Calculation of Motor Torque at Zero Speed: From Principles to Formulas

When selecting motors or discussing projects, many clients ask:

"Does a motor have torque at zero speed? If so, how is it calculated?"

While the simple answer is "yes," for engineering calculations, you must understand several key points to avoid selection errors. Based on field experience, here is a clear breakdown.

1. What is "Zero Speed Torque"?

Essentially, torque at zero speed is called Starting Torque or Locked-Rotor Torque.

It is the torque generated at the exact moment the motor is energized but has not yet started rotating. For induction motors, at zero speed, the slip equals 1. Even though the motor isn't performing "work" yet, it is already "exerting force," which allows it to start under load.

2. The Essential Engineering Formula

For project selection, you don't need complex electromagnetic models. This formula is sufficient:

Rated Torque Formula:

• T: Torque (N·m)

• P: Power (kW)

• n: Rated Speed (rpm)

3. How to Calculate at Zero Speed?

The core problem: If you plug in $n = 0$, the formula fails.

The answer is: You cannot directly substitute 0. This formula applies only to the "running state," not the "starting state."

4. Correct Calculation Methods (Common Practice)

• Method 1: Conversion from Rated Torque

  In engineering, we use: Zero Speed Torque = Multiplier $times$ Rated Torque.

  For typical 3-phase induction motors, the starting torque is generally 0.75 to 2.75 times the rated torque.

• Method 2: Theoretical Calculation (For Design)

  Starting torque is proportional to the square of the voltage (T ∝ V²). This is mostly used in motor design or simulations, rarely in the field.

5. Torque Differences by Motor Type

• Induction Motors: Medium starting torque; suitable for fans and pumps.

• Wound Rotor Motors: High starting torque (via external resistance); suitable for crushers and hoists.

• Permanent Magnet Motors: Excellent low-speed performance; can achieve constant torque with a VFD.

• Servo Motors: Can output rated or even peak torque at zero speed; ideal for precision control.

6. Why Zero Speed Torque Matters

In heavy-duty applications like crushers, mixers, and conveyors, the equipment starts under a heavy load rather than at no-load. If the starting torque is insufficient, the motor will fail to start and may trip the circuit breaker.

Conclusion:

Zero speed torque is estimated by multiplying the rated torque by a factor. It represents starting capability, not running capability.