CN111929736B - Asymmetric fractional turn coil winding method for measuring alternating magnetic field - Google Patents
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Abstract
The invention provides an asymmetric fractional turn coil winding method for measuring an alternating magnetic field, which comprises the following steps: the disk for winding the coil is equally divided into an even number of sector areas passing through the center of a circle, and the sector areas are arranged in a clockwise mode from 1 to sectorA region N; each turn of coil is divided into N-1 fractional sub-turns, each fractional sub-turn is wound in a sector area, the winding directions of the fractional sub-turns of two adjacent sector areas are opposite, and a sector area N is left; the sub-turn coefficient ratio of the fractional sub-turns wound in the sector areas from 1 to N-1 is
(ii) a Each fractional sub-turn comprises a circumferential arc part and a radial straight line part, wherein the circumferential arc part is wound on the circumferential part of the fan-shaped area, and the radial straight line part is wound on the radial tangent plane part of the fan-shaped area passing through the center of a circle; and judging the size and direction of the magnetic field by the rotating coil according to the size and the rotating angle of the induced electromotive force. The invention can realize the measurement processing of the magnetic field in the space.
Description
Technical Field
The invention relates to the technical field of measurement, in particular to an asymmetric fractional turn coil winding method for measuring an alternating magnetic field.
Background
With the rapid development of scientific technology, the research content of scientific calculation visualization is the measurement of the key research three-dimensional vector field. The existing method for measuring the non-uniform three-dimensional vector field is to convert the vector field into a scalar or tensor to output, and azimuth information of the vector field is difficult to accurately represent, so that the non-uniform three-dimensional vector field is inaccurately evaluated. The measurement of non-uniform three-dimensional vector fields is more challenging compared to three-dimensional scalar fields. Meanwhile, the development of measuring instruments and equipment for the non-uniform three-dimensional vector field is still incomplete, so that research and development of detecting instruments and imaging technologies for the non-uniform three-dimensional vector field have become a research trend.
In the field of geological exploration, with the development of technologies, the traditional exploration method cannot meet the requirement of geological exploration, and the application of a pre-detection technology in geological exploration is more and more extensive. The front detection sensors can detect stratum information in advance and can evaluate advanced stratum, but because the detection performance of the current front detection sensors on stratum boundaries is poor, when an instrument moves in the stratum, reflected signals of the stratum boundaries cannot be accurately received due to the interference of background signals, serious misjudgment occurs in the aspects of geological guidance and stratum evaluation, and the positions and the sizes of the stratum boundaries cannot be effectively detected. Therefore, it is necessary to develop an antenna structure capable of remotely detecting the distance and the orientation of the formation interface.
Therefore, an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field is urgently needed in the prior art, relates to the field of measurement of vector magnetic fields, and is also used for rapidly solving the aspects of direction, distance and the like of a layer interface in the field of geological exploration.
Disclosure of Invention
Objects of the invention
In order to overcome at least one defect in the prior art, the invention provides an asymmetric fractional turn coil winding method for measuring an alternating magnetic field, which can realize the measurement processing of the magnetic field in space; the method can be used in the field of vector magnetic field measurement and in the field of geological exploration for rapidly solving the direction, distance and other aspects of the layer interface.
(II) technical scheme
As a first aspect of the present invention, there is disclosed an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field, comprising:
a disc for winding a coil is equally divided into even fan-shaped areas passing through the center of a circle and is clockwise arranged from the fan-shaped area 1 to the fan-shaped area N; n is more than or equal to 4;
based on the sector areas, each turn of coil is divided into N-1 fractional sub-turns, each fractional sub-turn is wound on one sector area, the winding directions of the fractional sub-turns of two adjacent sector areas are opposite, and at the moment, the sector area N is empty;
based on the fractional sub-turns, the sub-turn coefficient ratio of the sector areas 1 to N-1 winding the fractional sub-turns satisfies:
Wherein the content of the first and second substances,Nthe number of the sector areas;J iis the sector areaiThe corresponding sub-turn coefficient;
based on the fractional sub-turns, each fractional sub-turn comprises a circumferential arc part and a radial straight line part, wherein the circumferential arc part is wound on the circumferential part of the sector area, and the radial straight line part is wound on the radial tangent plane part of the sector area passing through the center of a circle;
the asymmetric fractional turn coil wound based on the winding method judges the size and the direction of the magnetic field according to the size and the rotating angle of the induced electromotive force through the rotating coil.
