Electric rotating machines are used for the conversion of energy. The motor converts electrical energy into mechanical energy, and the generator converts mechanical energy into electrical energy. During energy conversion, the input energy in one form can not be fully converted into output energy in another form. The difference in the output energy and input energy is called the losses.
Pragmatically, no machine is 100 % efficient, and some losses always take place during the energy conversion process. The losses raise the temperature of the machine, and the efficiency of the machine gets lowered. In a DC machine, the energy loss takes place in the form of heat energy. The losses occur in the armature and field of the DC machine. There are five types of losses: copper loss, brush loss, iron loss, stray loss, and mechanical loss, which take place in a DC machine.
Losses in DC Machines
Types of Losses in a DC Machine
We shall discuss the types of losses in a DC machine for better understanding.
We shall discuss the types of losses in a DC machine for better understanding.
1. Copper Loss in DC Machine winding
The copper loss is caused by the ohmic resistance offered by the winding of the DC machine. When the current flows through the winding, heat loss takes place. The heat loss is proportional to the square of the current and the resistance of the winding. The copper loss in the winding is I2R. Where I is the current flowing through the winding, and R is the resistance of the winding. Copper loss is also known as variable loss because it depends on the percentage loading of the machine. The loss increases with the increase of loading on the machine.
The DC machine has two types of winding- field and armature winding- and losses occur in both windings. The supply is fed to the armature through the carbon brushes, and losses also occur due to ohmic voltage drops across the carbon brush.
1 a). Copper Loss in Armature Winding
The armature of the DC machine has very low resistance. The resistance of the armature is denoted by Ra.
Armature copper loss = Ia2Ra
Where
Ia is the armature current
Ra is the armature winding resistance.
The maximum copper loss occurs in the armature winding because the load current flows through it. The copper loss in the armature is about 25 to 30 % of the full load loss.
1 b). Copper Loss in the Field Winding
DC supply is fed to the field winding for the production of the flux in the DC machine. The resistance of the field winding is much more than the resistance of the armature winding. That is why the substantial copper loss takes place in the field winding, even at the low field current. The copper loss in the field winding is expressed as;
Field winding copper loss = If2Rf
Where, If is the field current and Rf is the field winding resistance.
The field winding copper loss is about 20-25 % of the full load loss of the DC machine. The copper loss in the field winding is practically constant because the field current and the field resistance remain almost constant in the DC machine.
2. Brush Contact Resistance Loss
The armature is a rotating part of the DC machine, and brushes are used to provide a DC supply to the rotating part of the DC machine. Ideally, the contact resistance between the brush contacting area and the commutator surface must be zero. However, in reality, it is impossible to have zero contact resistance.
The voltage drop takes place across the carbon brushes. The brush power drop depends upon the voltage drop across the brush and armature current.
Power Drop in Brush = PBD = VBD Ia
Where,
PBD = Power drop in Brush
VBD = Voltage Drop in Brush
Ia = Armature Current
If the brush voltage drop is not given, it is generally assumed that 2-volt drops across the carbon brush, and the power drop in the brush is 2Ia. The brush power loss can not be calculated separately, but it is included in the armature copper loss of the DC machine.
3. Core Losses or Iron Losses in DC Machine
The armature winding of the DC machine is wound around the magnetic core. The flux generated by the field coil gets linked to the armature conductors through a magnetic core. Two types of losses, namely hysteresis and eddy current loss, occur in the magnetic core. The iron loss is almost constant; therefore, the iron loss or core loss is also called constant loss. The total core loss is about 20-25 % of the full load losses.
3 a). Hysteresis Loss in DC Machine
The armature of the DC machine rotates in a magnetic field, and in one complete rotation, the magnetic field reversal happens. The part of the armature remains under the S-pole for half a revolution, and after completing half the revolution under the S-pole, the part of the armature goes under the P-pole for the remaining half cycle. Thus, in one complete cycle, the magnetic field reversal happens in the armature core. The frequency of the magnetic reversal can be found by the following mathematical expression.
Due to constant magnetic reversal in the armature, some energy consumed during magnetic reversal is called hysteresis loss. The hysteresis loss depends on the quality and volume of the core material.
The hysteresis loss in the DC machine can be calculated using the Steinmetz formula.
Steinmetz formula of Hysteresis Loss in a Dc Machine
| Steinmetz formula Ph = η Bmn f V Ph = η Bm1.6 f VWhere, Ph = hysteresis loss (Watt) η = Steinmetz hysteresis coefficient, depending on the material (J/m3) Bm = Maximum flux density (Wb/m2) n =Steinmetz exponent, ranges from 1.5 to 2.5, depending on the material f = frequency of magnetic reversals per second (Hz) V = volume of magnetic material (m3) |
3 b). Eddy Current Loss in DC Machine
The armature of the DC machine is wound on the magnetic core, and the magnetic core rotates in the magnetic field. According to Faraday’s law of electromagnetic induction, an EMF is induced in the core. The magnetic core has a certain resistance, and the induced EMF causes current to circulate within the piece of the magnetic core. The circulation current, called eddy current, causes the wastage of electrical energy. The loss caused by the eddy current is called the eddy current loss in a DC machine. The eddy current loss can be minimized by the use of a laminated core. The eddy current loss can be calculated by following mathematical expressions.
Eddy Current Loss Formula
| Pe=KBm2f2t2V Where, Pe= Eddy current loss(watt) B= Maximum flux density Wb/m2 f= frequency in Hz t= thickness of lamination (m) V= Volume of the material (m3) K= Eddy Current Constant |
4. Mechanical Loss in DC Machine
In a DC machine, the field is a stationary part, and the armature is a rotating part. The armature rotates on the bearings. The energy loss in the form of heat occurs due to friction between the inner cage and outer cage of the bearing.
The other mechanical loss is the windage loss. The air surrounding the shaft offers resistance, and when the DC machine rotates, the loss caused by air resistance is called windage loss. The DC machine draws extra power from the source to overcome the air resistance, and the extra energy is equal to the windage loss of the DC machine. The windage loss increases with an increase in the speed of the rotating machine.
5. Stray Losses in DC Machine
Stray losses are miscellaneous losses that are difficult to determine. The various reasons for the stray losses in DC machines are short circuit current undergoing commutation, distortion of flux, etc. The stray losses in the DC machine are about 1 % of the total losses.