What Determines the Back EMF of a Brushless DC (BLDC) Motor?

The Bottom Line (Key Takeaway): In a Brushless DC (BLDC) motor, Back EMF (Electromotive Force) acts as a natural speed regulator. Once a motor is manufactured, its physical properties are fixed, meaning the Back EMF is entirely dependent on the rotor’s angular velocity (speed). As the motor spins faster, Back EMF increases, which eventually limits the maximum speed and torque the motor can produce.

What Is Back EMF in a Motor?

According to Lenz’s Law, when the rotor of a BLDC motor rotates, the changing magnetic field induces a reverse voltage in the stator windings. This induced voltage is known as Back EMF.

Crucially, Back EMF always pushes against the primary voltage supplied to the motor winding.

What Are the Main Factors Determining Back EMF?

The magnitude of the Back EMF generated in a BLDC motor depends on three primary physical and operational factors:

1. The Angular Velocity of the Rotor (ω): How fast the motor is spinning.

2. The Magnetic Field Strength (B): The magnetic flux density of the rotor’s permanent magnets.

3. The Stator Coil Design (N & l): The number of turns in each phase winding and the physical length of the rotor.

The Back EMF Calculation Formula

Mathematically, the relationship is expressed as:

E ∝ N × l × B × ω

Wo:

• E = Back Electromotive Force (Back EMF)

• N = Number of coils in each phase winding

• l = Length of the rotor

• B = Magnetic flux density of the rotor

• ω = Angular velocity of the rotor (Speed)

Engineering Insight: Once a BLDC motor rolls off the production line at Faradyi Motors, variables N, l, and B are physically locked in. Therefore, the Back EMF becomes strictly proportional to the rotor’s angular velocity (ω). To simplify system design, motor manufacturers provide a Back EMF Constant (Ke), allowing engineers to easily estimate the reverse voltage at any given RPM.

How Does Back EMF Affect Motor Speed and Torque?

Understanding the interaction between supply voltage, Back EMF, and torque is critical for motion control applications.

The effective voltage driving the motor is the difference between the power supply and the Back EMF:

Effective Voltage = Supply Voltage – Back EMF

Here is how the motor behaves as it accelerates:

1. Acceleration Phase: The manufacturer selects a specific Back EMF constant during design so that there is a sufficient voltage difference to drive current and generate working torque.

2. High-Speed Phase: As the motor exceeds its rated speed, the Back EMF continues to rise. Consequently, the effective voltage drops, causing a decrease in electrical current and a proportional drop in mechanical torque.

3. Maximum Speed Limit: When the Back EMF perfectly equals the power supply voltage, the effective voltage becomes zero. The current drops to 0, the torque becomes 0, and the motor reaches its absolute speed limit (no-load speed).

When engineering precision automation systems, selecting a BLDC motor with the correct Back EMF constant is crucial for ensuring sufficient torque at your target operating speed.

Explore Faradyi-Motoren‘ range of highly optimized BLDC motors tailored for advanced industrial applications.