Stability is examined with respect to the torque in the elastic element between motor and load in semi-definite systems exhibiting unstable self-excitation during start-up. Equations are provided for optimizing a motor-mounted damped absorber to minimize the torque fluctuations in the shafting between motor and load in semi-definite systems. Minimum damper inertia needed to stabilize the system is computed assuming optimum damping. Stability and damper optimization equations are applied to two cases involving unstable self-excitation in electric submersible pump systems. In the first case, unstable growth of torque amplitude in shafting between an electric induction motor and an inertial load was observed during start-up in laboratory testing. A computer simulation of the system dynamics demonstrated that the torque could be stabilized by adding a damped absorber to the motor. In a computer simulation for the second case, unstable torque fluctuations in the shafting of an electric submersible pump system were dramatically reduced by the addition of a damped absorber; however, stability was not achieved until the damper inertia was sufficiently increased. Stability is not always required for safe operation of electric submersible pumps. A computational model of the system dynamics during startup should be used to determine when stability is required.

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