DC Motor Speed Equation Calculator

DC Motor Speed Formula:

\[ \omega = \frac{V - I \times R}{K} \]

Voltage (V):

volts

Current (I):

amperes

Resistance (R):

ohms

Motor Constant (K):

V/(rad/s)

Motor Speed (ω):

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1. What is the DC Motor Speed Equation?

Definition: This equation calculates the angular velocity (speed) of a DC motor based on the applied voltage, current, resistance, and motor constant.

Purpose: It helps engineers and technicians understand and predict motor performance under different electrical conditions.

2. How Does the Equation Work?

The calculator uses the formula:

\[ \omega = \frac{V - I \times R}{K} \]

Where:

\( \omega \) — Angular velocity (radians per second)
\( V \) — Applied voltage (volts)
\( I \) — Current (amperes)
\( R \) — Armature resistance (ohms)
\( K \) — Motor constant (volts per radian/second)

Explanation: The numerator represents the back EMF (voltage minus voltage drop across resistance), which when divided by the motor constant gives the speed.

3. Importance of Motor Speed Calculation

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

4. Using the Calculator

Tips: Enter the applied voltage, current draw, armature resistance, and motor constant (from datasheet). All values must be ≥ 0 except voltage and K which must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What if I don't know the motor constant?
A: The motor constant (K) is typically provided in the motor's datasheet. It can also be calculated from no-load speed and voltage.

Q2: Why does current affect motor speed?
A: Current causes a voltage drop across the armature resistance (I×R), reducing the effective voltage available to produce motion.

Q3: What's a typical motor constant value?
A: This varies widely by motor size and type. Small hobby motors might have K ≈ 0.01 V/(rad/s), while industrial motors could be several V/(rad/s).

Q4: How do I convert rad/s to RPM?
A: Multiply by 60/(2π) ≈ 9.5493. Our result shows rad/s for engineering accuracy.

Q5: Does this account for load torque?
A: Indirectly - the current I reflects the load torque. Higher torque demands increase current, which decreases speed per the equation.