STUDY OF THE DYNAMIC CHARACTERISTICS OF A MULTIFUNCTIONAL ROTARY WORKING UNIT

Abstract

A mathematical model of the dynamics of a multifunctional rotary working unit was developed, and the influence of its structural and kinematic parameters on the critical shaft rotation speed and the amplitude-frequency characteristics was investigated. The working unit is considered as a complex mechanical system comprising an elastic shaft with discretely placed concentrated masses, as well as hinge-mounted flail hammers. The relevance of the study lies in establishing the characteristic rotation frequency zones under the condition of ensuring resonance-free operation of the rotor. To construct the dynamic model, an energy-based approach and the Lagrange equations of the second kind were used. The model accounts for the energy of the shaft, the discretely placed masses, and the variable position of the flail hammers, as well as energy losses due to damping and the destruction of plant mass. As a result of the simulation, the equation of motion of the rotor was obtained, on the basis of which an expression was derived for determining the critical shaft rotation speed and the amplitude-frequency characteristic of the system. A numerical experiment was conducted for an experimental rotor sample, which established that at an effective mass of 50.087 kg and a radial shaft stiffness of N/m, the critical rotation speed is 220.078 rad/s. The influences of effective mass, radial shaft stiffness, viscous damping coefficient, and imbalance magnitude on the position of the resonance zone and the oscillation amplitude were substantiated. It was established that an increase in the rotor's effective mass reduces the critical rotation speed, while an increase in shaft stiffness contributes to its growth. It is shown that an increase in damping significantly reduces the maximum oscillation amplitude in the resonance zone, whereas an increase in imbalance causes a proportional increase in vibrational loads. Based on the simulation results, it was established that the working range of the rotor rotation frequency of 1200-1300 rpm lies in the pre-resonance zone and is characterized by insignificant oscillation amplitudes. The obtained value of the safety factor with respect to the critical frequency is 1.617, which indicates a sufficient distance of the operating mode from the resonance region.