7.1 Problems - chapter 7  (Page 5/6)

7.18 A 7.5-kW, 230-V shunt motor has 2000 shunt-field turns per pole, an armature resistance (including brushes) of 0.21 $\Omega$ , and a commutating-field resistance of 0.035 $\Omega$ . The shunt-field resistance (exclusive of rheostat) is 310 $\Omega$ . When the motor is operated at no load with rated terminal voltage and varying shunt-field resistance, the following data are obtained:

The no-load armature current is negligible. When the motor is operating at full load and rated terminal voltage with a field current of 0.554 A, the armature current is 35.2 A and the speed is 1185 r/min.

a. Calculate the full-load armature reaction in equivalent demagnetizating ampere-turns per pole.

b. Calculate the full-load electromagnetic torque at this operating condition.

c. What starting torque will the motor produce with maximum field current if the starting armature current is limited to 65 A? Assume that the armature reaction under these conditions is equal to 160 ampere-turns per pole.

d. Design a series field winding to give a speed of 1050 r/min when the motor is loaded to an armature current of 35.2 A and when the shunt field current is adjusted to give a no-load speed of 1200 r/min. Assume the series field will have a resistance of 0.05 $\Omega$ . (Hint: This problem can be solved either graphically or by use of the MATLAB "spline0" function to represent the magnetization curve.)

7.19 When operated at rated voltage, a 230-V shunt motor runs at 1750 r/min at full load and at no load. The full-load armature current is 70.8 A. The shunt field winding has 2000 turns per pole. The resistance of the armature circuit (including brushes and interpoles) is 0.15 $\Omega$ . The magnetization curve at 1750 r/min is

a. Compute the demagnetizing effect of the armature reaction at full load.

b. A long-shunt cumulative series field winding having four turns per pole and a resistance of 0.038 $\Omega$ is added to the machine. Compute the speed at full-load current and rated voltage. The shunt field current will remain equal to that of part (a).

c. With the series-field winding of part (b) installed, compute the internal starting torque in N. m if the starting armature current is limited to 125 A. Assume that the corresponding demagnetizating effect of armature reaction is 230 ampere-turns per pole. (Hint: This problem can be solved either graphically or by use of the MATLAB "spline0" function to represent the magnetization curve.)

7.20 A 230-V dc shunt motor has an armature-circuit resistance of 0.23 $\Omega$ . When operating from a 230-V supply and driving a constant-torque load, the motor is observed to be drawing an armature current of 60 A. An external resistance of 1.0 $\Omega$ is now inserted in series with the armature while the shunt field current is unchanged. Neglecting the effects of rotational losses and armature reaction, calculate

a. the resultant armature current and

b. the fractional speed change of the motor.

7.21 A common industrial application of dc series motors is in crane and hoist drives. This problem relates to the computation of selected motor performance characterstics for such a drive. The specific motor concerned is a series-wound, 230-V, totally-enclosed motor having a 1/2-hour crane rating of 100 kW with a ${\text{75}}^{0}C$ temperature rise. The performance characteristics