# Number of rotor teeth

## Concept

The number of rotor teeth is calculated according to the number of segments of the stator and rotor cores of the stepping motor. The number of segments of the stator and rotor cores is divided into two types: single-stage and multi-stage. The single-stage type is that the stator and rotor are a piece of iron core. Because the windings of each phase are evenly arranged in the circumferential direction, it is also called the radial split type. It is the most used structure in stepping motors and is a three-phase reaction type. Stepping motor. The stator and rotor cores are laminated with silicon steel sheets, the stator poles are salient poles, and the pole faces of the poles have small teeth. There are three sets of control windings on the stator, and each set has two series of centralized control windings, which are respectively wound on two diametrically opposed magnetic poles. Each set of windings is called a phase, and the three-phase windings are connected in a star shape, so the number of stator poles It is usually twice the number of phases. There are no windings on the rotor, and there are even small teeth along the circumference. The pitch of the small teeth must be equal to the pitch of the small teeth on the stator poles, and the number of teeth of the rotor is limited. The advantages of this structure are simple manufacturing, easy to ensure accuracy, smaller step angles, and higher starting and running frequencies. The disadvantage is that when the diameter of the motor is small and the number of phases is large, it is difficult to separate the phases in the radial direction, the power consumption is large, and there is no positioning torque when the power is cut off.

Multi-section is that the stator and rotor cores are divided into m sections according to the number of phases along the axis of the motor. Since the windings of each phase are distributed along the axial direction, it is also called the axial split type. According to the structural characteristics of the magnetic circuit, there are two types: one is that the main magnetic circuit is still radial, and the other is that the main magnetic circuit contains an axial part. The structure of the multi-segment radial magnetic circuit stepping motor, the structure of each segment is similar to the single-segment radial phase split structure. Usually each phase winding is on each magnetic pole of a section of the stator core. The number of magnetic poles of the stator is determined by reasonable consideration of the structure, and can be equal to the number of teeth of the rotor at most. The circumference of the stator and rotor cores has uniform small teeth with similar tooth shapes and the same pitch. The number of rotor teeth is usually a multiple of the number of stator poles. Every two adjacent segments of the stator core or rotor core are staggered by 1/m pitch along the circumference. In addition, two-phase or three-phase windings can also be placed on one segment of the core. The stator core or rotor core must be staggered by the corresponding tooth pitch for every two adjacent segments, which can increase the flexibility of motor manufacturing. The common feature of the multi-segment structure is that the core segmentation and dislocation assembly process is more complicated, and the accuracy is not easy to guarantee. Especially for motors with small step angles, it is more difficult, but the step angle can be made very small, the starting and running frequency is high, the space utilization rate of the stator of the axial magnetic circuit is high, the ring control winding is convenient to wind, and the rotor The inertia is low.

## Analysis of the influence of the number of rotor teeth on the harmonic characteristics of the flux switching motor

Compared with the electrically excited motor, the permanent magnet motor has no excitation coil, which makes the whole motor simple in structure and reliable in operation Improve, the maintenance cost of the motor is relatively low, and there is no excitation loss. Permanent magnet motors are widely used in various fields of industry due to their high power density.

The existing permanent magnet motors are mostly rotor permanent magnet structures, and the permanent magnets are all surface-mounted or embedded structures, which rotate together with the rotor to provide a rotating magnetic field. For high-speed rotating permanent magnet motors, the rotor-type permanent magnet structure makes the permanent magnets in a high-speed motion state. The permanent magnets have a relatively large centrifugal force relative to the rotor, which puts forward higher requirements for the installation and fixation of the permanent magnets; secondly, the rotor Excessive temperature rise during the rotation will affect the working point of the permanent magnet, and in severe cases, the permanent magnet will be irreversibly demagnetized.

The flux switching motor can avoid the above-mentioned problems of traditional permanent magnet motors due to its unique topological structure. The difference between its structure and the traditional permanent magnet motor is that its permanent magnet and armature coil are both placed on the stator side, which avoids excessive centrifugal force of the permanent magnet caused by the rotation of the rotor, thereby reducing the requirements for permanent magnet installation and fixing; The excessive temperature rise of the rotor has a bad influence on the permanent magnets. The flux-switching motor has a higher power density than ordinary permanent magnet motors due to the magnetizing effect of the flux-switching motor, and it has better application prospects in the fields of electric vehicles and aviation.