In one possible embodiment, in the case of winding a plurality of sets of coils, the ratio of the pitches of the fractional sub-turn winding wires of the sector areas 1 to N-1 is the ratio of the inverses of the sub-turn coefficients of the sector areas 1 to N-1 winding.
In a possible embodiment, the winding direction of the sector N/2 is defined as the forward direction, and the forward direction is the clockwise or counterclockwise direction. For any of the fan-shaped areas i, the winding direction is
(ii) a Wherein the direction of-1 indicates that the winding direction of the sector region N/2 is opposite, the direction of 1 indicates that the winding direction of the sector region N/2 is the same, and the winding manner result shows that the winding directions of the fractional sub-turns of the two adjacent sector regions are opposite.
In a possible embodiment, for a coil wound by M turns, each of the sector winding methods is a single one-time winding method.
In a possible embodiment, the single one-time winding method is that for any sector i, the winding fractional number of the sub-turns is equal to
And M is a magnification factor, and one-time winding is completed through the routing of the radial straight line part and the circumferential circular arc part of the fan-shaped area.
In a possible implementation, the sub-turn coefficient corresponding to the sector N/2
The occupied weight is larger than the occupied weight of the sub-turn coefficients of other sector areas.
In a possible implementation manner, based on the asymmetric fractional turn coil, the magnitude and the direction of the magnetic field are determined by rotating the coil according to the magnitude and the rotation angle of the induced electromotive force, specifically:
step 1: placing the asymmetric fractional turn coil in the magnetic field, and approximately regarding the magnetic field at the position of the coil as a vector field with the same direction and different field intensity;
step 2: rotating the coil for a circle, and judging the field intensity of the vector field according to the amplitude of the induced electromotive force of the coil;
and step 3: and judging the direction of the vector field according to the rotation angle of the coil and the amplitude change of the induced electromotive force.
In one possible embodiment, in step 2, the asymmetric fractional turn coil forms a plurality of peaks during rotation.
In a possible embodiment, in step 2, the sub-turn coefficients corresponding to the sector N/2 are obtained
The weight is maximum, the induced electromotive force generated by the weight is maximum, if the peak value is maximum, the field intensity is maximum at the position of the fan-shaped area N/2, and if the peak value is minimum, the field intensity is minimum at the position of the fan-shaped area N/2; the other peak values are between the maximum value and the minimum value, and the corresponding field intensity at the position of the fan-shaped area N/2 is between the maximum value and the minimum value.
In a possible implementation manner, in step 3, a power line is drawn according to the field intensity corresponding to each position in the rotation process given in step 2, so that the direction of the magnetic field is obtained according to the direction of the power line.
(III) advantageous effects
Compared with the prior art, the asymmetric fractional turn coil winding method for measuring the alternating magnetic field, provided by the invention, has the advantages that the coil model obtained according to the winding method can realize the measurement of the magnetic field, and further, the three-dimensional vector magnetic field is measured by adopting a plurality of coil models, and the imaging of the complex three-dimensional vector magnetic field is realized; in the field of geological exploration, the direct coupling electromotive force of a transmitting coil can be effectively eliminated, so that signals received by a receiving coil all come from reflected waves of a layer interface, and the position of the layer interface is effectively identified through the amplitude and the phase angle of the received signals; according to the asymmetric model of the winding coil, the measurement of the layer interface orientation is realized through rotating the coil according to the peak value change of the induced electromotive force; as the distance of the layer interface becomes farther, the layer interface reflection signal weakens, and as the direct coupling signal of the transmitting coil is completely eliminated, the receiving coil can only effectively receive the signal reflected by the layer interface, so that the receiving coil can remotely detect the position of the layer interface and judge the azimuth information of the layer interface, and the tasks of geological guidance and formation evaluation can be completed in the complex stratum.
