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One-, two-, and three-mass vibration machines with translational motion of platforms and a vibration exciter of a ball, roller, or pendulum type with several loads were studied. The empirical criterion for the onset of auto-balancing was applied in the extended formulation. It has been established that a single-mass vibration machine has one resonant speed, and: – at the after-resonance speeds of rotation of loads synchronously with the rotor, the auto-balancing mode becomes stable; – at the pre-resonance speeds of rotation of loads, loads tend to gather together. In a dual-mass vibration machine, there are two resonant speeds and one additional speed located between two resonant ones. The auto-balancing mode is stable when the loads rotate synchronously with the rotor at the following speeds: – between the first resonant speed and the additional speed; – greater than the second resonant speed. At other speeds of rotation of loads, loads tend to gather together. The three-mass vibration machine has three resonant speeds and two additional speeds, located one by one between adjacent resonant speeds. The auto-balancing mode is stable when the loads rotate synchronously with the rotor at the following speeds: – between the first resonant speed and the first additional speed; – between the second resonant speed and the second additional speed; – greater than the third resonant speed. At other speeds of rotation of loads, loads tend to gather together. In a single-mass vibration machine, the value of the resonant speed does not depend on the viscosity of supports. In dual-mass and three-mass vibration machines, all characteristic speeds depend on the viscosity of supports. With small forces of viscous resistance, the values of these speeds are close to the characteristic speeds found in the absence of resistance forces.

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