In the rotor system, depending upon the ratio of rotating (internal) damping and stationary (external) damping, above the critical speed may develop instability regions. The crack adds to the rotating damping due to the rubbing action between two faces of a breathing crack. Therefore, there is a need to estimate the rotating damping and other system parameters based on experimental investigation. This paper deals with a physical model based an experimental identification of the rotating and stationary damping, unbalance, and crack additive stiffness in a cracked rotor system. The model of the breathing crack is considered as of a switching force function, which gives an excitation in multiple harmonics and leads to rotor whirls in the forward and backward directions. According to the rotor system model considered, equations of motion have been derived, and it is converted into the frequency domain for developing the estimation equation. To validate the methodology in an experimental setup, the measured time domain responses are converted into frequency domain and are utilized in the developed identification algorithm to estimate the rotor parameters. The identified parameters through the experimental data are used in the analytical rotor model to generate responses and to compare them with experimental responses.
In the present work, an experimental investigation of a transverse fatigue crack has been carried out. A mathematical modelling of cracked rotor system along with the measured vibration is used to find crack parameters that not only detect the fault but also quantify it. Many experimental studies on cracks considered the crack as a slit or notch, which remains open. However, such flaws do not mimic a fatigue crack behavior, in which crack front opens and closes (i.e., breathes in a single revolution of the rotor). The fatigue crack in rotors commonly depicts 2× frequency component in the response, as well as higher frequency components, such as 3×, 4× and so on. In rotors, both forward and backward whirling take place due to asymmetry in rotor, and thus the fatigue crack gives the forward and backward whirl for all such harmonics. A rotor test rig was developed with a fatigue crack in it; rotor motions in two orthogonal directions were captured from the rig at discrete rotor angular speeds using proximity probes. The directional-spectrum processing technique has been utilized to the measured displacements to get its forward and backward whirl components. Subsequently, it is executed in a mathematical model-based estimation procedure to obtain the crack forces, residual unbalances, and remaining rotor system unknown variables. Estimation of crack forces during rotation of the shaft gives its characteristics, which can be used further to develop newer crack models.
In the present work, a procedure for the estimation of internal damping in a cracked rotor system is described. The internal (or rotating) damping is one of the important rotor system parameters and it contributes to the instability of the system above its critical speed. A rotor with a crack during fatigue loading has rubbing action between the two crack faces, which contributes to the internal damping. Hence, internal damping estimation also can be an indicator of the presence of a crack. A cracked rotor system with an offset disc, which incorporates the rotary and translatory of inertia and gyroscopic effect of the disc is considered. The transverse crack is modeled based on the switching crack assumption, which gives multiple harmonics excitation to the rotor system. Moreover, due to the crack asymmetry, the multiple harmonic excitations leads to the forward and backward whirls in the rotor orbit. Based on equations of motions derived in the frequency domain (full spectrum), an estimation procedure is evolved to identify the internal and external damping, the additive crack stiffness and unbalance in the rotor system. Numerically, the identification procedure is tested using noisy responses and bias errors in system parameters.
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