Synthesizing a resonance anti-phase two-mass vibratory machine whose operation is based on the Sommerfeld effect

This paper reports the synthesized two-mass antiphase resonance vibratory machine with a vibration exciter in the form of a passive auto-balancer. In the vibratory machine, platforms 1 and 2 are viscoelastically attached to the stationary bed and are tied together viscoelastically. A passive auto-balancer is mounted on platform 2. It has been established that the vibratory machine has two resonant frequencies and two corresponding forms of platform oscillations. Such values for the supports’ parameters have been analytically selected at which: ‒ there is an antiphase mode of motion at which platforms 1 and 2 oscillate in the opposite phase and the principal vector of forces acting on the bed (when disregarding the forces of gravity) is zero; ‒ the frequency of platform oscillations under an antiphase mode coincides with the second resonance frequency. The antiphase mode occurs when the loads in an auto-balancer get stuck in the vicinity of the second resonance frequency, which is caused by the Sommerfeld effect. The dynamic characteristics of a vibratory machine have been investigated by numerical methods. It has been established that in the case of small internal and external resistance forces: ‒ there are five theoretically possible modes of load jamming; ‒ the antiphase (second) form of platform oscillations is theoretically implemented under jamming modes 3 and 4; ‒ jamming mode 3 is locally asymptotically stable while jamming mode 4 is unstable; ‒ for the loads to get stuck in the vicinity of the second resonance frequency, the vibratory machine must be provided with the initial conditions close to jamming mode 3, or the rotor must be smoothly accelerated to the working frequency; ‒ the dynamic characteristics of the vibratory machine during operation can be controlled in a wide range by changing both the rotor speed and the number of loads in the auto-balancer. The reported results are applicable for the design of resonant antiphase two-mass vibratory machines for general purpose