Nonlinear Normal Modes and the Dahl Friction Model Parameter Identification

Abstract

Fretting wear of steam generator tubes due to vibration induced by fluid flow remains a serious problem in the nuclear industry. Azizian and Mureithi [1] have recently developed a hybrid friction model to simulate the friction behavior of tube-support interaction. However, identification of the model parameters remains unresolved. To identify the parameters of the friction model, the following quantities are required: contact forces (tangential force (friction) and normal force (impact)), the slip velocity and displacement in the contact region. Direct measurement of these quantities by using a steam generator tube interacting with its supports is difficult. To simplify the problem, a beam, clamped at one end and simply supported with consideration of friction effect at the other is used. The beam acts as a mechanical amplifier of the friction effects at the microscopic level. Using this simple setup, the contact forces, the sliding velocity and the displacement can be indirectly obtained from the beam’s vibration response measurements. A new method based on nonlinear modal analysis was developed to calculate the contact forces. This method is based on the modal superposition principle and Fourier series expansion. The nonlinear normal modes (NNMs) and the generalized coordinates (GCs) have been identified experimentally as functions of the excitation level, the frequency, the preload in the contact area, with and without lubrication. Three hypotheses and related analyses to identify the NNMs and GCs were tested; the analysis based on the harmonic balance method gives the best results for reconstructing the accelerometer signals with an error less than 2% for all excitation levels compared to more than 2% for other methods. The successful signal reconstruction makes it possible to accurately identify the parameters of the Dahl friction model. This is also the first step to identify the parameters of the hybrid friction model.