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Unformatted text preview: Name: Section: ’0 ,1 EE331 Homework PSS — spring 2011 Problem 1: You are given a aircraft launch system that has a catapult length of 80m, a maximum
ﬂux density of B = 1T, an effective length across of L = 100m, a maximum power supply current
of 30kA, a maximum average power available from the ship power system of 7.5MW, and we
desire that the pilot be subject to no more than 4g of acceleration (1 g = 9.817;).
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a. Determine the minimum launch time and the terminal velocity (Hint: velocity is the time
integral of acceleration and distance is the time integral of velocity). Ans: (2.025, 79.2
m/s)
b. Determine the maximum mass (largest plane and payload) that can be launched at this
acceleration. Ans: (76,531 kg)
c. Determine the energy required to launch the plane (ﬁnd the induced voltage, calculate the
power, then integrate to ﬁnd the energy). Ans: (2.41 * 108 J)
(1. Determine the total required energy if only 75% of the total energy goes to launching the
plane (the rest is lost in heat and overcoming drag). Ans: (3.21*108 J)
e. Given the restriction on available average power from the ship power system, ﬁnd the
minimum time required between catapult shots. Ans: (42.85) Problem 2: You are given a PM DC motor intended for use in an electric car that uses a 72V
battery. You wish to determine the three parameters of the model: rd , Kv , and TIM. You run the following two tests:
Test 1: Apply 72VDC and measure In 2 4.196A and a) =198.6rad/s with no load Test 2: Apply 72VDC and measure Ia = 61A and a) =180.0rad/s with a load a. Determine ra, K, and Tm“.
[ra = 0.1189, Kv = 0.36Vs, TLOSS = 1.51Nm] P . .
"0"" j of the motor for the conditions of Test 2. In b. Determine the efﬁciency [ [83.8%] c. If we set Va = SOVDC and TLW = 7.5Nm , determine the resultant armature current and rotor speed (Assume that TL” is constant with speed).
[Ia = 25A, (1) = 130.7rad/s] Page 1 of 2 Name:
Section: EE331 Homework PSS — spring 2011
Problem 3: Given a 24VDC PM motor with ra = 0.2279!) and Kv = 0.1253Vs, a. Sketch the electromagnetic torque versus speed (0) on the x—axis) characteristic. Calculate the yintercept, xintercept, and slope. (yint = 13.1953 Nm, x—int = 191.5
rad/s, slope = 0.0689) b. If de = (250x10‘6N ms2)a)2 and TLOSS is negligible, what is the steadystate operating speed and the armature current?
[(0 =130.1 rad/s, Ia = 33.78A] c. What is the efﬁciency at this operating point?
[17 = 67.9%] Problem 4: We wish to reduce the speed of the motor above to half its current value by
adjusting the armature voltage. a. Find the load torque at this speed. (1.056 Nm)
b. Find the new armature current. (8.43 A)
c. Find the required armature voltage. (10.1 V) d. What is the efﬁciency at this operating point? (80.6%) Problem 5: A 10HP PM DC motor is controlled by a power converter that can adjust its
terminal voltage between 0 and 120VDC. The input voltage to the power converter is 144VDC. The parameters of the machine are ra = 0.143 Q, Kv = 1.104Vs and T Loss is negligible. If T Load is
ﬁxed at 70Nm (regardless of speed): a. To achieve a rotor speed of 60rad/s,
i. Find the required armature current and armature voltage. [Ia = 63.4A, Va = 75.3V] ii. Find the converter duty cycle.
[D = 52.3%] iii. If the converter is 93% efﬁcient, determine the average current out of the
144V source.
[Is = 35.6A] Additional Problems (Instructor Option):
0 Any as assigned by instructor Page 2 of 2 /
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 Fall '11
 Rudd
 Electrical Engineering, Electric motor, armature voltage, PM DC motor

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