1.2 Health monitoring of rotating machinery
1.2.1 Vibration based monitoring on rotating machinery
Vibration signatures of rotor defects are not as unique as to be distinctly identifiable, due to overlapping dynamics and statistical reasons. After the pioneering works of Hookes (1660), Bernoulli (1705), Bernoulli (1751), Euler (1774) and others, researchers were able to solve the problem of vibrations of a bar. Continuous beam theories appeared and established after the work of many later scientists, including Rayleigh and Timoshenko. However, due to complexities associated with the crack mechanism, theories on damaged beams and rotors are far from being established. Even after a volume of papers published on cracked structures in the last three decades, a consistent cracked beam theory is yet to be developed. Downham (1976) made a comprehensive study about vibration based analysis of recent advancement in fault diagnosis in rotating machinery by outlining various case studies of rotor faults, such as the gear and bearing wear and turbine blade failure. Thomas (1984) illustrated vibration monitoring technique for large (above 500 MW) turbo-generator using the frequency measurement and its type for the data analysis. Gottlich (1988) adopted the idea of offline performance map of vibration based condition monitoring to describe the performance efficiency of a rotating machine. The performance map is constructed relative to the actual maximum efficiency data and the design efficiency, whose combination with the measured vibration data enhances the running conditions of system. Smalley et al. (1996) illustrated a method for assessing the severity of fault using
vibrational data and its related cost effectiveness using the net present value method. Some guidelines were formulated in comparison of maintenance and downtime cost against the possible cost after damage of machinery. Vibration based condition monitoring aided an immense performance of machinery fault diagnosis and is examined by Stewart (1976), Smith (1980) and Taylor (1995). Smith (1980) analyzed the faults qualitatively using vibration characteristic including the nonlinear effects. In the same way Stewart (1976) and Taylor (1995) included how the measured vibration data can be utilized for the fault diagnosis process.
Vibration signatures of a cracked rotor are not unique and the cost associated with failure due to cracks is high, hence the investigation of cracked rotors draws considerable attention from academia and industry alike. Using signal based methods researchers, such as Bently and Muszynska (1986a), Allen and Bohanick (1991), and Eisenmann (1998), reported the crack detection onto the shaft for the various cases. The root cause of shaft cracks for various cases are studied, such as due to the misalignment, fretting corrosion, and heavy side loads in generators, compressors, gears and nuclear coolant pumps. Based on the vibration method for the crack detection, Bently and Muszynska (1986a) presented a work in which spectrum amplitude at 1x gradually increases during rotation of shaft.
However, other researchers illustrated that 2x component is the good indicator of shaft cracks. The judgement by Werner (1993) was that spectral at 1x trend is a better indicator for crack in the shaft response, but at 2x it is mainly because of the local asymmetric stiffness of shaft owing to the crack. Also he gave the recommendation that the response at 2x spectral is too much sensitive owing to other factors, like misalignment, side loads, support system asymmetry, etc., to be a reliable behaviour of cracks onto the shaft. Various authors have also recommended in their studied the spectral at 2x response for the crack detection in the shaft, such as Saavedra
and Cuitino (2002). They demonstrated the spectral at 2x behaviour in theoretical and experimental analysis of a cracked shaft. They observed based on the vibration at half of the critical speed of cracked rotor for horizontal shafts, and found that it is clearer in behaviour as the crack indicator. As per the study through fracture mechanics by Lazzeri et al. (1992), it is observed that in monitoring of operational diagnosis, the utilization of 2x spectral in a machineries to identify the cracks is better. Bently and Muszynska (1986b) illustrated 2x spectral based on comparison of start-up/coast-down of rotor, which is more useful than steady-state operation. Sanderson (1992) presented detection of crack based on the propagation of crack in a nuclear plant of 935 MW turbo-generator. Herein, the crack was detected when it reaches 25%
of the shaft diameter and then machine was sent for maintenance. Muszynska et al. (1992) illustrated that the torsional vibrations are excited even through purely radial forces in a cracked shaft due the presence of unbalance and misalignment. Based on observation in the horizontal and vertical machines during monitoring of torsional vibrations they studied that the spectrum at 4x, 6x, 8x, etc. were found to the lowest torsional frequency, which was helpful in the detection of crack.
Gasch and Liao (1996) illustrated the detection of crack based on orbit shape method.
Herein, the vibration of shaft in the spectrums are forward orbits of 1x, 2x and 3x frequencies and same also for backward frequencies. The monitoring on backward harmonics, particularly in transients case, can be used to detect presence of cracks. An experimental verification of the above method has been illustrated by Liao and Gasch (1992) based on a different depth levels of crack in a test rig. Plaut et al. (1994) studied the transient behaviour of a cracked shaft based on a constant acceleration or deceleration passed a critical speed. The review paper of Dimarogonas (1996) emphasizes the importance of analysis of cracks. Goldman and Muszynska (1999)
presented the periodicity of major rotor malfunctions, most defects cause rotor vibration component at multiples (nX) or fractions {(n / m) X} of the shaft spin speed. Tiwari (2005) discussed improving estimation of the bearing dynamic parameters along with residual unbalance in a two-degree of freedom rotor-bearing system using a specific identification algorithm with the help of regression matrices. Zhao et al. (2012) used multivariate empirical mode decomposition (EMD) and full spectrum for the condition monitoring of centrifugal pumps. A brief summary of defects and their periodicity is presented in Table 1.1, based on the compilation of Goldman and Muszynska (1999), and Bachsmid et al. (2010).
Table 1.1 Periodicity of common rotor defects
S. N. Defect Frequency Nature
1 Mass unbalance, rotor eccentricity
1X generally an elliptical orbit
2 Bearing misalignment 1X, 2X, 3X Axial and radial vibration components present
3 Bearing wear off 0.5X, 1X
4 Shaft bow 1X
5 Rotor stator rub 0.33X, 0.5X bifurcation diagrams and Poincare maps helpful
6 Transverse crack 1X, 2X 2X components are the indicators
7 Axial rotor asymmetry 2X native vibration due to intrinsic asymmetry
8 Flexible coupling misalignment
1X, 2X, 3X 1X predominant but other harmonics present
9 Rigid coupling misalignment
1X
10 Loosening bearing bushes 2X up to 6X may be present, out of phase with 1X