Derive the formula of motor ????
Answers
Explanation:
Torque Equation of a DC Motor
When a DC machine is loaded either as a motor or as a generator, the rotor conductors carry current. These conductors lie in the magnetic field of the air gap. Thus, each conductor experiences a force. The conductors lie near the surface of the rotor at a common radius from its centre. Hence, a torque is produced around the circumference of the rotor, and the rotor starts rotating.
When the machine operates as a generator at a constant speed, this torque is equal and opposite to that provided by the prime mover. When the machine is operating as a motor, the torque is transferred to the shaft of the rotor and drives the mechanical load. The expression is same for the generator and motor.
When the current carrying current is placed in the magnetic field, a force is exerted or it which exerts turning moment or torque F x r. This torque is produced due to the electromagnetic effect, hence is called Electromagnetic torque. The torque which is produced in the armature is not fully used at the shaft for doing the useful work. Some part of it where lost due to mechanical losses. The torque which is used for doing useful work in known as the shaft torque.
Since,
torque-equation-of-dc-motor-eq1
Multiplying the equation (1) by Ia we get
torque-equation-of-dc-motor-eq2
Where,
VIa is the electrical power input to the armature.
I2aRa is the copper loss in the armature.
We know that,
Total electrical power supplied to the armature = Mechanical power developed by the armature + losses due to armature resistance
Now, the mechanical power developed by the armature is Pm.
torque-equation-of-dc-motor-eq3
Also, the mechanical power rotating armature can be given regarding torque T and speed n.
torque-equation-of-dc-motor-eq4
Where n is in revolution per seconds (rps) and T is in Newton-Meter.
Hence,
torque-equation-of-dc-motor-eq5
But,
torque-equation-of-dc-motor-eq6
Where N is the speed in revolution per minute (rpm) and
torque-equation-of-dc-motor-eq7
Where, n is the speed in (rps).
Therefore,
torque-equation-of-dc-motor-eq8
So, the torque equation is given as
torque-equation-of-dc-motor-eq9
For a particular DC Motor, the number of poles (P) and the number of conductors per parallel path (Z/A) are constant.
torque-equation-of-dc-motor-eq10
Where,
torque-equation-of-dc-motor-eq11
Thus, from the above equation (5) it is clear that the torque produced in the armature is directly proportional to the flux per pole and the armature current.