Permanent magnet auxiliary synchronous reluctance motor based on mixed silicon steel material

Abstract

The invention provides a permanent magnet auxiliary synchronous reluctance motor based on a mixed silicon steel material, and belongs to the field of novel topology of motors, and the permanent magnet auxiliary synchronous reluctance motor comprises a stator and a rotor which are coaxially arranged; an air gap with uniform length exists in the radial direction between the rotor and the stator; the rotor comprises a permanent magnet, a main magnetic circuit and a central magnetic bridge; the permanent magnet is arranged in the rotor magnetic barrier; the central magnetic bridge passes through the center of each layer of magnetic barrier; the cross section of the central magnetic bridge magnetic steel is in a strip shape with smooth boundaries, and the widths of the central magnetic bridge magnetic steel and the joint part in each layer of magnetic barrier are fixed and are not related; the central magnetic bridge is used for supporting the rotor multi-layer magnetic barrier structure and providing a magnetic circuit for the straight-axis flux linkage. The motor rotor is high in rigidity, high in salient pole ratio and obvious in reluctance torque component.

Description

Technical Field

[0001] The present application belongs to the field of novel topologies of electric motors, and more specifically, to a permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material. Background Art

[0002] The permanent magnet assisted synchronous reluctance motor combines the characteristics of permanent magnet synchronous motor and synchronous reluctance motor, and has been widely used in household appliances, transportation, aerospace and industrial production. Compared with permanent magnet synchronous motor, permanent magnet assisted synchronous reluctance motor has low dependence on high-performance rare earth permanent magnet materials and low cost. Compared with synchronous reluctance motor, permanent magnet assisted synchronous reluctance motor increases permanent magnet torque and improves power density.

[0003] In order to improve the reluctance torque of the motor, the rotor structure of the permanent magnet assisted synchronous reluctance motor mostly adopts the design concept of multi-layer magnetic barriers of the synchronous reluctance motor, including square, arc, "U" type, streamlined and hybrid magnetic barriers. At the same time, in order to improve the power density of the motor, permanent magnets are installed in the above-mentioned magnetic barriers. However, the above-mentioned rotor structure poses a challenge to the high-speed operation of the permanent magnet assisted synchronous reluctance motor. The complex multi-layer magnetic barrier structure and the embedded permanent magnets may cause the rotor core to deform or even break under the action of mechanical compressive stress, which seriously affects the reliability of the motor. If the speed is reduced so that the rotor meets the mechanical stress requirements, the power density of the motor will also decrease.

[0004] In addition, complex rotor magnetic circuit design often causes the problem of local rotor core saturation, which reduces the torque output capacity of the motor and has an adverse effect on the power density of the motor. Especially in the fields of aerospace and electric vehicles with limited space and high loss density, power density is a key indicator for the successful application of motors. Therefore, it is necessary to urgently study new permanent magnet assisted synchronous reluctance motor topologies that take into account both motor power density and rotor stiffness. Summary of the invention

[0005] In view of the defects of the prior art, the purpose of this application is to provide a permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material, aiming to solve the problem that the power density and mechanical strength of the existing permanent magnet assisted synchronous reluctance motor are mutually restricted, resulting in poor motor reliability, low power density and low torque output capacity.

[0006] To achieve the above-mentioned objectives, in the first aspect, the present application provides a rotor, comprising: permanent magnets, a main magnetic circuit and a central magnetic bridge; the permanent magnets are installed in the rotor magnetic barriers; the central magnetic bridge passes through the center of each layer of magnetic barriers; the cross-section of the central magnetic bridge magnetic steel is a long strip with smooth boundaries, and the width of the intersection with each layer of magnetic barriers is fixed, and the widths are independent of each other; the central magnetic bridge is used to support the rotor multi-layer magnetic barrier structure and provide a magnetic circuit for the direct-axis magnetic flux.

