Modeling effect of a "stuck" pendulum for a mechanical system with two degrees of freedom

The present work is devoted to new results of investigations of the effect of “sticking” of a pendulum on the rotating shaft of a mechanical system with two degrees of freedom. The essence of this phenomenon is that for a pendulum installed with the possibility of free rotation on the motor shaft of a mechanical system, at a certain ratio between the friction in the pendulum support and its moment of inertia, there is a mode of motion when the shaft rotates with a given angular velocity, and the angular velocity (rotation frequency) of the pendulum coincides with one of the natural frequencies of oscillations of the mechanical system. The studies included the compilation of equations of motion of a mechanical system with a pendulum in generalized coordinates without damping, the introduction of a small parameter to separate stationary and unsteady motion, the transition to the main coordinates with damping, the derivation of an algebraic expression that determines the conditions for the occurrence of the effect of “sticking” of the pendulum on the rotating shaft of the mechanical system, numerical integration of the differential equations of motion of the model in the unsteady mode of motion. As a result of research, the algebraic expression allowing to establish conditions of occurrence of the effect of “sticking” of a pendulum on a rotating shaft of a mechanical system depending on parameters of a pendulum and properties of a mechanical system, also to study possibility of use of a pendulum for experimental finding of natural frequencies of vibrations of mechanical systems is received.

pendulum, mechanical system, principal coordinates, damping, "sticking" effect, natural frequency of oscillations