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In mechanical structures where the components are joined by bolts, the vibration damping depends mainly on energy dissipation due to friction at the contact surfaces. In this paper, we propose a method for estimating modal damping ratios of bolted structures with partial overlap region by the dynamic finite element contact analysis. First, the eigenvalue analysis considering the contact surface stiffness is performed and the natural frequencies are evaluated to determine the pressure load to be applied to the contact surface in the contact analysis. Then the transient analysis is performed with a single frequency sinusoidal forced displacement to obtain the frictional dissipated energy for each mode shape and the modal damping ratios are estimated from the dissipated energy. The validity of the proposed method is confirmed by comparing the estimated damping ratios with the experimental results. We carry out the contact analyses by varying the excitation amplitude to examine the amplitude dependence of the damping ratio and reveal the reason for its amplitude dependence based on the slip velocity and the frictional force on the contact surface. The results show that the modal damping ratios have a strong amplitude dependence. The damping ratios change drastically in the lower amplitude range while they indicate a small change in the higher amplitude range. This is because the transitions from sticking to slipping occur over the whole contact area in the lower amplitude range, as a result, the dissipated energy rapidly increases compared to the vibration energy. In contrast, the dissipated energy increases at the same rate as the vibration energy in the high amplitude range.

The present paper describes edge contact analyses for power transmission gears using tooth-flank-film elements, which have been proposed for finite element analyses of tooth stresses. For edge contact analyses, the tooth-flank-film elements are placed not only on usable flanks but also over tooth edges. Finer elements on edge neighboring areas and on the parts of usable tooth flanks where tend to contact with mating edges enable the edge contact to be analyzed. Comparisons of calculated distributions of tooth contact stress with observed tooth flanks after a running test showed the validity of the proposed method for edge contact analyses.

Mechanical joints such as bolted and spot welded joints are widely used to join plate structures. The existence of contact interface in the joint increases the vibration damping in the structure because the energy dissipation due to friction occurs at the interface. In this paper, we propose a procedure for calculating the energy dissipation at the interface using finite element analysis to estimate the damping for the fundamental and the higher modes. We use the static contact analysis instead of the dynamic contact analysis to reduce computational effort and use the mode shapes of linear FE model of the joined plate structure as the forced displacement in the static contact analysis. This enables us to obtain the energy dissipation depending on the mode shape for each mode. To improve the calculation accuracy of the energy dissipation, we apply a surface load on the overlap (interface) region and find the necessary value of surface load. To validate the proposed procedure, the modal damping ratios estimated from the dissipated energy are compared with the measured damping ratios. The results show that the proposed procedure enables to accurately estimate the energy dissipation of the joined plate structure. The necessary surface load increases with increasing mode number and varies almost proportionally with the square of the angular frequency.