GB2614105A

GB2614105A - Hybrid magnetic source magnetic lead screw having high positioning precision, and multi-harmonic collaborative modulation method therefor

Info

Publication number: GB2614105A
Application number: GB2208487.5A
Authority: GB
Inventors: Ling Zhijian; Kang Mei; Zhao Wenxiang; Ji Jinghua
Original assignee: Jiangsu University
Current assignee: Jiangsu University
Priority date: 2021-05-13
Filing date: 2021-05-25
Publication date: 2023-06-28
Also published as: GB202208487D0

Abstract

A hybrid magnetic source magnetic lead screw having a high positioning precision, and a multi-harmonic collaborative modulation method therefor. The magnetic lead screw comprises a magnetic nut and a magnetic screw rod, which are coaxially arranged. According to the characteristics of a spiral structure, a new effective harmonic order is introduced by means of spatial matching between a permanent magnet and a magnetic modulation module, thus satisfying not only a modulation mechanism in a linear direction, but also satisfying a modulation mechanism in a circumferential direction, such that multi-harmonic collaborative modulation is achieved. An excitation winding is wound inside the magnetic modulation module, so that an air-gap magnetic field of the magnetic lead screw is adjustable, thereby improving the positioning precision. In the hybrid magnetic source magnetic lead screw having a high positioning precision, on the premise of ensuring high reliability and high thrust density, the defects of an existing magnetic lead screw such as single modulation of a magnetic field, large magnetic flux leakage and insufficient positioning precision are overcome.

Description

HYBRID MAGNETIC SCREW WITH HIGH POSITIONING PRECISION AND MULTI-HARMONICS MODULATION METHOD THEREOF

Technical Field

The present invention relates to a hybrid magnetic screw with high positioning precision and a design method of multi-harmonics modulation. In particular, it involves helical magnetic transmission and hybrid multi-harmonics modulation technology, which is suitable for aerospace, high-end machine tool applications. It belongs to the field of electric actuators.

Background

Magnetic screw is a new type of linear actuator, which exhibits high force density and non-contact transmission. Thus, it is extensively employed for many applications, ranging from artificial heart to aerospace actuation and ocean power generation. However, most of the research on the magnetic screws have focused on the surface-mounted magnetic screws, which have disadvantages such as single magnetic modulation, magnetic flux leakage and air-gap magnetic field un-adjustable.

The paper IEEE Transactions on Industrial Electronics, 65(9): 7536-7547, 2018 "Design optimization and test of a radially magnetized magnetic screw with discretized PMs" introduces a permanent magnet (PM) surface-mounted magnetic screw, which attaches the radially magnetized permanent magnets with N and S poles alternately on the back-iron. Compared with the other topologies, the surface-mounted magnetic screw has a higher force density and can greatly simplify the manufacturing process. However, the air-gap magnetic field of the surface-mounted magnetic screw cannot be adjusted, which reduces the positioning precision and thrust force density. Thus, it restricts the application of magnetic screw in high dynamic fields such as aerospace.

The paper IEEE Transactions on Magnetics, 50(11): 8205004, 2014 "Electromagnetic lead screw for potential wave energy application-introduces an electromagnetic type magnetic lead screw. The coils are wound in the helical slots, and the direct currents are injected into the coils to obtain the helical electric magnetic field in the air-gap. The electromagnetic lead screw realizes the adjustment of the air-gap magnetic field, thereby improving the positioning precision.

However, compared with the permanent magnetic fields, the magnetic field density of the electromagnetic lead screw will decrease significantly. Under the same volume, the thrust force of electromagnetic lead screw is reduced by 75%.

The Chinese Patent 201610821273.1 disclosed a field modulation magnetic screw, which is actually a magnetic screw topology that satisfies magnetic field modulation effect. In the field modulation magnetic screw, the relationship between the pole-pair numbers of the inner, outer permanent magnet parts and ferromagnetic iron pole-pieces can be derived as: "t =pi+ P2 (1) where ni is the ferromagnetic iron pole-pieces, pi is the inner part permanent magnet pole-pairs, and p2 is the outer part permanent magnet pole-pairs.

