Unequal-tooth permanent magnet linear vernier motor and thrust enhancement mechanism analysis method

Abstract

The invention provides an unequal-tooth permanent magnet linear vernier motor and a thrust enhancement mechanism analysis method. The motor comprises a stator module and a rotor module. The stator module comprises a permanent magnet and a stator core. The N pole and the S pole of the permanent magnet are alternately installed on the surface of the stator core. The rotor module comprises an armature winding, a rotor yoke, auxiliary teeth and main teeth, each main tooth is provided with split teeth, and the split teeth and the auxiliary teeth are unequal in tooth width, so that an unequal-tooth structure is formed; the armature winding is wound on the main teeth; and an air gap exists between the stator module and the mover module. According to the magnetic field modulation principle, the stator permanent magnet and the unequal tooth structure interact to modulate a new working harmonic wave type, the auxiliary teeth weaken magnetic field coupling between phases, and the fault tolerance performance of the motor is improved. And meanwhile, thrust generated by each working harmonic wave is calculated by using a Maxwell stress tensor method to analyze and improve a thrust enhancement mechanism of the motor, and the motor is verified to have effectiveness in thrust improvement.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet linear motor technology, and particularly relates to an unequal tooth permanent magnet linear vernier motor and a thrust enhancement mechanism analysis method, which is applicable to linear motion applications such as short-stroke transportation and direct-drive elevators. Background Technology

[0002] Traditional permanent magnet linear vernier motors have advantages such as low speed and high thrust, high positioning accuracy, and good reliability, and are currently used in direct drive motion systems. However, applications requiring high thrust density in linear servo systems place higher demands on the thrust performance of permanent magnet linear vernier motors.

[0003] Traditional permanent magnet linear vernier motors structurally satisfy the magnetic field modulation relationship P. a =|P PM -Z mt To generate greater thrust, armature windings often use a full-pitch τ = Z. mt / (2P a Integer slot windings have problems such as a large number of coils, difficulty in winding, excessively long ends, and large copper consumption. To solve these problems, a common method is to change the integer slot full-pitch winding to a fractional slot winding to facilitate winding. However, this reduces the winding factor of the motor, resulting in a decrease in no-load back EMF and thrust.

[0004] To improve the thrust density of permanent magnet linear vernier motors, the shape of the permanent magnets and the amount of permanent magnets used can be modified to enhance the magnetic field strength. For example, Halbach permanent magnet arrays can be used, utilizing their magnetic focusing effect to effectively increase the thrust density of the linear motor and improve the permanent magnet magnetic field, thereby reducing thrust fluctuations. However, the manufacturing process of Halbach permanent magnet arrays is relatively complex and the production cost is high. Alternatively, the theory of bilateral magnetic field modulation can be used, with permanent magnets installed on both the stator and mover sides. However, this results in a large number of permanent magnets, difficulties in winding and coiling, and significant thrust fluctuations. While using an alternating pole arrangement can effectively reduce the amount of permanent magnets used and improve their utilization rate, solving the problem of excessive permanent magnet usage in traditional permanent magnet linear motors, the alternating pole arrangement leads to uneven air gap magnetic field, significant harmonic magnetic field influence, and problems such as high permanent magnet leakage and low thrust density. Summary of the Invention

[0005] To address the shortcomings of the aforementioned background technology, this invention proposes an unequal-tooth permanent magnet linear vernier motor and a thrust enhancement mechanism analysis method. By merging the armature teeth between each phase winding of a traditional integer-slot winding permanent magnet linear vernier motor to obtain the main teeth, the armature winding is concentrated and wound on the main teeth. The auxiliary teeth between phases retain their original structure. To satisfy the magnetic field modulation effect, three split teeth are opened on each main tooth. The split teeth and auxiliary teeth have the same tooth width, forming an equal-tooth structure concentrated winding permanent magnet linear vernier motor structure with the largest winding factor. To further enhance thrust, the unequal tooth widths of the split teeth and auxiliary teeth are used to fully utilize the motor's magnetic field modulation capability, resulting in a permanent magnet linear vernier motor with a concentrated winding and unequal tooth structure. Based on the principle of magnetic field modulation, the interaction between the stator permanent magnet and the unequal tooth structure modulates new operating harmonic types. Using the unequal tooth structure can better improve the thrust density of the permanent magnet linear vernier motor and solve the problems of low permanent magnet utilization and winding difficulties in existing permanent magnet linear vernier motors. Simultaneously, the auxiliary teeth weaken the magnetic field coupling between phases, improving the motor's fault tolerance. The contribution of each operating harmonic to the total thrust is analyzed using the Maxwell stress tensor method to understand the thrust-enhancing mechanism of the unequal tooth structure.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] A permanent magnet linear vernier motor with unequal teeth includes a stator module and a mover module. The stator module includes a permanent magnet and a stator core, with the N and S poles of the permanent magnet alternately mounted on the surface of the stator core. The mover module includes an armature winding, a mover yoke, auxiliary teeth, and main teeth. Each main tooth has split teeth, and the tooth widths of the split teeth and auxiliary teeth are unequal, thus forming an unequal tooth structure. The armature winding is wound on the main teeth. An air gap exists between the stator module and the mover module.

