Refinement of the dynamic model building method of vibroisoled gyroscopic system

Abstract

The expediency of the movement equations compiling of a vibro-insulated housing of a gyroscopic system of classical type in a coordinate system, the start of which coincides with the center of mass of the entire device, is studied in this paper. The vibration protection system is believed to be formed by the elastic elements of the passive type. The gyroscopic system consists of a sensitive element - a three-step gyroscope, which is located on a platform with a triaxial gimbal. The general (basic) dynamics theorems are used to compile the movement equations. The movement equation of each element of a gyroscopic system is written in a moving coordinate system connected with its axis of suspension. The movement equations of a vibration insulated device case are written in a coordinate system that is tightly connected to it, the starting point of which coincides with the point corresponding to the position of the center of mass of the gyroscopic system in the absence of mechanical perturbances. The suspension centers of the platform frames are considered not to coincide with the specified point. In turn, it is also assumed that the platform centers of mass and the outer frame do not coincide with their axises of suspension. The system of equations of the rotational motion of a gyroscopic system is obtained by the method of Ishlinsky O. Yu., which excludes the unknown components of the moments of interaction reactions between the gyro device elements. The obtained scalar equations of the case rotational motion include components that are projections of the moments of the housing inertia forces and the device elements caused by the absolute acceleration of the center of mass of the gyroscopic system together with the case. Since the gyroscopic system has moving elements, the resultant of these inertia forces is not applied at the center of mass of the gyroscopic device and the case, but at a point whose position can be determined by the coefficients of the translational motion acceleration in the expressions of these inertia forces moments equating them to zero. The last equalities allow us to find the position of the point at which the center of rigidity of the vibration protection system should be located. This enables to avoid the appearance of interrelated angular and translational oscillations of the case caused by the potential forces distribution. The translational motion equations of the gyroscopic system instrument are obtained by the theorem of the main vector change of the motion quantities applied to each element of the gyroscopic system with the subsequent exclusion of the interaction forces between these elements. Angular velocities and angular accelerations of the device elements, which are included in the expressions of linear accelerations, are proposed to be expressed through angular velocity and angular acceleration of the case. This allows to distinguish terms that determine the impact of the angular movement of the suspension elements on the translational motion of the device case. Thus, the refinement of the motion equations compiling method of the passive vibration protection system of the gyroscopic system is given in the paper. These equations are proposed to be written in the coordinate system axes connected with the center of mass of the gyroscopic system together and the vibration insulated case. The obtained equations allow to determine the requirements for rational installation of the vibration protection system, to evaluate the influence of the gyroscopic system on the angular and translational motion of the vibration insulated case of the gyroscopic instrument.