Contact modeling of heterogeneous materials of the machine tool bed–foundation interface based on the gradient of contact stress distribution

The machine tool bed and concrete foundation of heavy machine tools are typically connected by anchor bolts. The dynamic characteristics of the bolted joint's bed and foundation contact surfaces have an important influence on the machining accuracy and service life of the machine tool. This paper proposes a virtual material model based on the gradient of contact stress distribution for modeling the contact interfaces between the heterogeneous material of the machine tool bed and the foundation. An expression for the equivalent elastic modulus of the metal-concrete contact surface is derived by considering the nonlinear properties of concrete. Concrete crushing is assumed, and the evaluation basis of critical deformation parameters of asperity is established. Based on Fractal theory and Hertz contact theory, theoretical models of the elastic moduli, Poisson's ratios, densities, and thicknesses of the virtual material are established. Due to the uneven distribution of contact stress, a gradient equation with virtual material parameters is obtained according to the contact stress distribution curve. Then, the contact surface is stratified based on the virtual material parameters. The theoretical model was verified by simulations and experiments. The first-order natural frequency error was found to be 1.3%. The proposed method provides a new approach for modeling the contact between heterogeneous materials of the machine tool bed–foundation interface.