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This paper focuses on a topic frequently involved in the dynamics of transient phenomena on rotary machines driven by an AC induction motor supplied by a three-phase four-wire electrical system: the free response of the dynamic system mirrored in the torsional vibrations of its rotor. This dynamic system is reducible at a single degree of freedom system, equivalent of a spring-mass-damper but as a torsional vibratory system composed of the motor rotor (having a moment of inertia) the rotating magnetic field (having a torsional stiffness) and a hypothetical damper (generating a viscous damping mainly due to the air friction). This free response is useful mostly to characterize the transmissibility related to the conversion of information from mechanical to electrical power through this dynamic system. A simple computer-assisted setup is used to describe indirectly and to analyze the free response (generated when the motor is switched-on or after star to delta commutation sequence), using the active electrical power absorbed by the motor.

This paper focuses on the evolution of instantaneous supplying current absorbed by an AC motor used to drive a lathe headstock gearbox during a transient regime characterised by a strong acceleration and deceleration and a strong variations of the absorbed active electrical power (with positive and negative power flows). A relationship between the current root mean square and active electrical power evolutions was established and proved in experimental terms. A severe limitation of the electrical current evolution was revealed: the impossibility to describe a negative flow of absorbed electrical power.