[0007] In the second aspect, the present application provides a permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material, comprising: a stator and a rotor arranged coaxially; there is an air gap of uniform length in the radial direction between the rotor and the stator; the rotor comprises: permanent magnets, a main magnetic circuit and a central magnetic bridge; the permanent magnets are installed in the rotor magnetic barriers; the central magnetic bridge passes through the center of each layer of magnetic barriers; the cross-section of the central magnetic bridge magnetic steel is a long strip with smooth boundaries, and the width of the intersection with each layer of magnetic barriers is fixed, and the widths are independent of each other; the central magnetic bridge is used to support the rotor multi-layer magnetic barrier structure and provide a magnetic circuit for the direct-axis magnetic flux.

[0008] Further preferably, the stator includes a hollow cylindrical stator core and a conductive coil; the stator core has a plurality of stator teeth evenly distributed along the circumferential direction, the stator teeth face the rotor direction, there are stator slots between adjacent stator teeth, a conductive coil is arranged in each stator slot, and the conductive coil is energized or de-energized.

[0009] Further preferably, the rotor has three magnetic barrier layers; the magnetic barrier is streamlined, and the shape of the magnetic barrier is determined by streamlined equipotential lines.

[0010] Further preferably, the number of rotor poles is eight, and the rotor structure of each pole is centrally symmetrical; the number of permanent magnets per pole is six, which are evenly distributed in each layer of magnetic barriers.

[0011] Further preferably, the central magnetic bridge is perpendicular to each layer of magnetic barriers and passes through the center of each layer of magnetic barriers, and the width of the magnetic bridge gradually increases from the inner layer of magnetic barriers to the outer layer of magnetic barriers.

[0012] Further preferably, two ends of the central magnetic bridge are provided with I-shaped clamping positions, and the ends of the clamping positions are in a smooth wedge shape.

[0013] Further preferably, the stator and the main magnetic circuit are made of high saturation magnetic induction intensity iron-cobalt-vanadium soft magnetic alloy material, which is stacked by silicon steel sheets; the central magnetic bridge is made of high-strength non-oriented silicon steel material; and the permanent magnet is made of high remanence samarium cobalt permanent magnet material.

[0014] On the third aspect, based on the above-mentioned rotor, the present application provides a method for installing the rotor, specifically: installing the main magnetic circuit on the rotating shaft, inserting the central magnetic bridge into the central empty slot of the main magnetic circuit, and then installing the permanent magnet in the rotor magnetic barrier.

[0015] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art:

[0016] The present application provides a rotor, including a central magnetic bridge, which passes through the center of each layer of magnetic barriers. The central magnetic bridge is made of high-strength silicon steel material with large magnetic resistance, so the central magnetic bridge width has a high degree of freedom in design, which is beneficial to improving the stiffness of the motor rotor.

[0017] The present application provides a permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material, wherein the magnetic resistance of the central magnetic bridge is much greater than the magnetic resistance of the main magnetic circuit. The proposed permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material has a high salient pole ratio and an obvious reluctance torque component.

[0018] The permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material provided in the present application adopts high-strength silicon steel material to support the multi-layer magnetic barrier structure, which improves the upper limit of rotor stress compared with the prior art, so it has good rotor stiffness and is suitable for high-speed operation. In addition, the volume and mass of the permanent magnets embedded in the rotor are less constrained by mechanical strength, which can effectively improve the magnetic load and electromagnetic torque of the motor. The proposed permanent magnet assisted synchronous reluctance motor can achieve higher power density. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a cross-sectional view of a conventional permanent magnet assisted synchronous reluctance motor provided in an embodiment of the present application;

[0020] Figure 2 is a cross-sectional view of a permanent magnet assisted synchronous reluctance motor provided in an embodiment of the present application;

[0021] FIG3( a ) is a diagram showing the rotor magnetic lines of force of a conventional permanent magnet assisted synchronous reluctance motor provided in an embodiment of the present application at a current angle of 0°;

[0022] FIG3( b ) is a diagram showing the rotor magnetic lines of force of the permanent magnet assisted synchronous reluctance motor of the present application at a current angle of 0° provided by an embodiment of the present application;

[0023] FIG4( a ) is a diagram showing the rotor magnetic lines of force of a conventional permanent magnet assisted synchronous reluctance motor provided in an embodiment of the present application at a current angle of 90°;

