Learning summary of motor winding

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Mar 26, 2020

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Case 1. Integer-slot winding

A. EMF vector star diagram

e.g. Calculated . The EMF vector of the conductor in slot 2 lags behind slot 1 by 30°. Arranging according to the AZBXCY phase sequence gives a star diagram of the slot EMF.

Single-layer winding. Pole pitch () = 6 slots, coil span () = 6 slots. Full-pitch coil.

Double-layer winding. Pole pitch () = 6 slots, coil span () = 5 slots. Short-pitch coil.

As shown below, (a) is a schematic diagram of the full and short pitch coil, (b) is an expanded view, and (c) is an EMF vector diagram.

B. Pitch factor

For the full-pitch coil, the single-turn coil EMF is:

Single-turn coil effective value is:

For the short-pitch coil, the EMF of a single-turn coil is:

Single-turn coil effective value is:

So the pitch factor (can be understood as a discount) of the coil is:

C. Distribution factor

The q coils of the same phase under a pole are connected in series to form a pole phase group. Each coil is embedded in a different slot, and the space position of the coils is different, forming a distributed winding. The EMF of the phase A is the composite EMF of a pole phase group multiplied

So the distribution factor is:

D. Winding factor

The winding factor can be expressed as

In particular, for single-layer windings, to simplify calculations, it is envisaged that the ends of each coil are removed and reconnected so that all coils become full-pitch coils. So the pitch factor of the single-layer winding is .

Case 2. Fractional-slot winding

Case 3. Concentrated winding

Concentrated winding is a type of fractional-slot winding, so let’s discuss them together.

Advantages of fractional-slot: (a) Fewer slots, fewer coils; (b) Increase pitch and distribution effects, and improve the sinusoidal waveform of EMF; (c) Concentrated windings have short coils and ends, which reduces copper usage; (d) ……

Disadvantages of fractional-slot: (a) and pp are restricted; (b) is low; (c) The inductance is large; (d)There are a lot of harmonics; (e) ……

A. Unit motor

Propose unit motor concept.

The original motor can be composed of unit motors, and the entire winding can be divided into identical units.

There are many combinations of optional fractional slots and , but the combination of optional unit motors and is much smaller.

Analyze the fractional slot concentrated winding, , that is, (in electrical angles). In order to obtain a higher winding coefficient, it is desirable that the difference between the EMF on both sides of the coil is close to , that is, , that is , the difference between and as small as possible.

B. Constraint

has constraints. Discuss two cases according to the numbers of .

From the figure Get:

Example calculation:

Define: Get:

Introduce the concept of a virtual motor, The multi-pole motor EMF vector star diagram is regarded as a vector diagram of a virtual motor with . Calculate virtual motor:

Find:

It can be obtained that the fractional slot winding with and the integer-slot virtual motor with have the same slot EMF vector star diagram.

From the figure Get:

Example calculation:

Get:

Calculate virtual motor:

Find:

This virtual motor is still a fractional slot, so a new virtual motor is created with a slot number of , which is an even number. So the new virtual motor is an integer-slot motor. Get:

Summary

The fractional-slot motor with and the integer-slot motor with and have the same distribution factor.

The fractional-slot motor with and the integer-slot motor with and have the same distribution factor.

Regardless of whether is even or odd, the distribution coefficient of the fractional slot unit motor is the same as that of the integer-slot motor with .

C. Calculation of winding factor

The distribution factor of the integer-slot winding is For the 60 ° phase zone,

For fractional-slot concentrated winding, define , get:

The pitch factor of the integer-slot motor is For fractional-slot concentrated windings, , get:

Whether is even or odd, Get:

For unit motor,

The winding factor of the unit motor is:

Summary

The winding factor of the fractional-slot concentrated winding is related to and , and has nothing to do with .

Unit motors with the same and , although is different, but and are the same, so they have the same winding factor.

The winding factor of the basic unit motor is only related to .

When is the same, the single-layer winding has greater inductance than the double-layer winding, which is not conducive to high-speed operation, and the end portion is extended twice, the amount of copper is increased, and the harmonics are large.

D. Examples

Q: Knowing , find and winding unrolled graph.

(a) Single-layer:

(b) Double-layer:

Case 4. Unbalanced winding.

If a winding is feasible, i.e. balanced, depends solely on the number of slots and the number of poles . A winding layout will yield unsymmetrical phase coils, whenever the number of slots per phase per machine periodicity is not an integer. Unbalanced winding:

Postscript

Harmonics in windings are also a noteworthy research point, which can affect motor losses and vibration. To be added.

Recommend a web page: Emetor There is a quick design tool for motor winding connection.

References

[1] 汤蕴璆. 电机学 [D]. 北京: 机械工业出版社, 2011. [2] 谭建成. 永磁无刷直流电机技术 [D]. 北京: 机械工业出版社, 2011. [3] F. Meier, S. Meier and J. Soulard, “Emetor - An educational web-based design tool for permanent-magnet synchronous machines,” 2008 18th International Conference on Electrical Machines, Vilamoura, 2008, pp. 1-6.

关于绕组的连接方式一直都是采用软件计算的方法，每次需要手算的时候都会忘记原理，需要重新翻看课本笔记，所以最近认真翻看了电机学教材，总结了一些方法规律。当然总结的相对比较浅显，而且这里面还有许多问题没有考虑，所以会留着以后慢慢解决。电机学这本书已经看了很多次了，但每看一次都会有新的收获。大学课程用的是华科的电机学教材，以前觉得很难，现在再看许多内容感觉不够深入，所以现在一直看的是汤蕴璆的电机学，感觉丰富了许多，当然还有许多疑问，留着慢慢解决吧。

关于集中绕组的布局方法，J. Soulard的一篇文章“Investigation on Pole-Slot Combinations for Permanent-Magnet Machines with Concentrated Windings“介绍了一种1，0相互交替选择布局的方法，研究后发现有些内容没能理解，特此mark一下。

To be continued.🍺