Winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes

Abstract

The present invention relates to the field of motors and provides a multi-operation-mode variable-winding split-tooth permanent-magnet synchronous vernier motor. Permanent magnets of the motor of the

Description

Technical Field The present invention relates to the electric machine field, which specifically involves a winding-changing split-tooth permanent magnet (PM) synchronous vernier machine with multiple operation modes. Background Conventional PM synchronous machines own advantages of high efficiency, high torque density, and so on, so this kind of machine has been widely used in fields demanding high torque density and high operation efficiency, such as electric vehicles. But the excitation field of conventional PM synchronous machine is provided by PMs, which is difficult to regulate. Thus, the speed range of conventional PM synchronous machine is limited. Therefore, mechanical gearings are usually adopted to realize variable speed operation, thus leading to disadvantages such as mechanical fatigue, friction loss, vibration, and noise. PM vernier machines operating based on the magnetic field modulation theory own output characteristics of low speed and high torque. However, this kind of machine still has the problems of limited speed range, just the same with conventional PM synchronous machines. By adding a set of three-phase auxiliary winding between small split teeth of a split-tooth PM vernier machine, a dual three-phase PM vernier machine was invented in Chinese patent (CN108336837). By changing an amplitude and a phase of a current in the auxiliary winding, tZ-axis magnetic field and magnetic g-axis field in its air-gap can be regulated effectively. Then, low speed / high torque and high speed / high efficiency operations can be realized. But the machine topology and its drive control system are more complex because two three-phase alternative current (AC) windings are adopted. Summary Aiming at the deficiencies of existing technologies, the present invention provides a winding-changing split-tooth PM synchronous vernier machine with multiple operation modes, which makes the machine own performances of both low speed / high torque and wide speed regulation range. The invention realizes the abovementioned technical purpose by following technical means. The winding-changing split-tooth PM synchronous vernier machine with multiple operation modes includes a stator and a rotor, between which there is an air-gap. A set of armature winding is wound in stator slots, and outgoing lines of each armature winding coil are connected by switching components. The stator core adopts a split-tooth structure, and numbers of small split-teeth on each two adjacent stator teeth are different, which forms a non-uniformed modulation tooth structure. The rotor contains a rotor core and rotor PMs. The rotor PMs are installed on a surface of the rotor. A relation between a number of small split-teeth ns and the number of stator slots N is: N n j \      N                                        N , where 2 means that the number of stator slots is divided into 2 modules, each module contains two big stator teeth of the machine, and big stator tooth contains small split-teeth. The number of split-teeth on each big tooth can be combined arbitrarily. Ad is a number of small split-teeth on the first big stator tooth, Az is a number of small split-teeth on the second big stator tooth, Ad and Az are positive integers, and ki^ki. The armature winding links excitation fields with different pole-pair numbers before and after an armature winding changing. The stator slot number and pole-pair numbers should satisfy: Pl =Pr* F Pl where pi is a pole-pair number of excitation field harmonic linked by the armature winding before the armature winding changing, pi is a pole-pair number of excitation field harmonic linked by the armature winding after the armature winding changing. Furtherly, there are three kinds of magnetic field harmonics with kns-jpr, kns+jpr and pr pole-pair numbers in the airgap, where pr is a pole-pair number of PMs, ns is the number of small split-teeth, 7 is a positive odd integer and equals to 1, 3, 5..., k is an integer and equals to 0, 1,2... Furthermore, the pole-pair numbers are obtained according to an expression of air-gap flux density as: +oo = A0 • S COS[jPr ~     + 7=1,3 +co                            +co S cos(kns0) • £ Faa cos[ jpr (e - ry / )] £=1,2                        7=1,3 +oo =Ao • S Fagj cos[m (0 -     + 7=1,3 +“ +“ A F . r            ( in (kns+jpr) e—1— W, 17=1,3 2 L           V   kF+JPr k1 —— COS 2 (kF-JPr) d + JPr ———ort kF ~ JP r where Fag is an air-gap magnetomotive force, 9 is a rotor circumferential position, Fagj is an amplitude of / pole-pair harmonic. A is an air-gap permeance. Ao is a direct current (DC) component of the air-gap permeance, Nk is an amplitude of the £h harmonic component. cor is a mechanical angular speed of the rotor. Furthermore, Slot pitch angles relative to pi and pi pole-pair harmonics are: z   x360p.    .   z    36()k.p. ai = sign(0j——1 = sign(^)--- TV                   ns z  x360p,    .   z  ~.36Qk2p2 a2 = sign          = sign(^)---- TV                    ns where sign (coP) is a direction function, TV is the stator slot number. Furthermore, when p\>ns, 360(            = 180^ 360(^ + k2} 2ns (Pi + Pz) (a+a) Furthermore, when pi<ns, = 180(^ + ^) The beneficial effects of the present invention are: the excitation field generated by PMs is modulated by the stator core with split-tooth structure. Thus, PM excitation field harmonics with different pole-pair numbers are generated. The outgoing lines of the armature winding components are connected by switching components to realize different switch states, based on which armature reaction fields with different pole-pair numbers are generated to couple with the excitation field generated by PMs with different pole-pair numbers effectively to realize multi-mode operation of the machine. Thus, the machine owns characteristics of both low speed / high torque and wide speed regulation range. The machine operates based on the magnetic field modulation theory, so it is still a PM synchronous vernier machine essentially with the characteristic of high torque density. Brief Description of the Drawings FIG. 1 is a schematic diagram of a PM arrangement described in the present invention. FIG. 2 is an equivalent diagram of an air-gap excitation magnetomotive force waveform described in the present invention. FIG. 3 is a schematic diagram of a simplified stator modulation teeth structure described in the present invention. FIG. 4 is a schematic diagram of a simplified air-gap permeance waveform described in the present invention. FIG. 5 is a structure schematic diagram of the winding-changing split-tooth PM synchronous vernier machine with multiple operation modes in an embodiment of the present invention. FIG. 6 is slot electric potential star diagram in an embodiment of the present invention. FIG. 7 is a schematic diagram of the armature winding changing in an embodiment of the present invention. FIG. 8 is a T-n curve diagram of the winding-changing split-tooth PM synchronous vernier machine with multiple operation modes in an embodiment of the present invention. In the drawings: 1-inner stator, 1-1-inner stator core, 2-outer rotor, 2-1-outer rotor yoke core, 3-PM, 4-armature winding, 5-shaft, 6-inner stator yoke, 7-inner stator tooth, 8-inner stator slot, 9-small split-tooth, 13-the first wire, 14-the second wire, 15-the first single-pole double-throw switch, 16- the second single-pole double-throw switch, 17-the third wire, 18-the fourth wire, 19-the third single-pole double-throw switch, 20- the fourth single-pole double-throw switch, 21-the fifth wire, 22-the fifth single-pole double-throw switch, 23-the sixth wire, 24-the sixth single-pole double-throw switch, 25-U-phase bus line, 26-V-phase bus line, 27- W-phase bus line. Detailed Description of the Embodiments Combining with attached figures and a specific embodiment, a further explanation of the present invention is presented. But the protection domain is not limited to this embodiment. A winding-changing split-tooth PM synchronous vernier machine with multiple operation modes contains a stator, a rotor and a shaft. The rotor is installed on the shaft. An air-gap is set between the stator and the rotor. A set of armature winding is set inside stator slots. Outgoing lines of each coil of the armature winding are connected by switching components. The rotor contains a rotor core and rotor PMs. The rotor PMs are installed on a surface of the rotor. A split-tooth structure is adopted for a stator core, and numbers of small split-teeth between each two adjacent stator teeth are different, which forms a non-uniformed modulation tooth structure. When symmetrical AC current is injected into the armature winding, armature reaction fields with different pole-pair numbers are generated based on different switch connection states, which effectively couple with PM excitation field harmonics generated by a modulation of the unequal modulation teeth. Thus, a multi-mode operation of the machine can be realized. The multi-mode contains a low speed / high torque operation mode and a wide speed regulation operation mode. The rotor PMs can be installed inside the rotor, by adopting surface-mounted, interior-mounted, interior embedded, or other installation ways to generate a PM excitation field required for the machine. To realize the scheme described above, a pole-slot ratio (a ratio of pole-pair number and stator slot number) of the machine is designed based on following processes: (1) Excitation field with different pole-pair numbers of the winding-changing split-tooth PM synchronous vernier machine with multiple operation modes FIG. 1 is an arrangement schematic diagram of surface-mounted rotor PMs of a described vernier machine in the present invention. An excitation magnetomotive force in the air-gap of the winding-changing split-tooth PM synchronous vernier machine with multiple operation modes can be equivalent to a square wave