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Torque Equation For DC Motor

Torque Equation for DC Motor

Torque is a rotational force that helps for rotating the armature of DC motor. Torque is produced by electromagnetic effect. In simple words we can say that, when a conductor carrying current placed in a magnetic field or flux a mechanical force experienced by the conductors and conductor moves in a particular direction. In this article we will drive torque equation for dc motor.

Torque is measured by the product of force F and radius r.

T = F × r

Let us suppose that the DC machine working as a motor

                                                       P = number of poles

                                                     Φ = Flux per pole in Weber (Wb)

                                                     B = Flux density in Tesla or Wb/m2

                                                      r = radius of armature in meters

                                                      l = length of the conductor in meters

                                                      i = current flowing through the conductor

Now we will calculate force on each conductor

                                                     F = Bil newtons

Torque due to one conductor

T = F ×r Newton-meter (Nm)

In above equation, we have find torque due to one conductor. But if the number conductors are more than one then the above equation is multiplied by Z. Z denotes the total number armature conductors.

Now total armature torque developed is

T = Z Fr Newton-meter (Nm)

If i is the current in each conductor then total armature conductor is Ia and number of parallel paths are A, then

  Conclusion:- From the above torque equation for dc motor, we arrived at a conclusion, which are discussed below:-

The torque developed is directly proportional to the flux per pole. If the flux is increased torque is also increased.

The torque developed is directly proportional to the number of armature conductor.

Torque depends on number of poles.

The torque depends on armature current or current flowing through the armature conductor.

Torque is inversely proportional to the number of parallel path.

 

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EMF Equation for DC Machine

EMF Equation for DC Machine

DC machine may be either works as a dc motor or dc generator. EMF equation is important for both. In case of DC generator an induced emf is called generated emf and in case of DC motors generated emf is called Back or Counter emf  The DC generator is rotate with the help of prime mover. Prime mover is directly coupled to the generator. When armature of dc generator rotates its conductor cuts by the magnetic flux that is produce in field winding and this results of an emf is induced in it. The induced emf depends upon the type of winding of dc generator whether it is wave or lap. In this article, we will drive the emf equation for dc machine.





Let,

Φ = flux per pole in weber

Z = total number of armature conductor

= number of slots * number of conductors per slot

P = number of parallel paths in armature

N = rotation speed of the armature in revolution per minute (r.p.m)

E = emf induced in any parallel path in armature

Eg = Generated emf

Flux cut by one conductor in one revolution = PΦ wb

Time to complete one revolution, t = 60/N seconds.

Average induced emf in one conductor,

emf equation for dc machine

The number of conductors connected in series in each parallel path = Z/A

The emf generated across terminals,

E = Average emf induced in one conductor * the number of conductors connected in series in each parallel path

Number of parallel paths in wave winding, A = 2

Number of parallel paths in lap winding, A = P

Conclusions from EMF Equation for DC Machine

  • In above equation, poles remain constant.
  • The emf induced in the armature is directly proportional to the flux per pole and speed.
  • The polarity of induced emf in armature is depends upon the connections of field winding and the direction of rotation. If reversed the connection of field winding and direction of rotation, the polarity induced emf will change.
  • The induced emf is fundamental phenomenon to all dc machines either it is operated as generator or motor.
  • When the machine is operating as a generator, this induced emf is called the generated emf Eg.
  • When the machine is operating as a motor, this induced emf is called back or counter emf, Eb. This emf plays an important role in dc motor. By using this equation we can find back emf.
  • Wave winding is used for high  voltage and low current applications and where as Lap winding used where large current at low voltage is generated.




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Speed Control of DC Series Motor

Speed Control of DC Series Motor

The Speed control of dc series motor can be obtained by changing the field, called field control method and by changing the back emf is called armature control method.

Flux or Field Control Method

In this method , the speed varied by  changing the field or flux. The following methods are adopted in field control method

Field Diverters

In this method, a variable resistance is connected in parallel with series field winding.

