Measurement method for determining the magnetic hysteresis effects of reluctance actuators by evaluation of the force and flux variation

A measurement method is presented which identifies the magnetic hysteresis effects present in the force of linear reluctance actuators. The measurement method is applied to determine the magnetic hysteresis in the force of an E-core reluctance actuator, with and without pre-biasing permanent magnet. The force measurements are conducted with a piezoelectric load cell (Kistler type 9272). This high-bandwidth force measurement instrument is identified in the frequency domain using a voice-coil actuator that has negligible magnetic hysteresis and eddy currents. Specifically, the phase delay between the current and force of the voice-coil actuator is used for the calibration of the measurement instrument. This phase delay is also obtained by evaluation of the measured force and flux variation in the E-core actuator, both with and without permanent magnet on the middle tooth. The measured magnetic flux variation is used to distinguish the phase delay due to magnetic hysteresis from the measured phase delay between the current and the force of the E-core actuator. Finally, an open loop steady-state ac model is presented that predicts the magnetic hysteresis effects in the force of the E-core actuator.