Modern day rotors are designed and for achieving high rotation speed. Researchers have put in considerable effort to develop a foolproof and reliable strategy to detect cracks in rotors. In this research, the dynamic behavior of a rotor system with a slant crack on the shaft is investigated. A Jeffcott rotor with a slant crack under arbitrary crack orientation angles on the midpoint of its shaft is considered. This solution relates to three crack model; open crack, close crack and breathing one. Breathing phenomenon is explained in detail; some of the existent models that are used in literature are discussed. Equations of the motion are obtained in four directions i.e. two transversal directions, one torsional direction and one longitudinal direction. The effects of gravity and external torsional excitation are also taken in to account. By considering the effects of crack on the stiffness matrix only, nonlinear equations of the system are solved using numerical method. Also effects of crack depth and the amplitude of external torsional excitation on the spectrum of the responses are investigated. In this research, the elements of compliance matrix for different crack orientations are calculated. The influence of crack orientations on the flexibility coefficients and steady response of the system is also investigated. It is shown that some of the flexibility coefficients take their maximum values for (approximately) 60 o crack orientation unexpectedly. It is concluded that any increase in the amount of crack angle from 30 o to 90 o (transverse crack), does not increase (or decrease) all of the flexibility coefficients monotonously. Spectrums of the responses indicate same characteristics. Although the elements of compliance matrix for slant cracks have been already reported in literature, some corrections in to the matrix elements were introduced in this thesis. For the first time, crack compliance matrix for crack orientations more than 90 o is calculated. Based on the changes in these elements that are in third row and - due to symmetry - third column of the crack compliance matrix, a novel way for crack detection are introduced and developed. It is shown that a slant cracked shaft under two directions of rotation has different compliance matrix; therefor it can be used as a criteria for crack detection in real rotor systems. This simple, practical and effective method can be used for any rotating systems especially rotors. Improving one of the available crack breathing models (CCLP) is another innovation that is introduced in this thesis. The introduced model (ICCLP) represents crack breathing behavior more accurately. Key Words: Rotor Dynamics, Slant crack, compliance matrix, crack detection, Breathing Model.
