Effects of angular vibration on the performance of a single-degree-of-freedom integrating gyroscope

Abstract

Recent studies have shown that various inaccuracies occur when a single-degree-of-freedom gyroscope is subjected to an angular vibra­tory environment. Under such conditions the performance of the gyroscope has been analyzed and the nature of the inaccuracies investigated. Errors due to "coning", "dynamic unbalance", and "sculling" have been included in the investigation. Values of the inaccuracies representative of those expected from tests using the precision angular vibrator developed by the Instrumentation Laboratory of the Massachusetts Institute of Technology are presented. By reference to a dynamic model the equation of motion was obtained. A suitable solution to the equation was determined in series form for the case of sinusoidal inputs simultaneously applied about two axes. No restrictions are placed on the frequency of the applied motions. The terms in the series solution reveal the nature of the angular displacement of the float with respect to inertial space about the output axis for two cases: (1) zero elastic restraint, (2) finite elastic restraint. It is strongly recommended that correlation of actual experimental results with the developed theory be obtained prior to further theoretical considerations.