This paper presents a novel way to detect fatigue slant cracks in rotors based on theoretical discussion. Hence, the dynamic behaviour of a Jeffcott rotor system with a mid-span slant crack under arbitrary crack orientations is studied. First, using concepts of fracture mechanics, the flexibility matrix and subsequently the system’s stiffness matrix are calculated. A symmetric relation for a global stiffness matrix is presented and proved. Next, the motion equations of the system that are obtained in four directions, two transverse, one torsional and one longitudinal, are solved using the Runge–Kutta numerical method. The characteristics of crack orientations for angles greater than 90° (transverse crack) are investigated in detail and their influence on the elements of the crack compliance matrix is presented. Also, slant crack characteristics with complementary angles are compared to each other. It is shown that the difference between cracked systems with complementary angles is only in 3rd row (3rd column) of the crack compliance matrix, and also it is shown that due to the presence of a slant crack, the system responses in forward and backward motion are different. Using the frequency responses of the shaft obtained, a technique to detect the existence of slant cracks on the shaft was proposed. This novel method is a simple way that can be used for slant crack detection in rotors.
Rotor system Slant crack Complementary crack angles Backward and forward whirl