A Stiffness Model for Bolted Joints Considering Asperity Interactions of Rough Surface Contact

Abstract A revised fractal contact model considering asperity interactions is proposed. The displacement of the mean of asperity heights is used to represent the effects of the asperity interactions. Then, the critical contact area will be dependent on the contact load, and the contact stiffness will be an integral whose integrand is an implicit expression. The fractal dimension and the fractal roughness are obtained by the measurement of the surface profile to calculate the theoretical contact stiffness. The measurement of deformation is conducted to obtain the actual contact stiffness for verification, and the results show that the proposed model is closer to the experimental results than other models without considering asperity interactions. Once the contact stiffness is determined, a new equivalent normal stiffness model for bolted joints considering the contact of two rough surfaces is also proposed. Since the contact stiffness is dependent on the clamped force, the equivalent normal stiffness for bolted joints is calculated iteratively at given initial preload and external separating force. Different from the classical model, the equivalent normal stiffness for bolted joint decreases with the external separating force increases, and this stiffness loss will become larger with initial preload decreases. In this sense, the proposed equivalent normal stiffness model is a way to determine the suitable initial preload for different sizes of bolts when the stiffness loss is restricted to a certain range.