[0024] FIG4( b ) is a diagram showing the rotor magnetic lines of force of the permanent magnet assisted synchronous reluctance motor of the present application at a current angle of 90° provided by an embodiment of the present application;

[0025] Figure 5 This is a comparison diagram of simulated torques of the permanent magnet assisted synchronous reluctance motor provided in an embodiment of the present application and a traditional permanent magnet assisted synchronous reluctance motor. DETAILED DESCRIPTION

[0026] The following specific implementation is provided below to help the reader gain a comprehensive understanding of the method described herein. However, after understanding the disclosure of the present application, various variations, modifications and equivalents of the methods, devices and / or devices described herein will be apparent. For example, the motor topology described herein is merely an example and is not limited to the topology set forth herein, but in addition to the structure that must be designed in a specific form, changes may be made that will be apparent after understanding the disclosure of the present application. In addition, in order to improve clarity and conciseness, feature descriptions known in the art may be omitted. In order to enable those skilled in the art to better understand the present invention, specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0027] The present application provides a novel permanent magnet assisted synchronous reluctance motor topology based on hybrid silicon steel material, including a stator and a rotor; the rotor includes: a permanent magnet part, a main magnetic circuit part and a central magnetic bridge part; wherein the permanent magnet is installed in the rotor magnetic barrier, and the central magnetic bridge passes through the center of each layer of magnetic barrier; the cross-section of the central magnetic bridge magnetic steel is a long strip with smooth boundaries, and the width of the intersection with each layer of magnetic barrier is fixed, and the widths are independent of each other; the function of the central magnetic bridge part is to support the rotor multi-layer magnetic barrier structure and provide a magnetic circuit for the direct-axis magnetic flux.

[0028] Further preferably, the number of magnetic barrier layers of the rotor is three, taking into account the thickness of each magnetic barrier layer and the width of the main magnetic path; the magnetic barrier is streamlined, and in order to maximize the salient pole effect of the motor rotor, the streamlined equipotential lines are used to determine the shape of the magnetic barrier, which is determined by Joukowski airfoil formulas (1) and (2);

[0029] More specifically, it is determined by the Joukowski airfoil formula:

[0030]

[0031] Where r is the radius, θ is the angle with the d-axis; D ri is the inner diameter of the rotor; p is the number of motor pole pairs, and Ψ is the equipotential line constant, which is a constant value for a given equipotential line and can be calculated using the following formula:

[0032]

[0033] For any equipotential line, if a point on it can be determined, the value of the equipotential line constant can be calculated, and then the streamlined equipotential line can be drawn using formula (1);

[0034] Further preferably, the number of rotor poles is eight, and the rotor structure of each pole is centrosymmetrical;

[0035] Further preferably, the number of permanent magnets per pole is six, which are evenly distributed in each layer of magnetic barriers;

[0036] Further preferably, the central magnetic bridge is perpendicular to each layer of magnetic barriers and passes through the center position of each layer of magnetic barriers;

[0037] Further preferably, the width of the central magnetic bridge crossing the magnetic barrier is fixed, and the width of the magnetic bridge of each layer of magnetic barrier is independent of each other, and the width of the magnetic bridge gradually increases from the inner layer of magnetic barrier to the outer layer of magnetic barrier;

[0038] Further preferably, "I"-shaped latches are provided at both ends of the central magnetic bridge portion, the ends of the latches are in a smooth wedge shape, and the boundaries of the central magnetic bridge are all smooth curves.

[0039] Further preferably, the main magnetic circuit parts of the stator and the rotor are made of high saturation magnetic induction intensity iron-cobalt-vanadium soft magnetic alloy material, which is laminated by silicon steel sheets;

[0040] Further preferably, the central magnetic bridge part of the rotor is made of high-strength non-oriented silicon steel material, and the part is an integral magnetic bridge block;

[0041] Further preferably, the rotor permanent magnet part is made of high remanence samarium cobalt permanent magnet material, and the part is composed of six permanent magnet blocks;

[0042] More specifically, the rotor is installed as follows: first, the main magnetic circuit part formed by stacking high magnetic permeability silicon steel sheets is installed on the rotating shaft, then a high-strength silicon steel central magnetic bridge is inserted into the central empty slot of the main magnetic circuit part, and finally, permanent magnets are installed in the rotor magnetic barrier.

