CN109728697B - Design method for multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure pole slot - Google Patents
Design method for multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure pole slot Download PDFInfo
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Abstract
The invention discloses a multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure with fractional slot concentrated windings and a pole slot design method. Including stator core and fixed stator core's aluminium fastener, stator winding, rotor core and rotor winding be located the stator both sides respectively, stator and rotor winding coil adopt axial space to carry out the coiling, are showing and have promoted the magnetic circuit magnetic conductance, have reduced the motor diameter. The characteristic that a pair of dominant pole pair components can be generated by a fractional slot concentrated winding is utilized, the space harmonic magnetic field pole pair number and the slip are used as independent variables, a function of a stator and rotor induction flux linkage and induction voltage is constructed, and for different pole slot combinations of a stator and a rotor, the highest electromagnetic power transmitted by the dominant pole harmonic magnetic field in a group of stator and rotor pole slot combinations exists. The pole slot selection method improves the power density and the power factor, and further realizes the direct drive/semi-direct drive operation of the motor.
Description
Technical Field
The invention relates to a multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure based on fractional slot concentrated windings and a pole slot selection method, and belongs to the technical field of motors.
Background
The double-fed wind power induction generator (the winding form is an integer slot) is simple and reliable in process and small in capacity of a matched converter, but the power factor is remarkably reduced along with the increase of the pole pair number, direct drive cannot be realized, a high-speed gear is required, the complexity of a transmission chain is increased, and the system performance is seriously influenced. Moreover, when power reaches a certain level, the manufacture and maintenance of high speed gears is extremely difficult.
Under the background, compared with a mechanical gear, the magnetic field modulation type permanent magnet gear and the low-speed induction motor system based on the permanent magnet gear speed change have the advantages of non-contact speed change transmission, no friction loss, low vibration, low noise, no need of lubrication, high inherent overload protection capability and reliability and the like. However, the scheme has complex process and depends on high-performance permanent magnet materials, and the torque pulsation is large when the power angle of the magnetic gear is unstable and automatic overload protection is carried out.
In recent years, many researchers have intensively studied fractional-slot concentrated windings, aiming at realizing multiple pairs of poles with few slots and applying the fractional-slot concentrated windings to large-sized low-speed permanent magnet synchronous generators. Compared with the traditional distributed winding motor, the fractional-slot concentrated winding motor has the advantages of small torque pulsation, high back electromotive force waveform sine degree, strong fault-tolerant capability, high torque density, low cogging torque and the like. However, the characteristics of high self-inductance and low mutual inductance of the fractional-slot concentrated winding cause the following problems: when the harmonic pole pair magnetic field rotates at a high speed relative to the rotor, eddy current is induced in the permanent magnet, additional eddy current loss and permanent magnet temperature rise are generated, and even demagnetization is caused; the harmonic wave pole pair magnetic field and the permanent magnet rotor are in weak electromagnetic coupling due to different pole pairs, and the power factor and the torque density of the permanent magnet motor are reduced although the high self-inductance and the low mutual inductance are favorable for improving the fault-tolerant performance of the motor. Therefore, the asynchronous induction motor directly adopts the winding scheme, which results in lower power factor and torque density and is difficult to realize direct drive.
Disclosure of Invention
The technical problem is as follows: aiming at the problems, the multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure of the fractional-slot concentrated winding is provided, based on the axial magnetic field motor structure, the fractional-slot concentrated winding with the polar slot ratio close to 1 is adopted, double-rotor alternating current excitation is carried out aiming at a pair of dominant components in stator magnetomotive force polar logarithm frequency spectrum, and the structure is suitable for low-speed large-torque environments, such as wind power generation.
The technical scheme is as follows:
the utility model provides a multifrequency antipodal magnetic field coupling directly drives double-fed motor structure which characterized in that: the magnetic coupling permanent magnet synchronous motor comprises an annular disc-shaped stator and rotors respectively positioned on two sides of the stator, an axial magnetic field structure is adopted between the rotors and the stators, air gaps exist between the two rotors and the stators, and a dominant pole pair harmonic magnetic field generated by a stator winding at the air gaps is respectively coupled with magnetic fields generated on the two rotors through selected pole slot matching.
Further, the stator includes a stator core, a stator winding, and a ring that fixes the stator core.
Further, the rotor includes a rotor winding and a rotor core.
Further, the stator and both rotors employ double layer windings with fractional slot concentration.