Drawings
The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining and illustrating the present invention and should not be construed as limiting the scope of the present invention.
Fig. 1 is a flow chart of an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention.
Fig. 2 is a schematic structural diagram of a model of a winding completion of an asymmetric fractional-turn coil (N = 4) in an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention.
Fig. 3 is a schematic structural diagram of a model of a winding completion of an asymmetric fractional-turn coil (N = 6) in an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention.
Fig. 4 is a schematic diagram of the magnitude and direction of the magnetic field of an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention.
Fig. 5 is a power line diagram of an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.
It should be noted that: in the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described are some embodiments of the present invention, not all embodiments, and features in embodiments and embodiments in the present application may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings, which are used for convenience in describing the invention and for simplicity in description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the scope of the invention.
A first embodiment of an asymmetric fractional-turn coil winding method for measuring an alternating magnetic field according to the present invention is described in detail below with reference to fig. 1 to 5. As shown in fig. 1-5, the winding method of the asymmetric fractional-turn coil provided in this embodiment mainly includes:
the disc for winding the coil is equally divided into an even number of sector areas passing through the center of a circle, and the sector areas are clockwise arranged as sector area 1, sector area 2, … and sector area N; n is more than or equal to 4;
based on the sector areas, each turn of coil is divided into N-1 fractional sub-turns, each fractional sub-turn is wound on one sector area, the winding directions of the fractional sub-turns of two adjacent sector areas are opposite, and at the moment, the sector area N is empty;
based on the fractional sub-turns, the sub-turn coefficient ratio of the sector areas from 1 to N-1 winding the fractional sub-turns is
And the ratio satisfies the equation
And is
(ii) a WhereinNThe number of the sector-shaped areas is,J iis a sector areaiThe corresponding sub-turn coefficient. Sub-turn coefficient of coil
Satisfy the requirement of
And is
In order to ensure that the signal received by the coil in the uniformly changing magnetic field is zero; the induced electromotive forces generated by the forward winding coil and the reverse winding coil are equal in magnitude and opposite in direction, so that mutual cancellation is realized.
Based on the fractional sub-turns, each fractional sub-turn comprises a circumferential arc part and a radial straight line part, wherein the circumferential arc part is wound on the circumferential part of the sector area, and the radial straight line part is wound on the radial tangent plane part of the sector area passing through the center of a circle;
the asymmetric fractional turn coil wound based on the winding method judges the size and the direction of the magnetic field according to the size and the rotating angle of the induced electromotive force through the rotating coil. The magnetic field is an alternating magnetic field.
In the actual measurement process, the coil usually adopts a plurality of turns to improve the signal strength of the transmitting or receiving coil, and the asymmetrically wound fractional turn coil adopted in the embodiment has the advantages that the winding turns directions of all the fan-shaped areas are different, and the ratio of the 1 to N-1 sub-turn coefficients of the fan-shaped areas is equal to
Therefore, the method of individually winding and integrally assembling the fan-shaped areas can be adopted to realize the integral winding of the coil.
Wherein, in the case of winding a plurality of sets of coils, the ratio of the pitches of the fractional sub-turn winding wires of the sector areas 1 to N-1 is the ratio of the inverses of the sub-turn coefficients of the sector areas 1 to N-1. In the case of winding a plurality of sets of coils, the ratio of the distances between two adjacent fractional sub-turns of the sectorial regions 1 to N-1 is:
ensuring that the axial length of the coils in each sector area is equal after a plurality of groups of coils are wound, keeping the field at the position of each sector area the same and reducing the measurement error,
representing the sub-turn coefficients of the sector 1 to N-1 windings.
Wherein, for an asymmetrically wound fractional turn coil, the winding direction of the sector N/2 is defined as a forward direction, and the forward direction is a clockwise or counterclockwise direction. For any of the fan-shaped areas i, the winding direction is
And the direction is-1, namely the winding direction of the fan-shaped area N/2 is opposite, the direction is 1, namely the winding direction of the fan-shaped area N/2 is the same, and the winding mode result shows that the fractional sub-turn winding directions of the two adjacent fan-shaped areas are opposite, namely the arc parts of the two adjacent fan-shaped areas are opposite in winding direction.
