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PROBLEM 1: DC Motor Characterization A shunt DC motor designed for railway service has the nameplate ratings shown in the following table; two tests were conducted

Electrical Engineering

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PROBLEM 1: DC Motor Characterization

A shunt DC motor designed for railway service has the nameplate ratings shown in the following table; two tests were conducted. For the no-load test, both field and rotor had rated voltage applied; the rotor current was measured to be 0.5% of its rated value. On the other hand, for the locked-rotor test the rotor reached its rated current at 3% rated voltage.

Parameter	Value	Unit
Power Output	1.2	MW
Speed	600	Rpm
Rotor Current	1.2	kA
Rotor Voltage	1.5	kV
Field Current	25	A
Field Voltage	600	V

 

1. Draw the equivalent circuit of this motor.

2. What are the values for the no-load speed, and no-load damping coefficient of this motor??

3. Find the external armature resistance required to limit the starting torque to 150% of its rated value at rated armature voltage. Assume that the field also has rated voltage applied.

PROBLEM 2: Regenerative Braking

DC motors of the rating presented in Problem 1 find their common use as traction motors in railways. With their massive inertias, a considerable amount of energy can be recovered for later use, or for powering utility functions aboard the train. This is done by operating the motor as a generator, where the armature terminals are temporarily connected to a load instead of a supply.

Parameter	Value	Unit	Remarks
Inertia	100000	Kg.m2
Damping	11.8	W.s	Train mechanisms only
Load Torque	15	kN-m

 

A freight train has the effective properties in the preceding table. Initially, the train runs such that the motor is spinning at its rated value. Upon application of regenerative braking, the motor’s controls draw 100A out of the armature while maintaining a 25A supply to the field.

1. Derive an expression for the angular speed w as a function of time.

2. Derive an expression for the instantaneous voltage V, (¢) across the armature terminals.

3. Determine how long it will take for the train to stop.

4. Determine the total energy recovered from the machine.

HINT: The complete solution for a non-homogenous first-order differential equation of the form

dy/dx + p(x)y = r(x)

is

y = e^-u(x) (òe^u(x)r(x)dx + c)

u(x) = òp(x) dx

PROBLEM 3: Hoisting Duties

DC motors also find applications such as in hoists, where torque characteristics need to be precisely controlled to avoid mechanical shock to the load, and possibly rope failure due to such jerking forces.

Parameter	Value	Unit
Power Output	100	kW
Speed	900	rpm
Rotor Current	500	A
Rotor Voltage	250	V
Field Current	6	A
Field Voltage	300	V

 

A hoist motor, whose nameplate values are shown in the preceding table, is used to drive a 0.5m-diameter rope-drum hoist through a 10:1 reduction gearbox. Without any load attached, applying rated voltages causes the rotor speed to be 5% larger than nameplate, and the motor to consume a total of 2.8kW.

1. Find the armature current required to maintain a 200kg crate suspended in the air.

2. Find the armature current required to lift a 4-ton bulldozer at a vertical speed of 180 feet per minute.

NOTE: Assume for this problem that the rope diameter and gearbox friction losses are negligible; the rope strength is sufficient;* and rated field voltage is always applied.