[0008] Preferably, the armature winding is constructed by a concentrated winding wound on the main teeth, with a coil span of 1 slot and a fundamental winding factor of 1.

[0009] A thrust enhancement mechanism analysis method for an unequal-tooth permanent magnet linear vernier motor, the steps of which are as follows:

[0010] Step 1: Describe the structure of a traditional permanent magnet linear vernier motor, satisfying the magnetic field modulation relationship P. a =|P PM -Z mt Furthermore, the armature winding is a single-layer full-pitch winding with integer slots, and the coil span is a full-pitch τ = Z. mt / (2P a ); where P PM P is the number of pole pairs of the stator permanent magnet. a Z represents the number of pole pairs in the armature winding. mt Modulate the number of teeth for the mover;

[0011] Step 2: While ensuring the motor performance remains unchanged, the mover structure of the traditional permanent magnet linear vernier motor is improved by merging the three teeth between windings AX, BY, and CZ into one main tooth, and windings AX, BY, and CZ are wound on the main tooth respectively, while keeping the structure of the auxiliary teeth unchanged, to obtain a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure.

[0012] Step 3: Analyze the no-load air gap magnetic flux density of the uniform tooth structure concentrated winding permanent magnet linear vernier motor based on the magnetomotive force-magnetic permeability model;

[0013] Step 4: Perform parametric analysis on the split tooth width of the unequal tooth structure concentrated winding permanent magnet linear vernier motor to obtain the unequal tooth structure concentrated winding permanent magnet linear vernier motor with greater thrust. The tooth width lengths of its split teeth and auxiliary teeth are not equal. Analyze the no-load air gap magnetic flux density of the unequal tooth structure concentrated winding permanent magnet linear vernier motor based on the magnetomotive force-permeability model.

[0014] Step 5: Under motor load, the Maxwell stress tensor method is used to analyze the thrust of the unequal tooth structure concentrated winding permanent magnet linear vernier motor and derive the thrust expression.

[0015] Step 6: Based on the thrust expression, use the finite element analysis method to obtain the thrust generated by each harmonic magnetic field of the unequal tooth structure concentrated winding permanent magnet linear vernier motor.

[0016] Preferably, the coil span of the concentrated winding of the equal-tooth structure permanent magnet linear vernier motor is 1 slot, and the number of turns per phase winding is the same as that of a traditional permanent magnet linear vernier motor; while satisfying the magnetic field modulation relationship P a =|P PM -Z mt Under the premise of |, the equal-tooth structure concentrated winding permanent magnet linear vernier motor has three split teeth on the main teeth, so that the tooth width of the split teeth is the same as the armature tooth width of the traditional permanent magnet linear vernier motor, and the magnetic flux, no-load back EMF and thrust of each phase of the equal-tooth structure concentrated winding permanent magnet linear vernier motor are consistent with those of the traditional permanent magnet linear vernier motor.

[0017] Preferably, the calculation method for the no-load air gap magnetic flux density of the uniform tooth structure concentrated winding permanent magnet linear vernier motor is as follows:

[0018] Traditional permanent magnet linear vernier motors and permanent magnet linear vernier motors with concentrated windings and equal tooth structure have the same stator structure. Therefore, the magnetomotive force of the stator permanent magnets in both types of motors can be expressed as:

[0019]

[0020] Among them, F pk Let L1 be the kth harmonic amplitude of the magnetomotive force of the permanent magnet, L1 be the length of the mover, and x be the position of the mover.

[0021] The uniform-tooth structure concentrated winding permanent magnet linear vernier motor has the same number of permanent magnet pole pairs, armature winding pole pairs, and modulation tooth structure as the traditional permanent magnet linear vernier motor. Therefore, the permeability function of both types of motors can be expressed as:

[0022]

[0023] Among them, Λ m0 Let Λ be the DC component of the j-th permeability harmonic. mj Let v be the amplitude of the j-th magnetic permeability harmonic, v represent the mover velocity, and t represent time.