Furthermore, the stator is formed by embedding a plurality of integral I-shaped magnetic core steel sheets into a ring which plays a role in fixing, each I-shaped silicon steel sheet is arranged at intervals of a section of gap, namely, two sides of the stator are provided with grooves, and a stator winding is embedded into the grooves in a 0 shape.
Furthermore, the two rotors are both provided with slots on one side, a yoke-free rotor core is adopted, the inner side surface of the yoke-free rotor core is provided with a plurality of winding slots, and the winding coil is embedded into the winding slots in a 0-shaped manner.
A design method for a pole slot of a multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure is characterized by comprising the following steps:
1) fractional slot concentrated winding pole slot selection
The short-range coefficient of the v antipodal harmonic of the winding is:
the selected polar grooves Q are in the following three conditions:
taking a mechanical angle theta as an abscissa, when a magnetic circuit of the motor is linear, namely the magnetic circuit is unsaturated and the cogging effect is ignored, and the magnetomotive force drop on the magnetic circuit of the iron core part is not considered, decomposing the rectangular magnetomotive force generated by a single coil into a series of harmonic magnetomotive forces:
in the formula: v is the harmonic order, p is the number of pole pairs of the winding, kyvIs the short-distance coefficient of v antipodal harmonic wave of winding, Q is the number of slots of unit motor, theta is mechanical angle, omega is angular frequency of exciting current, N is the number of turns of coil, N is the number of coil, ImIs the effective value of the exciting current, t is time, and F is the harmonic magnetomotive force of a single coil;
harmonic magnetomotive force superposition of each phase winding:
in the formula kqvIs the winding distribution coefficient, FOne phaseIs a one-phase synthetic magnetomotive force.
At this time, the winding coefficient kwvIn which k iswvRepresenting the winding coefficient:
kwv＝kyv*kqv(5)
at this time kyv、kqv、kwvAre all increased with v and are periodically and symmetrically varied, wherein
Wherein k is a positive integer, and the absolute value of the harmonic winding coefficient is maximum; under the condition of constant number of turns and current, the magnetomotive force amplitude of each subharmonic is in positive correlation with the winding coefficient, so that a pair of dominant pole pairs (p) exist in the fractional slot concentrated winding1、p2) The harmonic magnetomotive force is maximum;
the pole slot fits in the stator slot and the two rotor slots are both selected from the pole slot fits contained in equation (2);
2) stator winding pole slot selection
According to the formula (2), the pole slot matching of the stator slot winding is selected from one of three conditions, and the dominant pole pair number p of the pole slot matching is determined3、p4；
3) Wherein one rotor pole slot is selected
Selecting a rotor slot, constructing a two-dimensional working interval of the magnetic induction strength of the stator and the rotor by using a winding function and taking the pole pair number and the slip of a space harmonic magnetic field as independent variables, and respectively determining the amplitude and the frequency of an induction flux linkage of the stator and the rotor and the amplitude of induced electromotive force of the stator and the rotor in the interval;
when the number of dominant pole pairs of fractional slot concentrated windings in the rotor side is p5、p6Formula (6) must be satisfied:
{p5、p6}∩{p3、p4}＝1 (6)
4) selection of another rotor pole slot
The selection mode of the other rotor side winding is the same as that of one rotor;
when the dominant pole pair number of the other rotor side winding is { p }7、p8When it is, formula (7) must be satisfied,
{p7、p8}∩{p3、p 41 and { p } ═ 17、p8}∩{p5、p6}＝0 (7)
From the above steps 1) -4), it is necessary to satisfy the equations (2), (6), (7) at the same time, and the selected stator and two rotors are actually selected.
Further, the distribution coefficients under the three polar grooves are:
in which is provided with alpha0＝2π/Q，INT1And INT2Are respectively a numerical value [ k/2 ]]And [ (k +1)/2]And (6) taking the whole.
Further, in step 3), the three-phase synthetic magnetomotive force of each subharmonic is derived from equation (4):
the influence of the cogging on the magnetic field is not considered, the slip ratio is introduced, and the magnetic induction intensity under different slip is obtained
Wherein lagAir gap length, s slip, μ0And (B) is a radial component of air gap flux density relative motion.