Based on the magnetic field modulation theory, the thrust force of the field modulation magnetic screw has been improved. However, it is composed of three parts, a translator, a stator, and a rotor. There are two layers of air-gaps, which greatly increases the manufacturing difficulty. The paper IEEE Transactions on Industry Applications, 54(6): 5736-5747, 2018 "Designing and experimentally testing a magnetically geared lead screw" designed and manufactured a prototype to verify the electromagnetic characteristic of the field modulation magnetic screw. But, due to the manufacturing complexity and machining accuracy, the measured thrust force is 40% less than the theoretical analysis.

Summary

The objective of the present invention is to provide, in view of the deficiencies of the existing magnetic screw, a hybrid magnetic screw with high positioning precision and a design method of multi-harmonics modulation. The purpose is to introduce the multi-harmonics modulation into a hybrid magnetic screw. The shortcomings of the existing magnetic screw, such as single magnetic field modulation and air-gap magnetic field un-adjustable are avoided. The thrust force density and positioning precision of the magnetic screws have been significantly improved.

Specifically, the magnetic screw of the present invention is implemented using the following technical solution: the hybrid magnetic screw comprises a magnetic nut (1) and a magnetic translator (2), which are placed coaxi ally. There is an air-gap between the magnetic nut (1) and the magnetic translator (2), and the length of the air-gap is selected based on the size and requirement of the magnetic screw.

The magnetic nut (I) comprises a plurality of first units arranged in sequence, and each of the first units comprises a helical permanent magnet Al which is axially magnetized, a helical magnetic modulation module B1, and a helical permanent magnet A2 which is axially magnetized. The helical magnetic modulation module B1 is sandwiched between the helical permanent magnet Al and helical permanent magnet A2. The magnetization directions of the helical permanent magnet Al and helical permanent magnet A2 are concentrated in the helical magnetic modulation module Bl. The helical magnetic lead lengths of the helical permanent magnet Al, helical permanent magnet A2, and the helical magnetic modulation module B I are all 1.

The magnetic translator (2) comprises a plurality of second units arranged in sequence, and each of the second units comprises a helical permanent magnet A3 which is axially magnetized, a helical permanent magnet A4 which is axially magnetized, a helical magnetic modulation module B2, a helical coil Cl, and a helical coil C2. The helical magnetic modulation module B2 is sandwiched between the helical permanent magnet A3 and helical permanent magnet A4. The magnetization directions of the helical permanent magnet A3 and helical permanent magnet A4 are concentrated in the helical magnetic modulation module B2. Then, the helical coil Cl and the helical coil C2 are wound on the helical magnetic modulation module B2. The current directions of the helical coil Cl and the helical coil C2 are opposite. When the hybrid magnetic screw needs to improve a thrust force at fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are positive and negative, respectively. Similarly, when the hybrid magnetic screw needs to reduce the thrust force at the fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are negative and positive, respectively. By changing the currents amplitudes and the current directions of the helical coil Cl and the helical coil C2, the air-gap magnetic field adjustment of the hybrid magnetic screw is realized. The helical magnetic lead lengths of the helical permanent magnet A3, helical permanent magnet A4, the helical magnetic modulation module B2, the helical coil Cl and the helical coil C2 are all 2.

In the magnetic nut (1), the permanent magnetic field is generated by the helical permanent magnet Al and the helical permanent magnet A2. Then, the permanent magnetic field is modulated by the helical magnetic modulation module Bl. Due to the helical modulation effect, the Pt, 3', and 5th harmonics are generated in the axial and circumferential directions, respectively. Similarly, in the magnetic translator (2), the permanent magnetic field is generated by the helical permanent magnet A3 and the helical permanent magnet A4. Then, the permanent magnetic field is modulated by the helical magnetic modulation module B2. The same harmonics as the magnetic nut (1) are generated. By changing the amplitudes and directions of the currents in the helical coil CI and helical coil C2 to adjust amplitudes of the harmonics. Therefore, the multi-harmonics modulation of the magnetic nut (1) and magnetic translator (2) is realized.

Further, the magnetization directions of the helical permanent magnet Al and the helical permanent magnet A2 are concentrated in the helical magnetic modulation module B 1; the helical permanent magnet A3 and the helical permanent magnet A4 are concentrated in the helical magnetic modulation module B2. In the above methods, the principle of minimum reluctance is adopted, and the helical permanent magnetic field is drawn out through the helical magnetic modulation module B1 and the helical magnetic modulation module B2, which significantly reduces the leakage of the magnetic field.

