INSTABILITAS PARAMETRIK SISTEM POROS ROTOR DENGAN CACAT RETAK MELINTANG (PARAMETRIC INSTABILITY OF CRACKED ROTOR SHAFT SYSTEMS) - Jabir, A.
Dynamic loading on shaft-rotor system coupled with material production process imperfection may lead to crack on the system. This phenomenon must be taken into consideration if catastrophic failure is to be avoided In this research, the effects of transversal crack on the dynamic behavior and stability of shaft-rotor system is investigated. Due to the complexity in the modeling of natural crack, as afirst attempt, this study considers artificial crack. Crack is introduced by cutting the shaft transversally at a particular location along the shaft. The cut simulates a crack with a certain depth and width. The existence of this crack results in position-dependent area moment of inertia which in turns effect the flexural rigidity of the shaft. For shaft rotating at constant speed, the flexural rigidity becomes time dependent and periodic. Hence, the shaft-rotor system flexural deformation will be governed by a second-order linear differential equation with time-varying coefficients. Such systems could not be solved analytically. The solution may be obtained via a closed-form numerical solution algorithm developed based upon discretization of the parameters continua. Floquet theory is employed to evaluate the system stability. Results are presented as parametric stability charts depicting the stability of the system for various crack depth and rotational speed. The stability charts show unstable regions emanate from ? / ?n = 1/ n ; where ? is the shaft rotational frequency, € is the equivalent natural frequency of the system, and n = 1, 2, 3, .... Runge-Kutta direct integration method is utilized to validate the algorithm and stability analysis. Results from the Runge- Kutta integration and those obtained via the algorithm are in close agreement. Evaluation of results in the unstable regions by direct integration yields unstable response which further validate the algorithm and the stability analysis algorithm based on Floquet Theory.