A 6/4 VRM of the form of Figure has the following properties: Stator pole angle ? = 30 ?, Rotor pole angle ? = 30 ?, Air-gap length g = 0.35 mm, Rotor outer radius R = 5.1 cm, Active length D = 7 cm. This machine is connected as a three-phase motor with opposite poles connected in series to form each phase winding. There are 40 turns per pole (80 turns per phase). The rotor and stator iron can be considered to be of infinite permeability and hence mutual-inductance effects can be neglected.

a. Defining the zero of rotor angle ?_m at the position when the phase-1 inductance is maximum plot and label the inductance of phase 1 as a function of rotor angle.

b. On the plot of part (a), plot the inductances of phases 2 and 3.

c. Find the phase-1 current I0 which results in a magnetic flux density of 1.0 T in the air gap under the phase-1 pole face when the rotor is in a position of maximum phase-1 inductance.

d. Assuming that the phase-1 current is held constant at the value found in part (c) and that there is no current in phases 2 and 3, plot the torque as a function of rotor position. The motor is to be driven from a three-phase current-source inverter which can be switched on or off to supply either zero current or a constant current of magnitude I₀ in phases 2 and 3; plot the torque as a function of rotor position.

e. Under the idealized assumption that the currents can be instantaneously switched, determine the sequence of phase currents (as a function of rotor position) that will result in constant positive motor torque, independent of rotor position.

f. If the frequency of the stator excitation is such that a time T₀ = 35 msec is required to sequence through all three phases under the excitation conditions of part (e), find the rotor angular velocity and its direction of rotation.

Transcribed Image Text:

Phase 1 Rotor Phase 2 30 Stator Phase 3