Some aspects of gyroscope stability and dynamic response

[摘要] The thesis describes the results of some investigations into the causes of instability in free gimbal-mounted gyroscopes. Considerable use has been made of analogue and digital computation to isolate the effects of various types of reaction forces which may occur in the spin axis bearings, and the effect of rotor asymmetry is also considered. Rotor asymmetry and variation of radial stiffness in the spin axis bearings were both found to give rise to I inear differential equations with periodic coefficients, and an analytical procedure of general applicability has been developed for obtaining the width of the unstable zones and the degree of instability at the parametric resonances. This procedure gives excellent agreement with the results of direct computer solution of the equations of motion. Slackness in the spin axis bearings of a gyroscope did not appear, per se, to produce instability. It may do so, however, as a secondary effect since forces which otherwise would be negligible become significant when other restraints on shaft displacement are removed. Tangential forces in the spin axis bearings in either direction were found to produce instability but different modes of vibration were excited according to the direction of the forces. The effect of cage accelerations in the spin axis bearings has been considered and has been shown to be small. Likewise, transverse couples which arise due to non uniformity of the motor magnetic field when the rotor tilts relative to the stator, have been shown to be negligible. Shaft and bearing compliance has also been considered, mainly from the point of view of natural frequency and frequency response to externally applied torques. Bearing eccentricity has been shown to cause a forced nutation at the frequency of rotation of the ball cage, giving rise to a simple resonance if this frequency should coincide with a natural frequency of the gyro. Experimental work has been carried out with a view to establishing the nature of the dynamic forces and deflections in the spin axis bearings. Because these are of such small amplitude and of such a complex waveform, analysis of the experimental results has proved difficult. Sinusoidal forcing of a casing containing a gyro rotor in order to obtain the frequency response of the shaft and bearing deflections was moderately successful while the rotor was stationary but no readings were possible with the rotor running because of a seemingly random variation in the response.

[发布机构] University:University of Glasgow

[关键词] Mechanical engineering, Aerospace engineering