Selection and research of stability of the steady state motions of a single-mass resonance vibromating machine working on the Somerfeld effect

Abstract

This paper has defined and investigated for stability the steady state modes of motion of a single-mass resonant vibratory machine. The vibratory machine has a platform that is supported by viscoelastic supports. The platform moves rectilinearly translationally. A vibration exciter is installed on the platform. The vibration exciter consists of N identical loads – balls, rollers, or pendulums. The center of mass of each load can move in a circle of a certain radius with a center on the longitudinal axis of the rotor. Each load, when moving relative to the body of the vibration exciter, is exposed to a viscous resistance force. It was established theoretically that with small forces of viscous resistance and any number of loads, the vibratory machine has jamming modes under which the loads that are collected form a conditional combined load and lag behind the rotor. In this case, there are two bifurcation speeds of the rotor. At speeds less than the first bifurcation speed, the vibratory machine has one single (first) jamming mode. When the first bifurcation speed is exceeded, the second and third jamming modes appear. When the second bifurcation speed is exceeded, the first and second jamming modes disappear. The first jamming mode is resonant. In the cases of two or more loads, the vibratory machine also has an auto balancing mode (no vibrations), under which the loads rotate synchronously with the body of the vibration exciter and mutually balance each other. With small forces of viscous resistance, the computational experiment found that odd jamming modes are stable if they are numbered in ascending order of the frequency of load jamming. An auto-balancing mode is stable at the rotor speeds above the resonance. For the onset of a resonant mode of motion of the vibratory machine, it is enough to slowly accelerate the rotor to a speed lower than the second bifurcation speed. The results reported here are applicable in the design of resonant single-mass vibratory machines with inertial vibration exciters of the ball, roller, or pendulum type.