MOTOR EFFICIENCY
The purpose of obtaining characteristic curves of a machine is to get a permanent record of its behavior by which to judge its performance and suitability for different applications. The availability of a motor for any particular duty is determined almost entirely by two factors-the variation of its torque with load and the variation of its speed with load.
The more common characteristics of motors obtained by tests are:
1. Efficiency, torque, and speed as a function of current ,
2. Saturation curves,
3. Speed-torque curves (series, shunt, cumulative, and differential compound).
In addition, friction, core loss, and miscellaneous load and heat -run tests are frequently made.
Efficiency-The efficiency of a motor is the ratio of its useful output to its total input, and it is written:
This may also be written:
If the losses in a motor are summarized, equation (2) may be rewritten and the efficiency found by:
where,
Vt is the terminal voltage,
IL is the line current,
Vf If are the copper losses in the shunt field,
Is2 Rs are the copper losses in the series field,
Ia2 Ra are the copper losses in the armature,
Psp are the stray power losses.
Terms within parentheses are the combined total motor losses.
The copper losses in a machine may be readily calculated in each case. The stray power losses (P-.p) consist of frictional losses in the bearings and brushes, windage resistance, and hysteresis and eddy currents in the armature and pole faces, but cannot be calculated directly, as they are all some function of speed or flux, or both.
Dynamometers
There are generally two classes of dynamometers, namely:
1. Absorption .
2. Transmission .
They differ mainly in that , while an absorption dynamometer absorbs the total power delivered by the motor being tested, the transmission dynamometer absorbs only that part represented by friction in the dynamometer itself. A typical absorption dynamometer is represented by the Prony brake.
The Prony Brake
If the output of a motor is measured by a Prony brake (Fig. 6), then the output measured in horsepower is:
Where.
Bhp is brake horsepower,
F is force in pounds,
R is radius of brake arm,
N is revoul tions per minute.
But since (FR) is the torque, (T), of the motor in foot-pounds, it follows that:
![Fig. 6. A Prony brake. It is generally necessary to provide cooling water to_thumb[1]](http://machineryequipmentonline.com/electric-equipment/wp-content/uploads/2020/06/Fig.-6.-A-Prony-brake.-It-is-generally-necessary-to-provide-cooling-water-to_thumb1.jpg "Fig. 6. A Prony brake. It is generally necessary to provide cooling water to_thumb[1]")
To convert to kilogram-meters per minute multiply hp by 4,564. The principal forms of transmission dynamometers are the torsion and the cradle types. In the torsion type, the deflection of a shaft or spiral spring which mechanically connects the driving and driven machines is used to measure the torque. The spring is calibrated statically by noting the angular twist corresponding to that of a known weight at the end of a measured lever arm perpendicular to the axis. The angle when testing may be measured by electrical or optical methods.
In the cradle type of dynamometer, the power is absorbed electrically by a generator whose shaft is connected to the motor under test. The term “cradle” is derived from the mounting of the generator in a trunnion-supported cradle. The pull exerted between the armature and the field tends to rotate the latter. This torque is counterbalanced and measured by weights moved along an arm in the conventional manner.
Speed-Torque Characteristics
Series Motor-The speed-torque characteristic curve of a series motor is obtained by running the motor at its rated voltage and absorbing the power by a brake. Readings of torque and speed are recorded (the speed should not be allowed to exceed four times the rated speed). The motor, under a moderate load to prevent its running away, is started by cutting out its series resistance.
The load should be gradually reduced by adjusting the brake until the maximum safe speed is recorded. At this point, the speed and torque should be recorded. Then the load should be increased step by step,
taking simultaneous readings of speed and torque. The load should be increased until either the motor stops or the current exceeds the heating limit of the motor, which for a few minutes may be taken as two or three times the normal full-load current. An ammeter of sufficient rating should be connected to record the current. A voltmeter is required to make certain that the impressed voltage remains constant and equal to the rated voltage of the motor. The readings of the speed in r/min are plotted against the torque in pound- feet. Fig. 7 shows the characteristic curves of a series motor.
![Fig. 7. Characteristic curves of a typical series motor_thumb[1]](http://machineryequipmentonline.com/electric-equipment/wp-content/uploads/2020/06/Fig.-7.-Characteristic-curves-of-a-typical-series-motor_thumb1.jpg "Fig. 7. Characteristic curves of a typical series motor_thumb[1]")
Shunt Motor-The motor is started by an ordinary shunt-motor starting rheostat, the brake being adjusted to absorb no power, and the speed of the motor measured. Then the load is increased, step by step, until the maximum safe overload or breakdown torque is reached. A 1ine ammeter and voltmeter to record the current and voltage, respec .tively, are required. The readings of the speed in r/min are plotted against the torque in foot-pounds. Fig. 8 shows the characteristic curves of a shunt motor.