[0024] Based on the magnetomotive force and permeability function of the stator permanent magnet, the expression for the no-load air gap magnetic flux density of the uniform tooth structure concentrated winding permanent magnet linear vernier motor is obtained:

[0025]

[0026] From the expression for the no-load air gap magnetic flux density, it can be seen that the main harmonic type of the uniform tooth structure concentrated winding permanent magnet linear vernier motor is kP. PM and |kP PM ±jZ mt |

[0027] Preferably, the method for calculating the no-load air gap magnetic flux density of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is as follows:

[0028] Because the tooth widths of the split teeth and auxiliary teeth in a permanent magnet linear vernier motor with unequal tooth structure and concentrated winding are not equal, the magnetomotive force of the permanent magnet in a permanent magnet linear vernier motor with unequal tooth structure and concentrated winding is the same as that in a permanent magnet linear vernier motor with equal tooth structure and concentrated winding. However, the air gap permeability function changes, as shown below:

[0029]

[0030] Among them, P Λ The relative air gap permeability period;

[0031] Therefore, the no-load air gap magnetic flux density of a permanent magnet linear vernier motor with unequal tooth structure and concentrated winding is expressed as:

[0032]

[0033] From the expression for the no-load air gap magnetic flux density, it can be seen that the main harmonic type of the unequal tooth structure concentrated winding permanent magnet vernier motor is kP. PM 、|kP PM ±jZ mt |and|kP PM ±jP Λ |

[0034] Preferably, the method for analyzing the thrust of a permanent magnet linear vernier motor with concentrated windings and unequal tooth structure using the Maxwell stress tensor method is as follows:

[0035] The unequal-tooth structure concentrated winding permanent magnet linear vernier motor introduces a new type of harmonic. Under motor load, the Maxwell stress tensor method is used to calculate and analyze the contribution of each operating harmonic magnetic field to the total thrust, and the thrust expression is derived:

[0036]

[0037] Among them, l st Let μ be the axial length of the iron core, μ0 be the air permeability, and k be the magnetic permeability. F Let be the thrust constant.

[0038] B yi Let θ be the vertical amplitude of the i-th air gap magnetic flux density harmonic. yi (t) represents the vertical phase of the i-th air gap magnetic flux density harmonic, B xi Let θ be the horizontal amplitude of the i-th air gap magnetic flux density harmonic. xi (t) represents the horizontal phase of the i-th air gap magnetic flux density harmonic.

[0039] Preferably, the method for obtaining the thrust generated by the harmonic magnetic fields of a permanent magnet linear vernier motor with unequal tooth structure and concentrated winding using finite element analysis is as follows:

[0040] S6.1: Using finite element analysis, the value of B at time t within one electric cycle y (θ,t) and B x (θ,t), and perform Fourier series analysis to obtain B. yi 、B xi θ yi (t) and θ xi (t);

[0041] S6.2: B yi 、B xi θ yi (t) and θ xi Substituting (t) into the thrust expression, we obtain the thrust generated by each harmonic magnetic field at time t;

[0042] S6.3: Calculate the average magnetic flux density amplitude B over one electric cycle. yi and B xi cos[θ yi (t)-θ xi The average value of cosθ (t)] i The average thrust F generated by each harmonic magnetic field xi and its proportion.

[0043] The beneficial effects of this invention are:

[0044] (1) The concentrated winding structure is adopted, which makes winding insertion convenient, the fundamental winding factor is large, and reduces the number of coils, the length of the end winding, the amount of copper used in the winding and the copper loss. The auxiliary teeth reduce the coupling degree between phases and improve the fault tolerance of the motor.

[0045] (2) The unequal tooth structure design fully utilizes the magnetic field modulation capability of the motor, further increasing the thrust density of the permanent magnet linear vernier motor and reducing the cogging force, making it suitable for applications with high thrust.

[0046] (3) Based on the Maxwell stress tensor method, the thrust generated by each working harmonic is calculated, revealing the thrust enhancement mechanism of the unequal tooth structure concentrated winding permanent magnet linear vernier motor. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of a traditional permanent magnet linear vernier motor.

[0049] Figure 2 This is a structural diagram of a 12-slot, 8-pole armature winding.

[0050] Figure 3 This is a schematic diagram of a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure.

[0051] Figure 4 This is a diagram showing the evolution of armature structure.

[0052] Figure 5 This is a diagram of the moving gear structure of a traditional permanent magnet linear vernier motor.

[0053] Figure 6 This is a diagram of the moving tooth structure of a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure.

[0054] Figure 7 This is a comparison diagram of the flux linkage between a traditional permanent magnet linear vernier motor and a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure.

[0055] Figure 8 This is a comparison diagram of the no-load back electromotive force of a traditional permanent magnet linear vernier motor and a permanent magnet linear vernier motor with concentrated windings and equal tooth structure.

[0056] Figure 9These are the air gap relative magnetic permeability waveforms of traditional permanent magnet linear vernier motors, and permanent magnet linear vernier motors with concentrated windings of equal and unequal tooth structures.

[0057] Figure 10 This is a comparison diagram of the no-load air gap magnetic flux density of traditional permanent magnet linear vernier motors, and permanent magnet linear vernier motors with concentrated windings of equal and unequal tooth structures.

[0058] Figure 11 This is a schematic diagram of the structure of the present invention.

[0059] Figure 12 This is a schematic diagram of the unequal tooth structure of the present invention.

[0060] Figure 13 This is a comparison chart of the thrust of traditional permanent magnet linear vernier motors, and permanent magnet linear vernier motors with concentrated windings of equal and unequal tooth structures.