The winding function is the same as the magnetomotive force waveform generated by the winding, so the winding function is obtained by Fourier decomposition:
therefore, by substituting the formulas (10) and (11) into the formula (12), the formula (13) is obtained:
from equation (13), the flux linkage amplitude generated on the rotor side by each harmonic magnetomotive force is known, except for the harmonic of v ═ 1 or 3 k-1:
bringing formula (13) into formula (14), to obtain formula (15)
The amplitude of the induced voltage generated on the rotor side by the magnetomotive force of each subharmonic other than the harmonic of v 1 or 3k-1 is known from equation (16):
in the formula, QsThe number of the slots of the motor stator and the rotor is respectively; m motor phases; psirA-vThe open circuit v-th harmonic of the rotor generates a flux linkage in the phase A; b isS(θ) is the radial component of the air gap flux density relative motion produced by the stator; n is a radical ofrA(θ) stator and rotor a-phase winding functions; r the radius of the winding; lefA stator core; n is a radical ofSA、nrAThe number of turns of the stator winding and the rotor winding; k is a radical ofs-wv、kr-wvWinding coefficients of certain harmonic magnetomotive force excited by the stator winding and the rotor winding respectively; s slip ratio; erA-vInduced electromotive force, | ψ, generated by open-circuit v-order harmonic of rotor in phase ArA-vI is the amplitude of each harmonic flux linkage, | ErA-vAnd | is the amplitude of each harmonic induction voltage.
The invention achieves the following beneficial effects:
the invention discloses a multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure with fractional-slot concentrated windings and a method for selecting specific pole slots. The motor comprises a stator core, an aluminum fastener for fixing the stator core, a stator winding, a rotor core and a rotor winding, wherein the aluminum fastener, the stator winding, the rotor core and the rotor winding are respectively positioned on two sides of the stator, and coils of the stator winding and the rotor winding are wound by adopting an axial space, so that the groove area is obviously reduced, the axial magnetic conduction area is increased, and the power factor is improved. The specific pole slot selection method is based on a multi-frequency antipodal magnetic field coupling principle, a winding function is introduced, a two-dimensional stator and rotor induction flux linkage and induction voltage working interval are constructed by taking the space harmonic magnetic field pole pair number and the slip as independent variables, and the amplitude and the frequency of the stator and rotor induction flux linkage and the amplitude of the stator and rotor induction electromotive force are respectively researched in the interval. The specific pole slot is selected, so that the coupling degree of a harmonic wave pole pair magnetic field generated by the fractional slot concentrated winding in the space is improved, and the electromagnetic power, the power factor and the torque density are improved. Compared with the conventional double-fed induction generator, the double-fed induction wind driven generator has the advantages of simple structure and low cost, adopts the fractional slot concentrated winding, utilizes the generation of a pair of dominant pole pair number components, and effectively improves the coupling degree of a harmonic pole pair magnetic field generated by the fractional slot concentrated winding in the space by selecting the pole pair combination of the stator and the rotor, improves the electromagnetic power, the power factor and the torque density, and can realize the direct-drive/semi-direct-drive operation of the double-fed motor without adopting a gear box.
Drawings
FIG. 1 is a three-dimensional structural diagram of a multi-frequency antipode magnetic field coupling direct-drive double-fed motor structure of a fractional slot concentrated winding.
Fig. 2 is a stator core assembly diagram.
FIG. 3 is a structural working principle diagram of a multi-frequency antipode magnetic field coupling direct-drive double-fed motor with fractional slot concentrated windings.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific examples.
As shown in fig. 1 and fig. 2, the multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure with fractional-slot concentrated windings comprises a stator consisting of a stator core 1, a stator winding 2 and an aluminum iron ring 3 for fixing the stator core, one of rotors consisting of a 1# rotor winding 4 and a 1# rotor core 5, and the other rotor consisting of a 2# rotor winding 6 and a 2# rotor core 7.
The stator and the two rotors are both in annular disc shapes, an axial magnetic field structure is adopted, the two rotors are located on two sides of the stator, air gaps exist between the two rotors and the stator, and proper pole slots are selected for matching, so that the dominant pole pair harmonic magnetic fields generated by the stator winding at the air gaps are respectively coupled with the magnetic fields generated on the two rotors, and the low-speed and high-torque operation of the motor is realized.
The stator and the two rotors both adopt fractional slot concentrated windings and double-layer windings.
The stator is composed of a plurality of rings which are integrally embedded with I-shaped magnetic core steel sheets to play a role in fixing, the rings are aluminum circular rings, each I-shaped silicon steel sheet is arranged at intervals, namely, slots are formed on two sides, and windings are embedded in the rings in a 0 shape, as shown in figure 2.