The flow of current through field winding divided into two paths, in this way some value of current passes through variable resistance and it reduces the value of current through the field winding. In this way, flux is reduced and speed of the motor is increased.

speed control of dc series motor

The lowest speed is obtained by reducing the current through diverter to zero.

By this method, speed above normal only can be obtained.

Armature Diverters

In this method, a variable resistance is connected across the armature. The current flowing through the armature divided into two paths(I = Ia + ID).

The flow of current through the variable resistance or diverter depends on the value of resistance.

Divert current reduces the current passes through the armature. Due to reduction in armature current, the speed of the motor is decreased.

speed control method of dc series motor armature diverter

By this method, speeds below normal only can be obtained.

Tapped Field Control

In this method, the flux is reduced by decreasing the number of turns of the series field winding. The flux produces in the field winding depends on the current flows through field winding and number of turns.

Φ α Ise * N

When the number of turns is decreased that decrease the flux. Hence, speed is increased by this relation (N α 1/Φ).

By this method, speed higher than normal can be achieved.

Armature Resistance Control Method

In this method, a variable resistance is connected in series with series field winding and armature.

By increasing the value of resistance, the voltage across the armature terminals reduces and speed is also reduce.

This method has poor speed regulation and considerable power loss in it.

 

 

 

 

 

 

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Speed Control of DC Shunt Motor

Speed Control of DC Shunt Motor

We Know that, the operating characteristics of dc shunt motor is same as the phase induction  motors. But speed of motors can not be changed easily in case of three phase induction motors. So that, where speed control of motor is required in  that cases dc shunt motor is employed. The speed of dc motor can be varied by varying the value of back emf and flux. Speed of DC motor is directly proportional to the back emf and inversely proportional to the flux. In this article we will discuss about speed control of DC shunt motor.

speed control of DC Shunt motor

Field or Flux Control Method

In this method the speed control of dc shunt motor is done by varying the flux per pole, hence the name is field or flux control method.

speed control of dc shunt motor field control

We know that, the speed of dc motor is inversely proportional to the flux, as the above relation is shown. In this method, a variable resistance or rheostat is inserted in series with the field winding. By varying the value of resistance connected in series speed can be changed (increased or decreased). At  high value of resistance less current less current will pass through the field winding and vice versa. This results reduces the flux and speed increases. So that, lowest speed attainable is that corresponding to maximum value of field current (If α Φ) and maximum speed depends on the minimum value of field current.

By this method, the speed above normal only can be obtained.  This method allows increasing the speed in the ration6:1 wider speed ranges tend to produce power commutation.

Armature Control Method

In this method of speed control, Voltage across the armature is varied by connecting a variable resistance in series with the armature circuit.

SPEED CONTRL OF DC SHUNT MOTOR ARMATURE CONTRAL METHOD

By changing the value of resistance the back emf is changed, hence the speed of dc motor changes. More value of resistance give rise more losses which reduce the speed of dc shunt motor.

By this method, the speed below normally only can be obtained.

In this method field current is unaffected because the shunt field is directly connected across the supply voltage.

From above explanation, it is clear that the speed of dc shunt motor is directly proportional to the back emf. This method is widely used for ‘speed control of dc shunt motor’.

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DC Motor

DC Motor

DC motor is a electrical machine which converts electrical energy into mechanical. There are three types of dc motors which are employed at various industrial applications. The dc motors are classified on the basis of connection of field winding with respect to armature. Most important application of dc motor found in traction system. Dc series motors are most suitable for traction system.


Working Principle of DC Motor

When a current carrying conductor placed in a magnetic field a mechanical force experienced by the conductor. The twisting movement of shaft about its axis due to force produced by interaction of field produced by current carrying conductor in armature and field produced by field winding is called torque. This type of toque is called electromagnetic torque.

Dc motor, opeartion, types of dc motors, characteristis of dc motors, speed control of dc motors

Pole-N and S are field magnets. It may be electromagnet or permanent magnet. The armature conductor is carrying current and placed in the magnetic field. Interaction between field magnet and field produce by armature conductor producing a driving torque.

Back E.M.F

The e.m.f induced in armature conductor due to flow of direct current which opposes the applied voltage is called back e.m.f or counter e.m.f.

