Analytic expression of AM mechanical static characteristic

So, in correspondence with mentioned above scheme, the value of secondary current will be:

where – total resistance of stator and rotor windings (circuit acdb);

(3.27)

Motor power (for slidingvalue)is equal

(3.28)

On the other hand this power is an electrical power loss of a circuit acdb:

(3.29)

This value is for one phase, and on a whole motor (m=3) the power loss will be

(3.30)

After (3.28) and (3.30) equalization

The value of AM moment can be determined:

. (3.31)

The value of secondary current from (3.27) will be substituted into (3.31), it will be obtained the expression of AM electromagnetic moment:

. (3.32)

In the right part of equation (3.32) all parameters for a given motor and static mode are constant, and for independent variable there is a sliding, that’s why the equation (3.32) can be expressed as general function

. (3.33)

Equations (3.32) and (3.33) are the AM mechanical characteristic, expressed in terms or sliding S. Electromagnetic moment is a complex function of a sliding, and the curve has two extremums - one in a motor mode, and other - as a generator. For obtaining of this extremums it is sufficiently to investigate the curve (3.32) on extremum by general method.

It should to take for this the first derivative of M by sliding S and equalize it to zero:

. (3.34)

Solving the equation (3.32) on conditions of (3.34), it will be obtained the sliding (), at which the motor will make the maximal moment:

. (3.35)

Substituting the value from (3.35) into equation (3.32), will obtain the expression of maximal moment:

. (3.36)

The sign „+” in equations (3.35) and (3.36) is correspond to motor mode (or braking mode with counter switching), and the sign „-” corresponds to generator mode of recuperative braking.

If equation (3.32) divide by equation (3.36) and to make respective transformation, it will:

, (3.37)

where .

From equations (3.32) and (3.36) is seen, that at given sliding the moment made by AM is proportional to the square of supplied voltage, furthermore the other parameters, that are in equations (3.32) and (3.36) are constant values for certain motor, because the AM moment is determined only by supply voltage. Such parameter as secondary resistance can be easily changed for a certain type of a motor by connecting of additional resistance in rotor circuit (if AM is the motor with phase rotor).

Mentioned above information result to very important conclusion:

Дата добавления: 2014-01-05