The research of ball automatic balancing device mainly focused on single ball automatic balancing device and mostly to study its plane motion. A two-plane ball automatic balancing device for rigid rotors was analyzed. The mathematical models of two-plane automatic ball balancing device for double eccentric disk were established and derived the vibration differential equation by the Lagrange equation,the autonomous system was obtained by rotating coordinate transformation. The stability was analyzed by Lyapunov first approximation theory. Then,the numerical simulation was carried out by Matlab software to analyze the vibration suppression characteristics of two-plane ball automatic balancing device and the movement rule of the balance ball at different rotational speeds and eccentric phases. The research result shows that the two-plane ball balancing device can restrain the plane motion and the space rotation significantly above the second-order critical speed.