Learn the Speed Equation of DC Motor with detailed explanations and formulas. Understand how voltage, flux, and back EMF affect the speed of a DC motor. Includes examples and calculations for better grasp of the DC motor speed formula.
The Speed Equation of DC Motor is a fundamental concept in electrical engineering that helps determine how fast a DC motor will rotate under various electrical and mechanical conditions. This is essential knowledge for engineers, students, and professionals dealing with motor-driven systems.
In this article, we’ll explore the speed equation of DC motor, understand the underlying physics, and walk through a practical example. We’ll also introduce related concepts like the voltage equation of DC motor and the formula for motor speed in various conditions.
Basic Understanding of a DC Motor
A DC motor converts electrical energy into mechanical energy through electromagnetic principles. The speed at which it rotates depends on several factors:
- Applied voltage
- Armature resistance
- Magnetic flux
- Back EMF (Electromotive Force)
To analyze and predict the performance of a DC motor, we use dc motor formulas that relate these quantities.
Voltage Equation of DC Motor
Before we derive the speed of DC motor formula, it’s essential to understand the voltage equation.
For a DC motor,
Where:
- V = Supply Voltage (Volts)
- Eb = Back EMF (Volts)
- Ia = Armature Current (Amperes)
- Ra = Armature Resistance (Ohms)
This equation tells us that the supply voltage is used to overcome both the back EMF and the voltage drop across the armature.
Speed Equation of DC Motor
The speed of a DC motor is directly proportional to the back EMF and inversely proportional to the magnetic flux:
Where:
- Eb = Back EMF (Volts)
- ϕ = Flux per pole (Weber)
- Z = Total number of armature conductors
- N = Speed of the motor (RPM)
- P = Number of poles
- A = Number of parallel paths in the armature winding
Rearranging the above equation:
Now, value of the back EMF(Eb) from the voltage equation:
Now, substituting the back EMF(Eb) from the voltage equation:
We can write above equation as,
60A/ZP has a constant value and can be denoted by K.
So, Speed Equation of DC Motor
The above motor speed equation clearly shows that:
- Speed (N) increases with Back EMF (Eₐ)
- Speed (N) decreases with increasing flux (ϕ)
- The other term 60A/ZP is constant for a given motor design.
Based on the derived speed equation, the speed of a DC motor can be regulated by adjusting either the magnetic flux or the armature voltage. Therefore, the two primary methods of DC motor speed control are the flux control method and the armature voltage control method.
This is the Speed Equation of DC Motor, often referred to as the dc motor speed formula or speed of motor formula.
Speed of DC Motor Formula – Simplified
For practical applications, especially under steady-state conditions:
Where K is a constant that depends on the motor’s construction. The value of K is 60A/ZP
This formula for motor speed helps in predicting how speed varies with voltage, current, resistance, and flux.
Torque and Speed Equation in DC Motors
We know from earlier derivations that the speed of a DC motor is given by:
And the torque equation is:
From these two equations, we notice that:
- Increasing flux (ϕ) increases the torque (T),
- But the same increase in flux would reduce the speed (N), since speed is inversely proportional to ϕ.
Summary of Relations:
| Motor Type | Torque Equation | Speed Relation | Key Feature |
|---|---|---|---|
| Series Motor | T∝I2a | N∝1/Ia | High starting torque, variable speed |
| Shunt Motor | T∝Ia | N≈constant | Constant speed, good for steady loads |
Example: Speed Equation of DC Motor
Let’s go through an example.
Given:
- Supply Voltage, V=220 V
- Armature Resistance, Ra=0.5 Ω
- Armature Current, Ia=20 A
- Magnetic Flux, ϕ=0.05 Weber
- Motor Constant, K=0.36
Step 1: Calculate Back EMF (Eb)
Step 2: Use the speed formula
So, the motor runs at 1512 RPM under these conditions.
Key Takeaways
- The speed of a DC motor depends on voltage, current, resistance, and magnetic flux.
- The dc motor speed formula helps optimize motor control systems.
- Reducing flux (weakened field) increases speed — a principle used in field control methods.
- Increasing armature resistance or load current reduces motor speed.
Conclusion
Understanding the Speed Equation of DC Motor is vital for accurate motor selection, speed control, and performance evaluation. Whether you’re working with robotics, conveyor belts, or electric vehicles, knowing the speed of DC motor formula gives you a technical edge.
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