CN113849775A - Method for calculating motor distribution factor of fractional slot concentrated winding unit - Google Patents

Method for calculating motor distribution factor of fractional slot concentrated winding unit Download PDF

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CN113849775A
CN113849775A CN202111238174.8A CN202111238174A CN113849775A CN 113849775 A CN113849775 A CN 113849775A CN 202111238174 A CN202111238174 A CN 202111238174A CN 113849775 A CN113849775 A CN 113849775A
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郑军强
茅靖峰
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Abstract

The invention relates to the technical field of permanent magnet motor electromagnetic performance calculation, in particular to a method for calculating motor distribution factors of fractional slot concentrated winding units, which meets gZ requirements by introducing slot poles matched with normalized ordered number pairs (g, h)0＝h(2p0) The relation of +/-k (k is equal to 1,2,4 and g is not equal to h is not equal to 1) can analogize any unit motor winding into a basic unit motor winding arrangement mode, so that the unit motor winding arrangement has a regular centralized distribution characteristic, and the distribution factors of the unit motor winding arrangement are calculated uniformly. Meanwhile, the method converts the unit motor windings with complex and various structural forms into regular concentrated branches by establishing the relation between the fractional slot concentrated winding unit motor and the corresponding basic unit motorThe distributed winding realizes the unified calculation of the motor distribution factors of the fractional slot concentrated winding units, and provides a theoretical basis for the calculation of the distribution factors of the permanent magnet motor and the analysis of spatial harmonics.