The two rotors are both provided with slots on one side, the design of a yoke-free iron core is adopted, the inner side surface is provided with a plurality of winding slots, and the winding coil is embedded in a 0 shape, as shown in figure 2.
A design method of a multi-frequency antipode magnetic field coupling direct-drive double-fed motor structure of a low-speed large-torque fractional slot concentrated winding comprises the following steps:
1) the pole slots of the fractional slot concentrated winding select the short distance coefficient of the v antipodal harmonic of the winding as follows:
the selected polar grooves Q are in the following three conditions:
taking a mechanical angle theta as an abscissa, when a magnetic circuit of the motor is linear, namely the magnetic circuit is unsaturated and the cogging effect is ignored, and the magnetomotive force drop on the magnetic circuit of the iron core part is not considered, decomposing the rectangular magnetomotive force generated by a single coil into a series of harmonic magnetomotive forces:
in the formula: v is the harmonic order, p is the number of pole pairs of the winding, kyvIs the short-distance coefficient of v antipodal harmonic wave of winding, Q is the number of slots of unit motor, theta is mechanical angle, omega is angular frequency of exciting current, N is the number of turns of coil, N is the number of coil, ImIs the effective value of the exciting current, t is time, and F is harmonic magnetomotive force;
harmonic magnetomotive force superposition of each phase winding:
in the formula kqvIs the winding distribution coefficient;
distribution coefficients under three polar channels:
in the formula, k is a positive integer，INT1And INT2Are respectively a numerical value [ k/2 ]]And [ (k +1)/2]And (6) taking the whole.
At this time, the winding coefficient kwvComprises the following steps:
kwv＝kyv*kqv(6)
at this time kyv、kqv、kwvAre all increasing with v and vary periodically and symmetrically. Wherein at least
The absolute value of the harmonic winding coefficient is maximum; under the condition of constant number of turns and current, the magnetomotive force amplitude of each subharmonic is in positive correlation with the winding coefficient, so that a pair of dominant pole pairs (p) exist in the fractional slot concentrated winding1、p2) The harmonic magnetomotive force is maximum;
2) stator winding pole slot selection
According to the formula (2), three selection methods are used for matching the pole slots of the stator slot winding, one of the three selection methods is selected randomly, and the dominant pole pair number of the pole slot matching is p according to the formula (2)3、p4。
3)1# rotor pole slot selection
The invention is based on the principle of multi-frequency antipodal magnetic field coupling. The rotor slot is selected according to the principle that the harmonic magnetomotive force generated by the stator side and the induced current generated by the rotor side influence the transmission of the electromagnetic power. The ranges selected are also the three cases in equation (2). And constructing a two-dimensional stator and rotor magnetic induction working interval by using a winding function and taking the pole pair number and the slip of the space harmonic magnetic field as independent variables. In the interval, the amplitude and the frequency of the stator and rotor induced magnetic linkage and the amplitude of the stator and rotor induced electromotive force are respectively researched.
And (4) deducing the three-phase synthetic magnetomotive force of each subharmonic:
the influence of the cogging on the magnetic field is not considered, the slip ratio is introduced, and the magnetic induction intensity under different slip is obtained
Wherein lagAir gap length, mu0The vacuum magnetic conductivity, s is slip ratio, f (theta) is three-phase synthetic magnetomotive force, and B (theta) is radial component of air gap flux density relative motion.
The winding function is the same as the magnetomotive force waveform generated by the winding, so the winding function is obtained by Fourier decomposition:
therefore, by substituting the formulas (10) and (11) into the formula (12), the formula (13) is obtained:
from equation (13), the flux linkage amplitude generated on the rotor side by each harmonic magnetomotive force is known, except for the harmonic of v ═ 1 or 3 k-1:
bringing formula (13) into formula (14), to obtain formula (15)
The amplitude of the induced voltage generated on the rotor side by the magnetomotive force of each subharmonic other than the harmonic of v 1 or 3k-1 is known from equation (16):
in the formula, QsThe number of the slots of the motor stator and the rotor is respectively; m motor phases; psirA-vThe open circuit v-th harmonic of the rotor generates a flux linkage in the phase A; b isS(θ) is the radial component of the air gap flux density relative motion produced by the stator; n is a radical ofrA(θ) stator and rotor a-phase winding functions; r the radius of the winding; lefA stator core; n is a radical ofSA、nrAThe number of turns of the stator winding and the rotor winding; k is a radical ofs-wv、 kr-wvWinding coefficients of certain harmonic magnetomotive force excited by the stator winding and the rotor winding respectively; s slip ratio; erA-vInduced electromotive force, | ψ, generated by open-circuit v-order harmonic of rotor in phase ArA-vI is the amplitude of each harmonic flux linkage, | ErA-vAnd | is the amplitude of each harmonic induction voltage.
