A novel way to detect transverse surface crack in a rotating shaft

Abstract

This paper presents a novel way to detect fatigue transverse cracks in rotating shafts. The proposed detection methodology exploits both the typical nonlinear breathing phenomenon of the crack and the coupling of bending–torsional vibrations due to the presence of crack for its diagnosis. A transient torsional excitation is applied for a very short duration at specific angular orientation of the rotor and its effect in the lateral vibrations is investigated. Wavelet transforms (WTs) is used in revealing the transient features of the resonant bending vibrations, which are set up for a short duration of time upon transient torsional excitation. Variation of peak absolute value of wavelet coefficient (of the transient lateral vibration response) with angle at which torsional excitation is applied is investigated. The correlation of this variation with the breathing pattern of the crack is studied. The sensitivity of the proposed methodology to the depth of crack is investigated. The detection methodology gives a vibration response signature that closely correlates with and is very specific to the behaviour of the transverse surface crack in a horizontal rotor. The response features are not likely to be exhibited by other common rotor faults under similar excitation conditions making the proposed detection methodology unambiguous. The fact that the rotor is not required to stop and that the detection process is applied for a rotating shaft with only a short period transient external excitation makes the methodology more convenient.

Introduction

Fatigue cracks are a potential source of catastrophic failures in rotors. Researchers have put in considerable effort to develop a foolproof and reliable strategy to detect cracks in rotors. One of the approaches investigated in detail is the phase and amplitude variation in the 2x component of steady-state (unbalance) response. Due to the asymmetry of the stiffness due to the existence of crack, several authors [1], [2], [3], [4], [5], [6], [7] have focused their attention on 1x and 2x components of rotor vibration and discussed the effect of crack on these frequency components. Experience, however, has shown that even for shallow to moderate cracks, the presence of 2x component of vibration cannot be considered as a reliable indicator of the presence of a crack in the rotor since there are several other mechanisms in rotor that generate second harmonic (2x) component. Although the crack breathing is responsible for the presence of higher harmonic component (3x) in the response, its amplitude is very small. The presence of higher harmonics cannot conclusively single out the crack as a fault in the rotor as there are several other mechanisms in the rotor bearing system that generate the higher harmonics.

Alternative to the detection of cracks using higher harmonic components in bending vibration, another detection methodology explored the effect of coupling between lateral, axial and torsional vibrations caused by the presence of crack in a rotor. Papadopoulos and Dimarogonas [8], [9] first proposed this effect as a useful and more reliable source for the detection of cracks. The presence of bending vibration frequencies in torsional spectra had been cited as potential crack indicators. Muszynska et al. [10] analysed torsional/lateral cross-coupled vibration response. Ostachowicz and Krawczuk [11] analysed coupled torsional and bending vibrations of a rotor with an open crack using finite element model. They applied an external torsional moment to the rotor and found the effect on lateral vibrations due to coupling effect of crack. Papadopoulos and Dimarogonas [12] studied coupling of lateral and longitudinal vibrations and have proposed the coexistence of lateral and longitudinal vibration frequencies in the same spectrum as an unambiguous crack indicator. Papadopoulos and Dimarogonas [13] have studied the stability of cracked shaft in coupled vibration mode. The effect of closing crack was taken into account by representing variation in stiffness in the form of a truncated cosine series. A case study on 300 MW steam turbine, wherein the lateral vibration spectrum showed subharmonics of fundamental longitudinal natural frequency was reported. Darpe et al. [14], [15] and Collins et al. [16] studied the detection of cracks using axial impulses to a rotating cracked shaft. They reported the presence of combination harmonics in the lateral vibration spectrum. Gounaris and Papadopoulos [17] investigated coupled vibration response between bending and longitudinal vibration by applying lateral excitation and measuring longitudinal vibrations on a rotating shaft with open crack assumptions.

Although [14], [15], [16] were perhaps the only studies on coupled vibrations of cracked rotors with breathing crack model, most of the previous reported work focused on open crack model. The open crack model in early studies served the purpose of reducing the stiffness of the rotor to account for the effect of the crack. However, to represent the actual breathing behaviour of the cracked rotor, change in the stiffness due to rotation of the rotor under gravity must be appropriately modelled. The crack breathing is a significant source of several nonlinear phenomena that cannot be revealed through the open crack model. Recently, this fact has been explored extensively by Darpe et al. [18]. They studied the effect of using exact breathing model for rotating shaft and investigated the coupling between all modes of vibration for cracked rotor. They proposed several new crack indicators and showed that these indicators are sensitive to crack depth.

Using Alternate Frequency/Time Domain (AFT) and path following method, Sinou and Lees investigated the change of natural frequencies, harmonic components and evolution of orbital pattern of the cracked rotor at half the critical speed [19]. Recently, model-based identification of crack has also been attempted [20], [21].

In the recent past several researchers have applied the wavelet transforms (WTs) for analysis of dynamic signals of the variety of mechanical systems to detect faults such as crack, bearing defects, rotor rub, etc. Adewusi and Al-Bedoor [22] applied WT to experimental signal of propagating transverse crack to track the growth of important harmonic components of the rotor speed. Zou and Chen [23] made a comparative study on time–frequency feature of transient response of cracked rotor by Wigner–Ville distribution and WT. Wan et al. [24] carried out vibration analysis of cracked rotor sliding bearing system with rotor-stator rubbing by harmonic WT. Zou et al. [25] analysed the torsional vibrations of a rotor with transverse crack using switching crack model and time–frequency features of torsional vibrations of the rotor are presented using WT. Prabhakar et al. [26] investigated the use of continuous wavelet transforms (CWTs) for crack detection and monitoring in a cracked rotor system during its transient passage through critical speed. In none of the above studies on application of WT to crack detection, an unambiguous detection strategy of crack with certainty could be proposed. The major problem, of distinguishing the cracked rotor response from that of the nonlinear response generated by other similar faults, still remains unsolved.

In this paper, the breathing crack model is used to investigate a novel use of transient external torsional excitation for crack detection. The torsional excitation is applied at specific angular position of the rotating shaft so that the periodic opening and closing of the crack is exploited to generate distinguishing response characteristics that is typical to the cracked rotor and cannot be expected in case of other rotor faults. The proposed crack detection strategy uses the coupling of vibrations of cracked rotor and breathing behaviour of crack. The proposed detection strategy is more reliable and unambiguous.

In this work, finite element model of a simple single disc rotor is considered. The rotor is modelled with Timoshenko beam elements and a rotor segment containing a transverse surface crack at centre of the span is modelled with a Timoshenko beam element with modified stiffness matrix derived in Ref. [18]. The modified stiffness matrix takes into account all the coupling phenomena that exists in a cracked rotor, i.e., bending-longitudinal, bending-torsion, longitudinal-torsion. The FE model of the rotor with six degrees of freedom per node and modified stiffness matrix for cracked region is used to study lateral vibration response of the rotor subjected to transient torsional excitation.