[0061] The main markings in the attached figures are: 1-Stator module; 2-Motor module; 1-1-NS pole permanent magnet; 1-2-Stator core; 2-1-Armature winding; 2-2-Motor yoke; 2-3-Auxiliary tooth; 2-4-Main tooth; 2-5-Split tooth. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] To verify the correctness of the method proposed in this invention, the structure of a traditional permanent magnet linear vernier motor is first given, such as... Figure 1 As shown, the motor has 10 permanent magnet pole pairs, 12 mover slots, and 2 armature winding pole pairs. The motor satisfies the magnetic field modulation relation P. a =|P PM -Z mt Furthermore, the armature winding is a single-layer full-pitch winding with integer slots, and the coil span is a full-pitch τ = Z. mt / (2P a The winding pitch is 3, and the N and N pole permanent magnets are mounted on the stator surface. Among them, P... PM P is the number of pole pairs of the stator permanent magnet. a Z represents the number of pole pairs in the armature winding. mtThe number of teeth is modulated for the mover. At this point, the fundamental winding factor of the traditional permanent magnet linear vernier motor reaches its maximum of 1, thus generating the maximum no-load back EMF and thrust. However, the coil span is not one slot, leading to difficulties in winding insertion. To facilitate coil insertion into the armature, directly embedding windings AX, BY, and CZ into the slots using the traditional method will result in a 12-slot, 8-pole armature winding structure, such as... Figure 2 As shown, although this simplifies winding, the fundamental winding factor becomes 0.866, which reduces the no-load back EMF and thrust. Therefore, while maintaining the same phase performance, the armature structure of the traditional permanent magnet linear vernier motor is improved into a permanent magnet linear vernier motor with concentrated windings and an equal-tooth structure with a pitch of 1 slot. Its structure is as follows: Figure 3 As shown.

[0064] To obtain Figure 3 The structure, the armature structure improvement process of this invention is as follows: Figure 4 As shown, the remaining two-phase winding coils between the AX windings are removed, converting the winding structure into a concentrated winding. The three moving teeth between the AX windings are merged into a single main tooth structure. Similarly, windings CZ and BY are configured in the same way, while the auxiliary teeth between each phase remain unchanged. After merging into a main tooth, to enable the motor to generate stable thrust, three split teeth are added to the main tooth, with the tooth width being the same as the armature tooth width of a traditional permanent magnet linear vernier motor, to satisfy the magnetic field modulation effect. Therefore, the resulting concentrated winding permanent magnet linear vernier motor with equal tooth structure has three windings, three main teeth, and three auxiliary teeth, with a coil span of one slot. The concentrated winding permanent magnet linear vernier motor with equal tooth structure and the traditional permanent magnet linear vernier motor have the same number of permanent magnet pole pairs, armature winding pole pairs, modulation teeth, and winding factor. Unlike traditional permanent magnet linear vernier motors, the equal-tooth structure concentrated winding permanent magnet linear vernier motor reduces the span of each phase winding from three slots to one slot, making it easier to embed into the slots. The auxiliary teeth also reduce the coupling between phases, improving the motor's fault tolerance. Traditional permanent magnet linear vernier motors and equal-tooth structure concentrated winding permanent magnet linear vernier motors are similar... Figure 5 and Figure 6 As shown. Figure 7 , 8 The A-phase flux linkage waveform and no-load back EMF waveform of a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure and a conventional permanent magnet linear vernier motor are shown respectively. Figure 7 , 8 It can be seen that the flux linkage and no-load back EMF of each phase winding of the two types of motors are basically the same, so the winding factors of the two types of motors are also the same, thus enabling the motor to generate maximum thrust.

[0065] Based on the magnetomotive force-permeability model, the no-load air gap magnetic flux density of a toothed, concentrated-winding permanent magnet linear vernier motor and a conventional permanent magnet linear vernier motor is analyzed to reveal their working principles. Since both motors have the same stator structure, the stator permanent magnet magnetomotive force of the conventional permanent magnet linear vernier motor and the toothed, concentrated-winding permanent magnet linear vernier motor can be expressed as:

[0066]

[0067] Among them, F pk L1 is the kth harmonic amplitude of the permanent magnet magnetomotive force, L1 is the mover length, and x is the mover position.

[0068] The uniform-tooth structure concentrated winding permanent magnet linear vernier motor has the same number of permanent magnet pole pairs, armature winding pole pairs, and modulation tooth structure as the traditional permanent magnet linear vernier motor. Therefore, the permeability function of both types of motors can be expressed as:

[0069]

[0070] Among them, Λ m0 Let Λ be the DC component of the j-th permeability harmonic. mj Let v be the amplitude of the j-th magnetic permeability harmonic, v represent the mover velocity, and t represent time.