Reports and researches on flux-switched motors mainly focus on motor topology, optimized design, electromagnetic characteristics and losses. The analysis and research on the harmonic characteristics of flux-switched motors are also involved, but there are few reports on the harmonic characteristics based on the number of rotor teeth. Based on the traditional flux-switching motor, the research proposes a method to change the number of rotor teeth to optimize the harmonic characteristics of the flux-switching motor. The analysis results show that different numbers of rotor teeth have a significant impact on the harmonic characteristics of the motor flux and back EMF.

### Principle of Flux Switching Motor

Flux switching, as the name implies, refers to the switching of the magnetic flux of the armature winding turns. In the existing magnetic flux switching motor, the magnitude and direction of the magnetic flux of the coil turn chain are mainly determined by the relative position of the rotor teeth and the stator teeth. One electrical cycle of a magnetic flux switching motor corresponds to a mechanical angle corresponding to one pole pitch of the rotor. Assuming that the positive direction of the magnetic flux is passing through the coil, the rotor teeth and stator teeth in Figure 1 (a) are directly opposite, and the magnetic flux passes through the coil. According to the principle of minimum reluctance, the magnetic flux of the coil turns is the maximum in the positive direction; When the rotor teeth move to the position shown in Figure 1(b), the rotor teeth and the stator slots are directly opposite. At this time, the magnetic flux passing through the coil is equal to the magnetic flux passing through the coil, and the magnetic flux of the coil turns is zero. ; The rotor teeth continue to move in the same direction to the position shown in Figure 1 (c). At this time, the rotor teeth and the stator teeth are still facing each other. Due to the magnetizing direction of the permanent magnets, the magnetic flux direction of the coil turns at this time is Passing through the human coil is opposite to the assumed positive direction, that is, the magnetic flux of the coil turns is the maximum in the reverse direction. Based on the above analysis, it is found that when the relative position of the rotor teeth and the stator teeth changes, the magnetic flux of the corresponding coil turn chain always closes along the path of least reluctance. The direction of the magnetic flux changes from passing through the coil to passing through the human coil, and the magnetic flux changes from the forward maximum to the reverse maximum. The above process completes the switching of the magnetic flux, including the magnitude and direction of the magnetic flux.

### Flux analysis

In order to study the influence of the number of rotor teeth on the harmonic characteristics of a flux-switched motor, it is first necessary to study the effect of the change of the number of rotor teeth on the flux linkage of the coil. Two types of flux-switching motors, 12/10 and 12/11, are selected as the research object, and the flux linkage is the target for comparative analysis. The finite element model of the flux-switching motor with two structures of 12/10 type and 12/ll type is established as shown in Figure 2. During the rotation of the rotor teeth for one pole pitch, five special rotor positions are selected according to the structures of the two motors to determine the size and polarity of the flux linkage of each coil. The positional relationship between the A-phase flux linkage and the rotor of the two motors is shown in Table 1 and Table 2.

Taken together, the change in the number of rotor teeth changes the sign and phase of the flux linkage of each coil in the A-phase winding. The change of the sign of each coil's flux linkage changes the harmonic components in the phase A composite flux linkage; the change of the phase of each coil's flux linkage changes the amplitude of the phase A composite flux linkage.

### Research conclusions

The principle of flux-switching motors is studied, the flux linkages of the turns of each coil when the rotor is at different positions are analyzed, and the finite element method is used to compare and analyze 12 The flux linkage and back electromotive force of /10 type motor and 12/11 type motor have the following conclusions:

1) The difference in the number of rotor teeth will change the complementarity between the single-phase coils;

2) The difference in the number of rotor teeth will change the polarity of the flux linkage of the coil turns, which will affect the harmonic components of the single-phase coil flux linkage, and then affect the harmonic characteristics of the motor;

< p>3) The difference in the number of rotor teeth will change the phase difference between the individual coils, thereby changing the amplitude of the flux linkage of the single-phase coil turn chain, thereby affecting the power density of the motor.

