Shenhar: Gyroscope with elastic bearings

ABSTRACT: This work deals with an analytical study of an unusual gyroscope suspension. In contrast to usual gyroscopes, this has elastic gimbal bearings and the conventional arrangement of two outer gimbals is replaced by a single internal gimbal. This gimbal has an oscillatory motion caused by Hooke's joint.

This suspension was developed by E.W. Howe (1964) and was developed by him for small offset angles of the rotor spin axis. A somewhat more extensive discussion was given by P.H. Savet (1966), but there too, the equations of motion were established for a specific case of small angles, neglecting load torque and internal and external friction. No stability criteria were discussed, no relations between parameters were defined and no conclusions were stated.

The purpose of the research is to formulate the equations of motion for a gyroscope on elastic suspensions for any offset angle of the motor drive axis from the axis of rotor and to solve the case of small offset angles. In addition it was desired to establish rotor stability criteria in order to obtain a free rotor which preserves its direction in space.

As a first step, the kinematic equations for Hooke's joint on which the mechanism is based were developed. The expressions for the torques exerted on the rotor at any offset angle and subject to influence of general spring and inner damping-friction were formulated. Equations of motion for a symmetric rotor at small angle of nutation were then derived.

As a specific case, the equations of motion for a rotor in vacuum and without internal damping were solved. The solution showed that it is possible to cancel the frequency of the slow precession by the correct tuning of spin-velocity to a fixed value. The effect of a dynamical "antispring" (dynamical spring with a negative spring constant) was described. This antispring completely cancels the influence of spring torques on the rotor.

In another case, a solution for the equations of motion of a rotor subject to load-torque and internal damping was obtained. In order to reach a stable solution of zero slow precession, damping by Coulomb friction proportional to the offset angle was assumed.

In comparison to a usual gyroscope, the structure of the system under discussion is very simple. The outstanding advantage of the elastic bearing system and the oscillating gimbal in the described gyroscope, lies in the elimination of the damaging influence of frictional torque which is found to traditional gyroscope gimbal bearing.

The state of knowledge relating to this problem has been enlarged by the analysis, given in this work, of the influence of load torque and friction on the behavior at large offset angles and is the solution of the problem of stability at small offset angles.

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