On obtaining machine tool stiffness by CAE techniques

In this paper, a single module method and a newly developed hybrid modeling method for analyzing the stiffness of machine tools are introduced in detail. Techniques include building suitable finite element models, determining equivalent loads, simulating the interface between two modules, considering boundary constraints, and interpreting results. By taking a detailed finite element mesh for one of the five modules (the headstock, the column, the table, the saddle and the bed), together with simplified meshes for the other four modules, a hybrid finite element model is assembled. The elastic modulli of the four simplified meshes are kept several orders higher than that of the detailed one. Therefore, the calculated stiffness of the hybrid model is essentially the stiffness of the softer module with the detailed mesh. The stiffness of the five modules can be obtained one after another in the same manner. By supporting the hybrid model only at the middle of the short edge on the bottom surface of the bed, the machine tool can be properly constrained, and its stiffness can be estimated correctly. The controversial issue as to how to simulate properly the boundary condition of the casters under the bed will not occur in this method. A cumbersome procedure to transform the external loads into the equivalent forces as required in SMM is also avoided. There is no local effect due to unevenly distributed nodal forces. It is shown that the hybrid modeling method is better than the single module method in accuracy and efficiency.