A new method of virtual material hypothesis-based dynamic modeling on fixed joint interface in machine tools

The dynamic characteristics of joint interfaces affect the dynamic behaviors of a whole machine tool structure notably. An analytic method of virtual material hypothesis-based dynamic modeling on fixed joint interface in machine tools was conducted so as to improve the modeling accuracy of whole machine tools. The microcontact part of two contact surfaces in fixed joint interface was assumed as a virtual isotropic material, which is rigidly connected with two components composing fixed joint interface. The interaction between normal and tangential characteristics of fixed interface was taken into account, a set of analytic solutions of elastic modulus, shear modulus, Poisson ratio and density was deduced from virtual material by adopting Hertz contact theory and fractal theory. Using the finite element structural dynamic modeling approach in existence, when some parameters of material’s elastic modulus, Poisson ratio, density, etc. are known, the dynamic model for virtual material composing a component could be established; therefore, the dynamic model for whole structure, including joint interface, would be obtained. The theoretical mode shapes were compared with the experimental ones (qualitative comparison of similar mode shape and quantitative comparison of the corresponding natural frequency). The comparison results show that the theoretical mode shapes are in excellent agreement with the experimental ones. The relative errors between the theoretical natural frequencies and the experimental ones are less than 9%. The good agreements of theoretical results with experimental ones confirm analytic solutions for virtual material’s parameters. The present solutions would be useful to the precise dynamic modeling of fixed joint interfaces in CNC machine tools in practice.