Direct-Current Motors: Compound-Wound DC Motor Calculations

Compound-wound dc motor construction is similar to series-wound dc motor construction, as shown in FGR. 103. The major difference is that this motor has both a series and a shunt field. The shunt field limits the maximum motor speed, in a manner similar to that in the PMDC and shunt-wound motors. The series winding increases starting torque and limits the starting current of the motor. The inductance of the series winding also helps to reduce flashover under rapid load changes.

There are two common types of compound motor connections. The long-shunt connection has the shunt winding across the power source, as shown in FGR. 104.

Here the shunt field flux is a function of the line voltage and the shunt field resistance.

The short-shunt connection is shown in FGR. 105. In this configuration, the shunt winding is across the armature but in series with the series winding. Here the shunt field current is a function of the voltage across the armature and the voltage drop in the series winding. At stall there is no generated voltage in the armature, so the shunt winding sees a voltage Vsh.

Vline = Vse + Vsh + Ra

Vline = IseRse + Ise

FGR. 103 Compound-wound dc motor field.

FGR. 104 Compound motor long-shunt connection diagram.

FGR. 105 Compound motor short-shunt connection diagram.

This is a function of the series winding resistance Rse and parallel combination of the shunt winding resistance Rsh and the armature resistance Ra.

As the speed increases, the generated voltage component is added, which effectively increases Ra, causing the equivalent parallel resistance to increase. This results in an increase in voltage across the shunt winding. This causes an increase in the field flux. At the same time, the current through the series winding is decreasing, which results in a decrease in field flux.

The shunt winding turn counts for the short and long connections would have to be different to get the same resultant and field flux because of the different voltages across them.

There are two different types of compound motors in common use. They are the cumulative compound motor and the differential compound motor. In the cumulative compound motor, the field produced by the series winding aids the field produced by the shunt winding. The speed of this motor falls more rapidly with increasing current than does that of the shunt motor because the field flux increases.

In the differential compound motor, the flux from the series winding opposes the flux from the shunt winding. The field flux, therefore, deceases with increasing load current. Because the flux decreases, the speed may increase with increasing load.

Depending on the ratio of the series-to-shunt field ampere-turns, the motor speed may increase very rapidly.

Performance Calculations

Calculation of motor performance for this motor is done in a fashion similar to that for the series motor discussed earlier in this section. All of the slot areas, magnetic paths, and other geometric properties are virtually identical to those of the series motor. The flux and mmf drops for this motor must be calculated at each desired speed or load point. This is necessary because the series winding causes the total field flux to change as the load current changes. The changes for the cumulative connection are not as dramatic as those of the series motor because the shunt field adds a constant component of flux. The flux change for the differential connection can, however, be very dramatic.

Cumulative Connected Motor

It’s typical practice to initially proportion the available field winding space to allow 80 percent for the shunt winding and 20 percent for the series winding. The ratio of series field ampere-turns to shunt field ampere-turns is chosen in the range of 15 to 30 percent. The full-load current is estimated. From this the wire sizes are chosen to keep the I^2xR less and current densities within reasonable limits.

Select the no-load speed and calculate the necessary flux.

No-load flux fgnl:

Where Eg = back emf at no load, estimated to be Vline - IaRa - IaRse

P = number of poles

Pa = number of parallel armature paths

Zact = effective number of armature conductors

Snl = desired no-load speed, rpm

Next, estimate the full-load current Ifl required for the desired output power.

Where:

Wo = watts output

Win = watts input

?= assumed efficiency

This typically ranges between 25 percent on very small motors to 90 percent on very large motors. You need to have a reasonable estimate for the type of product upon which you are working.

Use this value to solve the magnetic circuit for the air gap flux fgfl.

The back-emf E is estimated from ...

The full-load torque Tfl can be found as follows:....

Differentially Connected Motor Performance

The procedure for calculating the performance of differentially connected motors is the same as for cumulative motors except for the full load air gap flux fgfl. In this case, the magnetic circuit is solved by subtracting flux due to the ampere-turns of the series winding from the shunt field flux. From the preceding formulas, one can see that a smaller full load air gap flux fgfl will cause the full-load speed to increase over the no-load speed.

One can see that if the efficiency is estimated incorrectly, the calculated performance results will be incorrect. This is, in effect, an iterative process which can be done rapidly and accurately with the aid of modern computers.