Interfacial Element for Finite Element Modal Analysis of Bolted Joints

Abstract

Multi-material structures are going to be a main scheme to construct automobiles. For the construction of multi-material structures, techniques to join dissimilar materials are required. The major joining techniques are classified into welding, adhesion and mechanical fastening such as bolted joints and riveting. Especially, bolted joints enable joining of metallic materials (steel and aluminium alloy, etc.) and non-metallic materials (CFRP, etc.) with high joint strength. However, the total stiffness of structures with bolted joints is relatively low because interfaces in bolted joints just contact each other, and its interfacial stiffness is lower than elastic modulus of base materials. Moreover, interfacial stiffness of bolted joints depends on clamping force of bolt and nut. This study has proposed an interfacial element for finite element modal analysis of bolted joints. The interfacial element simulates interfacial stiffness of bolted joints. Contact of interfaces is assumed to be the Hertzian contact of elastic asperities whose peak heights obey the Gaussian distribution. Based on this assumption, the stiffness of the interfacial element is derived from the compressive stress and the surface texture of the interfaces. By using the finite element model with the interfacial element, the modal analysis computes the natural frequency and the vibration mode. Finite element simulations and hammering tests have been conducted with several bolted joints. In general, the natural frequency of the bolted joints in the hammering tests increases with the increase in the clamping force, but it is lower than the calculation results in which the stiffness reduction of the jointed interfaces is ignored. The calculation results by using the proposed interfacial element agree with the hammering tests. Therefore, the proposed interfacial element contributes to improvement of modal analysis of bolted joints by mathematically modelling stiffness reduction of jointed interfaces based on tribology.