shown in FIG. 2. Based on the square wave shown in FIG. 2 and considering a rotation of rotor, the expression of magnetomotive force in the air-gap Fag with a rotor circumferential position 9 can be obtained by using Discrete Fourier Transformation (DFT): +00 Fag 0 = E F^ ^s[jpr(0-cort)] -^3 (1) where pr is a pole-pair number of PMs, cor is a mechanical angular speed of rotor rotation, Fagj is a amplitude of the   harmonic, which can be expressed as: F^r—h F„(eyos(jpfi)do 71 = —\ lPr(~F }cos(jpr0)d0 + 71 Tr 71 — Fagm COS( jPrO)dO + 71 Wr 71 77 Wr 2F (     ( ITT \ = -^ 2sin -sinjx J77 \ V 2 7 J (2) where Fagm is an amplitude of air-gap magnetomotive force. FIG. 3 is a schematic diagram of the small split-teeth on the described vernier machine in the present invention. A simplified air-gap permeance waveform shown in FIG. 4 can be obtained according to FIG. 3. Based on the simplified air-gap permeance shown in FIG. 4, the expression of the air-gap permeance A with the rotor circumferential position 0 can be obtained by using DFT: +00 A(0) = Ao + ^Ai cos(h?^) (3) where Ao is a DC component of the air-gap permeance, A* is an amplitude of the Ath harmonic component, ns is a number of small split-teeth. The DC component Ao can be described as: a0=-t(M + aa) (4) where Ar is a permeance of stator tooth, As is a permeance of stator slot, Ot is a crossing angle of one stator tooth, Os is a crossing angle of one stator slot. The harmonic component A* can be expressed as: n f*— A, =    A(^)cos(^)^ y z j By equation (1) and equation (3), an expression of an air-gap flux density of the winding-changing split-tooth PM synchronous vernier machine with multiple operation modes is: = V' 2 >, cos [ jp, (9 - o / )] + Y \ (^) • X C0S [j'Pr (e “ £=1,2                       7-1,3 = A0 • S FagJ C0S [j'Pr (e ~ M] + ~k agi 2 'k agi 2 cos (kns - jpr)\ 0 + JPr -—-Op kns + jpr JPr „ . ------------CD t -JPr (6) It can be seen from equation (6) that there are three different kinds of harmonic fields existing in the air-gap with pole-pair numbers of kns-jpr, kns+jpr and pr, respectively. And their angular speeds are * JPr ,         / P- . and (jj respectively. Conventional PM synchronous machines work based on the pr pole-pair harmonic. The invented machine can use not only pr pole-pair harmonic, but also kns-jpr and kns+jpr pole-pairs harmonics, so that the multi-mode operation can be realized. (2) The armature winding should link excitation fields with different pole-pair numbers before and after an armature winding changing To realize an effective operation of electric machines, the armature winding should be wound according to the pole-pair numbers of PM excitation fields. By the analysis of excitation fields, it can be seen that the pole-pair numbers of excitation fields are abundant in the invented machine. Theoretically, a pitch and a connection of the armature winding can be designed according to the pole-pair number of any one harmonic. In the present invention, different winding component connection modes are obtained by changing states of switching components connected with the outgoing lines of the armature winding components per phase. Thus, armature reaction fields with different pole-pair numbers can be obtained. By changing the connection among the outgoing lines of armature winding components, the armature reaction fields with different pole-pair numbers, so that an effective coupling between the armature reaction fields and the PM excitation fields with different pole-pair numbers in the air-gap can be realized. According to the corresponding slot phasor diagrams of harmonics of the PM excitation fields with different pole-pair numbers, different connection modes can be designed. The pole-slot ratio before and after the armature winding changing should satisfy corresponding limitations, specifically as: Suppose that N is a number of stator slot, ns is a number of small split-teeth, pole-pair numbers of stator winding before and after the winding changing are pi and pi. Then, a relation between the number of small split-teeth and the number of stator slots in a split-tooth machine satisfies: ns =^(kl+kl) A                           N where 2 means the number of stator slots is divided into 2 modules. Each module contains two big stator teeth of the machine, and each big stator tooth contains small split-teeth, the number of which can be combined arbitrarily, ki is a number of small split-teeth on the first big stator tooth, ki is a number of small split-teeth on the second big stator tooth. Zn and ki are positive integers. When ki=ki, the small split-teeth are uniformly distributed; when kpAki, the small split-teeth are non-uniformly distributed. 1) k\=ki (the small split-teeth are uniformly distributed) ns=k\N=kiN, corresponding slot pitch angles of p\ and pi pole-pairs harmonics are: z x360p.    . z ,36Qk.p. ai = sign(64)—= sign(^)---- TV                  ns z x360p,    . z , 360Tb / ?, «2 = sig" (« / ,)—— = signH)--- TV                  ns where sign^*) is a direction function, which expresses a rotation direction of one harmonic. When the rotation direction of one harmonic is the same with the rotor rotation direction U)r, sign( ¢4^)=1. When the rotation direction of one harmonic is opposite to the rotor rotation direction (P, sign( 01 / ,)=-1. To ensure that the pole-pair numbers of the harmonics linked by the armature winding are different, namely p\ and pi pole-pairs harmonics are linked before and after the winding changing, respectively, Ch and CXi should satisfy: -a2 ^360 / ? where n is an integer. According to equation (8) and equation (9), *     *                       (10) According to equation (6), a magnetic gear modulation equation can be obtained as: P>j=\jpr+H (11) where pkj is a pole-pair number of harmonic after a modulation by small split-teeth, j=l, 3, 5... A=0, ±1, ±2... When j=l, A=-l, a space harmonic with the largest amplitude except the fundamental harmonic can be generated. Make pkj=pi, pr=pi,j=l, k=-l, then an equation can be obtained as (12) In equation (12), when pi>ns, pi=p\-ns, the angular speed of pi pole-pair harmonic is Pr ------ar ?r Hs , and the rotation direction of pi pole-pair harmonic is the same with that of pi, and the direction functions sign^*) in the corresponding slot pitch angles C(i and Oi of pi and pi pole-pairs harmonics are both 1. When pi<ns, pi= ns-pi, the angular speed of pi pole-pair harmonic Pr -----ar is ?r Hs   ,which is opposite to that of pi, and the direction functions sign(&k) of the corresponding slot pitch angles C(i and Oi of pi and pi pole-pairs harmonics are -1 and 1, respectively. (1) When pi>ns, Pi Pi ns Q3) 360p. 360p? 360k z . a a =---Pl--Pl =----1( p _ p ) = 360k N     N ns      ^27        (14) It does not satisfy (10) and should be abandoned. (2) When pi<ns. Pl=ns-Pl (15) 360 / ?. 360p? 360k z A --— +--— =----{Pi+Pil N N n v 1   27 360^ Pi+Pi (Pi+Pi) = 360^ (16) It does not satisfy equation (10) and should be abandoned. Thus, it can be known that the uniformly distributed arrangement of small split-teeth cannot satisfy a design requirement of the present invention. 2) k\ (the small split-teeth are non-uniformly distributed) (17) a. 360 / ^ 360 / ^ N    2ns 360p2 360p2 ai~ N    2n M2) M) (18) _ 360(4,+¾) Cvi (^■'l (19) (1) When p\>ns. A Pi ns (20) aY-a2 = 360(VM^ - A) = 180 + ) (21) k, + k^ ,          _ . —---- n(n = 1,2,3...) When 2                  , equation (10) satisfies the design requirement of the present invention, so, it is an optional solution. (2) When p\<n P[ (22) a. _360(k1 + k2) 2ns _ 180(^+^) A + A = 180(^ + ^) (23) k, + A —---- n(n = 1,2,3...) When 2                  , equation (10) satisfies the design requirement of the present invention, so, it is an optional solution. To sum up, when the pole-slot ratio meets equation (24), the armature winding can link excitation fields with different pole-pair numbers before and after the winding changing: P\=Pr ns a=K-a| * kx k2 k. + k, . _ _T —---- ^n,n = 1,2,3L I 2                     (24) Embodiment As shown in FIG. 5, an outer rotor structure is adopted in a winding-changing split-tooth PM synchronous vernier machine with multiple operation modes in this embodiment. The machine contains an inner stator 1, an outer rotor 2, PMs 3, an armature winding 4 and a shaft 5. The outer rotor 2 is set on the shaft 5. There is an air-gap set between the inner stator 1 and the outer rotor 2. A thickness of the air-gap is related to a power level of the machine, selected PM materials and processing and assembling technics of the inner stator 1 and the outer rotor 2. The inner stator 1 contains an inner stator core 1-1 and the armature winding 4. The inner stator core 1-1 contains an inner stator yoke 6 and 12 inner stator teeth 7. Twelve inner stator slots 8 are formed between adjacent inner stator teeth 7. Two and three small split-teeth 9 are set on each two adjacent inner stator teeth, respectively. Therefore, there are thirty non-uniformly distributed small split-teeth 9 with the same width. The armature winding 4 is embedded in the stator slots 8. The outer rotor 2 contains an outer rotor yoke 2-1 and fifty tile-type PMs 3 with the same thickness. PMs 3 are distributed uniformly on a surface of the outer rotor 2. PMs 3 are magnetized in a radial direction, and magnetization directions of adjacent PMs 3 are opposite. The inner stator core 1-1, the small split-teeth 9 and the outer rotor yoke core 2-1 are made of laminated silicon steel sheets and can be manufactured easily. Different PM materials, such as NdFeB or SmCo can be adopted for PMs 3. The pole-slot ratio is selected according to equation (24): «5=30, / ?i=25. Then, pi can be obtained and equals to 5. Therefore, there are harmonic components of 5 and 25 pole-pair numbers existing in the excitation fields. So the armature winding can be wound according to harmonic fields of 5 and 25 pole-pair numbers. Corresponding slot phasor diagrams are shown in FIG. 6(a) and (b), in which angles between adjacent slot phasors are the same. A sum of slot pitch angles of the harmonics with two pole-pair numbers calculated according to equation (8) are odd multiples of 180°. So