Brushed Motor Speed Calculator with Acceleration

Motor Speed Equation:

\[ RPM = \frac{(V - I_a \times R_a)}{(K \times \Phi)} \]

Voltage (V):

volts

Armature Current (Ia):

amps

Armature Resistance (Ra):

ohms

Motor Constant (K):

V/(rad/s)

Magnetic Flux (Φ):

Acceleration Time:

seconds

Motor Speed:

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1. What is the Brushed Motor Speed Equation?

The brushed motor speed equation calculates the rotational speed of a brushed DC motor based on the applied voltage, armature current, resistance, motor constant, and magnetic flux. It's fundamental for understanding and controlling motor performance.

2. How Does the Calculator Work?

The calculator uses the motor speed equation:

\[ RPM = \frac{(V - I_a \times R_a)}{(K \times \Phi)} \times \frac{60}{2\pi} \]

Where:

\( V \) — Applied voltage (volts)
\( I_a \) — Armature current (amps)
\( R_a \) — Armature resistance (ohms)
\( K \) — Motor constant (V/(rad/s))
\( \Phi \) — Magnetic flux (Weber)
The 60/2π factor converts rad/s to RPM

Explanation: The equation shows that motor speed is proportional to the applied voltage minus the voltage drop across armature resistance, and inversely proportional to the motor constant and magnetic flux.

3. Importance of Motor Speed Calculation

Details: Accurate speed calculation is crucial for motor selection, performance prediction, and control system design in applications ranging from industrial machinery to electric vehicles.

4. Using the Calculator

Tips: Enter all required values in appropriate units. For acceleration calculation, provide the time taken to reach full speed. Typical motor constants range from 0.01 to 1.0 V/(rad/s).

5. Frequently Asked Questions (FAQ)

Q1: What affects motor speed most significantly?
A: Applied voltage has the most direct impact, followed by load (which affects armature current). Magnetic flux is typically constant in permanent magnet motors.

Q2: Why does speed decrease with load?
A: Increased load causes higher armature current, which increases the voltage drop across armature resistance (Ia×Ra), effectively reducing the voltage available to produce speed.

Q3: How accurate is this calculation?
A: It provides theoretical no-load speed. Actual speed under load will be lower due to additional factors like brush drop and mechanical losses.

Q4: What's typical RPM range for brushed motors?
A: Small DC motors typically operate between 1,000-20,000 RPM, though specialized motors can exceed 50,000 RPM.

Q5: How does acceleration calculation work?
A: Acceleration is calculated by dividing the final speed by the time taken to reach that speed, assuming constant acceleration.