Further, the magnetic lead lengths of the helical permanent magnet Al and the helical permanent magnet A2, and helical magnetic modulation module B1 are all 1. The axial lengths of the helical permanent magnet Al and the helical permanent magnet A2 are the same can be expressed as (2) where // is the axial length of the helical magnetic modulation module Bl.

Further, the helical magnetic lead lengths of the helical permanent magnet A3 and the helical permanent magnet A4, the helical magnetic modulation module B2, and the helical coil Cl, and the helical coil C2 are all 2 The axial lengths of the helical permanent magnet A3 and the helical permanent magnet A4 are the same as that of the helical permanent magnet Al and the helical permanent magnet A2. The axial length of the helical magnetic modulation module B2 is the same as the helical magnetic modulation module Bl. In helical magnetic modulation module B2, the axial length of the modulated tooth 6 can be expressed as 1, -2 /" (3) where /" is the axial length of the helical coil Cl and the helical coil C2.

The technical solution of the method of the present invention includes the following steps: step 1: the magnetic lead lengths of the helical permanent magnet At and the helical permanent magnet A2, and helical magnetic modulation module B1 are all A. It should be noted that the helical magnetic lead lengths of the helical permanent magnet A3 and the helical permanent magnet A4, the helical magnetic modulation module B2, and the helical coil C 1, and helical coil C2 are also A; step 2: the lengths of helical magnetic lead A of magnetic nut (1) and magnetic translator (2) are the consistent. Then, the axial lengths of the helical permanent magnet Al, the helical permanent magnet A2, helical permanent magnet A3 and the helical permanent magnet A4 are all /m Moreover, the axial lengths of the helical magnetic modulation module B1 and the helical magnetic modulation module B2 are all h. The topologies of the helical magnetic modulation module B1 and helical magnetic modulation module B2 are both designed as the "E-type" structures. The axial lengths of the modulated tooth are h., which satisfies the multi-harmonic modulation of the hybrid magnetic screw; step 3: take the circumferential and axial cross-sectional view of the hybrid magnetic screw, respectively. The circumferential and axial magnetic fields range from 0 to 2r and 0 to >I, respectively. By extracting the magnetic flux density within an axial magnetic lead A, the l', 3 rd, and 5111 harmonic orders can be obtained in the axial direction. Similarly, by extracting the magnetic flux density within a circle of 27r, the 1S1 3rd and 5(11 harmonic orders can be obtained in the circle direction. Therefore, the innovation of this hybrid magnetic screw is achieved fully helical magnetic coupled, which satisfies the modulation in the circumferential and axial direction, respectively; step 4: in the helical magnetic modulation module B2, the helical coil Cl and the helical coil C2 are wound in the "E-type" slot. According to the operating conditions, currents of different directions and amplitudes are injected into the helical coil Cl and the helical coil C2, and the air-gap magnetic field can be adjusted. Then, the multi-harmonic amplitudes of different orders are changed; step 5: the air-gap magnetic field densities of hybrid magnetic screw are subjected to Fourier analysis in the circumferential and axial direction, respectively. The feasibility of the above modulation principle is verified, also the thrust density and positioning precision of the proposed hybrid magnetic screw are verified.

With the aforementioned design solutions, the present invention can have the following beneficial effects: 1. Based on the spatial configuration of the magnetic modulation module and permanent magnetic field, the multi-harmonic modulation of the helical magnetic field is realized, thereby improving the thrust force; 2. By winding the helical coils in the magnetic modulation module, the air-gap magnetic field of the hybrid magnetic screw can be adjusted, thereby improving the positioning precision; 3. The multi-harmonic modulation of the hybrid magnetic screw is realized, which significantly improves the thrust force and positioning precision. The permanent magnets are placed between the magnetic modulation modules, the magnetic flux leakage can be reduced significantly.

The hybrid magnetic screw of the present invention has the advantages of high positioning precision and high thrust force. It realizes the torque-force conversion by helical magnetic field transmission, which satisfies the modulation in the circumferential and axial direction, respectively. Compared with the traditional magnetic screws, the thrust force can be significantly improved. Moreover, the helical coils are wound in the magnetic modulation module, which improves the positioning precision while ensuring the high force density. It is especially suitable for aerospace, high-end machine tool fields.