Description

Method for calculating motor distribution factor of fractional slot concentrated winding unit
Technical Field
The invention relates to the technical field of permanent magnet motor electromagnetic performance calculation, in particular to a method for calculating motor distribution factors of fractional slot concentrated winding units.
Background
The distribution factor directly represents the distribution effect of the fractional slot concentrated winding permanent magnet motor, not only is the concentrated reflection of the electromagnetic performance of the permanent magnet motor, but also is the basis for calculating the winding factor and analyzing the magnetomotive force harmonic wave. In general, calculating the motor distribution factor requires the use of a slot vector radial diagram, specifically: based on the maximum principle of the synthetic magnetomotive force, the slot vectors formed by all coils belonging to one phase are subjected to vector superposition and then compared with the algebraic sum of the slot vectors, and the distribution factor can be obtained. However, the slot vector star maps of the unit motors are greatly different along with the diversity of slot pole matching, and the slot vector star maps of different orders of harmonics of the same unit motor are also different, so that the calculation difficulty of the distribution factors is greatly increased by the factors. Therefore, a unified calculation method for the motor distribution factors of the fractional slot concentrated winding units is explored, and a solid theoretical foundation can be laid for the magnetomotive force harmonic analysis and low-harmonic design of the permanent magnet motor winding.
Disclosure of Invention
Aiming at the problems, the invention provides a method for calculating the motor distribution factor of a fractional-slot concentrated winding unit.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating a motor distribution factor of a fractional-slot concentrated winding unit comprises the following steps:
firstly, calculating the number N of coils contained in each phase of winding of the unit motorcoilComprises the following steps:
Figure BDA0003318212220000011
in the formula, NLayerFor the number of winding layers, the number q of slots per pole and per phase of the unit motor can be expressed as follows:
Figure BDA0003318212220000012
wherein Q and D are true fractions, wherein Q represents the number of coils included in each coil group;
second step according to NcoilAnd the odd-even of Q, the matching relation of the motor slot poles of the fractional-slot concentrated winding unit can be uniformly expressed as follows:
Figure BDA0003318212220000013
in the formula, (g, h) is a slot pole matching normalization ordinal number pair;
step three, when N iscoilWhen the number of the fractional slot concentrated winding units is odd, the v-th harmonic distribution factor of the motor of the fractional slot concentrated winding unit is as follows:
Figure BDA0003318212220000021
wherein l ═ 2 (Q-1)/α0＝2π/Z0；
The fourth step, when NcoilWhen the number is even and Q is even, the v-order harmonic distribution factors of the motor with the single-layer and double-layer fractional slot concentrated winding unit can be respectively expressed as follows:
Figure BDA0003318212220000022
Figure BDA0003318212220000023
wherein c represents a downward rounding of Q/4, d is a remainder of Q/4, and alpha0＝2π/Z0；
The fifth step, when NcoilWhen the number is even and Q is odd, the calculation formula of the v-th harmonic distribution factor of the motor of the single-layer and double-layer fractional slot concentrated winding unit is respectively as follows:
Figure BDA0003318212220000024
Figure BDA0003318212220000025
wherein l ═ [ (Q-1)/2-1](Q-1)/2-l, s represents l/2 rounded down, l' is the remainder of l/2, alphas1、αs2And alphad1Can be respectively expressed as:
Figure BDA0003318212220000026
preferably, in the second step, (g, h) is selected to satisfy the following condition:
1) g and h are positive integers and need to be iteratively solved according to a specific slot pole matching relation formula (3);
2) g is an odd number in order to ensure that the arrangement mode of the unit motor windings is the same as that of the corresponding basic unit motors;
3) because of the existence of the periodic principle, the slot poles satisfying the relation of the formula (3) are matched with the normalized ordinal number pairs to have a plurality of groups, and one group with the minimum g value is selected when the distribution factor is calculated.
By adopting the technical scheme, the normalized ordered number pair (g, h) is matched by introducing the slot poles, and the normalized ordered number pair (g, h) meets gZ0＝h(2p0) The relation of +/-k (k is equal to 1,2,4 and g is not equal to h is not equal to 1) can analogize any unit motor winding into a basic unit motor winding arrangement mode, so that the unit motor winding arrangement has a regular centralized distribution characteristic, and the distribution factors of the unit motor winding arrangement are calculated uniformly. Meanwhile, the method is suitable for any groove number Z0The number of pole pairs is p0And the phase number is m (m is prime number), and the distribution factor of the motor of the single-layer and double-layer fractional slot concentrated winding unit is calculated.
The invention has the beneficial effects that:
the invention converts the unit motor windings with complex and various structural forms into regular concentrated distributed windings by establishing the connection between the fractional-slot concentrated winding unit motor and the corresponding basic unit motor, thereby realizing the unified calculation of the distributed factors of the fractional-slot concentrated winding unit motors and providing a theoretical basis for the calculation of the distributed factors of the permanent magnet motors and the analysis of space harmonics.
Drawings
FIG. 1 is a motor characteristic classification diagram of a fractional slot concentrated winding unit of the present invention;
FIG. 2 is a schematic view of example 1 of the present invention;
FIG. 3 is a schematic view of embodiment 2 of the present invention;
FIG. 4 is a schematic view of embodiment 3 of the present invention;
FIG. 5 is a schematic view of example 4 of the present invention;
fig. 6 is a schematic view of embodiment 5 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, so that those skilled in the art can better understand the advantages and features of the present invention, and thus the scope of the present invention is more clearly defined. The embodiments described herein are only a few embodiments of the present invention, rather than all embodiments, and all other embodiments that can be derived by one of ordinary skill in the art without inventive faculty based on the embodiments described herein are intended to fall within the scope of the present invention.
A method for calculating a motor distribution factor of a fractional-slot concentrated winding unit comprises the following steps:
firstly, calculating the number N of coils contained in each phase of winding of the unit motorcoilComprises the following steps:
Figure BDA0003318212220000031
in the formula, NLayerFor the number of winding layers, the number q of slots per pole and per phase of the unit motor can be expressed as follows:
Figure BDA0003318212220000032
wherein Q and D are true fractions, wherein Q represents the number of coils included in each coil group;
second step according to NcoilAnd the odd-even of Q, the matching relation of the motor slot poles of the fractional-slot concentrated winding unit can be uniformly expressed as follows:
Figure BDA0003318212220000033
in the formula, (g, h) is a slot pole matching normalization ordinal number pair; wherein, the selection of (g, h) meets the following conditions:
1) g and h are positive integers and need to be iteratively solved according to a specific slot pole matching relation formula (3);
2) g is an odd number in order to ensure that the arrangement mode of the unit motor windings is the same as that of the corresponding basic unit motors;
3) because of the existence of the periodic principle, the slot poles satisfying the relation of the formula (3) are matched with the normalized ordinal number pairs to have a plurality of groups, and one group with the minimum g value is selected when the distribution factor is calculated.
Step three, when N iscoilWhen the number of the fractional slot concentrated winding units is odd, the v-th harmonic distribution factor of the motor of the fractional slot concentrated winding unit is as follows:
Figure BDA0003318212220000041
wherein l ═ 2 (Q-1)/α0＝2π/Z0；
The fourth step, when NcoilWhen the number is even and Q is even, the v-order harmonic distribution factors of the motor with the single-layer and double-layer fractional slot concentrated winding unit can be respectively expressed as follows:
Figure BDA0003318212220000042
Figure BDA0003318212220000043
wherein c represents a downward rounding of Q/4, d is a remainder of Q/4, and alpha0＝2π/Z0；
The fifth step, when NcoilWhen the number is even and Q is odd, the calculation formula of the v-th harmonic distribution factor of the motor of the single-layer and double-layer fractional slot concentrated winding unit is respectively as follows:
Figure BDA0003318212220000044
Figure BDA0003318212220000045
wherein l ═ [ (Q-1)/2-1](Q-1)/2-l, s represents l/2 rounded down, l' is the remainder of l/2, alphas1、αs2And alphad1Can be respectively expressed as:
Figure BDA0003318212220000046
referring to fig. 1, a concentrated winding unit motor N according to fractional slotscoilAnd the parity of Q, and the number of winding layers can be divided into five types, and the winding arrangement characteristics of these five types of unit motors will be described next.
Example 1
Referring to fig. 2, fig. 2 is a partial slot vector star diagram of a first type unit motor. Due to NcoilThe number of the unit motors is odd, so the unit motor can only adopt a double-layer winding structure, and the winding arrangement rule is as follows: q coils are continuously arranged in a 2 pi/m interval, only the coil of the phase is placed in the interval, the Q coils are alternately arranged in the interval in the positive and negative directions, a slot vector marked by a dotted arrow indicates that the direction of the vector needs to be determined according to the slot pole number of a specific unit motor, and alpha-h (2 pi/Z) is shown in the figure0) And l is (Q-1)/2. And respectively solving the vector sum and the algebraic sum, and further calculating the distribution factor of the v-th harmonic of the unit motor of the type.
Example 2
Referring to fig. 3, fig. 3 is a partial slot vector star diagram of a second-type unit motor, and the two cases are divided according to parity of Q/2, but the winding arrangement rules are completely the same, specifically: q coils are equally placed in two pi/m intervals, the space phase difference of the two intervals is pi, the two intervals are only provided with the coil of the phase, one interval is provided with Q/2 forward coils, the other interval is provided with Q/2 reverse coils, and in the figure, the Q/2 forward coils are placed
Figure BDA0003318212220000051
Figure BDA0003318212220000052
Indicating that Q/4 is rounded down. Likewise, the vector sum and the algebraic sum of the Q coils are obtained, and the distribution factor of the v-th harmonic in the case is obtained.
Example 3
Referring to fig. 4, fig. 4 is a partial slot vector star diagram of a third type unit motor. In this case, Q is equal to NcoilAnd/2, the arrangement rule is as follows: the Q coils are continuously arranged in a pi/m interval, only the coil of the phase is placed in the interval, and the Q coils are alternately arranged in the interval in a positive and negative mode. After vector synthesis, the distribution factor of the v-th harmonic can be obtained.
Example 4
Referring to fig. 5, fig. 5 is a partial slot vector star diagram of a unit motor of the fourth type, and the four cases are divided into two cases according to parity of (Q-1)/2, but the winding arrangement rules are completely the same, and the arrangement rules are as follows: the Q coils are divided into two parts of unequal amounts of (Q-1)/2 and (Q +1)/2, if the part (Q-1)/2 is odd, the part (Q +1)/2 is necessarily even, and the former part is placed at two alpha of the difference pi1Within the interval and only the forward coil of the phase, alpha1Can be expressed as
Figure BDA0003318212220000053
And the (Q +1)/2 portions are placed at two alpha values of the mutual difference pi2Within the interval and only the counter-winding of the phase, alpha2Can be expressed as
Figure BDA0003318212220000054
Interval alpha1And alpha2The spatial phase difference is 3 pi/2 m. When the (Q-1)/2 portion is an even number, the portion is placed at α2In the interval, the (Q +1)/2 portions are placed at α1In the interval, the vector composition rules of the two cases are completely the same.
Example 5
Referring to fig. 6, fig. 6 shows a partial slot vector of a unit motor of the fifth typeAnd (4) a star diagram. When using double-layer windings, Q is equal to NcoilAnd/2, the arrangement rule is as follows: the Q coils are divided into two parts with unequal amounts of (Q +1)/2 and (Q-1)/2, the number of the coils of the two parts is odd and even, the two parts are respectively placed in an interval of 2 pi/m, the two parts of coils are not continuously arranged any more, the phase difference of the axial space of the two parts of coils is 3 pi/2 m, and the Q coils are alternately arranged in the interval in a positive and negative mode. The distribution factor of the v-th harmonic of the unit motor of the type can be obtained by solving the slot potentials represented by the Q coils and carrying out vector summation.
In summary, in the method for calculating the motor distribution factors of the fractional-slot concentrated winding unit, the unit motor windings with complex and diverse structural forms are converted into the regular concentrated distributed windings by establishing the connection between the fractional-slot concentrated winding unit motor and the corresponding basic unit motor, so that the unified calculation of the motor distribution factors of the fractional-slot concentrated winding unit is realized, and a theoretical basis is provided for the calculation of the permanent magnet motor distribution factors and the spatial harmonic analysis.
The embodiments of the present invention have been described in detail, but the description is only for the preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.

