#### 1. How is back electromotive force generated?

The generation of back electromotive force is easy to understand. The principle is that the conductor cuts the magnetic field lines, as long as there is relative movement between the two. It can be that the magnetic field does not move and the conductor cuts; it can also be that the conductor does not move and the magnetic field moves. For a permanent magnet synchronous motor, its coils are fixed on the stator (conductor), and the permanent magnets are fixed on the rotor (magnetic field). When the rotor rotates, the magnetic field generated by the permanent magnets on the rotor will rotate and be attracted by the stator. The coil on the coil is cut and a back electromotive force is generated in the coil. Why is it called back electromotive force? As the name suggests, the direction of the back electromotive force E is opposite to the direction of the terminal voltage U (as shown in Figure 1).

Figure 1

#### 2. What is the relationship between back electromotive force and terminal voltage?

It can be seen from Figure 1 that the relationship between back electromotive force and terminal voltage under load is:

For the test of back electromotive force, it is generally tested under no-load condition, no current, and the rotation speed is 1000rpm. Generally, the value of 1000rpm is defined, and the back electromotive force coefficient = the average value of the back electromotive force/speed. The back electromotive force coefficient is an important parameter of the motor. It should be noted here that the back electromotive force under load is constantly changing before the speed is stable. From equation (1), we know that the back electromotive force under load is less than the terminal voltage. If the back electromotive force is greater than the terminal voltage, it becomes a generator and outputs voltage to the outside. Since the resistance and current in actual work are small, the value of the back electromotive force is approximately equal to the terminal voltage and is limited by the rated value of the terminal voltage.

#### 3. The physical meaning of back electromotive force

Imagine what would happen if the back electromotive force did not exist? It can be seen from equation (1) that without back electromotive force, the entire motor is equivalent to a pure resistor and becomes a device that generates particularly serious heat. This is contrary to the fact that the motor converts electrical energy into mechanical energy.

In the context of electrical energy conversion equations,

UIt refers to the input electrical energy, such as the input energy to a battery, electric motor, or transformer. I2Rt represents the heat loss energy in various circuits. This energy is a type of thermal dissipation energy, and this value should be as small as possible. The difference between the input electrical energy and the heat loss electrical energy is the useful energy * E反It* corresponding to the back electromotive force (EMF). In other words, the back EMF is used to generate useful energy and is inversely related to heat loss. The larger the heat loss energy, the smaller the achievable useful energy.

Objectively speaking, the back electromotive force (EMF) consumes electrical energy in a circuit, but it is not a “loss.” The electrical energy corresponding to the back EMF is converted into useful energy for electrical devices. For example, in an electric motor, it is converted into mechanical energy, while in a battery, it is converted into chemical energy.

Therefore, the magnitude of the back EMF indicates the ability of an electrical device to convert the total input energy into useful energy. It reflects the efficiency of energy conversion in the electrical device.

#### 4. What does the size of the back electromotive force depend on?

The formula for calculating back electromotive force:

Based on the above formula, I believe everyone can probably tell a few factors that affect the size of the back electromotive force. Here is a summary of an article:

(1) The back electromotive force is equal to the change rate of the magnetic linkage. The higher the rotation speed, the greater the change rate and the greater the back electromotive force;

(2) The magnetic link itself is equal to the number of turns multiplied by the single-turn magnetic link. Therefore, the higher the number of turns, the larger the magnetic link and the greater the back electromotive force;

(3) The number of turns is related to the winding scheme, star-delta connection, number of turns per slot, number of phases, number of teeth, number of parallel branches, whole-pitch or short-pitch scheme;

(4) The single-turn magnetic linkage is equal to the magnetomotive force divided by the magnetic resistance. Therefore, the greater the magnetomotive force, the smaller the magnetic resistance in the direction of the magnetic linkage, and the greater the back electromotive force;

(5) The magnetic resistance is related to the cooperation of the air gap and the pole slot. The larger the air gap, the greater the magnetic resistance and the smaller the back electromotive force. The pole-groove coordination is relatively complex and requires detailed analysis;

(6) The magnetomotive force is related to the remanence of the magnet and the effective area of the magnet. The larger the remanence, the higher the back electromotive force. The effective area is related to the magnetizing direction, size, and placement of the magnet, and requires specific analysis;

(7) Residual magnetism is related to temperature. The higher the temperature, the smaller the back electromotive force.

In summary, the influencing factors of back electromotive force include rotation speed, number of turns per slot, number of phases, number of parallel branches, short overall pitch, motor magnetic circuit, air gap length, pole-slot coordination, magnet residual magnetism, and magnet placement position. And magnet size, magnet magnetization direction, and temperature.

#### 5. How to choose the size of the back electromotive force in motor design?

In motor design, the back electromotive force E is very important. I think if the back electromotive force is well designed (appropriate size selection and low waveform distortion rate), the motor will be good. The influence of back electromotive force on the motor is mainly in several aspects:

1. The size of the back electromotive force determines the field weakening point of the motor, and the field weakening point determines the distribution of the motor efficiency map.

2. The distortion rate of the back electromotive force waveform affects the ripple torque of the motor and the stability of the torque output when the motor is running.

3. The size of the back electromotive force directly determines the torque coefficient of the motor, and the back electromotive force coefficient is directly proportional to the torque coefficient. From this we can draw the following contradictions faced in motor design:

a. As the back electromotive force increases, the motor can maintain high torque under the controller’s limit current in the low-speed operating area, but cannot output torque at high speeds, or even reach the expected speed;

b. When the back electromotive force is small, the motor still has output capability in the high-speed area, but the torque cannot be reached under the same controller current at low speed.

Therefore, the design of the back electromotive force depends on the actual needs of the motor. For example, in the design of a small motor, if it is required to still output sufficient torque at low speed, then the back electromotive force must be designed to be larger.