[0043] The novel permanent magnet assisted synchronous reluctance motor provided in the present application is beneficial to improving the power density of the motor while taking into account the mechanical strength of the rotor.

[0044] Example

[0045] Figure 1 This is a cross-sectional view of a conventional permanent magnet assisted synchronous reluctance motor. Due to the symmetry of the electrode topology under each pole, only one eighth of the cross section is given. There is an air gap of uniform length in the radial direction between the rotor and the stator. The stator may include a hollow cylindrical stator core and a conductive coil. The stator core has a number of stator teeth evenly distributed along the circumference, the stator teeth face the rotor direction, and there are stator slots between adjacent stator teeth. A conductive coil can be set in each stator slot and the coil can be powered on / off. Both the rotor core and the stator core can be formed by stacking multiple layers of silicon steel sheets. The stator can adopt the existing stator topology, which will not be described in detail here. The main parameters of this topology are shown in Table 1.

[0046] Table 1

[0047] Parameter name Numeric Stator outer diameter (mm) 190.0 Stack length(mm) 194.0 Stator inner diameter (mm) 140.4 Number of stator slots 48 Pole pairs 4 Air gap length(mm) 2.2 Inner permanent magnet width (mm) 9.3 Width of middle layer permanent magnet (mm) 11.0 Outer permanent magnet width (mm) 13.8

[0048] The novel permanent magnet assisted synchronous reluctance motor topology based on hybrid silicon steel material involved in the present application includes a rotor and a stator arranged coaxially; according to the structure of the above-mentioned traditional permanent magnet assisted synchronous reluctance motor, the embodiment of the present application proposes a novel permanent magnet assisted synchronous reluctance motor topology based on hybrid silicon steel material, Figure 2 is a cross-sectional view of the proposed permanent magnet assisted synchronous reluctance motor. Figure 1 Schematic diagram of a variant example of a permanent magnet assisted synchronous reluctance motor. For the sake of fairness in comparison, the embodiment of the present application does not adopt a streamlined magnetic barrier structure, but adopts Figure 1 The same “U” type magnetic barrier structure as the permanent magnet assisted synchronous reluctance motor shown; Figure 2 The main parameters of the motor topology and Figure 1 The conventional permanent magnet assisted synchronous reluctance motor is shown in Table 1.

[0049] The stator core material and the rotor main magnetic circuit part of the permanent magnet assisted synchronous reluctance motor provided in the embodiment of the present application are made of high saturation magnetic induction intensity iron-cobalt-vanadium soft magnetic alloy material, the central magnetic bridge part of the rotor is made of high strength non-oriented silicon steel material, and the permanent magnet material is made of high remanence samarium cobalt permanent magnet.

[0050] In the embodiment of the present application, the motor slot-pole combination is preferably 48 slots and 8 poles, and the stator winding adopts a double-layer short-distance five-pole distributed winding; in the embodiment of the present application, the rotor magnetic barrier is preferably a three-layer "U" shape, and each layer of the magnetic barrier is a symmetrical structure; Figure 1 Compared with the conventional permanent magnet assisted synchronous reluctance motor shown, the number of magnetic barrier layers, position, length and width of the embodiment of the present application remain unchanged, but the embodiment of the present application eliminates the magnetic bridge between the magnetic barriers on both sides and the central magnetic barrier.

[0051] The preferred number of permanent magnets in the embodiment of the present application is six, which are evenly distributed in each layer of magnetic barriers, and the permanent magnets in different magnetic barrier layers are parallel to each other; the amount of permanent magnets in the embodiment of the present application is Figure 1 The permanent magnet assisted synchronous reluctance motors shown are identical and the amount of permanent magnets in each layer of magnetic barriers is also consistent, with only slight differences in distribution positions.

[0052] In the embodiment of the present application, the central magnetic bridge is preferably perpendicular to each layer of magnetic barriers and passes through the center of each layer of magnetic barriers; the width of the central magnetic barrier passing through the magnetic barrier is fixed, and the width of the magnetic bridge of each layer of magnetic barriers is independent of each other, and the width of the magnetic bridge gradually increases from the outer layer of magnetic barriers to the inner layer of magnetic barriers; wedge-shaped clamps are provided at both ends of the central magnetic bridge part, and the boundaries of the central magnetic bridge are all smooth curves.