From the formulas (11) to (15), the flux linkage amplitude is related to the number of turns, the length of the stator core, the length of an air gap, the pole slots of the stator and the rotor and the winding coefficient of the stator and the rotor under each harmonic magnetic field; the induced voltage amplitude is, among other things, related to slip. When the number of turns, the length of the stator core, the length of the air gap, the pole slots of the stator and the rotor and the slip ratio are fixed, the magnitudes of the flux linkage amplitude and the induction voltage amplitude are in positive correlation with the coefficient of each subharmonic magnetomotive winding.
When the number of dominant pole pairs of fractional slot concentrated windings in the rotor side is p5、p6. The requirements are as follows:
{p5、p6}∩{p3、p4}＝1 (18)
4)2# rotor pole slot selection
As can be seen from equations (11) to (15), the 2# rotor side winding is selected in the same manner as the 1# rotor. However, since the two rotors are distributed on two sides of the stator, the induced voltage and the induced flux linkage in the 1# rotor winding are affected by the 2# rotor winding. When the dominant pole pair number of the 2# rotor side winding is { p7、p8In the time, the following requirements are satisfied:
{p7、p8}∩{p3、p 41 and { p } ═ 17、p8}∩{p5、p6}＝0 (19)
Because the number of dominant pole pairs of the windings of the 1# rotor and the 2# rotor are different, the magnetomotive force frequency spectrum distribution is different, the mutual inductance is small, and the influence on the motor is small.
The stator slots are 14 poles and 15 slots, the 1# rotor is 14 poles and 18 slots, and the 2# rotor is 22 poles and 24 slots, which are selected by the formulas (14) - (16). The working principle of the motor, namely the flux linkage coupling principle, is briefly described.
The working principle of the invention is as shown in figure 3: the working principle of the multi-frequency antipode magnetic field coupling direct-drive double-fed motor structure of the fractional-slot concentrated winding is illustrated by a two-dimensional local expanded view of the figure. The three-phase winding of the stator is connected with a power grid, and the three-phase winding of the 1# rotor and the three-phase winding of the 2# rotor realize alternating current excitation through a converter respectively. The magnetic flux generated by the stator and rotor current excitation forms a loop through the 1# rotor yoke, the 1# rotor winding, the 1# rotor side air gap, the stator winding, the 2# rotor side air gap, the 2# rotor winding and the 2# rotor yoke.
Flux linkage coupling principle: a pair of dominant pole-pair harmonic magnetic fields and higher harmonics are generated in an air gap under the excitation of a stator, 7, 8, 11 and 13 pole-pair harmonic magnetic fields are generated by the 1# rotor and the 2# rotor after the excitation respectively, the harmonic spectrum characteristics of the 1# rotor and the 2# rotor are large in difference, and the mutual inductance is negligible. The dominant pole pair magnetic field of the stator winding unit motor is 7 and 11 pairs of poles, the mutual inductance between the 1# rotor and the stator winding mainly passes through 7 pairs of pole magnetic field coil chains, and the mutual inductance between the 2# rotor and the stator winding mainly passes through 11 pairs of pole magnetic field coil chains. Active and reactive decoupling control of stator current is realized through coordination of the double rotors and alternating current excitation.
