New Vector Description of Kinetic Pressures on Shaft Bearings of a Rigid Body Nonlinear Dynamics with Coupled Rotations around No Intersecting Axes

Abstract

New vector description of kinetic pressures on shaft bearings of a rigid body nonlinear dynamics with coupled rotations around no intersecting axes is first main result presented in this paper. Mass moment vectors and vector rotators coupled for pole and oriented axes, defined by K. Hedrih in 1991, are used for obtaining vector expressions for kinetic pressures on the shaft bearings of a rigid body dynamics with coupled rotations around no intersecting axes. A complete analysis of obtained vector expressions for kinetic pressures on shaft bearings give us a series of the kinematical vectors rotators around both directions determined by axes of the rigid body coupled rotations around no intersecting axes. As an example of defined dynamics, we take into consideration a heavy gyro-rotor- disk with one degree of freedom and coupled rotations when one component of rotation is programmed by constant angular velocity. For this system with nonlinear dynamics, series of graphical presentation transformations in realizations with changes of eccentricity and angle of inclination (skew position) of heavy rigid body-disk in relation to self rotation axis are presented, as well as in realization with changing orthogonal distance between axes of coupled rotations. Angular velocity of kinetic pressures components in vector form are expressed by using angular acceleration and angular velocity of component coupled rotations of gyrorotor-disk.