Wherein, for the coil wound by M turns, the winding mode of each sector area is a single one-time winding method, namely, for any sector area i, the winding fractional number of sub-turns is
And M is a magnification factor, and one-time winding is completed through the routing of the radial straight line part and the circumferential circular arc part of the fan-shaped area. For the coil wound by M turns, the integral winding of the coil is realized by adopting a method of independently winding and integrally assembling each sector area.
In order to embody the overall winding process of the coil, fig. 2 shows the winding manner of each sector area in the case of winding 1 turn by an N =4 model, wherein the ratio of the sub-turn coefficients of the sector areas 1 to 3 is 1:2:1, the sector areas 1 and 3 are reversely wound, and the sector area 2 is forwardly wound. In order to better embody the regular winding method, a one-turn coil is taken as an example for explanation, as shown in fig. 2, a sector area 1 is wound by 1 sub-turn, a sector area 2 is wound by 2 sub-turns, a sector area 3 is wound by 1 sub-turn, and a sector area 4 is wound by 0 sub-turn.
In order to improve the resolution of the asymmetric fractional sub-turn coil in measuring the size and direction of the magnetic field, the weight occupied by the sub-turn coefficient corresponding to the sector area N/2 is greater than the weight occupied by the sub-turn coefficients of other sector areas. Different resolution measurements can be achieved with different weights.
To embody the fractional sub-turn winding process of different sector areas, fig. 3 shows the winding manner of each sector area in the case where N =6 fractional sub-turn coil model is wound by 10 turns, where sector areas 1 to 5 are wound by sub-turn coefficient ratio of 0.2:1.5:2.6:1.5:0.2, where sector areas 1, 3 and 5 are forward winding and sector areas 2 and 4 are reverse winding, so that sector area 1 is wound by 2 sub-turns, sector area 2 is wound by 15 sub-turns, sector area 3 is wound by 26 sub-turns, sector area 4 is wound by 15 sub-turns, sector area 5 is wound by 2 sub-turns, and sector area 6 is wound by 0 sub-turns.
Integral turn winding illustrated by FIG. 2 and fractional sub-turn winding illustrated by FIG. 3Shake, can see that the more the sector area, the sub-turn coefficient corresponding to sector area N/2
The larger the occupied weight is, the higher the resolution is; for a clear, complete and visual description of the winding process, the present invention gives the models of fig. 2 and 3, the actual coil winding does not take into account the gaps between the sectors, the wires of each sector are coincidently wound, and the radii of all the wound sub-turns are the same.
It can be known from the above process that the asymmetric fractional-turn coil winding method provided by the present invention can effectively eliminate the direct-coupled electromotive force of the transmitting coil, so that the signals received by the receiving coil all come from the reflected waves of the layer interface, and the following describes a method for measuring the magnetic field signal by the asymmetric coil obtained according to the winding method, where the measurement model can be as shown in fig. 4, and the measurement steps can be step 1, step 2, and step 3 described below.
Based on the asymmetric fractional turn coil, the size and the direction of the magnetic field are judged by rotating the coil according to the size and the rotating angle of the induced electromotive force, and the specific expression is as follows:
step 1: the asymmetric fractional turn coil is placed in a magnetic field, and the radius of the coil is smaller than the wavelength of electromagnetic waves, so that the magnetic field at the position of the coil is approximately regarded as a vector field with the same direction and different field strengths;
step 2: rotating the coil for a circle, and judging the field intensity of the vector field according to the amplitude of the induced electromotive force of the coil;
wherein, in step 2, the asymmetric fractional turn coil forms a plurality of peaks during rotation due to asymmetry of coil winding.
