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In the previous part, the author explained how the detection, location and analysis of faults play a vital role in the field of rotor dynamics. This article discusses how shaft misalignment can be another cause of vibration due to reaction forces generated in the shaft couplings.
Coupling misalignment is a condition where the shaft of the driver machine and the driven machine are not on the same centerline. For discussion purposes, the non-coaxial condition can be parallel misalignment or angular misalignment. The more common condition is a combination of the two in both the horizontal and vertical directions. This compounding of misalignment, parallel and angular in both vertical and horizontal directions, is what has made the correction of misalignment so frustrating. Correcting one affects another, and the alignment technician hunts his or her way to a better alignment with repeated measurement and move, then another.
Other situations include: Bent shaft defects sometimes develop on a motor that has been allowed to sit stationary – after about six months deflection can become permanent; a fatigue crack can lead to catastrophic failure; and rotating unbalance, the uneven distribution of mass around an axis of rotation, which is caused when the center of mass (inertia axis) is out of alignment with the center of rotation (geometric axis).
Unbalanced forces lead to excessive vibrations and premature failure of system components such as bearings and couplings. The reasons for unbalance include inaccurate production procedures (machining, casting, forging, assembly), wear and tear, loading conditions (mechanical), environmental conditions (thermal loads and deformation) and component failure. Unbalance has become a bigger issue in recent times due to higher-speed machinery. It is estimated that the speed of operation of machinery has doubled during the past 50 years. This means that the level of unbalance forces may have quadrupled during the same.
Model-based fault detection is, at this time, directly employed in most areas of fault diagnosis. The model-based approach involves the establishment of a suitable process model, either mathematical or signal-based, which can estimate and predict process parameters and variables. At the heart of fault diagnosis lies the model-based approach, whereby as many variables and system parameters are taken into account as possible, in order to construct a detailed mathematical model of the system under observation. Once the dynamic behavior of the system has been adequately modeled it should theoretically be possible to detect faults via analysis of changes in input parameters to the model.
Eshleman reviewed many aspects of significance, including the vibration analysis of faults in rotors, bearings, seals, dampers and foundations. Isermann described the main principles involved in model-based procedures and outlined their importance for the realistic modeling of faults. Smith covered the general kinds of faults listed above and described qualitatively how they may be recognized from their vibration characteristics, and included effects caused by non-linearity.
Markert outlined the procedure for model-based approach used in fault diagnosis of rotors. He mentioned basic steps to perform diagnosis and optimized the fault parameters using the least square fitting. Platzfurther used this model-based approach for on-line identification of fault in rotor systems. Model-based fault identification in rotor systems by the least square method has been accomplished by Richard Markert, Roland Platzo and Siedler at Darmstadt University of Technology, Germany whose procedure is used extensively in this work.
An experimental stress analysis lab has been established in the mechanical engineering department of the Indian Institute of Technology (ITT), Kharagpur. This comprises a shaft with a disc at mid-span and one bearing at each end enclosed in a housing, with the shaft coupled with motor shaft. Real-time data was gathered using a data acquisition system. Initial experimental simulation results appear to show that unbalance is the only fault isolated by the model.
(Siwani Adhikari is a mechanical engineer at IIT Kharagpur, India. For a detailed rendition of the modeling of unbalance, a full mathematical description and the results obtained to date, contact the author at email@example.com)