[0071] Based on the magnetomotive force and permeability function of the stator permanent magnet, the expression for the no-load air gap magnetic flux density of the uniform tooth structure concentrated winding permanent magnet linear vernier motor is obtained:

[0072]

[0073] From the expression for the no-load air gap magnetic flux density, it can be seen that the main harmonic types of both types of motors are kP. PM and |kP PM ±jZ mt |

[0074] To further improve the thrust density of the motor, a parametric analysis was performed on the split tooth width of the concentrated winding permanent magnet linear vernier motor with an equal tooth structure. This yielded a concentrated winding permanent magnet linear vernier motor with an unequal tooth structure, which has a greater thrust. The tooth widths of the split teeth and auxiliary teeth in this unequal tooth structure concentrated winding permanent magnet linear vernier motor are not equal. The magnetomotive force of the permanent magnet in the unequal tooth structure concentrated winding permanent magnet linear vernier motor is the same as that in the equal tooth structure concentrated winding permanent magnet linear vernier motor, but the air gap permeability function changes, as shown below:

[0075]

[0076] Among them, P Λ The relative air gap permeability period.

[0077] Therefore, the no-load air gap magnetic flux density of a permanent magnet linear vernier motor with unequal tooth structure and concentrated winding is expressed as:

[0078]

[0079] From the expression for the no-load air gap magnetic flux density, it can be seen that the main harmonic type of the unequal tooth structure concentrated winding permanent magnet vernier motor is kP. PM 、|kP PM ±jZ mt |and|kP PM ±jP Λ Compared to a permanent magnet vernier motor with a concentrated winding and equal tooth structure, a permanent magnet vernier motor with a concentrated winding and unequal tooth structure can generate a richer harmonic working magnetic flux density.

[0080] like Figure 11 As shown, an unequal-tooth permanent magnet linear vernier motor includes a stator module 1 and a mover module 2. The stator module 1 includes a permanent magnet 1-1 and a stator core 1-2, with the N and S poles of the permanent magnet 1-1 alternately mounted on the surface of the stator core 1-2. The mover module 2 includes an armature winding 2-1, a mover yoke 2-2, auxiliary teeth 2-3, and main teeth 2-4. Each main tooth 2-4 has a split tooth 2-5, and the tooth width of the split tooth 2-5 is unequal to that of the auxiliary tooth 2-3, thus forming an unequal-tooth structure. Figure 12 As shown, the armature winding 2-1 is wound on the main tooth 2-4; there is an air gap 3 between the stator module 1 and the mover module 2. In order to facilitate the embedding of the coil into the armature slot, the armature winding 2-1 adopts a concentrated winding structure wound on the main tooth 2-4, with a coil span of 1 slot and a fundamental winding factor of 1, while reducing the end winding length, the amount of copper used in the winding, and the copper loss.

[0081] In order to satisfy the magnetic field modulation relation P a =|P PM -Z mt |, where P PM P is the number of pole pairs of the stator permanent magnet. a Z represents the number of pole pairs in the armature winding. mt To determine the number of modulated teeth for the mover, the mover module of this motor consists of main teeth and auxiliary teeth. The main teeth have three split teeth, and the number of auxiliary teeth is equal to the number of main teeth. The number of modulated teeth for the mover is equal to the number of split teeth plus the number of auxiliary teeth. The interaction between the stator permanent magnet magnetomotive force and the magnetic permeability harmonics of the unequal tooth structure introduces a new type of harmonic magnetic flux density. The unequal tooth structure can increase thrust by changing the magnitude and phase difference of the horizontal and vertical directions of the air gap magnetic flux density, and the auxiliary teeth reduce the magnetic circuit coupling between phases, thereby improving the fault tolerance of the motor.

[0082] The air gap relative permeability waveforms of traditional permanent magnet linear vernier motors, and those with equal and unequal tooth structures and concentrated windings, are as follows: Figure 9As shown, traditional permanent magnet linear vernier motors and uniformly toothed concentrated winding permanent magnet linear vernier motors have regular modulated tooth structures, evenly distributed along the x-axis. From Figure 9 As can be seen from (a) and (b), the relative magnetic permeability waveforms of the two motors are almost identical and exhibit periodic changes, with the number of cycles being the same as the number of moving teeth. Figure 9 As shown in (c), the relative magnetic permeability period P of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is... Λ The value is 3, which corresponds to the number of moving tooth units, not the number of moving teeth.

[0083] The no-load air gap magnetic flux density waveforms of traditional permanent magnet linear vernier motors, equal-tooth structure and unequal-tooth concentrated winding permanent magnet linear vernier motors are as follows: Figure 10 As shown in the figure, the magnetic flux density waveforms of the traditional permanent magnet linear vernier motor and the permanent magnet linear vernier motor with concentrated windings and equal tooth structure are basically the same. The main operating harmonic present in all three types of motors is 2... nd (k=j=1,|kP PM -jZ mt |) 10 th (k=1,kP PM ) and 22 nd (k=j=1,kP PM +jZ mt In addition to the harmonics mentioned above, the unequal tooth structure concentrated winding permanent magnet linear vernier motor also has 1 st (k=1,j=3,|kP PM -jP Λ |), 7 th (k=1,j=1,|kP PM -jP Λ |), 13 th (k=1,j=1,|kP PM +jP Λ |) and 19 th (k=1,j=3,|kP PM +jP Λ Harmonics, although the amplitudes of these harmonics are very small. Compared with traditional permanent magnet linear vernier motors and permanent magnet linear vernier motors with equal tooth structure and concentrated windings, permanent magnet linear vernier motors with unequal tooth structure and concentrated windings can generate a richer range of operating harmonics.

