7.1 Problems - chapter 7  (Page 4/6)

7.14 A 150-kW, 600-V, 600 r/min dc series-wound railway motor has a combined field and armature resistance (including brushes) of 0.125 $\Omega$ . The full-load current at rated voltage and speed is 250 A. The magnetization curve at 400 r/min is as follows:

Determine the internal starting torque when the starting current is limited to 460 A. Assume the armature reaction to be equivalent to a demagnetizing mmf which varies as the square of the current. (Hint: This problem can be solved either graphically or by use of the MATLAB "spline0" function to represent the magnetization curve.)

7.15 A 25-kW, 230-V shunt motor has an armature resistance of 0.11 $\Omega$ and a field resistance of 117 $\Omega$ . At no load and rated voltage, the speed is 2150 r/min and the armature current is 6.35 A. At full load and rated voltage, the armature current is 115A and, because of armature reaction, the flux is 6 percent less than its no-load value. What is the full-load speed?

7.16 A 91-cm axial-flow fan is to deliver air at 16.1 $m^3$ /sec against a static pressure of 120 $P_a$ when rotating at a speed of 1165 r/min. The fan has the following speed-load characteristic

It is proposed to drive the fan by a 12.5 kW, 230-V, 46.9-A, four-pole dc shunt motor. The motor has an armature winding with two parallel paths and $C_a$ = 666 active conductors. The armature-circuit resistance is 0.215 $\Omega$ . The armature flux per pole is ${\phi }_d$ = ${\text{10}}^{-2}$ Wb and armature reaction effects can be neglected. No-load rotational losses (to be considered constant) are estimated to be 750 W. Determine the shaft power output and the operating speed of the motor when it is connected to the fan load and operated from a 230-V source. (Hint: This problem can be easily solved using MATLAB with the fan characteristic represented by the MATLAB "spline()" function.)

7.17 A shunt motor operating from a 230-V line draws a full-load armature current of 46.5 A and runs at a speed of 1300 r/min at both no load and full load. The following data is available on this motor:

Armature-circuit resistance (including brushes) = 0.17 $\Omega$

Shunt-field turns per pole = 1500 turns

The magnetization curve taken with the machine operating as a motor at no load and 1300 r/min is

a. Determine the shunt-field current of this motor at no load and 1300 r/min when connected to a 230-V line. Assume negligible armature-circuit resistance and armature reaction at no load.

b. Determine the effective armature reaction at full load in ampere-turns per pole.

c. How many series-field turns should be added to make this machine into a long-shunt cumulatively compounded motor whose speed will be 1210 r/min when the armature current is 46.5 A and the applied voltage is 230 V? Assume that the series field has a resistance of 0.038 $\Omega$ .

d. If a series-field winding having 20 turns per pole and a resistance of 0.038 $\Omega$ is installed, determine the speed when the armature current is 46.5 A and the applied voltage is 230 V. (Hint: This problem can be solved either graphically or by use of the MATLAB "spline0" function to represent the magnetization curve.)