Brief Description of the Drawings

FIG. 1 is a schematic view of a hybrid magnetic screw of the present invention; FIG. 2 is a cross-sectional view of hybrid magnetic screw. (a) Circular side view, (b) Axial side view; FIG. 3 is a schematic of the operation principle; FIG. 4 is a schematic diagram of magnetic field distribution of hybrid magnetic screw. (a) Aligned position, (b) Adjustable thrust force position; FIG. 5 is the air-gap helical magnetic field harmonic order; FIG. 6 is the thrust force adjustable range of the hybrid magnetic screw.

In the drawings, 1. Magnetic nut; 2. Magnetic translator; Al. Helical permanent magnet for magnetic nut 2; A2. Helical permanent magnet for magnetic nut 2; A3. Helical permanent magnet for magnetic translator 2; A4. Helical permanent magnet for magnetic translator 2; BI. Modulation module for magnetic nut 2; B2. Modulation module for magnetic translator 1; Cl. Helical coil 1; C2. Helical coil 2.

Detailed Description of the Embodiments

In order to make the objectives, technical solutions, and effects of the present invention clearer, the structural features and beneficial effects of a hybrid magnetic screw in the present invention are described in detail below with reference to the accompanying drawings and specific embodiments.

As shown in FIG. I, the magnetic nut (I) comprises a plurality of first units arranged in sequence, and each of the first units comprises a helical permanent magnet Al which is axially magnetized, a helical magnetic modulation module B 1, and a helical permanent magnet A2 which is axially magnetized. The helical magnetic modulation module B1 is sandwiched between the helical permanent magnet Al and helical permanent magnet A2. The magnetization directions of the helical permanent magnet Al and helical permanent magnet A2 are concentrated in the helical magnetic modulation module BI. The helical magnetic lead lengths of the helical permanent magnet Al, helical permanent magnet A2, and the helical magnetic modulation module BI are all 2.

comprises a plurality of second units arranged in sequence, and each of the second units comprises a helical permanent magnet A3 which is axially magnetized, a helical permanent magnet A4 which is axially magnetized, a helical magnetic modulation module B2, a helical coil Cl, and a helical coil C2. The helical magnetic modulation module B2 is sandwiched between the helical permanent magnet A3 and helical permanent magnet A4. The magnetization directions of the helical permanent magnet A3 and helical permanent magnet A4 are concentrated in the helical magnetic modulation module B2. Then, the helical coil C1 and the helical coil C2 are wound on the helical magnetic modulation module B2. The current directions of the helical coil Cl and the helical coil C2 are opposite. When the hybrid magnetic screw needs to improve a thrust force at fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are positive and negative, respectively. Similarly, when the hybrid magnetic screw needs to reduce the thrust force at the fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are negative and positive, respectively. By changing the currents amplitudes and the current directions of the helical coil Cl and the helical coil C2, the air-gap magnetic field adjustment of the hybrid magnetic screw is realized. The helical magnetic lead lengths of the helical permanent magnet A3, helical permanent magnet A4, the helical magnetic modulation module B2, the helical coil Cl and the helical coil C2 are all 2.

As shown in FIG. 2, a cross-sectional view of the hybrid magnetic screw is given. It can be seen that the circumferential and axial magnetic fields range from 0 to 27c and 0 to 2, respectively. In the magnetic translator (2), the permanent magnetic field generated by the helical permanent magnet A3 and helical permanent magnet A4. Then, the permanent magnetic field is modulated by the helical magnetic modulation module B2. In addition, in the magnetic translator (2), the helical coil Cl and the helical coil C2 are wound in the "E-type" slot.

As shown in FIG. 3, when the magnetic translator (2) generates axially displacement, the magnetic field distributions alone the axially becomes significant, resulting in the development of thrust force. Then, the helical coil Cl and the helical coil C2 are wound in the "E-type" slot. According to the operating conditions, currents of different directions and amplitudes are injected into the helical coil Cl and the helical coil C2, and the air-gap magnetic field can be adjusted. Then the thrust force of the fixed operating point can be adjusted, and the positioning precision is also improved.