[0084] Since the magnetomotive force permeability method cannot explain the influence of asymmetric structure and tangential magnetic field on thrust, the Maxwell stress tensor method (MST) is used to analyze the thrust enhancement mechanism of permanent magnet linear vernier motor with concentrated winding and unequal tooth structure. Equation (5) shows that the interaction between the unequal tooth structure and the permanent magnet magnetomotive force generates new working harmonic magnetic fields. Under motor load, the Maxwell stress tensor method is used to calculate and analyze the contribution of each working harmonic magnetic field to the total thrust, deriving the thrust expression as follows:

[0085]

[0086] Among them, l st Let μ be the axial length of the iron core, μ0 be the air permeability, and k be the magnetic permeability. F Let be the thrust constant.

[0087] B yi Let θ be the vertical amplitude of the i-th air gap magnetic flux density harmonic. yi (t) represents the vertical phase of the i-th air gap magnetic flux density harmonic, B xi Let θ be the horizontal amplitude of the i-th air gap magnetic flux density harmonic. xi (t) represents the horizontal phase of the i-th air gap magnetic flux density harmonic.

[0088] The thrust generated by each harmonic is obtained by following the steps according to equation (6):

[0089] 1) Analyze B at time t within one electric cycle using the finite element method. y (θ,t) and B x (θ,t), and perform Fourier series analysis to obtain B. yi 、B xi θ yi (t) and θ xi (t);

[0090] 2) B yi 、B xi θ yi (t) and θ xi Substituting (t) into the thrust expression yields the thrust generated by the harmonic magnetic field at time t;

[0091] 3) Calculate the average magnetic flux density amplitude B over one electric cycle. yi and B xi cos[θ yi (t)-θ xi The average value of cosθ (t)] i The average thrust F generated by each harmonic magnetic flux density xi and its proportion.

[0092] Therefore, the following conclusions are drawn: (1) The magnitude of the thrust F generated by each harmonic is... xi With magnetic flux density amplitude B yi 、B xi and cos[θ yi (t)-θ xi (t)] Three factors are related, so the main working harmonic magnetic flux density and contribution degree of the thrust of the unequal tooth structure concentrated winding permanent magnet linear vernier motor are analyzed, and the main factors that increase the thrust of the unequal tooth structure concentrated winding permanent magnet linear vernier motor are also analyzed; (2) The harmonic number with the same number of pole pairs as the permanent magnet plays the main thrust role (such as P PM The thrust of other harmonics is relatively small (e.g., |kP) PM -jZ mt |times, P PM +Z mt (3) Compared with the unequal tooth structure and the equal tooth structure concentrated winding permanent magnet linear vernier motor, the increase in thrust is not necessarily due to the increase in the number of harmonics, but may also be due to the main active harmonics (such as P). PM cosθ (times) i (4) Because the magnetic field modulation effect is complex, the magnitude of the thrust generated by each harmonic of different structures may be different.

[0093] Without considering end effects, the average thrust of each operating harmonic of the two motors under rated operating conditions was calculated using equation (6), as shown in Table 1. The results show that the thrust is mainly generated by the 10th harmonic magnetic field, which has the same number of pole pairs as the permanent magnet, while the contribution of other harmonic magnetic fields to the thrust is negligible. Therefore, the increase in thrust is not necessarily due to the increase in the number of harmonics. The thrust of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is higher than that of the equal tooth structure concentrated winding permanent magnet linear vernier motor, which is attributed to the significant increase in thrust generated by the 10th harmonic magnetic field.

[0094] Table 1

[0095]

[0096] According to equation (6), the thrust generated by the 10th harmonic of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is related to B. y10 B x10 cos[θ y10 (t)-θ x10 The 10th harmonic magnetic flux density and thrust F of concentrated winding permanent magnet linear vernier motors with equal and unequal tooth structures are proportional. x10 The average values ​​are shown in Table 2. The 10th harmonic magnetic flux density and thrust F of these two motors were analyzed. x10 Analysis shows that the B of unequal tooth structure and equal tooth structure concentrated winding permanent magnet linear vernier motorsy10 and B x10 The changes are not significant, but the cosθ of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is... 10 The significant increase is the main reason for the increased thrust.