![Fig. 8. Characteristic curves of a typical shunt motor._thumb[1]](http://machineryequipmentonline.com/electric-equipment/wp-content/uploads/2020/06/Fig.-8.-Characteristic-curves-of-a-typical-shunt-motor._thumb1.jpg "Fig. 8. Characteristic curves of a typical shunt motor._thumb[1]")
Compound Motor-If the series field in a compound-wound motor is connected so that it aids the shunt field, the motor is said to be cumulatively compounded; if the series field is connected to oppose the shunt field, the motor is said to be differentially compounded.
In a differential-compound motor, the series field opposes the shunt field so that the magnetic flux is decreased when the load is applied. This results in the speed remaining substantially constant or even increasing with an increase in load. This speed characteristic is obtained with a corresponding decrease in the rate at which the torque increases with the load.
The cumulative-compound motor has characteristics which are a combination of shunt and series characteristics. As the load is applied, the series ampere-turns increase the magnetic flux, causing the torque for any given current to be greater than it would be for a shunt motor. On the other hand, this increase in flux causes the speed to decrease more rapidly than it does in the shunt motor. This type of motor develops a high torque with a sudden increase of load, has a definite no-load speed, and has no tendency to run away when the load is removed. The speed-torque curves are obtained in a manner similar to that previously described for the series and shunt motor.
Loading Back Tests
When a machine is loaded on a brake or a rheostat, the total power input is converted into heat, and is therefore wasted. This waste of power, particularly in the case of large machines, represents a consid erable expense, and may in some cases exceed the available amount of power in the testing room or factory. To overcome this loss of energy, various testing methods have been devised. These consist commonly in loading one machine with another, so that only the losses in the two machines need be supplied by the power source.
The connection arrangement for Kapp’s loading back test is shown in Fig. 9. With this method, the two machines are electrically connected in parallel and mechanically connected by means of a belt. One machine is run as a motor and the other as a generator. The output of the generator is fed back to the motor, so that the supply source has to supply only the difference between the input to the motor and the output of the generator.
![Fig. 9. Connections for Kapp's loading-back test._thumb[1]](http://machineryequipmentonline.com/electric-equipment/wp-content/uploads/2020/06/Fig.-9.-Connections-for-Kapps-loading-back-test._thumb1.jpg "Fig. 9. Connections for Kapp's loading-back test._thumb[1]")
In starting the test, the switch connecting the two machines is opened, and the motor is brought up to speed in the usual manner. The other machine is now being run as a generator through the belt
connection. The generator field rheostat is adjusted until its voltage becomes equal to that of the supply source, after which the switch is closed. From the indication of the various instruments shown, the losses may easily be determined, and from this the efficiency, by a simple application of Ohm’s law.
When the two machines are identical in construction, an approximate value of the efficiency of each may be obtained by measuring the current supplied by the power supply in addition to their terminal voltage. The total losses in the two machines are then equal to the potential across the circuit multiplied by the total current supplied. Thus, if the current and the back emf in the two machines are equal, the total power loss in each machine is simply El. In actual practice, however, this is not exactly true since the back emf on the motor will always be less than that on the generator. Also, the armature current of the motor will always be greater than that of the generator. Thus, the core loss of the motor will be less than the core loss of the generator, and the armature (l2R) loss of the motor will be somewhat greater than the armature (l2R) loss of the generator. From the foregoing, it is evident that the loss in each machine is only approximately equal to El/2.
Hopkinson’s loading back test differs principally from the previously described Kapp’ s method in that the supply losses are supplied me chanically by an auxiliary motor instead of being supplied electrically. The connections for this method are shown in Fig. 10. The auxiliary motor is used to supply all the losses, with the current in the armatures being circulated by weakening the field of one machine and strength ening that of the other. It should be observed, however, that the core losses in the machines are different, because the fields have different excitations. Therefore, while this method is quite satisfactory as a regulation and heating test, it is not satisfactory for efficiency tests.
![Fig. 10. Connections for Hopkinson's loading-back test._thumb[1]](http://machineryequipmentonline.com/electric-equipment/wp-content/uploads/2020/06/Fig.-10.-Connections-for-Hopkinsons-loading-back-test._thumb1.jpg "Fig. 10. Connections for Hopkinson's loading-back test._thumb[1]")