Wherein, in step 2, the sub-turn coefficient corresponding to the sector N/2
The maximum weight is used to generate the maximum induced electromotive force contribution, and if the peak value is maximum, the maximum induced electromotive force contribution represents the fanThe field intensity of the position where the N/2 shaped area is located is the largest, and if the peak value is the smallest, the field intensity of the position where the N/2 shaped area is located is the smallest; the other peak values are between the maximum value and the minimum value, and the corresponding field intensity of the position of the N/2 sector area is between the maximum value and the minimum value;
as can be seen from fig. 4NAn asymmetric fractional turn coil in case of =4, assuming an integral path at sector area 1 ofS 1The integration path at sector area 2 isS 2The integration path at sector area 3 isS 3The integration path at the sector area 4 isS 4(ii) a Assume field strengths at A, B, C and D asB 1、B 2、B 3、B 4Then, the expression of the induced electromotive force generated by the coil is:
as can be seen from the above equation, the sector area 2 contributes most to the induced electromotive force, and thus the magnitude of the field intensity can be determined from the peak value. Assuming that the field strength is at its maximumB 1Then the coil starts to rotate clockwise from the position of fig. 4; in the initial position, the sector region 1 is located in the region of maximum field strength, in which case the induced electromotive force is generatedV 1The expression is
When the rotation is 90 degrees, the sector area 4 is positioned in the area with the maximum field intensity, and the induced electromotive force generated at the moment isV 2The expression is
When the coil rotates 180 degrees, the sector area 3 is positioned in the area with the maximum field intensity, and the induced electromotive force generated at the moment isV 3The expression is
When the coil rotates 270 degrees, the sector area 2 is positioned in the area with the maximum field intensity, and the induced electromotive force generated at the moment isV 4The expression is
Comparing two conditions when the coil rotates by 0 degree and 180 degrees, the induced electromotive force at the moment is as follows:
The sector region N is not wound with the sub-turns, so that the contribution to the induced electromotive force is 0, so that
If, if
Greater than 0, thenB 2Is greater thanB 4If, if
Less than 0, thenB 2Is less thanB 4。
Comparing two conditions when the coil rotates by 90 degrees and 270 degrees, the induced electromotive force at the time is as follows:
since the sector area 3 and the sector area 1 are both wound by 1 sub-turn and the winding direction is the same, there is
，
. Since the sector area N is not wound with sub-turns, the contribution to the induced electromotive force is 0, i.e., there is
In the rotation process of the coil, because the sector area 2 has 2 sub-turns, the contribution of the sector area 2 in induced electromotive force is the largest, and when the field intensity at the position reaches the maximum value, the induced electromotive force V reaches the maximum value; when the field strength reaches the minimum value, the induced electromotive force V reaches the minimum value. When the coil rotates by 0 degrees, 90 degrees, 180 degrees and 270 degrees, the field intensity is judged according to the magnitude of the induced electromotive force, so that the field intensity at different positions can be judged according to the amplitude of the induced electromotive force of the coil rotating by one circle.
And step 3: and judging the direction of the vector field according to the rotation angle of the coil and the amplitude change of the induced electromotive force.
In step 3, a power line is drawn according to the field intensity corresponding to each position in the rotation process given in step 2, so that the direction (i.e. the azimuth) of the magnetic field (i.e. the vector field) is obtained according to the direction of the power line. Is differentNCorresponding coil model measurement principle andNthe principle of coil model measurement is the same for = 4. Suppose that through step 2, obtainedB 2Is less thanB 4、B 3Is less thanB 1The plotted power line can be as shown in fig. 5.
