Dynamics of a Gyroscope Having Oblique Gimbal Axes

Abstract

The effects are considered of obliquity in the suspension axes of a free two-axis gyroscope supported in gimbals. Three principal types of obliquity are considered, namely (1) non-orthogonality of the bearing axes of the outer and inner gimbals, (2) non-orthogonality of the bearing axes of the inner gimbal and the spin axis of the rotor, in a plane Oyz defined by their usual orthogonal directions, and (3) misalignment of the spin axis of the rotor and a principal axis of the inner gimbal, in a direction out of the plane Oyz. Such obliquities or misalignments could occur as a result of manufacturing errors or they might be introduced deliberately in order to obtain particular dynamical characteristics. The free motion of the system is shown to be described by two coupled second-order non-linear equations, which are solved to first and second approximations for the three cases in which misalignment occurs separately. The first approximation determines the nutational vibration and the second the drift rate. Both are shown to be affected by each type of misalignment: the nutation varies in frequency and mode, and the drift rate in magnitude but not in direction. The relations between misalignment of the spin axis and dynamic unbalance of the inner gimbal are also discussed.