Considering the needs of high rotating speed and high efficiency in the modern machines, the decreasing clearance between the rotor and the stator is a necessary design. To improve the performance efficiency of these kinds of machines, the radial clearance between the rotating rotor and the stator becomes smaller and smaller. As a result, it is easier for rotor-stator rub to happen and the normal operation of machines will be affected more severely. When a rub-impact happens, the partial rub arises at first. During a complete period, the rub and impact interactions occur between the rotor and stator once or fewer times. Gradual deterioration of the partial rub will lead to the full rub and then the vibration will affect the normal operation of the machines severely. The majority of works was focused on the development of some mathematical models in order to make the rubbing phenomenon more accurately to be understood in the past few decades. Now in our work general model of a rub-impact rotor-bearing system is set up and the corresponding governing motion equations are given. The rubbing model consists of the following forces i.e., radial elastic impact and the tangential Coulomb type of friction. Through numerical calculations, rotating speeds, unbalance and stiffness values are used as control parameters to investigate their effect on the rotor-dynamic system with the help of time histories, phase plane plots, whirl orbits. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed under different operating conditions. Stator flexibility effects are also studied using a modified Jeffcott rotor model .Numerical methods employed in our work are Newmarkβs method and Runge-Kutta method .The Graphs that have been obtained from both methods were compared Finite Element Model of the rotor dynamic system is developed with 2-noded Timoshenko beam elements. The rotary degrees of freedom are eliminated by static condensation. The Campbell diagram is obtained by accounting both gyroscopic effect and Viscous damping matrices. The Newmark time integration scheme is adopted again by incorporating the intermittent rubbing forces at the central node simulating the rigid disk stator interactions and we are trying to get the results, to compare with the obtained results. The thesis is organized as follows: Chapter-1 describes introduction to rotor dynamic problem and literature survey. Chapter-2 deals with the dynamic modeling and equations of motion of various models considered in the present work. Chapter-3 describes the results part as solution of these equations. Chapter-4 gives summary and conclusions of the work
