Simulating the junctions of basic machine-tool components

Abstract

In developing models of machine-tool supporting systems, it is important to determine the initial data. For the basic parts, handbook data are available; it is more difficult to determine the initial data for the junctions. For the example of special samples, the simulation of junctions between the basic parts in the form of a thin layer of isotropic material was described in [1]. It was shown that, on the basis of experimental data on the junction deformation in specified contact conditions, a model of the junction may be developed, and the elastic moduli E and G of the material simulating the junction may be determined. However, the handbook and specialized data refer to the rigidity of the junction and the damping there, but not to the deformation. Therefore, we need to determine the initial data for a model of the junction (values of E and G of the material modeling the junction) from the known rigidity and damping of the junction. Given the benefits of shell finite elements, we use a shell model in solving this problem. As an example, consider a chuck‐column junction in a 654 noncantilever milling machine. On the basis of the dimensions and configuration of the junction (Fig. 1a), a geometric model may be developed, in the form of two identical boxes of cellular structure (Fig.1b). The dimensions of the model in the XOZ plane conform to those of the junction. The box height z in the model and its wall thickness s are assumed to be 1 and 0.02 mm, respectively [1]. In this model, the junction between the chuck and column is oriented so that its rear face is connected to the guide surface of the column and its front face to the guide surface of the chuck. Given that it is very difficult to determine the initial data for junction calculation from the known rigidity and damping, we will first consider an elementary volume dV of the material simulating the junction. To determine E and G , we analyze the compression (Fig. 2a) and shear (Fig. 2b) of volume dV . In the compression of volume dV , the displacement of its points along the OX , OY , and OZ axes will be denoted by dm , dn , and dw , respectively. Only the deformation dw of volume dV (height dz , cross-sectional area dS xy ) under the action of force dF z in the direction of the OZ axis is shown in Fig. 2a. The deformation in the direction of the OX and OY axes is analogous.