As shown in FIG. 4, the schematic magnetic field distributions of the hybrid magnetic screw at two typical positions. As shown in FIG. 4(a), when the magnetic poles on both the magnetic nut (1) and the magnetic translator (2) are aligned with each other, the magnetic field distribution is symmetrical. Then, when the magnetic translator (2) generates axially displacement, the magnetic field distributions alone the axially becomes significant. In addition, the axial length of the helical permanent magnet Al, helical permanent magnet A2, helical permanent magnet A3 and helical permanent magnet A4, the axial length of the helical modulation module B1 and the helical modulation module B2, and the axial length of the "E-type" slot are optimized. The optimization of the permanent magnetic field and excitation magnetic field is realized to reduce the magnetic coupling.

As shown in FIG. 5, by extracting the magnetic flux density within an axial magnetic lead A, the 1st, 3rd and 5th harmonic orders can be obtained in the axial direction. Similarly, by extracting the magnetic flux density within a circle of 2r, the l', 31.11, and 5 th harmonic orders can be obtained in the circle direction. The innovation of this hybrid magnetic screw is achieved fully helical magnetic coupled, which satisfies the modulation in the circumferential and axial direction, respectively.

As shown in FIG. 6, the feasibility of the above modulation principle is verified, also the variation range of the thrust forces are verified.

