In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 − D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D − 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.
This work develops an analytical method to estimate the natural frequency splitting and principal instability of the rotating cyclic ring structures. An elastic model is built up under the ring-fixed frame by using the energy method. The modeling leads to a partial differential equation with time-variant coefficient. The eigenvalue is formulated to estimate the natural frequency splitting, principal instability and their relationships. The dependence of the basic parameters on the natural frequency splitting and principal instability is demonstrated. The principal instability can occur at the splitting natural frequencies but cannot at the repeating ones. A classical problem regarding the parametric instability of the rotating ring with stationary supports and the inverse problem are examined. The results verify that the natural frequency splitting does not mean unstable for the former problem, but for the latter the splitting implies unstable. Besides, the model is transformed into the support-fixed frame and thus an equivalent time-invariant model is obtained, which is solved by using the general vibration theory. The analytical method is validated through the comparisons with the results in the open literature and especially the comparisons between the results from the two types of frames.
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