A novel nonlinear contact stiffness model of concrete–steel joint based on the fractal contact theory

The heavy-duty machine tool is usually assumed in the concrete foundation, in which the machine tool-foundation joints have a critical effect on the working accuracy and life of heavy-duty machine tool. This paper proposed a novel contact stiffness model of concrete–steel joint based on the fractal theory. The topography of contact surface exist in concrete–steel joint has a fractal feature and can be described by fractal parameters. Asperities are considered as elastic, plastic deformation in micro-scale. However, the asperities of concrete surface will be crushed when the stress is larger than their yield limit. Then, the force balance of contact surfaces will be broken. Here, an iteration model is proposed to describe the contact state of concrete–steel joint. Because the contact asperities cover a very small proportion (less than 1%), the load on crushed asperities is assumed carried by other no contact asperities. This process will be repeated again and again until the crushed asperities are not being produced under external load. After that, the real contact area, contact stiffness of the concrete–steel joint can be calculated by integrating the asperities of contact surfaces. Nonlinear relationships between contact stiffness and load, fractal roughness parameter G, fractal dimension D can be revealed based on the presented model. An experimental setup with concrete–steel test-specimens is designed to validate the proposed model. Results indicate that the theoretical vibration mode shapes agree well with the experimental variation mode shapes. The errors between theoretical and experimental natural frequencies are less than 4.18%. The presented model can be used to predict the contact stiffness of concrete–steel joint, which will provide a theoretical basis for optimizing the connection characteristic of machine tool-concrete foundation.