STUDYING THE EXCITATION OF RESONANCE OSCILLATIONS IN A ROTOR ON ISOTROPIC SUPPORTS BY A PENDULUM, A BALL, A ROLLER

We have analytically examined the steady motion modes of the system, composed of a balanced rotor on the isotropic elastic-viscous supports, and a load (a ball, a roller, a pendulum), mounted inside the rotor, thus enabling its relative motion. In this case, the pendulum is freely mounted onto the rotor shaft, while the ball or roller rolling without slipping along a ring track centered on the longitudinal axis of the rotor. The physical-mathematical model of the system has been described. We have recorded differential equations of the system’s motion with respect to a coordinate system rotating at a constant speed of rotation in the dimensionless form. All steady motion modes of the system have been defined under which a load rotates at a constant angular velocity. In the coordinate system that rotates synchronously to a load, these motions are stationary. Our theoretical study has shown that under motion steady modes: – in the absence of resistance forces in the system, a load rotates synchronously with the rotor; – in the presence of resistance forces in the system, a load is lagging behind the rotor. The load jamming regimes are the one-parameter families of steady motions. Each jamming mode is characterized by the corresponding jam frequency. Depending on the system parameters, one, two, or three possible load jam velocities may exist. If, at any rotor speed, there is only a single angular velocity of a load jam, then the corresponding motion mode (a one-parameter family) is globally asymptomatically steady. If the number of jam velocities varies depending on the angular rotor speed, the asymptomatically steady are: – the only existent mode of jamming (globally asymptomatically steady when there are no others); – jamming modes with the smallest and greatest velocities. A load jam mode with the lowest angular velocity (close to resonance) can be used in order to excite resonance oscillations in vibration machines. The highest frequency of a load jam is close to the rotor speed. This mode can be used to excite the non-resonance oscillations in vibration machine