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Internal friction has been known to be a cause of whirl instability in built-up rotors since the early 1900's. This internal damping tends to make the rotor whirl at shaft speeds greater than a critical speed, the whirl speed usually being equal to the critical speed. Over the years of research, though models have been developed to explain instabilities due to internal friction, its complex and unpredictable nature has made it extremely difficult to come up with a set of equations or rules that can be used to predict instabilities accurate enough for design. This thesis deals with suggesting improved methods for predicting the effects of shrink fits on threshold speeds of instability. A supporting objective is to quantify the internal friction in the system by measurements. Experimental methods of determining the internal damping with non-rotating tests are investigated, and the results are correlated with appropriate mathematical models for the system. Rotating experiments were carried out and suggest that subsynchronous vibration in rotating machinery can have numerous sources or causes. Also, subsynchronous whirl due to internal friction is not a highly repeatable phenomenon.

This thesis reports on a design and modeling of a micro-machined gyroscope. The proposed sensor is a dual mass type, electro-statically driven to primary mode oscillation and senses, capacitively, the output signal. Full decoupling between drive and sense modes minimizes the mechanical crosstalk and based on this a novel gyroscope is designed and modeled which has separate sensing and driving masses. The dual mass gyroscope is designed such that driving and sensing resonant frequency is 23101 Hz with 0% mismatch (in simulation)with quality factor of 31.6227 and bandwidth of 730.51Hz. The gyroscope when actuated in simulation with 25V ac and 10V dc showed sensing capacitance variation of 126aF for 1 rad/s with base capacitance of 244.16fF. To the design of the gyroscope a new semi automatic tool was formulated for the noise analysis and noise based optimization of the resonant MEMS structures. Design of a sensitive gyroscope needs to take into account the noise shaping induced by damping phenomena at micro scale and is critical for optimization. The analysis was further extended to the design of the gyroscope and estimation shows that there is a trade of between the S/N ratio and the sensitivity and the design could be made much better in-terms of S/N by tuning its resonant frequency to 10⁶Hz.

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