According to the winding method of the asymmetric fractional turn coil for measuring the alternating magnetic field, the coil model is obtained according to the winding method, the measurement of the size and the direction of the magnetic field can be realized through the coil model, and then the measurement of the three-dimensional vector magnetic field is realized by adopting a plurality of coil models, and the imaging of the complex three-dimensional vector magnetic field is realized; in the logging-while-drilling process, the direct coupling electromotive force is eliminated through the designed asymmetric coil, and the receiving coil only receives a reflection signal of a layer interface, so that the calculation of the distance and the direction of the layer interface is realized.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (9)
1. An asymmetric fractional turn coil winding method for measuring an alternating magnetic field, comprising:
a disc for winding a coil is equally divided into even fan-shaped areas passing through the center of a circle and is clockwise arranged from the fan-shaped area 1 to the fan-shaped area N; n is more than or equal to 4;
based on the sector areas, each turn of coil is divided into N-1 fractional sub-turns, each fractional sub-turn is wound on one sector area, the winding directions of the fractional sub-turns of two adjacent sector areas are opposite, and at the moment, the sector area N is empty;
based on the fractional sub-turns, the sub-turn coefficient ratio of the sector areas 1 to N-1 winding the fractional sub-turns satisfies:
Wherein the content of the first and second substances,Nthe number of the sector areas;J iis the sector areaiThe corresponding sub-turn coefficient;
based on the fractional sub-turns, each fractional sub-turn comprises a circumferential arc part and a radial straight line part, wherein the circumferential arc part is wound on the circumferential part of the sector area, and the radial straight line part is wound on the radial tangent plane part of the sector area passing through the center of a circle;
the asymmetric fractional turn coil wound based on the winding method judges the size and the direction of a magnetic field according to the size and the rotating angle of induced electromotive force through a rotating coil, and specifically comprises the following steps:
step 1: placing the asymmetric fractional turn coil in the magnetic field, and approximately regarding the magnetic field at the position of the coil as a vector field with the same direction and different field intensity;
step 2: rotating the coil for a circle, and judging the field intensity of the vector field according to the amplitude of the induced electromotive force of the coil;
and step 3: and judging the direction of the vector field according to the rotation angle of the coil and the amplitude change of the induced electromotive force.
2. The asymmetric fractional turn coil winding method of claim 1 wherein, in the case of winding a plurality of sets of coils, the ratio of the pitches of the fractional sub-turn winding wire of the sector areas 1 to N-1 is the ratio of the inverses of the sub-turn coefficients of the sector areas 1 to N-1 winding.
3. The asymmetric fractional turn coil winding method of claim 1, wherein a winding direction of the sector region N/2 is specified as a forward direction, and the forward direction is a clockwise or counterclockwise direction; for any of the fan-shaped areas i, the winding direction is
(ii) a Wherein the direction of-1 indicates that the winding direction of the sector region N/2 is opposite, the direction of 1 indicates that the winding direction of the sector region N/2 is the same, and the winding manner result shows that the winding directions of the fractional sub-turns of the two adjacent sector regions are opposite.
4. The asymmetric fractional turn coil winding method of claim 1 wherein for a coil wound with M turns, each of said sectors is wound in a single one-time winding.
5. The asymmetric fractional turn coil winding method of claim 4, wherein said single one-time winding method is a method in which, for any of said sector areas i, a fractional number of winding sub-turns is
And M is a magnification factor, and one-time winding is completed through the routing of the radial straight line part and the circumferential circular arc part of the fan-shaped area.
6. The asymmetric fractional turn coil winding method of claim 1, wherein the fan is wound with a single windingThe sub-turn coefficient corresponding to the N/2 shaped region
The occupied weight is larger than the occupied weight of the sub-turn coefficients of other sector areas.
7. The asymmetric fractional turn coil winding method of claim 1 wherein in step 2, the asymmetric fractional turn coil forms a plurality of peaks during rotation.
8. The asymmetric fractional turn coil winding method of claim 7 wherein in step 2, the sub-turn coefficients corresponding to the sector N/2 are due to
The weight is maximum, the induced electromotive force generated by the weight is maximum, if the peak value is maximum, the field intensity is maximum at the position of the fan-shaped area N/2, and if the peak value is minimum, the field intensity is minimum at the position of the fan-shaped area N/2; the other peak values are between the maximum value and the minimum value, and the corresponding field intensity at the position of the fan-shaped area N/2 is between the maximum value and the minimum value.
9. The asymmetric fractional turn coil winding method of claim 1, wherein in step 3, the direction of the magnetic field is obtained by plotting the magnitude of the field strength corresponding to each position during the rotation given in step 2.
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