[0053] and Figure 1 Compared with the conventional permanent magnet assisted synchronous reluctance motor shown in FIG, the central magnetic bridge of the embodiment of the present application adopts high-strength non-oriented silicon steel material, which has better mechanical strength than conventional iron core material, so it can be Figure 1The three magnetic bridges of the conventional permanent magnet assisted synchronous reluctance motor shown in the figure are all concentrated in the center to form an embedded high-strength central magnetic bridge. The central magnetic bridge has a high degree of freedom in the width of each layer of magnetic barriers. The embodiment of the present application simply Figure 1 The three magnetic bridges of the conventional permanent magnet assisted synchronous reluctance motor shown in the figure are added to obtain the central magnetic bridge width, which can be flexibly adjusted in specific applications; Table 2 is Figure 1 The width of each layer of the three magnetic bridges in the conventional permanent magnet assisted synchronous reluctance motor is shown in Figure 1. Figure 2 The central magnetic bridge width of the embodiment of the present application is shown.

[0054] Table 2

[0055]

[0056] The magnetic resistance of high-strength non-oriented silicon steel material is higher than that of conventional core material, so the widened central magnetic bridge will not significantly increase the quadrature-axis inductance; Figure 3(a) and Figure 3(b) are respectively when the current phase angle is 0° and the effective current value is 498A. Figure 1 The conventional permanent magnet assisted synchronous reluctance motor shown in Figure 2 The rotor magnetic density cloud diagram of the embodiment of the present application is shown; it can be seen that the magnetic lines of force in the rotor of the conventional permanent magnet assisted synchronous reluctance motor and the embodiment of the present application hardly cross the rotor boundary, which indicates that the magnetic resistance of the quadrature axis magnetic circuit is large; Figure 4 (a) and Figure 4 (b) are respectively when the current phase angle is 90° and the effective value of the current is 498A, Figure 1 The conventional permanent magnet assisted synchronous reluctance motor shown in Figure 2 The rotor magnetic density cloud diagram of the embodiment of the present application is shown; it can be seen that the vast majority of magnetic lines of force come from outside the rotor boundary, indicating that the magnetic resistance of the direct axis magnetic circuit is small; the above simulation results prove that the rotor salient polarity of the embodiment of the present application is not reduced due to the use of mixed silicon steel material;

[0057] Figure 5 When the current phase angle is 45° and the effective current value is 1287A, Figure 1 The conventional permanent magnet assisted synchronous reluctance motor shown in Figure 2 The torque waveform of the embodiment of the present application is shown; the average torque of the traditional permanent magnet assisted synchronous reluctance motor topology is 411.96 Nm, and the torque pulsation is 8.68%; the average torque of the embodiment of the present application is 458.47 Nm, and the torque pulsation is 8.68%. It can be seen that the output power of the embodiment of the present application is 11.3% higher than that of the traditional permanent magnet assisted synchronous reluctance motor, and the torque pulsation is slightly increased; considering that the mechanical strength of the embodiment of the present application is higher than that of the traditional permanent magnet assisted synchronous reluctance motor, the amount of permanent magnets used can be further increased, and the central magnetic bridge structure can be further optimized. Therefore, the output torque of the embodiment of the present application still has huge room for improvement.

[0058] In summary, compared with the prior art, the present application has the following advantages:

[0059] The high-strength silicon steel material used in the central magnetic bridge of the motor rotor has a large magnetic resistance, so the design freedom of the central magnetic bridge width is high, which is beneficial to improving the stiffness of the motor rotor.

[0060] The magnetic resistance of the central magnetic bridge of the motor rotor is much larger than the magnetic resistance of the main magnetic circuit. The proposed new permanent magnet assisted synchronous reluctance motor topology based on hybrid silicon steel material has a high salient pole ratio and an obvious reluctance torque component.

