Sensor-less estimation of frictions and moment of inertia of a stepper motor in a machining device

Stepper motor are widely used for both, industrial and commercial applications because of their low cost, high reliability and high torque. The knowledge of mechanical parameters like load inertia and frictions are required in order to parametrize correctly the motor controller. Estimation of these parameters is possible with position sensors but they are expensive in comparison to the motor, furthermore it may not be possible the installation because of unavailability of space. Current sensors are supposed available. This paper proposes a new sensor-less identification method to evaluate static and viscous friction and moment of inertia in a stepper motor. For the identification of friction parameters an energy analysis is performed considering the effects of cogging and white noise on phase currents and a solution to avoid those disturbances is proposed. Propagation of uncertainty theory is used to calculate noise correlation and subsequently the bias correction of the estimated parameters. A frequency study is made to evaluate cogging effect. Identification of load inertia is performed evaluating the dynamic behavior of the motor currents with a given voltage excitation, in particular an analysis of the resonance frequency of phase currents is performed. All results are verified experimentally using a three phase hybrid stepper motor and validated using an optical encoder. Results of the study allows to makes valid the sensor-less estimation using only current sensors and implementing algorithms in a standard control board, saving the cost and space of mechanical sensor. The study is extensible to all synchronous motors.