Determination of the efficiency of a dc motor by loss summation method(Swinburne's test) Theory

## Introduction

Swinburne‟s test is the most commonly used method for testing of D.C machines. It is an indirect method of testing D.C machines. In this method, the no load losses of the machine are determined experimentally and the additional losses on load are estimated from the known data of the machine, and with the help of the losses and input power the efficiency at any desired load is predetermined.
For a D.C. shunt motor change of speed from no load to full load is quite small. Therefore, mechanical loss can be assumed to remain same from no load to full load. Also if field current is held constant during loading, the core loss too can be assumed to remain same. In this test, the motor is run at rated speed under no load condition at rated voltage.

## Losses

We are using the term machine in the discussion of power losses owing to the fact that no distinction need be made between the losses in the D.C generator and the motor. The law of conservation of energy dictates that the input power must always be equal to the output power plus the losses in the machine. There are three major categories of losses:
1) Mechanical losses
2) Iron losses
3) Copper losses

## Mechanical losses

Mechanical losses are the result of:
(a) The friction between the bearings and the shaft,
(b) The friction between the brushes and the commutator, and
(c) The drag on the armature caused by air enveloping the armature (winding loss).
The bearing-friction loss depends upon the diameter of the shaft at the bearing, the shaft‟s peripheral speed, and the coefficient of friction between the shaft and the bearing. To reduce the coefficient of friction, the bearing is usually lubricated.
The brush-friction loss depends upon the peripheral speed of the commutator, the brush pressure, and the coefficient of friction between the brush and the commutator. The graphite is the brush helps provide lubrication to lessen the coefficient of friction.
The winding loss depends upon the peripheral speed of the armature, the number of slots on its periphery, and its length.
Mechanical losses due to friction and winding Pfw can be determined by rotating the armature of an unexcited machine at its rated speed by coupling it to a calibrated motor. Because there is no power output, the power supplied to the armature is the mechanical loss.

## Iron loss

Since the induce E.M.F. in the conductors of the armature alternates with a frequency determined by the speed of rotation and the number of poles, a magnetic loss Pm (hysteresis and eddy-current) exists in the armature.
The hysteresis loss depends on the frequency of the induced E.M.F., the area of the hysteresis loop, the magnetic flux density, and the volume of the magnetic material. The area of the hysteresis loop is smaller for soft magnetic materials. This is one of the reasons why soft magnetic materials are used for electrical machines.
Although the armature is build using thin laminations, the eddy currents do appear in each lamination and produce eddy-current loss. The eddy-current loss depends upon the thickness of the lamination, the magnetic flux density, the frequency of the induced E.M.F. and the volume of the magnetic material.
A considerable reduction in the magnetic loss can be obtained by operating the machine in the linear region at a low flux density at the expense of its size and initial cost.

## Rotational losses

In the analysis of a D.C. machine, it is a common practice to lump the mechanical loss (Pf) and the magnetic loss (Pm) together. The sum of the two losses is called the rotational loss, PWe know that the speed of shunt motor is given by.
i.e. Pr= Pfw + Pm
The rotational loss of a D.C. machine can be determined by running the machine as a separately excited motor under no load. The armature winding voltage be so adjusted that the induced E.M.F. in the armature winding is equal to its rated value, Va . If VT is the terminal voltage and Ra is the armature-winding resistance, then the voltage that must be applied to the armature terminals is should.
Va = VT - IaRa

For the motor.
Apply Va across the armature terminals and adjust the field excitation until the machine rotates at its rated speed. Then measure the armature current. Because the armature current under no load is small fraction of its rated value and the armature winding resistance is usually very small, we can neglect the power loss in the armature winding. As there is no power output, the power supplied to the motor, VaIa, must be equal to the rotational loss in the machine. By subtracting the mechanical loss, we can determine the magnetic loss in the machine.

## Copper losses

Whenever a current flows in a wire, a copper loss, Pcu, is associated with it. The copper losses, also known as electrical or I2R losses, can be segregated as follows:
1. Armature-winding loss
2. Shunt field-winding loss
3. Series field- winding loss
4. Interpol field- winding loss
5. Compensating field-winding loss
6. Armature-winding loss
7. Shunt field-winding loss
8. Series field- winding loss
9. Interpol field- winding loss
10. Compensating field-winding loss

A machine always has some losses that cannot be easily accounted for; they are termed as stray-load losses. It is suspected that the stray-load losses in the D.C. machine s are the result of
(a) the distorted flux due to armature reaction and
(b) Short-circuit currents in the coils undergoing commutation.
As a rule of thumb, the stray-load loss is assumed to be 1% of the power output in large machines (above 100 horse power) and can be neglected in small machines.

## Power flow diagram for dc machine Various losses indicated in these figure are :
Pin = mechanical input in case of electrical generator
pout = mechanical out in case of electrical motor
Pwf =winding and friction losses
Pi = total core loss
Psh = shunt field loss in shunt machine
Pc= armature copper losses including loss in series winding and stray laod copper
Pb = brush contact losses

## Circuit diagram of Swinburne test ## Calculation of constant losses

VT = Terminal voltage
Ish = shunt field winding current
Pao = no-load armature copper losses (I2aoR)
Constant losses (Pc) = VTIo - Pao

## Calculation of efficiencies

Motor efficiency
Let us consider,
We have to find out the efficiency of the D.C. shunt motor at the load current of „IL‟ amperes
Then, IA=IL-ISh
Armature copper losses = I2aRa = (IL– Ish) 2Ra
Constant losses = Pc (we found them above)
Therefore, total losses = Armature copper losses + constant losses
Total losses = (IL- Ish) 2Ra + Pc
Input Rating PL= VTIL (IL depends open the mechanical load)
ῃ = 1 – losses / input
= 1-((IL-ISh) Ra+Pc+IshRSh)/VTIL

## Generator efficiency

Output Rating PL= VTIL (IL depend upon electrical load) Ia=IL+ISh
ῃ = 1 – losses / output + losses
= 1-(IL+ISh) Ra+Pc+I2ShRSh) / (VTIL+ (IL+ISh) Ra +Pc+I2ShRSh):