# Objective

To analyze the performance of a commercial DC motor available in the market by plotting the speed vs torque characteristics curve using the data sheet information.

# Introduction

The speed-torque curve of any DC motor is very important to study and analyze the performance of that motor. This analysis will help us to identify and select the perfect motor with optimum performance for any particular application. This blog discusses how to plot the speed-torque characteristics using matlab software.

# Technologies involved

## DC Motor

A DC motor is a device which basically converts DC electrical energy into mechanical energy.

### Working principle

**Faraday’s law of electromagnetic induction:** Whenever a current carrying conductor is placed in a varying magnetic field, it experiences a force/torque in it and at the same time an opposite polarity EMF is induced in this conductor according to Lenz’s law. The direction of the induced torque/force is determined by the Fleming’s left hand rule.

The magnitude of this force on conductor can be expressed using below equation:

F = B*I*L * SIN(Ө)

Where,

F = Force

B = Magnetic flux density (Strength of Magnetic Field)

I = Current passing through the conductor

L = Length of the conductor

Ө = Angle that the Conductor makes with the Magnetic field.

**Lenz’s law: **The direction of the induced emf or current in a moving conductor placed in a changing magnetic field will be in such a way that it opposes the cause which makes it move.

**Fleming’s left hand rule: **It is possible to predict the direction of force/torque acting on a current carrying conductor placed in a changing magnetic field if the direction of current or magnetic field is known.

# Involved Softwares

## MATLAB

MATLAB (an abbreviation of “MATrix LABoratory”) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.

### MATLAB Scripting

Matlab Script is a sequence of various commands, which are most likely used to represent some program and is executed in the same way as a program or single command in the Matlab command window.

# Implementation

## MATLAB script creation

Created below script in matlab which contains commands for taking input values from user and then calculates the torque values corresponding to predefined speed values..

## DC motor selection

Selected “ C42-L50-W30 “ model brushed DC motor manufactured by Moog Components group which is available in the market.(data sheet link provided in references section)

## Data collection

Collected the required input variables mentioned in the code from the motor data sheet as below:

- V (DC input voltage) = 84 V
- Nr (Rated speed) = 160 rad/sec
- Ia (Armature current) = 2.4 A
- Kt (Torque constant) = 0.4590 Nm/amp
- Ke (Back EMF constant) = 0.4584 voltssec/rad

## Result

Executed the script and provided all the required input variables. Below curve was generated as output.

# Conclusion

From the above result, we can conclude that the torque of the motor decreases when speed increases linearly. The no load speed of the motor is 1700 rpm and the stalk torque is 8.6 Nm.

# References

Link: Speed-Torque Analysis of DC motor – Google Docs

DC Motor data sheet:Permanent Magnet DC Brush Motors Technical Data Sheet (moog.com)

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