Modeling of a linear PM machine including magnetic saturation and end effects: Maximum force-to-current ratio

The use of linear permanent-magnet (PM) actuators increases in a wide variety of applications because of their high force density, robustness, and accuracy. These linear PM motors are often heavily loaded during short intervals of high acceleration, so that magnetic saturation occurs. This paper models saturation and end effects in linear PM motors using magnetic circuit models. The saturating parts of the magnetic circuit are modeled as nonlinear reluctances. Magnetomotive forces represent the currents and the magnets. This paper shows, that when saturated, a negative d-axis current increases the force developed by the motor. Although the increase is not large, it is nevertheless useful, because a negative d-axis current also results in a decrease in the amplifier rating. Further, the trajectory for the maximum force-to-current ratio is derived. The correlation between the calculated and the measured force justifies the model.