the winding pitches designed according to the harmonics with two pole-pair numbers are consistent. The armature winding changing can be realized conveniently based on a scheme as following: As shown in FIG. 6(a), the pitch of armature winding 4 can be obtained as 6 according to the slot phasor diagram. A coil a-g is formed by an armature winding component a and an armature winding component g, a coil h-b is formed by an armature winding component h and an armature winding component b, coil a-g and coil h-b are connected in series in the same direction to form U-phase winding. A coil e-k is formed by an armature winding component e and an armature winding component k, a coil / -f is formed by an armature winding component I and an armature winding component f, coil e-k and coil / -f are connected in series in the same direction to form V-phase winding. A coil i-c is formed by an armature winding component i and an armature winding component c, a coil d-j is formed by an armature winding component s and an armature winding component j, coil i-c and coil d-j are connected in series in the same direction to form W-phase winding. Finally, a winding connection as shown in FIG. 7(a) is formed. Then, an armature reaction field with 5 pole-pair can be generated to couple with a PM excitation field harmonic with 5 pole-pair effectively. As shown in FIG. 6(b), a coil a-g is formed by an armature winding component a and an armature winding component g, a coil h-b is formed by an armature winding component h and an armature winding component b, coil a-g and coil h-b are connected in series in opposite directions to form U-phase winding. A coil e-k is formed by an armature winding component e and an armature winding component k, a coil / -f is formed by an armature winding component I and an armature winding component f, coil e-k and coil / -f are connected in series in opposite directions to form V-phase winding. A coil i-c is formed by an armature winding component i and an armature winding component c, a coil d-j is formed by an armature winding component s and an armature winding component j, coil i-c and coil d-j are connected in series in opposite directions to form W-phase winding. Finally, a winding connection as shown in FIG. 7(b) is formed. Then, an armature reaction field with 25 pole-pair can be generated to couple with a PM excitation field harmonic with 25 pole-pair effectively. As shown in FIG. 7, FIG. 7(a) shows the winding connection state when the stator winding couples with the PM excitation field harmonic with 5 pole-pair. U-phase winding is formed by the armature winding components a, g, b, h, in which the armature winding component a is connected with the U-phase bus line 25 using the first wire 13, the armature winding component g is connected with the first single-pole double-throw switch 15 using the second wire 14, the second single-pole double-throw switch 16 is connected with a lead of U-phase winding. V-phase is formed by the armature winding components e, k, f, I, in which the armature winding e is connected with the V-phase bus line 26 using the third wire 17, the armature winding component k is connected with the third single-pole double-throw switch 19 using the fourth wire 18, the fourth single-pole double-throw switch 20 is connected with a lead of V-phase winding. W-phase is formed by the armature winding components i, c, j, d, in which the armature winding component i is connected with the W-phase bus line 27 using the fifth wire 21, the armature winding c is connected with the fifth single-pole double-throw switch 22 using the sixth wire 23, the sixth single-pole double-throw switch 24 is connected with a lead of W-phase winding. In FIG. 7, "+" means the in-line direction, means the out-line direction. As shown in FIG. 7, FIG. 7(b) shows the winding connection state when the stator winding couples with the PM excitation field harmonic with 25 pole-pair. The first single-pole double-throw switch 15 and the second single-pole double-throw switch 16 of U-phase, the third single-pole double-throw switch 19 and the fourth single-pole double-throw switch 20 of V-phase, the fifth single-pole double-throw switch 22 and the sixth single-pole double-throw switch 24 are switched from the state in FIG. 7(a) to the other connection state to complete the armature winding changing. At this time, the stator winding is changed from coupling with the PM excitation field harmonic with 5 pole-pair to the PM excitation field harmonic with 25 pole-pair. As shown in FIG. 8, a speed regulation range is widened after the armature winding changing. A base rotation speed increases from n to 1.93m, which realizes an expected speed expansion goal. The described embodiment is a preferred execution mode of the present invention. However, the present invention is not limited to the above execution mode. Without deviating from the essential content of the present invention, any obvious improvements, substitutions or variations that can be made by technical personnel in this field shall be protected by the present invention.

