Rubbing response comparisons between single blade and flexible ring using different rubbing force models

Abstract

In order to simulate the rubbing characteristics of the single blade-casing system with flexible supports, two types of the self-programmed elements (i.e., two-node Timoshenko beam and spring elements) are adopted to establish corresponding finite element models (FEMs) in sequence. Then a node to surface contact algorithm is programmed to build the interface contact between the blade tip and the casing. Next, the forward increment Lagrange multiplier and penalty methods in combination with the model order-reduction technique are separately utilized to solve the rubbing dynamic responses of the studied system under the effects of eccentricity and friction coefficient, and corresponding result comparisons are also made with each other. Finally, some main conclusions are summarized as follows: (1) Relative to the penalty method (PM), the Lagrange multiplier method (LMM) can eliminate the penetration between the blade tip and the casing, but results in the larger vibration amplitudes of rubbing force and displacement especially for the large penetration induced by the large eccentricity and the high rotating speed, generally speaking, those vibration amplitudes obtained from both methods are relatively consistent with each other under the small penetration; (2) Serious rubbing cause the appearance of resonance bands in the amplitude-frequency responses and sidebands in the spectrum; (3) Increasing friction coefficient makes the soft nonlinearity of the system more distinct, meanwhile, strain energy combining with the spectrum is very suitable for identifying the dominant mode of the system.