# Examples of calculations to Section 5 - Electric drive

## Examples of calculations for Section 5

Example 19

For an asynchronous motor with a phase rotor, calculate and construct natural and artificial mechanical characteristics: a) when a rotor is inserted into the chain ; b) with a reduced value of the supply voltage Engine data: Solution

Calculation of the mechanical characteristics of the induction motor will be carried out according to Closs's revised formula: where - the critical moment; - critical slip; Coefficient of reduction of resistances: The given values ​​of rotor resistance: Inductive short-circuit resistance: The critical moment of the motor at the nominal value of the supply voltage: where - with the ideal idle speed.

Critical slip on the natural characteristic: Equation of natural mechanical characteristics: Using this equation, the natural mechanical characteristic of an induction motor is calculated (Figure 10.27, curve 1). To construct the rheostatic mechanical characteristic at we define the total reduced resistance of the rotor chain: where - the amount of additional resistance introduced into the rotor circuit. Fig. 10.27. Mechanical characteristics of the induction motor:

1 - natural: 2, 3 - artificial

Critical slip on rheostat characteristic: Equation of rheostatic characteristic: The rheostatic mechanical characteristic corresponding to this equation has the form (Figure 10.27, curve 2).

To construct a mechanical characteristic with  Let's define the critical moment: The equation of the artificial mechanical characteristic at В looks like: The corresponding mechanical characteristic has the form (Figure 10.27, curve 3).

Example 20

For the engine considered in Example 19, calculate the resistance of the starting rheostat under the normal start-up mode in three steps and at , using the analytical method.

Solution

Since the starting mode is normal, the switching moment ( ) must exceed the static by 10 ... 20%.

We accept . The ratio of the maximum moment at start-up ( ) by the moment of switching is found by the formula (2): We perform a check for the maximum (peak) moment, which should be less than the critical one: Resistance of the stages of the starting rheostat when included in a single star: Example 21

For the engine considered in example 19, calculate the resistance of the starting rheostat under the normal starting mode in three steps and using the approximate facsimile method.

Solution

When calculating the starting resistances, the approximate graphic method is based on the straightness of the mechanical characteristic, and the calculation is carried out as for a direct current motor with parallel excitation. In Fig. 10.28. The starting characteristics of the engine for the specified starting conditions are constructed.

Maximum starting torque: Switching torque: According to the graph in Fig. 9.28 determine the resistance of the stages of the starting rheostat:  Fig. 10.28. Starting characteristics of an asynchronous motor built in an approximate way

Comparing the results of the resistance calculations in examples 20 and 21, we see that the discrepancy is not more than 5%. Therefore, in practical calculations, you can use any of the methods considered.

Example 22

For an induction motor with a squirrel cage rotor, calculate and construct the natural and artificial mechanical characteristics for the two values ​​of the stator current frequencies/= 35 Hz and/= 20 Hz, with the proportional law of the stator voltage: Engine data:  Solution

We will calculate the mechanical characteristics according to the procedure given in [8, 16]. With the proportional law of frequency regulation the electromagnetic moment of the engine is determined by the formula: where t is the number of stator phases; (/, "- phase nominal stator voltage at a frequency of 50 Hz; - relative frequency; is a coefficient dependent on the frequency .

The coefficient at a frequency of 50 Hz is equal to 1.03 and increases with decreasing frequency. At a frequency of 20 Hz . Without a large error, one can neglect the change in this coefficient.

Table 10.8

 5 M, Nm (O, C-1 M, Hm CO, with_ | M, Hm (About, With "1"/ 0.000 0 78.5 0 54.9 0 31.4 0.010 121 75.3 85 52.7 49 30.1 0.030 334 73.8 239 51.7 139 29.5 0.100 703 68.5 580 48.0 374 27.4 0.136 732 65.7 626 47.0 418 27.0 0.150 729 64.7 668 45.3 475 26.7 0.170 717 63.2 681 44.2 508 26 0.200 688 61.0 685 42.6 534 24.3 0.300 570 53.0 633 37.3 576 21.3 0.500 398 38.0 489 26.6 535 15.2 1,000 218 0 287 0 375 0   We calculate the motor speed at various frequencies using the formula: In Table. 10.8 shows the results of calculations of the natural mechanical characteristic at Hz.

In Fig. 10.29 built the natural (curve 1) and artificial (curves 2 for Hz and 3 for Hz) the mechanical characteristics of the induction motor

Example 23

Calculate and build the angular characteristic of a synchronous, explicitly polar motor

Engine data:  Solution

The equation for the angular characteristic of a synchronous, pole-pole motor is: Rated angular speed: Rated motor EMF: In Table. 10.9 shows the results of calculations of the angular characteristic of a synchronous motor, where the following notation is used: Fig. 10.29. Mechanical characteristics of the induction motor:

1 - natural: 2 - artificial at /= 35 Hz; 3 - artificial at /= 20 Hz

• Synchronous torque component • reactive torque component The results of calculating the angular characteristics of a synchronous motor are summarized in Table. 10.9.

Table 10.9    0 0 0 0 15 2.88 2.03 4.92 30 5.57 3.52 9.1 45 7.88 4.07 11.95 60 9.65 3.52 13.2 75 10.7 2.04 12.74 90 11.1 0 11.1 105 10.7 -2.03 8.7 120 9.65 -3.52 6.13 135 7.88 -4.07 3.8 150 5.57 -3.52 2 165 2.89 -2.04 0.85 180 0 0 0 Fig. 10.30. Angular characteristic of a synchronous motor:

1 - explicit pole, 2 - non-pole pole, 3 - reactive torque component

In Fig. 10.30 shows the angular characteristic of a pole-pole synchronous motor , constructed in accordance with the data in Table. 10.9.

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