Claims

1. A winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes, characterized by comprising a stator and a rotor, between which there is an air-gap; a set of armature winding coils is wound in stator slots, and outgoing lines of each armature winding coil are connected by switching components; a switch of a armature winding connection state is realized by switching the switching components, a stator core adopts a split-tooth structure, and numbers of small split-teeth on every adjacent two of stator teeth are different, which forms a non-uniform modulation tooth structure; the rotor contains a rotor core and rotor permanent magnets; the rotor permanent magnets are installed on a surface of the rotor;a relationship between a number of the small split-teeth and a number of stator slots is:N (   , .         N                                                   N2         , wherein 2 means that the number of the stator slots is divided into 2modules, each of the modules contains two big stator teeth of the machine, and each of the big stator teeth contains the small split-teeth; the number of the small split-teeth on each of the big teeth can be combined arbitrarily; k\ is a number of small split-teeth on the first big stator tooth, fe is a number of small split-teeth on the second big stator tooth, k\ and are positive integers, and k\the armature winding links excitation fields with different pole-pair numbers before and after an armature winding changing, the number of the small split-teeth and pole-pair numbers should satisfy:Pl= Pr^ ns Pi = K-a| ' k2 k + k2 —----- n, n = 1,2,3...I 2wherein p\ is a pole-pair number of excitation field linked by the armature winding before the armature winding changing; and pi is a pole-pair number of excitation field linked by the armature winding after the armature winding changing.

2. The winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes according to claim 1, characterized in that:there are three kinds of magnetic field harmonics with kns-jpr, kns+jpr and pr pole-pair numbers in the airgap, where pr is a pole-pair number of permanent magnets, ns is the number of small split-teeth, j is a positive odd integer and equals to 1, 3, 5..., k is an integer and equals to 0, 1, 2...

3. The winding-changing split-tooth permanent magnet synchronous vernier machine with multipleoperation modes according to claim 2, characterized in that:the pole-pair numbers are obtained according to an expression of air-gap flux density as:- A„ ■ y    cos[ jp, (0 - ffl / )] +7=1,3+co                            +coE cos(kns0) • £ Fagj cos[ jpr (0 - apt)]£=1,2                        7=1,3= A0 ’ E FagJ C0S[ JPr (0 ~     +7=1,3+“ +“ A F . F            (        inE E cos (kns + jpr) e- ---r— a>rt*=1,27=1,3   2 L             \         +JPr+co +coEE^£=1,2 7=1,3COS(H-7A) e +JPr--—--Opt ^s-JPrwhere Fag is an air-gap magnetomotive force, 9 is a rotor circumferential position, Fagj is an amplitude of j pole-pair harmonic. A is an air-gap permeance. Ao is a direct current component of the air-gap permeance, Ak is an amplitude of the £th harmonic component. a>r is a mechanical angular speed of the rotor.

4. The winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes according to claim 1, characterized in that:Slot pitch angles relative to p\ and pi pole-pairs harmonics are:z , 360p.    . z x360£p.«i = sign (¾) ——1 = sign (¾)---- A              nsz .360 / 2,    . z .360 / :, / 2,= sign(^)—= sign(^)--- A              nswhere sign (m*) is a direction function, N is the stator slot number.

5. The winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes according to claim 4, characterized in that:360(£ + £,) z , z, ,, «! - «2 =-------(Pi - A) =180(M Mwhen pi>ns,                s6. The winding-changing split-tooth permanent magnet synchronous vernier machine with multiple operation modes according to claim 4, characterized in that:when p\<n^ax --«2 ) =360(^ + ^)2m „= 180(^ + k2)(a+a)(a+a)

Images