In previous chapters, the measurement and signal processing techniques, transducers, signal conditioners and signal analysis equipments are described, which are used in the rotating machinery condition monitoring. It is very important to display the measured signal in convenient form so as to be useful for the interpretation of the condition of rotating machinery. In the present chapter, by looking at various forms of measured signal possible condition of machinery is provided. It also looks into the correlation of a particular signature with a particular failure in more details. Every fault has a specific signature in the measured signal and it is most convenient and cheapest way to identify possible fault in machinery. Now very advanced signal processing techniques (wavelet transform, neural network, fuzzy logic, genetic algorithms, genetic programming, and machine support vectors) are being applied in vibration signals of laboratory test set ups to detect, locate and quantify the faults and based on this even the life of the machinery is also being predicted. A brief review of applications of these techniques for rotating machinery condition monitoring is provided since detailed treatment to these newly emerging methods is beyond the scope of the present book. Proactive action to prevent a failure is the better than the detection of failure. The next chapter will be dealt with introduction of the active control of rotors by magnetic bearings, which is still a research and applied area in the field of rotor dynamics.
Many rotating machines, such as power station turbo-generators, may be considered as consisting of three major parts; the rotor, the bearings (often fluid bearings) and the foundations. In many modern systems, the foundation structures are flexible and have a substantial influence on the dynamic behaviour of the complete machine. These rotating machines have a high capital cost and hence the development of condition monitoring techniques is very important. Vibration based identification of faults, such as rotor unbalance, rotor bends, cracks, rubs, misalignment, fluid induced instability, based on the qualitative understanding of measured data, is well developed and widely used in practice. However the quantitative part, the estimation of the extent of faults and their locations, has been an active area of research for many years. Over the past three to four decades, theoretical models have played an increasing role in the rapid resolution of problems in rotating machinery.
Edwards et al. (1998) gave a brief review of the wider field of fault diagnosis. Parkinson (1991) and Foiles et al. (1998) gave comprehensive reviews of rotor balancing. Muszynska (1989) gave a thorough review of the analysis of rotor–stator rub phenomena. Doebling et al. (1998) gave an extensive survey on the crack detection methods. A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings was presented by Tandon and Choudhury (1999). The application of wavelets has emerged in the context of damage detection, and an excellent review of this is given by Staszewski (1998). A review of the research work performed in real-time active balancing and active vibration control for rotating machinery, as well as the research work on dynamic modeling and analysis techniques of rotor systems, is presented by Zhou and Shi (2001).
15.1 Rotor unbalance
In any rotating machinery the rotor unbalance is always present and it is one of the most common sources of severe vibration. The unbalance is defined in Chapter 2, which is the product of the rotor mass and its eccentricity (the eccentricity is a distance of the centre of gravity of the rotor from its centre of rotation). When a severely unbalanced rotor is rotated freely on frictionless bearings, it stops at nearly fixed orientation. It indicates that the gravity force acting at centre of gravity pulls the rotor to a fixed orientation due to its eccentricity. The position of the unbalance is also called the heavy (or hot) spot. This position is always remain fixed. The point on an unbalanced rotating shaft with the maximum displacement (Figure 15.1) is called the high spot. This is variable and depends upon the speed of rotor. It is observed by a vibration pickup as the point of maximum positive amplitude. The high and heavy spot may or may not coincide, depending on where the rotor is operating relative to its critical speeds. In the Jeffcott rotor it is observed that the high and heavy spot coincide below the critical speed and they are opposite above the critical speed. At critical speed they have 900 phase with heavy spot leading.
Example 15.1 Consider a two-DOF Jeffcott rotor mounted on two identical flexible bearings. The mass of disc is 54.432 kg and the stiffness of the shaft is 1.378×107 N/m. Consider the following properties of the each bearing: kxx = 1.01×107 N/m, kyy = 4.16×107 N/m, kxy = 4.16×105 N/m, and kyx = 3.12×107 N/m. Obtain the amplitude and phase variation with respect to the spin speed of the shaft. Plot the orbit (x-y plot) of the shaft by indicating its direction of rotation between critical speeds. Choose a suitable unbalance on the disc to generate the responses.
Solution: The unbalance response is generated by the procedure described in Chapter 4 and are shown in Figs. 15.1 and 15.2. It can be observed that the rotor-bearing system has two critical speeds (one around 400 rpm and other around 900 rpm). It can be seen that there are amplitude peaks corresponding to these critical speeds accompanied by phase changes. Figs. 15.3(a-c) show orbit plots for various spin speed of the rotor. It can be seen that there is a change in the sense of orbit rotation while crossing the critical speeds.