The forces due to the unbalance in a system cause undesired vibration and noise, and reduce the system life. One of the new and efficient methods used to reduce the unbalance is the use of automatic dynamic ball balancer. The automatic dynamic ball balancer is a typical passive balancer which doesn't need control systems to balance the rotor. Because these devices are used in the systems which have variable unbalance according to the operating conditions and the system may be switched on and off several times a day, therefore reducing the balancing time becomes a necessary task. In practice, the gyroscopic effect is created for several reasons, e.g. when the rotor is located offset from the shaft midspan. Previous studies have not determined the optimum values of the damping ratio and mass of balls of the automatic dynamic ball balancer under the gyroscopic effect. In this study, the effect of damping ratio and the mass of balls of the automatic dynamic ball balancer on the stability and balancing of the system under the gyroscopic effect have been investigated and, using the Nelder-Mead simplex algorithm, the optimum values of these parameters to minimize the time of balancing and converging the Euler angles to zero are obtained.