Identification of Friction Model Parameters Using the Inverse Harmonic Method

A hybrid friction model has been developed by Azizian and Mureithi (2013, “A Hybrid Friction Model for Dynamic Modeling of Stick–Slip Behavior,” ASME Paper No. PVP2013-97249) to simulate the general friction behavior between surfaces in contact. However, identification of the model parameters remains an unresolved problem. To identify the parameters of the friction model, the following quantities are required: contact forces (normal and tangential or friction forces), the slip velocity, and the displacement in the contact region. Simultaneous direct measurement of these quantities is difficult. In the present work, a beam clamped at one end and simply supported with the consideration of friction at the other is used as a mechanical amplifier of the friction effects at the microscopic level. Using this simplified approach, the contact forces, the sliding velocity, and the displacement can be indirectly obtained by measuring the beam vibration response. The inverse harmonic balance method is a new method based on nonlinear modal analysis which is developed in this work to calculate the contact forces. The method is based on the modal superposition principle and Fourier series expansion. Two formulations are possible: a harmonic form formulation and a subharmonic form formulation. The approach based on subharmonic forms coupled with spline fitting gave the best results for signal reconstruction. Signal reconstruction made it possible to accurately identify the parameters of the hybrid friction model with a multiple step approach.