[0061] The motor topology proposed in this application has good rotor stiffness and is suitable for high-speed operation. The volume and mass of the permanent magnets embedded in the rotor are less constrained by mechanical strength, which can effectively improve the magnetic load and electromagnetic torque of the motor. The proposed new permanent magnet assisted synchronous reluctance motor topology can achieve higher power density.

[0062] In the description of the embodiments of the present application, it should be noted that, unless otherwise clearly specified and limited, the term "connection" should be understood in a broad sense.

[0063] In addition, in the embodiments of the present application, the mathematical concepts mentioned, such as symmetry, equality, parallelism, and perpendicularity, are all limited to the current technological level, rather than being absolutely strict definitions in the mathematical sense, and a small amount of deviation is allowed, such as approximately symmetry, approximately equality, approximately parallelism, and approximately perpendicularity.

[0064] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A rotor, characterized in that: include: Permanent magnets, main magnetic circuit and central magnetic bridge; permanent magnets are installed in the rotor magnetic barriers; the central magnetic bridge passes through the center of each layer of magnetic barriers; the cross-section of the central magnetic bridge magnetic steel is a long strip with smooth boundaries, and the width of the intersection with each layer of magnetic barriers is fixed and independent of each other; the central magnetic bridge is used to support the rotor multi-layer magnetic barrier structure and provide a magnetic circuit for the direct-axis magnetic flux.

2. A permanent magnet assisted synchronous reluctance motor based on hybrid silicon steel material, characterized in that: include: A stator and a rotor arranged coaxially; There is an air gap of uniform length in the radial direction between the rotor and the stator; The rotor includes: permanent magnets, main magnetic circuit and central magnetic bridge; Permanent magnets are installed in the rotor magnetic barriers; the central magnetic bridge passes through the center of each layer of magnetic barriers; the cross-section of the central magnetic bridge magnetic steel is a long strip with smooth boundaries, and the width of the intersection with each layer of magnetic barriers is fixed and independent of each other; the central magnetic bridge is used to support the rotor multi-layer magnetic barrier structure and provide a magnetic path for the direct-axis magnetic flux.

3. The permanent magnet assisted synchronous reluctance motor according to claim 2, characterized in that: The stator includes a hollow cylindrical stator core and a conductive coil; the stator core has a number of stator teeth evenly distributed along the circumference, the stator teeth face the rotor direction, there are stator slots between adjacent stator teeth, a conductive coil is arranged in each stator slot, and the conductive coil is energized or de-energized.

4. The permanent magnet assisted synchronous reluctance motor according to claim 2, characterized in that: The rotor has three layers of magnetic barriers; the magnetic barriers are streamlined, and the shape of the magnetic barriers is determined by streamlined equipotential lines.

5. The permanent magnet assisted synchronous reluctance motor according to any one of claims 2 to 4, characterized in that: The rotor has eight poles, and the rotor structure of each pole is centrally symmetrical; there are six permanent magnets per pole, which are evenly distributed in each layer of magnetic barriers.

6. The permanent magnet assisted synchronous reluctance motor according to claim 2, characterized in that: The central magnetic bridge is perpendicular to each layer of magnetic barriers and passes through the center of each layer of magnetic barriers. The width of the magnetic bridge gradually increases from the inner layer of magnetic barriers to the outer layer of magnetic barriers.

7. The permanent magnet assisted synchronous reluctance motor according to claim 2 or 6, characterized in that: I-shaped clamping positions are arranged at both ends of the central magnetic bridge, and the end of the clamping position is in a smooth wedge shape.

8. The permanent magnet assisted synchronous reluctance motor according to claim 2, characterized in that: The stator and main magnetic circuit are made of high saturation magnetic induction intensity iron-cobalt-vanadium soft magnetic alloy material, which is stacked by silicon steel sheets; the central magnetic bridge is made of high-strength non-oriented silicon steel material; the permanent magnet is made of high remanence samarium cobalt permanent magnet material.

9. A method for installing a rotor according to claim 1, characterized in that: Specifically, the main magnetic circuit is installed on the rotating shaft, the central magnetic bridge is inserted into the central empty slot of the main magnetic circuit, and then the permanent magnet is installed in the rotor magnetic barrier.

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