Among the ways to reduce vibrations of rotary machines with a vertical or horizontal axis of rotation is the use of ball-type automatic balancing devices. At the same time, the acceleration of compensating masses in the automatic balancing device with an annular cross-section of the housing showed that to accelerate the compensating masses to the operating speed of the rotor, it is necessary to provide the initial velocity due to the influence of gravity at the initial stage of acceleration. The value of the initial velocity of compensating masses depends on the parameters of the elastic suspension of the rotor, the size of the compensating mass, the coefficient of rolling friction between the compensating mass and the inner surface of the housing of the automatic balancing device and other parameters. In this work, the influence of the rolling friction coefficient and other parameters of the rotor system on the acceleration of compensating masses is studied, recommendations on the selection of parameters are given.