Vibration Analysis of Multi Degree of Freedom Self-excited Systems

ABSTRACT: It is known that nonlinearities in the friction-velocity curves of dry friction may lead to instability of the steady frictional sliding, namely, friction-induced vibration. Therefore, stick-slip vibration is an important issue in mechanical engineering, and understanding the dynamics of stick-slip and its possible elimination also becomes important, especially for applications requiring high-precision motion. Among the many everyday examples of friction sounds, violin music and brake noise in automobiles represent the two extremes in terms of the sounds they produce and the mechanisms by which they are generated. Of the multiple examples of friction sounds in nature, insect sounds are prominent. In this thesis, multi-degree degree of freedom self-excited vibrating systems which are excited by the friction force imposed from a moving surface will be considered. A Coulomb friction law is introduced in the equations of the contact point taking into account all the possible status: separated, sliding or sticking. The vibration response and velocity of system’s components under various initial conditions will be calculated and reported. The effect of initial conditions, velocity of moving surface, mass, spring stiffness coefficient, damping and its coefficient of friction will be studied and discussed. The results are obtained for occurrence and nonoccurrence of stick slip phenomena. It is thought that this design guides may be useful in the control and reduction of the vibrations induced by dry friction. Furthermore, the result of this study provides an understandable structure for vibro-acoustical analysis of self-excited vibrating systems.Keywords: Friction Contact, Friction-Induced Vibrations, Self-Excited systems, Brake Noise, Non-linear Time-Series Analysis, Chaotic Dynamics. …………………………………………………………………………………………………………………………