contact stiffness at the interfaces and the bulk stiffnesses of the supports and the floor. The contact stiffness model proposed by Shimizu et al. is expanded to determine the contact stiffness in the normal and tangential directions of an interface. In the proposed model, the contact stiffness is obtained by multiplying the unit contact stiffness by the real contact area. The contact stiffness of concrete is experimentally investigated to estimate the stiffness between machine tool supports and the floor, and it was observed to be the primary determinant of the stiffness of interfaces between metal and concrete. Moreover, the unit contact stiffness of concrete is discovered to be less than 1/10 of those of the metals that were used for the study. The natural frequency and vibration mode shape of a model machine tool bed are also experimentally measured and used to verify the proposed stiffness model. The comparison of the results obtained from the two procedures shows that the natural frequency and vibration mode shape of a machine tool bed can be predicted using the proposed stiffness model.