Claims (2)

1. A method for calculating motor distribution factors of fractional slot concentrated winding units is characterized by comprising the following steps: the method comprises the following steps:
firstly, calculating the number N of coils contained in each phase of winding of the unit motorcoilComprises the following steps:
Figure FDA0003318212210000011
in the formula, NLayerFor the number of winding layers, the number q of slots per pole and per phase of the unit motor can be expressed as follows:
Figure FDA0003318212210000012
wherein Q and D are true fractions, wherein Q represents the number of coils included in each coil group;
second step according to NcoilAnd the odd-even of Q, the matching relation of the motor slot poles of the fractional-slot concentrated winding unit can be uniformly expressed as follows:
Figure FDA0003318212210000013
in the formula, (g, h) is a slot pole matching normalization ordinal number pair;
step three, when N iscoilWhen the number of the fractional slot concentrated winding units is odd, the v-th harmonic distribution factor of the motor of the fractional slot concentrated winding unit is as follows:
Figure FDA0003318212210000014
wherein l ═ 2 (Q-1)/α0＝2π/Z0；
The fourth step, when NcoilWhen the number is even and Q is even, the v-order harmonic distribution factors of the motor with the single-layer and double-layer fractional slot concentrated winding unit can be respectively expressed as follows:
Figure FDA0003318212210000015
Figure FDA0003318212210000016
wherein c represents a downward rounding of Q/4, d is a remainder of Q/4, and alpha0＝2π/Z0；
The fifth step, when NcoilWhen the number is even and Q is odd, the calculation formula of the v-th harmonic distribution factor of the motor of the single-layer and double-layer fractional slot concentrated winding unit is respectively as follows:
Figure FDA0003318212210000017
Figure FDA0003318212210000021
wherein l ═ [ (Q-1)/2-1](Q-1)/2-l, s represents l/2 rounded down, l' is the remainder of l/2, alphas1、αs2And alphad1Can be respectively expressed as:
Figure FDA0003318212210000022
2. the method for calculating the distribution factor of the motor with the fractional-slot concentrated winding unit according to claim 1, wherein the method comprises the following steps: in the second step, the selection of (g, h) meets the following conditions:
1) g and h are positive integers and need to be iteratively solved according to a specific slot pole matching relation formula (3);
2) g is an odd number in order to ensure that the arrangement mode of the unit motor windings is the same as that of the corresponding basic unit motors;
3) because of the existence of the periodic principle, the slot poles satisfying the relation of the formula (3) are matched with the normalized ordinal number pairs to have a plurality of groups, and one group with the minimum g value is selected when the distribution factor is calculated.
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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107579606A (en) * 2017-09-20 2018-01-12 江苏大学 A kind of low fractional-slot concentratred winding magneto and design method of performance of making an uproar that shake
US20190229573A1 (en) * 2016-10-10 2019-07-25 Jiangsu University Permanent magnet brushless motor having high winding factor, and design and fault-tolerant control methods thereof
CN111428387A (en) * 2020-04-28 2020-07-17 沈阳工业大学 Winding distribution coefficient calculation model and method considering distribution difference of motor slot conductors

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20190229573A1 (en) * 2016-10-10 2019-07-25 Jiangsu University Permanent magnet brushless motor having high winding factor, and design and fault-tolerant control methods thereof
CN107579606A (en) * 2017-09-20 2018-01-12 江苏大学 A kind of low fractional-slot concentratred winding magneto and design method of performance of making an uproar that shake
CN111428387A (en) * 2020-04-28 2020-07-17 沈阳工业大学 Winding distribution coefficient calculation model and method considering distribution difference of motor slot conductors

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
VANDANA RALLABANDI 等: "Multilayer Concentrated Windings for Axial Flux PM Machines", 《IEEE TRANSACTIONS ON MAGNETICS》 *
张炳义 等: "真分数槽集中绕组相带谐波比漏磁导系数研究", 《电机与控制学报》 *
郑军强 等: "分数槽集中绕组永磁电机低谐波设计方法综述", 《中国电机工程学报》 *

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