Speed of DC Motor Formula

DC Motor Speed Formula:

\[ RPM = \frac{V - I \times R_m}{K_v \times \Phi} \]

Voltage (V):

volts

Current (I):

amps

Resistance (R_m):

ohms

Motor Constant (K_v):

RPM/V

Magnetic Flux (Φ):

Motor Speed (RPM):

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1. What is the DC Motor Speed Formula?

Definition: This calculator determines the rotational speed (RPM) of a DC motor based on electrical and mechanical parameters.

Purpose: It helps engineers, technicians, and hobbyists predict or verify motor performance under different operating conditions.

2. How Does the Formula Work?

The calculator uses the formula:

\[ RPM = \frac{V - I \times R_m}{K_v \times \Phi} \]

Where:

\( RPM \) — Motor speed in revolutions per minute
\( V \) — Applied voltage (volts)
\( I \) — Armature current (amps)
\( R_m \) — Armature resistance (ohms)
\( K_v \) — Motor velocity constant (RPM/volt)
\( \Phi \) — Magnetic flux (Webers)

Explanation: The numerator represents the back EMF (voltage minus voltage drop across resistance), which is divided by the product of motor constant and flux to get speed.

3. Importance of Motor Speed Calculation

Details: Accurate speed prediction is crucial for motor selection, performance analysis, and system design in applications from industrial machinery to robotics.

4. Using the Calculator

Tips: Enter all parameters in their respective units. Typical values:

K_v: 100-1000 RPM/V for small motors
R_m: 0.1-10 ohms depending on motor size
Φ: Typically 0.001-0.1 Wb for permanent magnet motors

5. Frequently Asked Questions (FAQ)

Q1: What if I don't know the flux value?
A: For permanent magnet motors, Φ is usually constant and may be found in datasheets. For field-wound motors, it varies with excitation current.

Q2: How does load affect the speed?
A: Increased load raises current (I), which increases the voltage drop (I×R_m), reducing speed.

Q3: What's a typical K_v value?
A: This varies widely - small hobby motors might be 1000 RPM/V, while large industrial motors might be 50 RPM/V.

Q4: Can this be used for brushless DC motors?
A: The formula applies conceptually, but brushless motors require additional factors for precise calculations.

Q5: Why does speed decrease with higher current?
A: Higher current causes more voltage drop across the armature resistance, reducing the effective voltage available to produce rotation.