[0097] Table 2

[0098]

[0099] The thrust of traditional permanent magnet linear vernier motors, and permanent magnet linear vernier motors with concentrated windings of equal and unequal tooth structures, is as follows: Figure 13 As shown, the average thrust of the first two types of motors is basically the same, while the average thrust of the unequal tooth structure permanent magnet linear vernier motor is greater. Compared with the equal tooth structure concentrated winding permanent magnet linear vernier motor, the average thrust of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is increased by 36.43%, which verifies that the unequal tooth structure permanent magnet linear vernier motor is effective in increasing thrust.

[0100] In summary, the motor structure of this invention has significant advantages over existing traditional permanent magnet linear vernier motors and uniform-tooth structure concentrated winding permanent magnet linear vernier motors. With the same amount of permanent magnets, the thrust density is actually higher. The concentrated winding armature winding facilitates winding and reduces end winding length and copper losses. Auxiliary teeth reduce the magnetic circuit coupling between phases, improving the motor's fault tolerance. The unequal-tooth structure generates new operating harmonic magnetic flux density. Using the Maxwell stress tensor method, the thrust enhancement mechanism of the unequal-tooth structure is calculated and analyzed for each operating harmonic. The thrust generated by each operating harmonic is related to B... yi B xi and cosθ i The thrust of the motor is primarily contributed by the harmonic orders corresponding to the number of pole pairs of the permanent magnet; other harmonics play a smaller role in thrust generation. Compared to a permanent magnet linear vernier motor with a concentrated winding and equal tooth structure, the increased thrust of a permanent magnet linear vernier motor with a concentrated winding and unequal tooth structure is not necessarily due to a richer array of operating harmonics, but rather may be due to the higher cosθ of the main operating harmonics. i This increases thrust. Furthermore, due to the complexity of magnetic field modulation, the magnitude of thrust generated by each harmonic may vary under different structures.

[0101] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An unequal-tooth permanent magnet linear cursor motor, characterized in that: The invention comprises a stator module (1) and a mover module (2); the stator module (1) comprises a permanent magnet (1-1) and a stator core (1-2); the N pole and the S pole of the permanent magnet (1-1) are alternately mounted on the surface of the stator core (1-2); the mover module (2) comprises an armature winding (2-1), a mover yoke (2-2), auxiliary teeth (2-3) and main teeth (2-4); each main tooth (2-4) is provided with a split tooth (2-5); the tooth widths of the split teeth (2-5) and the auxiliary teeth (2-3) are unequal, thereby forming an unequal tooth structure; the armature winding (2-1) is wound on the main teeth (2-4); and an air gap (3) is provided between the stator module (1) and the mover module (2).

2. The unequal-tooth permanent magnet linear vernier motor according to claim 1, characterized in that: The armature winding (2-1) is structured such that concentrated winding is wound on the main teeth (2-4), the coil span is 1 slot, and the fundamental wave winding factor is 1.

3. A method for analyzing the thrust enhancement mechanism of an unequal-tooth permanent magnet linear vernier motor according to claim 1 or 2, characterized in that: The steps are as follows: Step 1: Give the structure of the traditional permanent magnet linear vernier motor to satisfy the magnetic field modulation relationship P a =|P PM -Z mt |, and the armature winding is an integer slot single-layer full-pitch winding, and the coil span is full pitch τ=Z mt / (2P a ), where P PM is the number of stator permanent magnet pole pairs, P a is the number of armature winding pole pairs, Z mt Modulate the number of teeth of the mover; Step 2: Under the premise of ensuring that the motor performance remains unchanged, the rotor structure of the traditional permanent magnet linear vernier motor is improved, the three teeth between the windings AX, BY, and CZ are merged into one main tooth, and the windings AX, BY, and CZ are respectively wound on the main teeth, and the structure of the auxiliary teeth is kept unchanged, so as to obtain an equal-tooth structure concentrated winding permanent magnet linear vernier motor; Step 3: Analyze the no-load air gap flux density of the equal-tooth structure concentrated winding permanent magnet linear cursor motor according to the magnetomotive force-permeability model; Step 4: parametrically analyze the split tooth width of the concentrated winding permanent magnet linear vernier motor with equal tooth structure, and obtain the unequal tooth concentrated winding permanent magnet linear vernier motor with greater thrust, in which the tooth width lengths of the split teeth and the auxiliary teeth are not equal; analyze the no-load air gap magnetic flux density of the concentrated winding permanent magnet linear vernier motor with unequal tooth structure according to the magnetomotive force-permeability model; Step 5: When the motor is loaded, the thrust of the unequal-tooth structure concentrated winding permanent magnet linear vernier motor is analyzed by using the Maxwell stress tensor method, and the thrust expression is derived; Step 6: According to the thrust expression, the finite element analysis method is used to obtain the thrust generated by each harmonic magnetic field of the unequal-tooth structure concentrated winding permanent magnet linear cursor motor.