Claims (3)
1. A design method for a pole slot of a multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure is characterized by comprising the following steps:
1) fractional slot concentrated winding pole slot selection
The short-range coefficient of the v antipodal harmonic of the winding is:
the selected polar grooves Q are in the following three conditions:
taking a mechanical angle theta as an abscissa, when a magnetic circuit of the motor is linear, namely the magnetic circuit is unsaturated and the cogging effect is ignored, and the magnetomotive force drop on the magnetic circuit of the iron core part is not considered, decomposing the rectangular magnetomotive force generated by a single coil into a series of harmonic magnetomotive forces:
in the formula: v is the harmonic order, p is the number of pole pairs of the winding, kyvIs the short-distance coefficient of v antipodal harmonic wave of winding, Q is the number of slots of unit motor, theta is mechanical angle, omega is angular frequency of exciting current, N is the number of turns of coil, N is the number of coil, ImIs the effective value of the exciting current, t is time, and F is the harmonic magnetomotive force of a single coil;
harmonic magnetomotive force superposition of each phase winding:
in the formula kqvIs the winding distribution coefficient, FOne phaseIs a one-phase synthetic magnetomotive force;
at this time, the winding coefficient kwvIn which k iswvRepresenting the winding coefficient:
kwv＝kyv*kqv(5)
at this time kyv、kqv、kwvAre all increased with v and are periodically and symmetrically varied, wherein
Wherein k is a positive integer, and the absolute value of the harmonic winding coefficient is maximum; under the condition of a certain number of turns and current, the magnetomotive force amplitude of each subharmonic is in positive correlation with the winding coefficient, so that a pair of dominant pole pairs p exists in the fractional slot concentrated winding1、p2The harmonic magnetomotive force is maximum;
the pole slot fits in the stator slot and the two rotor slots are both selected from the pole slot fits contained in equation (2);
2) stator winding pole slot selection
According to the formula (2), the pole slot matching of the stator slot winding is selected from one of three conditions, and the dominant pole pair number p of the pole slot matching is determined3、p4；
3) Wherein one rotor pole slot is selected
Selecting a rotor slot, constructing a two-dimensional working interval of the magnetic induction strength of the stator and the rotor by using a winding function and taking the pole pair number and the slip of a space harmonic magnetic field as independent variables, and respectively determining the amplitude and the frequency of an induction flux linkage of the stator and the rotor and the amplitude of induced electromotive force of the stator and the rotor in the interval;
when the number of dominant pole pairs of fractional slot concentrated windings in the rotor side is p5、p6Formula (6) must be satisfied:
{p5、p6}∩{p3、p4}＝1 (6)
4) selection of another rotor pole slot
The selection mode of the other rotor side winding is the same as that of one rotor;
when the dominant pole pair number of the other rotor side winding is p7、p8In this case, the formula (7) must be satisfied,
{p7、p8}∩{p3、p41 and { p } ═ 17、p8}∩{p5、p6}＝0 (7)
From the above steps 1) -4), it is necessary to satisfy the equations (2), (6), (7) at the same time, and the selected stator and two rotors are actually selected.
2. The method for designing the pole slots of the multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure according to claim 1,
the distribution coefficients under the three polar tanks are:
in which is provided with alpha0＝2π/Q，INT1And INT2Are respectively a numerical value [ k/2 ]]And [ (k +1)/2]And (6) taking the whole.
3. The method for designing the pole slots of the multi-frequency antipodal magnetic field coupling direct-drive double-fed motor structure according to claim 1,
in the step 3), the three-phase synthetic magnetomotive force of each subharmonic is deduced according to the formula (4):
the influence of the cogging on the magnetic field is not considered, the slip ratio is introduced, and the magnetic induction intensity under different slip is obtained
Wherein lagAir gap length, s slip, μ0The vacuum magnetic conductivity, f (theta) is three-phase synthetic magnetomotive force, and B (theta) is the radial component of air gap flux density relative motion;
the winding function is the same as the magnetomotive force waveform generated by the winding, so the winding function is obtained by Fourier decomposition:
therefore, by substituting the formulas (10) and (11) into the formula (12), the formula (13) is obtained:
from equation (13), the flux linkage amplitude generated on the rotor side by each harmonic magnetomotive force is known, except for the harmonic of v ═ 1 or 3 k-1:
bringing formula (13) into formula (14), to obtain formula (15)
The amplitude of the induced voltage generated on the rotor side by the magnetomotive force of each subharmonic other than the harmonic of v 1 or 3k-1 is known from equation (16):
in the formula, QsThe number of the slots of the motor stator and the rotor is respectively; m motor phases; y isrA-vThe open circuit v-th harmonic of the rotor generates a flux linkage in the phase A; b isS(θ) is the radial component of the air gap flux density relative motion produced by the stator; n is a radical ofrA(θ) stator and rotor a-phase winding functions; r the radius of the winding; lefA stator core; n is a radical ofSA、nrAThe number of turns of the stator winding and the rotor winding; k is a radical ofs-wv、kr-wvWinding coefficients of certain harmonic magnetomotive force excited by the stator winding and the rotor winding respectively; s slip ratio; erA-vInduced electromotive force, | y, generated by open-circuit v-order harmonic of rotor in A phaserA-vI is the amplitude of each harmonic flux linkage, | ErA-vAnd | is the amplitude of each harmonic induction voltage.
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