be made in advance for replacement in damaged part. Thus, in order to assure a safety and reliability in operation of a gear transmission system, it is necessary to understand the dynamics of the system under various possible failure conditions.

Presently, the prevention and management of premature failures in equipment has become a vital part of the maintenance program. Many researches have done for finding a reliable monitoring strategy in gear transmission systems. A variety of fault detection procedures have been developed. Mostly impractical procedure could be visual inspection because it is not easily to visualize faults in micro scale unless costly, specialized equipment is used. However, it is quite impossible to examine gear transmissions during operation. Practically, visual inspection is used mainly after machine failure has been experienced.

One of the most promising procedures for detecting incipient faults in gear-rotor-bearing system is the vibration analysis. The advantage of vibration signature analysis is no requirement of machinery shutdown and it can be carried out online by a computer-based machine health monitoring. However, current on-board condition monitoring systems for gear-rotor and bearing systems often fail to provide sufficient time between warning and failure otherwise safety procedures can be implemented. At times, a small fault in transmission system can quickly develop into a dangerous failure mode without any notable signs. Additionally, inaccurate interpretation of operational conditions may result in false alarms and unnecessary repairs and downtime. In the case of effects due to combined damage in bearing, shaft, and gears, vibration signatures usually cannot be identified immediately without special treatment. Therefore, all these needs motivate for the development and research in detecting and identifying faults in ball bearing, shaft, and gear before inducing system failure.

1.2 Literature Overview

Traditionally, the research in rotating machinery attempted to predict the performance of the rotor dynamic system during the operation. An amount of work [1-8] has been reported in machine life prediction based on statistical models where the fatigue life analysis was included in their models. Their prediction is based on statistical approach developed by Lundberg and Palmgren [4, 5] while the reliability models are based on classical fatigue theory and the Weibull failure distribution. However the condition of machine components and their corresponding under various operating environment were not considered.

Generally, rolling element bearing systems generate vibration even if they are in perfect condition.

The sources of excitation are due to the external disturbance, the internal excitation, and the varying structure compliance [9, 10]. The varying compliance vibration is generated by the relative motions between ball bearing and inner or outer race because the number of rolling elements and their position in the load zone changes with bearing rotation [11].

However, the presence of a defect causes a significant increase in the vibration level so it is important to understand the behavior of vibration signatures under different types of defect. Most of researchers studying on the detection and diagnosis of localized defects in bearing have done experimental works while others developed models for detecting defects and compared their results with experimental results. Mc Fadden and Smith [12, 13] proposed a model for the high-frequency vibration produced by a single defect or multiple defects on the inner race of a rolling element bearing under radial load and the model performance was confirmed experimentally by NASA researchers [14].

One of the common faults in large rotating machinery is the residual shaft bow. The existence of residual bow in shaft may result from various effects such as, gravity sag, thermal distortion, uneven shrink fits, and mechanical bow due to previous large unbalance. In the case of gravitational sag, it mostly occurs in the large horizontal turbines or compressors which are allowed to rest for long period of times. This may affect the shaft temporarily. The turbomachinery operating in particularly high temperature such as gas/steam turbines and water pumps in nuclear reactors is possible to developed temporary bow condition because the temperature distribution along the shaft temperature is uneven. However, uneven shrink fits of impellers or spacers on a shaft may produce a permanent mechanical bow due to the rubbing of a shaft on a seal.