The paper presents the structural diagram and mathematical model of a vibration diagnostic system to measure angular velocities of two interconnected electric motors. The system is based on vibration signals and the control signals of the motor mechanical parameters. The measurement procedure of the rotor rotational speed is based on vibration signals during synchronization. The procedure presented allows simultaneous measurement and synchronization frequencies of rotation to diagnose of the motors' mechanical parts. The calculated reduced error of synchronizing frequencies of rotation of the rotors, which is 0.45% of the measurement range of frequencies of rotation from 0 to 80Hz.