Abstract
Bolted joints have significant influence on the dynamic characteristic of the machine tool assembly. This study proposes a new modeling method using virtual gradient material. On the basis of Hertz contact theory and fractal geometry theory, the relationship between contact stiffness and normal contact load is deduced. The contact pressure distribution at the interface is obtained through finite element contact analysis. An orthogonal material model is introduced to describe the properties of virtual material. The virtual material is divided into several layers, and the elastic modulus and shear modulus in each sub-layer are derived based on Hooke’s Law. Both experimental and theoretical results for a bolted lap structure are obtained. The experimental results are compared with theoretical ones in terms of qualitative comparison of similar mode shapes and quantitative comparison of corresponding natural frequencies. The comparison shows that the theoretical first three-order vibration mode shapes are in good line with the experimental ones. The relative errors of corresponding natural frequencies between the virtual gradient material model and the experiment are less than 9%, which are smaller than those between the traditional virtual uniform material model and the experiment. The proposed virtual gradient material method would be useful to accurately model the bolted joint in CNC machine tools.
Published Version
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