Consider a shunt wound motor connected to the dc supply. A dc current start flowing through the armature conductor. Field magnets are also energized by dc supply which produces a magnetic field. When the interact armature field and main field driving torque is produced. As the armature rotates, back e.m.f is produced which opposes the applied voltage V.

Net voltage across armature circuit = V – Eb

Armature current Ia = V-Eb/Ra

Significance or Importance of Back EMF

The presence of back e.m.f makes the dc machine self regulating machine. The armature resistance is very small. If it carries the large current it will burn out. So the back e.m.f makes the motor to draw as much armature current as it just adequate to develop the torque required by the load

Armature current, Ia = V-Eb/Ra

Types of DC Motors

The DC motors are divided into three types according to their connections of field winding in relation to the armature.

  • DC series motor
  • DC shunt motor
  • DC compound motor

DC compound motor further into two types

  • Cumulative compound motor
  • Differential compound motor


DC Series Motor OR Series Wound Motor

In DC series motor the armature and field winding connected in series. The current flowing through the field winding is the same as that in the armature, if the mechanical load on the shaft increase the armature current also increases. The resultant increase in magnetic flux causes reduction in speed.

dc series motor

DC Shunt Motor or Shunt Wound Motor

DC shunt motor in which the field winding is connected in parallel with the armature. The shunt winding has fine and large number of coil. The shunt winding carries the constant current from the supply main.

types of dc motor shunt motor

Armature current, Ia = Ia – Ish

Shunt current, Ish = V/Rsh

DC Compound Motor or Compound Wound Motor

There are two types of DC compound motor or compound wound motors. Compound motors are those motors which has two field winding. One winding is connected in series with the armature and the other winding is connected in parallel with the armature series winding has less number of turns having large cross sectional area. Where as the shunt winding has more turns having small cross sectional area. There are two types of Compound Wound Motors.

  1. Cumulative compound wound motor
  2. Differential compound wound motor

Commulative Compound Wound Motor

When the shunt field winding directly connected across the armature terminals is called Cumulative Compound Motor.

Differential Compound Wound Motor

When the shunt field winding is connected in such a way that it shunts the series combination of armature and series field, it is called Differential Compound Motor.

dc compound motors

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Characteristics of DC Series Motors

Characteristics of DC Series Motors

The performance of DC motor can observe by its operating characteristics curve is called motor characteristics. In this article we will discuss about characteristics of DC series motors.

characteristics of DC series motors

Speed Armature Current (N-Ia) Characteristics

The speed of a dc series motor given by the relation.

Where is back emf and its value is equal to (V-Ia (Ra+Rse) and Φ is flux.

At starting time, the value of current is small and flux produce also small. We know that flux is proportional to the current.

According to above relation the speed is inversely proportional to the flux. The speed will be high at starting time.

 

Torque-Armature Current (T-Ia) Characteristics

We know that, torque dc motor is directly proportional to product of flux and armature current.

Tα Φ Ia

The current passes through the field winding is same as that in the armature. In case of dc shunt motor, the flux is constant but in case of dc series motor, flux depends upon the current.

Upto magnetic saturation, field flux is directly proportional to armature current.

Φ α Ia

Hence, the torque of dc series becomes proportional to square of armature current.

T α Ia Ia

T α Ia2

After magnetic saturation, the flux become constant and armature torque become proportional to the armature current.

T α Ia

Torque current characteristics of dc series motor is also called electrical characteristics of the motor.

The torque and armature current reveals that the dc series motor gives high starting torque. That is why applications of dc series motor found where high starting torque is required at the starting time such as in Electric Locomotives.

Speed and Torque (N-T) Characteristics

When mechanical load on a dc series motor increases, torque also increases which reduces the speed of a dc series motor.

 

 

 

 

So that torque is inversely proportional to the speed.

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Characteristics of DC Shunt Motors

Characteristics of DC Shunt Motors

In case of dc shunt motors, for constant supply voltage, the field current is constant. Hence, the flux in dc shunt motors is practically constant. In this article,we will discuss about various characteristics of dc shunt motor.

characteristics of dc shunt motor

Speed Current (N-Ia) Characteristics

The speed of dc motor is directly proportional to back emf and inversely proportional to flux.

