Several Calculation Formulas for Motors

1. Electromagnetic related

1) The induced electromotive force formula of the electric motor: E=4.44 * f * N* Φ， E is the coil electromotive force, f is the frequency, S is the cross-sectional area of the surrounding conductor (such as the iron core), N is the number of turns Φ It's magnetic flux.

How formulas are derived? We won't delve into these things anymore, we mainly focus on how to use them. Induced electromotive force is the essence of electromagnetic induction, and when a conductor with induced electromotive force is closed, it will generate induced current. Induced current in a magnetic field is subjected to an ampere force, generating a magnetic moment that drives the coil to rotate.

From the above formula, it can be seen that the magnitude of electromotive force is directly proportional to the power frequency, coil turns, and magnetic flux.

Magnetic flux calculation formula Φ= B*S*COS θ， When the plane with an area of S is perpendicular to the direction of the magnetic field, the angle θ 0, COS θ It's equal to 1, and the formula becomes Φ= B*S。

 

By combining the above two formulas, the formula for calculating the magnetic flux intensity of the motor can be obtained as follows:

B=E/（4.44*f*N*S）。

 

The other one is the Ampere force formula. To know how much force the coil is subjected to, we need this formula F=I * L * B * sin α， Where I is the current intensity, L is the conductor length, and B is the magnetic field intensity, α It is the angle between the direction of the current and the direction of the magnetic field. When the wire is perpendicular to the magnetic field, the formula becomes F=I * L * B (if it is an N-turn coil, magnetic flux B is the total magnetic flux of the N-turn coil, and there is no need to multiply it by N).

 

Knowing the force, you know the torque, which is equal to the torque multiplied by the radius of action, T=r * F=r * I * B * L (vector product). By using the two formulas of power=force * velocity (P=F * V) and linear velocity V=2 π R * rotational speed per second (n seconds), a relationship can be established with power, resulting in the formula number 3 below. However, it should be noted that the actual output torque is used at this time, so the calculated power is the output power.

 

2. The speed calculation formula for AC asynchronous motors: n=60f/P

This is very simple. The speed is directly proportional to the power frequency and inversely proportional to the number of motor pairs (remember it is a pair). Just apply the formula directly. However, this formula actually calculates the synchronous speed (the speed of the rotating magnetic field), and the actual speed of the asynchronous motor will be slightly lower than the synchronous speed, so we often see that the 4-pole motor is generally more than 1400 revolutions, less than 1500 revolutions.

 

3. The relationship between motor torque, power, and speed: T=9550P/n (P is motor power, n is motor speed)

It can be derived from the content of number 1 above, but we don't need to learn how to derive. Just remember this calculation formula. However, once again, please note that the power P in the formula is not the input power, but the output power. Due to the loss of the motor, the input power is not equal to the output power. However, in books, it is often idealized to equate input power with output power.

 

4. Motor power (input power):

1) Calculation formula for single-phase motor power: P=U * I * cos φ， If the power factor is 0.8, the voltage is 220V, and the current is 2A, then the power P=0.22 × two × 0.8=0.352KW。

2) Calculation formula for three-phase motor power: P=1.732 * U * I * cos φ （cos φ Is the power factor, U is the load line voltage, and I is the load line current.

However, this type of U and I is related to the connection method of the motor. In the star connection method, due to the common terminals of three coils separated by 120 ° voltage being connected together, forming a zero point, the voltage loaded on the load coil is actually the phase voltage; When using the triangular connection method, each coil is connected to a power line at both ends, so the voltage on the loaded coil is the line voltage. If we use the commonly used 3-phase 380V voltage, the coil in the star connection method is 220V, while the coil in the triangle connection method is 380V, P=U * I=U ^ 2/R. Therefore, the power in the triangle connection method is three times that in the star connection method, which is why high-power motors start with star delta voltage reduction.

 

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