Motor Principles and Several Important Formulas,Xinrun Microelectronics Technology (Shenzhen) Co., Ltd.

Motor Working Principle

The working principle of a motor is straightforward. Simply put, a motor generates a rotating magnetic field through energized coils and drives the rotor to rotate. As described by the law of electromagnetic induction, an energized coil placed in a magnetic field will generate a rotational force. This is the basic physical principle of all motors, which is fundamental basic physics knowledge.

Motor Structure

A motor is mainly composed of two core parts: a stationary stator and a rotating rotor. The detailed structure is as follows:

1. Stator (Stationary Part)

Stator Core: A key component of the motor magnetic circuit, used for embedding stator windings.

Stator Winding: The coil structure that forms the motor’s circuit. Connected to the power supply, it generates the rotating magnetic field required for motor operation.

Frame: Fixes the stator core and end covers, and provides mechanical protection and heat dissipation for the motor.

2. Rotor (Rotating Part)

Rotor Core: An essential part of the motor magnetic circuit, with slots reserved for installing rotor windings.

Rotor Winding: Cuts the rotating magnetic field produced by the stator to induce electromotive force and current, thereby generating electromagnetic torque to drive motor rotation.

Important Motor Calculation Formulas

1. Electromagnetic Related Formulas

1) Motor induced electromotive force formula: $$E=4.44\times f\times N\times \Phi$$

Where: E = coil electromotive force, f = power frequency, N = number of coil turns, Φ = magnetic flux.

This article focuses on practical application rather than formula derivation. Induced electromotive force is the essence of electromagnetic induction. A closed conductor with induced electromotive force generates induced current, which is subjected to Ampere force in the magnetic field to form a magnetic moment and push the coil to rotate.

It can be concluded from the formula that electromotive force is positively proportional to power frequency, coil turns and magnetic flux.

Magnetic flux formula: $$\Phi=B\times S\times \cos\theta$$

When the plane area S is perpendicular to the magnetic field direction, θ = 0° and cosθ = 1, the formula is simplified to: $$\Phi=B\times S$$.

By combining the above two formulas, the magnetic flux density calculation formula is derived:

$$B=E/(4.44\times f\times N\times S)$$

2) Ampere force formula: $$F=I\times L\times B\times \sin\alpha$$

Where: I = current intensity, L = conductor length, B = magnetic field intensity, α = angle between current direction and magnetic field direction.

When the conductor is perpendicular to the magnetic field, sinα = 1, and the formula is simplified to $$F=I\times L\times B$$. For multi-turn coils, B represents the total magnetic flux of all turns, so no additional multiplication by the number of turns is required.

Torque is defined as the product of force and acting radius: $$T=r\times F=r\times I\times B\times L$$ (vector product).

Combined with the power formula $$P=F\times V$$ and linear speed formula $$V=2\pi R\times n$$ (n = rotational speed per second), the torque can be correlated with power. It should be noted that the torque adopted here is the actual output torque, and the calculated power refers to motor output power.

2. Rotational Speed Formula of AC Asynchronous Motors

$$n=60f/P$$

Motor speed is positively proportional to power frequency and inversely proportional to the number of pole pairs. This formula calculates thesynchronous speed (rotating magnetic field speed). The actual speed of an asynchronous motor is slightly lower than the synchronous speed. For example, a 4-pole motor has a rated speed of approximately 1400 rpm instead of the theoretical 1500 rpm due to slip difference.

3. Relationship Between Motor Torque, Power and Speed

$$T=9550P/n$$

Where: P = motor output power, n = motor rotational speed.

This formula can be derived from the above electromagnetic formulas. Note that P refers to output power rather than input power. Due to motor internal losses, input power is always greater than output power, though theoretical textbooks often adopt an ideal equivalence for simplified calculation.

4. Motor Input Power Formula

1) Single-phase motor power formula: $$P=U\times I\times \cos\varphi$$

Example: With power factor cosφ=0.8, voltage=220V, current=2A, the power is calculated as P=0.22×2×0.8=0.352kW.

2) Three-phase motor power formula:$$P=1.732\times U\times I\times \cos\varphi$$

Where: cosφ = power factor, U = load line voltage, I = load line current.

The actual voltage borne by the coil varies with motor wiring modes. For star (Y) connection, three coils with 120° phase difference share a common neutral point, and the coil bears phase voltage (220V for 380V grid power). For delta (△) connection, both ends of each coil are connected to power lines, and the coil bears full line voltage (380V for 380V grid power).

According to $$P=U^2/R$$, the power of delta connection is three times that of star connection under the same conditions. This is the core reason why high-power motors adopt star-delta step-down starting to reduce starting current and power impact.

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