Dynamic Analysis of Presliding Friction via Skeleton Method

Friction, which evidently appears in any mechanical systems incorporating parts with relative motion, manifests itself as material nonlinearity. Depending on its application, friction can be a desirable thing or a drawback in the system. In order to optimally utilize or compensate for the frictional effect in a system, characterization of the frictional behaviour is very crucial. The classical Coulomb friction model has been widely used especially in the field of control engineering to compensate for the static force in a system. In spite of its simplicity, the effectiveness of the Coulomb model in capturing the frictional behaviour in the presliding regime is very low and it does not incorporate the hysteresis property that evidently appears. Hitherto, a question might arise whether the Coulomb model sufficient to characterize friction in mechanical systems. This paper deals with the characterization of equivalent modal parameters, namely the stiffness and damping elements, to effectively represent the dynamic behaviour of mechanical systems subjected to hysteresis friction forces. The analysis is carried out by using the skeleton technique, which employs the instantaneous amplitude and frequency of the excitation input and the response output of the system under a certain forced excitation. Observing the response signal of a free vibration system and performing mathematical manipulation on its analytic signal form, the equivalent modal parameters can be constructed. Subsequently, the dynamic analysis is performed in the equivalent system and as a conclusion the results show good agreement with the dynamic properties of the original system for wide range of excitation.