ECE321/ECE595
Homework 8
Problem 1 – Discrete Winding Function
The number of conductors in each slot of the a-phase of the stator of the machine
are as follows:
N as = [0 4 4 0 − 4 − 4 0 4 4 0 − 4 − 4]T
Compute and graph the winding function associated with this winding. Suppose the band c-phase conductor arrangement is the same, except moved back by 2 and 4 slots,
respectively. What would be the total number of conductors in each slot (as an absolute
value). Would it be the same for every slot ?
Problem 2 – Continuous Winding Function
Suppose the conductor density of a winding function is given by
nbr = 262 cos(8φrm − 2π / 3)
Compute the rotor b-phase winding function in terms of position measured from the
rotor.
Problem 3 – Continuous Winding Function
Find the winding function for
nas (φ sm ) = N s sin( Pφsm / 2) + N s 3 sin(3Pφsm / 2)
Problem 4 – Conductor density distribution (ECE595 Only)
Consider the conductor density given by
n as (φsm ) = Ns1 sin( Pφsm / 2) − N s3 sin(3Pφsm / 2)
nbs (φsm ) = N s1 sin( Pφsm / 2 − 2π / 3) − N s3 sin(3Pφsm / 2)
n cs (φsm ) = Ns1 sin( Pφsm / 2 + 2π / 3) − N s3 sin(3Pφsm / 2)
Define the total conductor density as
nt = nas + nbs + ncs
Defining α 3 = N s 3 / N s1 compute the value of α 3 which minimizes the peak value of
nt (φsm ) . A numerical answer is acceptable
Problem 5 – Rotating MMF (Everyone should do this problem and Problem 6)
The winding function of the a- and b-phase stator windings of a machine are
given by was = 100 cos(4φ s ) and wbs = 250 sin( 4φ s ) . The a-phase current of the machine is
given by i as = 10 cos(ω e t + π / 8) . Determine the b-phase current and the airgap needed to
achieve an airgap flux density of B(φ s , t ) = 1.2 cos(ω e t + π / 8 − 4φ s ) .
CONTINUED ON NEXT PAGE
Problem 6 – Rotating MMF
The conductor turns density of a two phase machine is given by
n as = 100 cos 2φ sm
n bs = −100 sin 2φ sm
The a- and b-phase currents are given by
i as = 5 cos(400t )
ibs = 5 sin( 400t )
Express the total stator MMF. What is the speed and direction of the MMF ?