Dynamic Analysis of a Slant-Cracked Functionally Graded Rotor-Bearing System

The dynamic response of a power law based functionally graded (FG) rotor-bearing system with a slant crack has been analysed in the present work. The vibration response of an FG rotor-bearing system with a slant crack has been simulated using the Houbolt time marching scheme for different crack depths. The time-domain vibration responses are converted into the frequency domain using Fast Fourier Transform (FFT) to identify the crack features in order to detect and monitor the cracks. The sub-harmonic frequency components of the steady-state frequency spectrum were centred on the FG rotor’s operating speed, separated by the interval frequency corresponding to the torsional frequency. The sub-harmonic frequency components of the transient state frequency domain were found to be centred on the critical speed of the FG rotor system. The subharmonic frequency components of the dynamic response confirm the existence of a crack in the FG rotor system, which could be used to detect the crack in an FG rotor system.

Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

The traditional modeling method of rotor system with a slant crack considers only integer-order calculus. However, the model of rotor system based on integer-order calculus can merely describe local characteristics, not historical dependent process. The occur of fractional order calculus just makes up for the deficiency in integer-order calculus. Therefore, a new dynamic model with a slant crack based on fractional damping is proposed. Here, the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method. The proposed model is simulated by Runge-Kutta method and continued fraction Euler method. The influence of the fractional order, rotating speed, and crack depth on the dynamic characteristics of rotor system is discussed. The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order. With the increase of the rotating speed, the amplitude of first harmonic component becomes gradually larger, the amplitude of the second harmonic becomes smaller, while the amplitude of the other frequency components is almost invariant. The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping. With the increase of the slant crack depth, the amplitude of the transverse response frequency in the rotor system with a slant crack increases, and the amplitude in the second harmonic component also increases significantly. In addition, the torsional excitation frequency and other coupling frequency components also occur. The proposed model is further verified by the experiment. The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Model-driven fault diagnosis of slant cracks in aero-hydraulic straight pipes

A model-driven fault diagnosis method for slant cracks in aero-hydraulic straight pipes is presented in this paper. First, fracture mechanics theory and the principle of strain energy release are used to derive an expression for the local flexibility coefficient of straight pipes with slant cracks. The inverse method of total flexibility is used to calculate the stiffness matrix of straight pipe elements with slant cracks. Second, the Euler-Bernoulli beam model theory is used in conjunction with the finite element method to construct a dynamic model of the cracked pipe. Finally, a contour map method is used to diagnose the slant crack fault and quantitatively determine the crack position and depth. Experimental results show that the proposed method can accurately and effectively identify a slant crack fault in aero-hydraulic pipelines.