Analysis Of Lathe Static Performance Based On Fractal Contact

The static performance of machine tool is the foundamental technical indicator. Good static performance plays an important role in guaranteeing the machining precision. This research subject is funded by National Key Technology Support Program "Concept-Unit Technology in Lightweight Design of Machine Tool"(No.2011BAF11B03).In this paper, the international, domestic and industrial backgrounds together with research significance are introduced firstly. Then the international and domestic research situations about both fractal contact model and finite element analysis of static performance are summarized. The relevant theories, like the finite element method, fractal theory and fractal contact theory, are stated later.Take the horizontal lathe as research object, build the mechanical model to get the load distributions on the contact surfaces between the components in the lathe. Build the equivalent models of fixed contact surfaces, bearing surfaces and ball screw contact surfaces, and solve the relavent equivalent parameters. Solve and analyze the nondimensional equivalent parameters of virtual materials based on the fractal contact model, and get the following conclusions. As the normal load of contact surface is increased, the real contact area increases, at the same time, the elasticity modulus and shear modulus of virtual material increase as well. As the tangential load of contact surfaces is increased, the shear modulus of the virtual material decreases. For a given normal load, as the fractal dimension is increased, both the elasticity and shear modulus of virtual material increase. Conversely, as the roughness parameter is increased, both the elasticity and shear modulus of virtual material decrease.Build the finite element model and analyze the static performance of the lathe by utilizing softwares Pro/E and Ansys. The result shows that the static stiffness of lathe in X direction is56631N/mm when replacing the fixed contact surface with virtual material, while without virtual material the static stiffness is61368N/mm. It indicates that the influence of fixed contact surface on lathe static stiffness can not be neglected. Conduct the static stiffness experiment on the lathe and process the experiment data according to the relevent experiment specification. The average stiffness is31850N/mm, the average correlation coefficient of linear fitting is0.99565, the average standard errors of slope and intercept are6.8965e-7and0.00215respectively. The correlation coefficient and standard error reveal that the fitting model is suitable and the data have a linear correlation. Comparing the experiment results with the results of finite element analysis, we find that the relative errors without virtual material and with virtual material are92.68%and77.80%respectively. So we conclude that replacing the fixed contact surface with the virtual material based on the fractal contact theory can increase the accuracy of the finite element calculation, which also prove the reasonability of this equivalent method.