Since flux of dc shunt motor is constant. In this way speed only depends upon back emf Eb.

N α Eb

N α V – IaRa

If the armature drop (IaRa) is negligible, the speed of the motor will remain constant for all values of load. As the armature current increases due to increase of load, armature drop IaRa increases and speed of the motor decreases slightly. Hence, actual speed curve is slightly drooping. But for all practical purposes, dc shunt motor is taken as a constant speed motor.

speed current characteristics

AB line shows constant speed.

AC line represents slight decreases in speed due to (I2aR) losses.

Because there is no change in the speed of a dc shunt motor from no load to full load. Therefore, shunt motors can be used for the loads which are totally and suddenly thrown off with out resulting in excessive speed. So shunt motor are suitable for driving shafting, machine tools and lathes and for all other purposes, where constant speed is required.

Torque-Armature Current(T-Ia) Characteristics

The torque of dc motors is directly proportional to the flux Φ.

Ta α Φ Ia

Ta α Ia

Since in case of dc shunt motor the flux per pole Φ is considered to be constant. Hence, the current increase in torque.

characteristics of dc shunt motor speed

This characteristic is also known as electrical characteristics. Electrical characteristics are straight line passing through the origin.

Speed-Torque (N-T) Characteristics

The speed torque characteristics are derived from the first two characteristics. When torque increases, armature current increases, the speed decreases slightly. Thus with increase in load or torque, the speed decreases.

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Necessity of Starter for DC Motors

Necessity of Starter for DC Motors

In this article we will discuss about necessity of starter for dc motors.

The starting of DC motor is not preferred with the use of starter. In case of DC motor starter contains resistance which limits the starting current and protective device such as over load relay, no volt release coils etc.

The armature current is given by the relation, Ia

                                                    Necessity of starter for DC Motors

When the motor is at rest, the induced back e.m.f Eb in the armature is zero because the back e.m.f is directly proportional to the speed of the motor, (Ebα N). At starting time, therefore, the armature current is limited only by the resistance of the armature circuit. The armature resistance is very low, however, and if full voltage is applied across the motor terminals, the armature will draw heavy current, since the armature current is inversely proportional to the resistance of armature circuit.

For example:-

10 n.p., 200 volt shunt motor has full load rated current 40A and armature resistance is about 0.2Ω. If the motor is directly switched on to supply, it would take armature current.

back emf 2

Since, At starting the back e.m.f is zero. The value of this current is 25 times the full load current. This high starting current may result in:-

  • Large current will flow through the armature winding causes production of heat and it will damage the armature.
  • It will cause excessive sparking over the Commutator.
  • Excessive voltage drops in the line to which the motor is connected. This, the operation of the appliances connected to the same line may refuse to work.

To avoid this excessive current at start, a variable resistance is connected in series with the armature circuit. This additional resistance limits the starting current. The value of additional resistance depends upon the current that flows the armature during starting time.

back emf 3

Once the motor picks up speed and back e.m.f is built up and resistance is gradually reduced. Resistance is cut out completely when the motor has attained full speed.

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Construction of DC Machine

Construction of DC Machine





DC machine consists of two main parts. One of them is armature and other is field system. The field system is stationary part of the dc machine and armature is rotating part.The construction of dc generator and dc motor is same. The Name of the parts  and function of these parts of dc machine will explain in this article .

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construction of DC machine

Yoke

It is a outer body of the machine. It is cylindrical in shape. It serves the following purpose in machine:
It supports inner part of the machines e.g. poles are fixed on it.
It provides mechanical protection to the inner parts of the machine.
It provides low reluctance part for the magnetic flux.
Cast Iron yokes are made for small machines and for large machine. It is made up of fabricated steel.

Poles

Pole consists of two main parts.
(i)    Pole Core
(ii)    Pole shoe

construction of DC machine Poles

Pole Core

The Pole Core is made of thin cast steel or wrought iron lamination which are riveted together. The pole core is circular in section and field coil is wound over it.

