A magnetic circuit with two coils and a given axis of movement is represented below. The cross section is uniform and equal throughout the upper and lower yoke, left leg, and middle leg, with the exception of the right leg being wider. N1 and N2 are 200 and 400 turns, respectively. Ignore the iron loss, fringing, and leakage.
a) Consider the magnetic material is linear with a µr of 8000. Calculate the inductances and plot the inductance change with respect to the middle leg air-gap between 2 mm ≤ x ≤ 5 mm on the same set of axes for each inductance value.
b) Plot the induced force with respect to the position interval in part a for currents of i1=4 A, i2=6 A.
c) For a fixed middle air-gap value of 3 mm, give a 3D surface plot of torque w.r.t. i1 and i2 change within the intervals of −12 A ≤ i1 ≤ 12 A, −8 A ≤ i2 ≤ 8 A.
Now consider an AC excitation (sinusoidal and 50 Hz) with i1 and i2 as 8 Arms and 5 Arms, respectively. The currents are in phase.
d) Calculate and plot the force with respect to time with an air-gap of 3 mm (the middle leg).
e) Calculate the induced voltages of coil 1 & 2 with a varying air-gap interval of part a.