4. The method for analyzing the thrust enhancement mechanism of the unequal-tooth permanent magnet linear vernier motor according to claim 3 is characterized in that: The coil span of the concentrated winding of the equal-tooth structure concentrated winding permanent magnet linear vernier motor is 1 slot, and the number of turns of each phase winding is consistent with that of the traditional permanent magnet linear vernier motor; when the magnetic field modulation relationship P is satisfied a =|P PM -Z mt |On the premise of equal tooth structure concentrated winding permanent magnet linear vernier motor, three split teeth are opened on the main teeth, so that the tooth width of the split teeth is the same as the armature tooth width of the traditional permanent magnet linear vernier motor, and the flux linkage per phase, no-load back EMF and thrust of the equal tooth structure concentrated winding permanent magnet linear vernier motor and the traditional permanent magnet linear vernier motor are consistent.

5. The method for analyzing the thrust enhancement mechanism of the unequal-tooth permanent magnet linear vernier motor according to claim 4 is characterized in that: The calculation method of the no-load air gap flux density of the equal-tooth structure concentrated winding permanent magnet linear vernier motor is: The conventional permanent magnet linear vernier motor and the equal-tooth structure concentrated winding permanent magnet linear vernier motor have the same stator structure. Therefore, the magnetomotive force of the stator permanent magnet of the two motors is expressed as: Among them, F pk is the kth harmonic amplitude of the permanent magnet magnetomotive force, L1 is the mover length, and x is the mover position; The equal-tooth structure concentrated winding permanent magnet linear vernier motor and the traditional permanent magnet linear vernier motor have the same number of permanent magnet pole pairs, armature winding pole pairs and modulated tooth structure. Therefore, the permeance function of these two motors is expressed as: Among them, Λ m0 is the DC component of the jth permeance harmonic, Λ mj is the amplitude of the jth permeance harmonic, v represents the mover speed, and t represents the time; According to the magnetomotive force and permeance function of the stator permanent magnet, the expression of the no-load air gap flux density of the equal-tooth structure concentrated winding permanent magnet linear vernier motor is obtained: From the expression of no-load air gap flux density, we can know that the main harmonic type of the equal-tooth structure concentrated winding permanent magnet linear cursor motor is kP PM and |kP PM ±j mt |.

6. The method for analyzing the thrust enhancement mechanism of the unequal-tooth permanent magnet linear vernier motor according to claim 4 is characterized in that: The calculation method of the no-load air gap magnetic flux density of the unequal tooth structure concentrated winding permanent magnet linear vernier motor is: Since the tooth width lengths of the split teeth and the auxiliary teeth of the unequal-tooth concentrated winding permanent magnet linear vernier motor are not equal, the permanent magnet magnetomotive force of the unequal-tooth concentrated winding permanent magnet linear vernier motor is the same as that of the equal-tooth concentrated winding permanent magnet linear vernier motor, but the air gap permeance function has changed, which is expressed as follows: Among them, P Λ is the relative air gap permeability period; Therefore, the no-load air gap flux density of the unequal-tooth structure concentrated winding permanent magnet linear vernier motor is expressed as: From the no-load air gap flux density expression, we can know that the main harmonic type of the unequal tooth structure concentrated winding permanent magnet vernier motor is kP PM 、|kP PM ±j mt | and |kP PM ±jP Λ |.

7. The method for analyzing the thrust enhancement mechanism of the unequal-tooth permanent magnet linear vernier motor according to claim 6 is characterized in that: The method for analyzing the thrust of the unequal-tooth structure concentrated winding permanent magnet linear vernier motor by using the Maxwell stress tensor method is as follows: The unequal-tooth structure concentrated winding permanent magnet linear vernier motor introduces a new type of harmonics. When the motor is loaded, the Maxwell stress tensor method is used to calculate and analyze the contribution of each working harmonic magnetic field to the total thrust, and the thrust expression is derived: Among them, l st is the axial length of the core, μ0 is the magnetic permeability of air, k F is the thrust constant, B yi is the vertical amplitude of the ith air gap magnetic flux harmonic, θ yi (t) is the vertical phase of the ith air gap magnetic flux harmonic, B xi is the horizontal amplitude of the i-th air gap magnetic flux harmonic, θ xi (t) is the horizontal phase of the i-th air gap magnetic flux harmonic.

8. The method for analyzing the thrust enhancement mechanism of the unequal-tooth permanent magnet linear vernier motor according to claim 7, characterized in that: The method for obtaining the thrust generated by each harmonic magnetic field of the unequal tooth structure concentrated winding permanent magnet linear cursor motor by using the finite element analysis method is: S6.1: Use finite element analysis to analyze the B at time t in an electrical cycle y (θ,t) and B x (θ, t), and perform Fourier series analysis on it to obtain B yi , B xi ,θ yi (t) and θ xi (t); S6.2: B yi , B xi ,θ yi (t) and θ xi (t) is substituted into the thrust expression to obtain the thrust generated by each harmonic magnetic field at time t; S6.3: Find the average magnetic flux density B within one electrical cycle yi and B xi , cos[θ yi (t)-θ xi (t)] is the average value cosθ i , the average thrust F generated by each harmonic magnetic field xi and its proportion.

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