Model-based prediction of normal contact stiffness values for bolted joints

Virtual testing of a technical product with respect to its acoustic behavior enables engineers to evaluate the design without the need for physical prototypes. In order to virtually test the acoustic behavior, the effects of both, the dynamic excitations of the system and the transfer behavior of sound from the excitation source to the user must be considered in simulation models. The transfer path is primarily influenced by resonance frequencies and damping. In structures connected via bolted joints, damping within the joint is the dominant source of damping along the transfer path. Therefore, appropriate structural dynamic models of bolted joint stiffness and damping are necessary. These models must represent both the normal and tangential stiffness and damping in bolted joints. Currently, experimental investigations are still required for the parameterization of bolted joint models. As an example, for the normal behavior, optical 3D measurements of the joint surfaces are conducted to obtain their topology. The surface topology is then used to identify parameters of an exponential contact law through elasto-plastic material modeling. To eliminate the need for complex measurements during model parameterization, this article presents a method for predicting the normal contact stiffness in bolted joints based on numerically generated surfaces. For this purpose, an algorithm is implemented to generate surfaces with different roughness properties. Based on these surfaces, the exponential contact law through elasto-plastic material modeling is performed. This calculation is used to determine the contact stiffness at different pressures. A Design of Experiments is conducted in which the surface roughness is varied to calculate the normal contact stiffness. Therefore, the surface parameters S A , S sk and S ku are varied. S A describes the average roughness and thus the size of the real contact area, S sk characterizes the asymmetry of the height distribution and provides information on load-bearing peaks or valleys, and S ku quantifies the sharpness of the distribution and thus the proportion of peaks. These properties significantly determine the microscopic deformation at the contact and therefore directly affect the stiffness and damping values of bolted joints. The resulting normal contact stiffness values are then used to create a regression model. This makes it possible, for the first time, to derive normal contact stiffness values for different surface roughnesses without performing any physical measurements. The normal contact stiffness values calculated from the regression model are used to parameterize a structural dynamic finite element model of the Brake-Reuß-Beam bolted structure. The model predicts the eigenfrequencies with a deviation of about 1.9% compared to experimental results, confirming the accuracy of the proposed approach.