Claims

Claims What is claimed is: 1. A hybrid magnetic screw with high positioning precision, characterized by comprising a magnetic nut (1) and a magnetic translator (2) in turn from outside to inside, wherein the magnetic nut (1) and the magnetic translator (2) are placed coaxially, there is an air-gap between the magnetic nut (1) and the magnetic translator (2), and a length of the air-gap is selected based on a size and requirement of the magnetic screw; the magnetic nut (1) comprises a plurality of first units arranged in sequence, and each of the first units comprises a helical permanent magnet Al which is axially magnetized, a helical magnetic modulation module Bl, and a helical permanent magnet A2 which is axially magnetized; the magnetic translator (2) comprises a plurality of second units arranged in sequence, and each of the second units comprises a helical permanent magnet A3 which is axially magnetized, a helical permanent magnet A4 which is axially magnetized, a helical magnetic modulation module B2, the helical coil CI, and a helical C2; the helical coil C 1 and the helical coil C2 are wound on the helical magnetic modulation module B2, the current directions of the helical coil C1 and the helical coil C2 are opposite; when the hybrid magnetic screw needs to improve a thrust force at fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are positive and negative, respectively; similarly, when the hybrid magnetic screw needs to reduce the thrust force at the fixed operating point, the amplitudes of the helical coil Cl and the helical coil C2 are negative and positive, respectively; by changing the currents amplitudes and the current directions of the helical coil C1 and the helical coil C2, the air-gap magnetic field adjustment of the hybrid magnetic screw is realized; in the magnetic nut (1), the permanent magnetic field is generated by the helical permanent magnet Al and the helical permanent magnet A2, the permanent magnetic field is modulated by the helical magnetic modulation module B1, and then, the 1S1, 3d, and 5'h harmonics are generated in axial and circumferential directions; similarly, in the magnetic translator (2), a permanent magnetic field is generated by the helical permanent magnet A3 and the helical permanent magnet A4, and the permanent magnetic field is modulated by the helical magnetic modulation module B2, and then, the same harmonics as the magnetic nut (1) are generated, and by adjusting the current amplitudes and the current directions in the helical coil Cl and the helical coil C2 to adjust amplitudes of the harmonics, the multi-harmonics modulation of the magnetic nut (1) and the magnetic translator (2) is realized; the magnetization directions of the helical permanent magnet Al and the helical permanent magnet A2 are concentrated in the helical magnetic modulation module B1, and magnetization directions of the helical permanent magnet A3 and the helical permanent magnet A4 are concentrated in the helical magnetic modulation module B2, in which a principle of minimum reluctance is adopted, and a helical permanent magnetic field is drawn out through the helical magnetic modulation module B1 and the helical magnetic modulation module B2.
2. The hybrid magnetic screw with high positioning precision according to claim 1, characterized in that the magnetic nut (1), the helical magnetic lead lengths of the helical permanent magnet Al and the helical permanent magnet A2, and the helical magnetic modulation module B1 are all A, the axial lengths of the helical permanent magnet Al and the helical permanent magnet A2 are the same, which can be expressed as //,,,,=1/2-4, where I is the axial length of the helical magnetic modulation module Bl.
3. The hybrid magnetic screw with high positioning precision according to claim I, characterized in that the magnetic translator (2), the helical magnetic lead lengths of the helical permanent magnet A3 and the helical permanent magnet A4, the helical magnetic modulation module B2, the helical coil C1, and the helical coil C2 are all A, the axial lengths of the helical permanent magnet A3 and the helical permanent magnet A4 are same as the helical permanent magnet At and the helical permanent magnet A2, in helical magnetic modulation module B2, the axial length of the modulated tooth can be expressed as /,=(6-21,,)/3, where 4, is the axial length of the helical coil Cl and the helical coil C2.
4. The hybrid magnetic screw with high positioning precision according to claim 1, characterized in that the topologies of the helical magnetic modulation module B1 and the helical magnetic modulation module B2 are both designed as the "E-type" structures.
5. A design method of multi-harmonics modulation for the hybrid magnetic screw with high positioning precision according to claim 1, characterized by comprising the following steps: step 1: the magnetic lead lengths of the helical permanent magnet Al, the helical permanent magnet A2, and the helical magnetic modulation module B1 are all 2, it should be noted that the helical magnetic lead lengths of the helical magnetic lead lengths of the helical permanent magnet A3 and the helical permanent magnet A4, the helical magnetic modulation module B2, the helical coil Cl, and the helical coil C2 are also).; step 2: the lengths of helical magnetic lead >I of magnetic nut (1) and magnetic translator (2) are consistent; then, the axial lengths of the helical permanent magnet Al, the helical permanent magnet A2, the helical permanent magnet A3, the helical permanent magnet A4 are all /p,,,, then, the axial lengths of the helical magnetic modulation module B1 and the helical magnetic modulation module B2 are all I,, moreover, the topologies of the helical magnetic modulation module B1 and the helical magnetic modulation module B2 are both designed as the "E-type" structures, the axial lengths of the modulated tooth are which satisfy the multi-harmonic modulation of the hybrid magnetic screw; step 3: take the circumferential and axial cross-sectional view of the hybrid magnetic screw, respectively, the circumferential and axial magnetic fields range from 0 to 27r and 0 to 2, respectively, by extracting the magnetic flux density within an axial magnetic lead A, the st, 3rd, and 5'1' harmonic orders can be obtained in the axial direction, similarly, by extracting the magnetic flux density within a circle of 2ir, the PE 3rd and 5th harmonic orders can be obtained in the circle direction, therefore, the innovation of this hybrid magnetic screw is achieved fully helical magnetic coupled, which satisfies the modulation in the circumferential and axial direction, respectively; step 4: in the helical magnetic modulation module B2, the helical coil Cl and the helical coil C2 are wound in the "E-type" slot, according to the operating conditions, currents of different directions and amplitudes are injected into the helical coil Cl and the helical coil C2, and the air-gap magnetic field can be adjusted, then, the harmonic amplitudes of different orders are changed; step 5: the air-gap magnetic field densities of hybrid magnetic screw are subjected to Fourier analysis in the circumferential and axial direction, respectively, the feasibility of the above modulation principle is verified, also the thrust density and positioning precision of the proposed hybrid magnetic screw are verified.
6. The design method according to claim 5, characterized in that the magnetization directions of the helical permanent magnet Al, the helical permanent magnet A2 are concentrated in the helical magnetic modulation module Bl; the magnetization directions of the helical permanent magnet A3, the helical permanent magnet A4 are concentrated in the helical magnetic modulation module B2, in the above methods, the principle of minimum reluctance is adopted, and the helical permanent magnetic field is drawn out through the helical magnetic modulation module B1 and the helical magnetic modulation module B2, which significantly reduces the leakage of the magnetic field.
7. The design method according to claim 5, characterized in that the magnetic nut (1), the helical magnetic lead lengths of the helical permanent magnet Al, the helical permanent magnet A2, and the helical magnetic modulation module B1 are all A, the axial lengths of the helical permanent magnet Al and the helical permanent magnet A2 are same as the helical permanent magnet A3 and the helical permanent magnet A4, in the helical magnetic modulation module B 1, the axial lengths of the modulated tooth I,. are same as the modulated tooth in the helical magnetic modulation module B2.