## Research on the influence of the number of teeth on the rotor of a hybrid magnetic flux switching motor

### Research background

Compared with an electrically excited motor, the permanent magnet motor has a simple structure. The operation reliability is high, and the maintenance cost is relatively low. Permanent magnets provide magnetomotive force so that the power density of permanent magnet motors is higher than that of traditional electric excitation motors. At the same time, the permanent magnet motor has no field winding, which can effectively reduce the copper loss of the motor. Therefore, permanent magnet motors have a wide range of applications in various fields of industry. Existing permanent magnet motors mostly adopt a rotor permanent magnet structure, and permanent magnets are attached to the surface of the rotor or embedded in the rotor to provide a rotating magnetic field. Decide how to place the permanent magnets according to different applications. Because the permanent magnet structure of the rotor makes the permanent magnet in motion, the permanent magnet has a large centrifugal force on the rotor, which puts forward higher requirements for the installation and fixation of the permanent magnet; secondly, the temperature rise during the rotation of the rotor is too high, It will affect the work of permanent magnets, and in severe cases, permanent magnets will be irreversibly demagnetized. Flux switching motors can solve the problems of traditional permanent magnet motors. The permanent magnets and armature windings are both placed on the stator side, avoiding the influence of the rotor centrifugal force and the excessive temperature rise on the permanent magnets. The magnetic flux-cutting motor has a higher power density than ordinary permanent magnet motor due to its magnetizing effect. It has good application prospects in the fields of electric vehicles and aviation. Based on the traditional flux-switching motor, a new type of hybrid-magnetized flux-switching motor is proposed, and the influence of different rotor teeth on the flux linkage and back electromotive force is analyzed. For the convenience of comparison, the 12/10 and 12/11 hybrid magnetizing flux-switching motors are taken as the research object.

### Topological structure and operating principle

The stator side structure of the hybrid magnetic flux switching motor proposed by the research is shown in Figure 3. The stator structure still uses a U-shaped stator yoke, and tangential magnetized permanent magnets are embedded between adjacent U-shaped stator yokes; compared with ordinary radial flux switching motors, the hybrid magnetizing flux switching has more power in the radial direction. The magnetized permanent magnets and the annular stator yoke outside the radial permanent magnets.

When there is no radial magnetizing permanent magnet, the motor is a traditional radial structure of magnetic flux switching motor, and the stator and the magnetic circuit in the stator are shown in Figure 4. The tangential magnetic circuit in Figure 4 is the main magnetic circuit on the stator side of the flux switching motor. Due to the existence of magnetic leakage outside the U-shaped stator yoke, the main magnetic link of the armature winding turn chain is reduced, and the induced electromotive force will be correspondingly reduced.

The magnetic flux path in the stator side of the hybrid magnetic flux switching motor proposed by the research is shown in Figure 5 (a), and the magnetic field line distribution of the motor is shown in Figure 5 (b) . Among them, tangential magnetism is produced by tangential magnetization permanent magnets, which is the main magnetic circuit of hybrid magnetization magnetic flux switching motors; radial magnetism is produced by radial permanent magnets, which serve as auxiliary magnetic circuits and have two main functions: one is It can reduce the leakage magnetic flux outside the stator to a certain extent, so that the permanent magnets magnetized in the tangential direction can be fully utilized; second, the existence of the tangential magnetic circuit increases the magnetic flux density in the U-shaped stator yoke, and then the U-shaped stator teeth The flux linkage between the middle and armature winding turns is increased.

### Research conclusions

A hybrid magnetizing magnetic flux switching motor is proposed, and the characteristics of its topological structure are analyzed. Based on the finite element calculation method, the 12/10 type and the 12/10 type are compared and analyzed. The flux linkage and back electromotive force of the 12/11 type motor have the following conclusions:

1) The winding structure of the hybrid magnetizing flux switching motor is complementary;

2) Rotor The change of the number of teeth will change the phase difference of each winding in the armature winding of one phase, change the phase difference between the harmonics in the flux linkage, and then affect the harmonic characteristics of the motor;

3 ) The change in the number of rotor teeth will cause the amplitude of the flux linkage of the armature windings of one phase to change, thereby affecting the power density of the motor;

4) In order to make full use of the complementarity of the magnetic flux switching motor windings, the rotor When the number of teeth changes, the arrangement of the armature windings also needs to be adjusted appropriately.

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