Project-1 (DC Motor)

Project-1 (DC MOTOR)

Google doc link- https://docs.google.com/document/d/1agFNY-oAs5rdP2VGmrp_ZyjJj8dcUNs9CFWYZsJWmIE/edit?usp=sharing

Objective

The aim of this project is to develop a MATLAB program which can produce torque-speed characteristics based on input from user.

Introduction

DC motor is a machine which convert electrical energy to mechanical energy. It works on the principle of Lorentz law which states that ‘ a current carrying conductor placed in a magnetic field experiences force’.

The direction of motor is found my Fleming’s left hand rule, in this we extend thumb, fore finger and middle finger perpendicular to each other(as shown)-

The magnitude of force can be found by, F=BILsinθ

where,

F= force (Newton)

B= magnetic field (Tesla)

I= Current (Ampere)

L= Length of conductor (meter)

θ= Angle between L and I (°)

As the name suggests it works on DC (Direct current). It has following components-

Involved software

MATLAB – Matrix Laboratory is a simulation tool where user is able to simulate real world problems before moving to model validation.

Implementation

Circuit diagram of DC motor

Here V is terminal voltage, I is armature current, R is armature resistance and EMF is back emf (It is generated due to faraday’s law of electromagnetic equation)

DC motor torque equation-

The relation between torque and armature current can be shown as-

Τ= kt*Ia   — 1

where,

Τ= Torque (Nm)

kt= Torque constant (Nm/A)

Ia= Armature current

Also,

The relation between back emf and motor speed can be shown as-

E=k*we  — 2

where,

E= Back emf (V)

k= back emf constant (V-s/rad)

we= rotor angular speed (rad/s)

From the circuit diagram by applying KVL – V=E+IaRa (where Ra is armature resistance)  — 3

From Eq.3

Ia= (V-E)/Ra  — 4

Putting eq. 4 in eq 1

T=kt*(V-E)/Ra — 5

Putting eq. 2 i n eq. 5

T=(kt*V/Ra)-(k*kt*we/Ra)

This equation shows relation between torque and speed and it will be used for MATLAB programming.

MATLAB programming

Result-

Tried with different value

1.

2.

3. For this time I chose following motor rating-

Here since value of stalling torque is very less (0.8Nm) so that’s why the curve is close to speed axis but the value of our model and actual stall torque is same i.e 0.8 Nm

Conclusion

This program will help user to find the torque-speed characteristics based on user input