Nonlinear dynamics of rotor of an auto-balancing ball device, considering eccentricity and changes in horizontal axes of rotation

This study is devoted to the dynamics of an auto-balancing device (ABD) when the rotor rotates at critical angular speeds. In this article, a model of an auto-balancing device (ABD) is proposed. The rotor is not only eccentric about the symmetry axis but also has a horizontal axis of rotation. A mathematical model is proposed based on the Lagrange equations; it describes the nonlinear motion of a balancing system (BS) with two running lines with a different number of balls, considering eccentricity, angular error, and changes in the horizontal axis of rotation. The nonlinear dynamics of the rotor motion with two running lines and two balls at a constant rotation speed and in the accelerating mode of the rotor motion is studied by a numerical method, taking into account the change in the horizontal axis of rotation.

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