Pole Shoes

Pole Shoes are also made of cast steel or wrought iron lamination and it screwed to the pole face. Pole shoes have larger cross section area. The poles sever following purposes.
•    It supports the filed coils.
•    It spreads out the magnetic flux in the air gap.

Field or Exciting Coils

Field coils are made of enameled copper. The coils are wound on the former then placed around the pole core as the field coils of all the poles are connected in series in such as way that when current flows through them, the adjacent poles attain opposite polarity. When direct current passed through the field coils, the required magnetic flux produced.

Armature

Armature is the rotating part of the dc machine. The conversion of energy takes place in the armature. The armature core is of laminated silicon steel. Laminations are used to reduce the eddy current loses and silicon steel is used to reduced the hysteresis losses. Armature is cylindrical in shape and keyed to the rotating shaft. At the outer periphery slots are cut, which accommodate the armature winding.

Armature Winding

Enameled copper is used for the construction of armature winding. The armature winding is housed in armature slots, which is suitably connected. The armature winding is heart of the dc machine.
On the basis of connections, there are two types of armature winding.
(a)    Lap Winding
(b)    Wave Winding

Commutator

It is the most important part of the DC machine. It is just a reversing switch. Commutator connects the rotating armature conductors to the stationary external circuit through brushes.
In generating action, it converts alternating voltage into direct voltage and in motoring action it converts unidirectional torque into alternating torque.
The commutator is a form of rotating switch placed between armature and external circuit and so arranged it will reverse the connections with the external circuit at the instant of each reversal of current in the armature.
The commutator is of cylindrical shape and is made up of wedge shape hard drawn copper segments. The segments are insulated from each other by a thin sheet of mica.



Brushes

The Brushes are pressed upon the commutator and make the connecting link between the armature winding and external circuit. Carbon is used for the construction of Brushes because it is conducting material and good lubricating material.

Brush Rocker

It holds the spindles of the brush holders. It is fitted on to the stationary frame of the machine with nut and bolts.

End Housing

End housings are attached to the ends of the main frame and support bearings. The front housing supports the bearings and the brush assemblies whereas the rear housing usually support the bearing only.

Bearings

The function of Bearings is to reduce friction between the rotating and stationary parts of the machine. Usually ball or roller bearing are used.

Shaft

The Shaft is made of mild steel. The shaft is used to transfer mechanical power from or to the machine.



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Applications of DC motors

Applications of DC motors

Different types of dc motors are available. These motors are used in different places. Applications of dc motors are as follows:-

Separately Excited DC Motor

We can obtain very accurate speed by using separately excited DC motors. So this motor is most suitable for the applications requiring speed variation from very low value to high value precisely. These motor are used in steel rolling mills, paper machines diesel electric propulsion of ships etc.



DC Shunt Motor

DC shunt motors are used where the speed required from no load to full load has to be maintained almost constant. The starting torque of DC shunt motor is medium limited to approximately 200%. This motor is also used where the load has to be driven at a number of speeds and any one of which is required to DC remain nearly constant. These motors are used in Lathes, Centrifugal pumps, Fans and Blowers, machine tools, wood working machines, spinning and weaving machines etc.

DC Series Motor

This motor is used where high starting torque is required at the starting time. The starting torque of DC series motor is very high up to 500%. This motor is also used where the load is subjected to heavy fluctuations and the speed is automatically adjusted with respect to load fluctuation. These motors are used in electric traction, cranes elevators, air compressors, sewing machines etc. But these motor are employed in electric traction system.




DC Compound Wound Motor

Commulative Compound Wound Motor

This motor is used where variable speed is required. These motors are suitable for drives requiring high starting torque and where the load may be thrown off suddenly. The operating torque of commulative compound wound motors is higher than DC shunt motors. These motors are used in shearing machines, punching machines, elevators conveyors, rolling mills etc.

Differential Compound Wound Motor

Differential compound wound motors are rarely used because of their poor torque characteristics. Theses motors are generally employed for experimental and research work.




Also Read:-

Construction of DC Machine

DC Motor

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