An analytical method for analyzing the loss characteristics of magnetic gears

Abstract

This invention relates to an analysis method for the loss characteristics of magnetic gears, belonging to the technical field of magnetic gear reducers for air turbine starters. The loss characteristic analysis method of this invention obtains the characteristics of the magnetic gear by analyzing the magnetic field harmonic distribution in the inner and outer air gaps between the stator of the adjusting magnetic ring and the inner and outer rotors. This results in accurate and widely applicable loss characteristic analysis results. Furthermore, it enables loss analysis and evaluation of magnetic gears under different connecting bridge structural configurations, enhancing the universality of magnetic gear loss characteristic analysis.

Description

Technical Field

[0001] This invention belongs to the technical field of magnetic gear reducers for air turbine starters, and specifically relates to an analysis method for the loss characteristics of magnetic gears, particularly an analysis method for the loss characteristics of magnetic gears in air turbine starters. Background Technology

[0002] A typical magnetic gear reducer structure mainly consists of five parts: an inner rotor, an inner rotor permanent magnet, a stator with a magnetic adjustment ring, an outer rotor permanent magnet, and an outer rotor. The inner rotor has an inner rotor magnetic ring, the outer surface of which has N-pole and S-pole permanent magnets arranged alternately with a small number of pole pairs. The permanent magnet surfaces are attached to a support frame and bound with a carbon fiber sheath to ensure structural strength at high speeds. The outer rotor has an outer rotor magnetic ring, the inner surface of which has N-pole and S-pole permanent magnets with a large number of pole pairs. The permanent magnets are embedded in the support frame, and epoxy resin is applied between the permanent magnets and the support frame for fixation. The stator with the magnetic adjustment ring is composed of alternating magnetic and non-magnetic materials, which modulate the magnetic field. The magnetic materials are made of amorphous superimposed materials, arranged alternately, with thermosetting plastic filling the spaces between them, which improves structural strength and reduces structural weight. There are inner and outer air gaps between the inner and outer rotor magnetic guide rings and the adjusting magnetic ring stator, respectively. The magnetic field harmonics in the inner and outer air gaps couple with each other, enabling the magnetic gear to work stably.

[0003] Magnetic gears are energy transmission devices in magnetic gear reducers, and loss and transmission efficiency are important indicators for evaluating their performance. However, in recent years, the research on the loss variation law and influence of magnetic gears by scholars has the following shortcomings: (1) The finite element method is the main method, and the theoretical analysis of the working magnetic field distribution and loss characteristics of magnetic gears is not perfect, resulting in inaccurate analysis results. (2) Existing loss characteristic analysis methods mainly focus on the loss characteristics of a certain component of the magnetic gear, and no loss characteristic analysis method for the entire magnetic gear has been given, making it difficult to compare the overall loss characteristics of magnetic gears with differences in component structures. Summary of the Invention

[0004] In view of the above problems, the present invention provides an analysis method for the loss characteristics of magnetic gears, which solves the problems of inaccurate analysis results of magnetic gear loss and difficulty in directly comparing the overall loss characteristics of magnetic gears under different structural forms in the prior art. It provides an analysis method for the overall loss characteristics of magnetic gears applicable to multiple structural forms, so as to achieve the goal of optimizing the loss characteristics of magnetic gears.

[0005] This invention provides an analysis method for the loss characteristics of magnetic gears, specifically including the following steps:

[0006] Step 1: Determine the parameters and materials of the magnetic gear according to the design requirements; establish a finite element analysis model of the magnetic gear based on the determined magnetic gear parameters and materials;

[0007] Step 2: Based on the finite element analysis model of the magnetic gear, obtain the simulated magnetic field line distribution and simulated magnetic field change frequency of the magnetic gear, and compare and verify them with the judgment conditions;

[0008] Step 3: Based on the eddy current loss model and the iron loss separation model, obtain the overall energy loss of the magnetic gear and its variation with the speed of the outer rotor;

[0009] Step 4: Analyze the transmission efficiency of the magnetic gear and its variation with the rotational speed of the outer rotor;

[0010] Step 5: Determine whether the overall energy loss of the magnetic gears obtained in Steps 3 and 4 and its variation with the speed of the outer rotor, as well as the transmission efficiency and its variation with the speed of the outer rotor, meet the optimal structural index. If they meet the optimal structural index, obtain the magnetic gear with the optimal structure.

[0011] Optionally, the design requirement is the gear ratio of the air turbine starter.

[0012] Optionally, the magnetic gear includes an inner rotor, an outer rotor, an inner rotor permanent magnet, an outer rotor permanent magnet, and a magnetic ring stator; the magnetic ring stator can be configured in the following ways: without a connecting bridge, with an internal connecting bridge, with an external connecting bridge, or with a double connecting bridge; finite element analysis is performed on the magnetic gear with a magnetic ring stator of the following types to obtain the finite element analysis model of the magnetic gear.

[0013] Optionally, the specific steps of step 2 are as follows: when the inner rotor permanent magnet and the outer rotor permanent magnet work simultaneously, the magnetic gear finite element analysis model of the magnetic ring stator based on the different setting methods is used to simulate and obtain the simulated magnetic field line distribution and simulated magnetic field change frequency of the corresponding magnetic gear.

[0014] Determine whether the simulated magnetic field line distribution of the magnetic gear meets the requirements based on the magnetic field line distribution criteria.

[0015] Determine whether the simulated magnetic field change frequency of the magnetic gear meets the requirements based on the magnetic field change frequency condition.

[0016] Optionally, the simulated magnetic field line distribution of the corresponding magnetic gear obtained in step 2 is as follows: based on the finite element analysis model of the magnetic gear of the adjusting ring stator with different settings, the simulated magnetic field line distribution of the adjusting ring stator with the corresponding settings and the simulated magnetic field line distribution in the air around the adjusting ring stator are obtained by simulation.

[0017] Optionally, the simulated magnetic field change frequency of the corresponding magnetic gear obtained in step 2 is obtained by simulating the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator, and the outer rotor, and obtaining the corresponding simulated magnetic field change frequency of the inner rotor, the adjusting magnetic ring stator, and the outer rotor through the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator, and the outer rotor.

[0018] Optionally, step 3 specifically involves: obtaining the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator, and the outer rotor; using the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator, and the outer rotor, respectively, obtaining the energy loss of the inner rotor magnetic ring, the outer rotor magnetic ring, the inner rotor permanent magnet, the outer rotor permanent magnet, and the adjusting magnetic ring stator of the magnetic gears in the different configurations; and obtaining the total energy loss of the magnetic gears from the obtained energy losses of the inner rotor magnetic ring, the outer rotor magnetic ring, the inner rotor permanent magnet, the outer rotor permanent magnet, and the adjusting magnetic ring stator of the magnetic gears in the different configurations.

[0019] Optionally, the energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and magnetic ring stator of the magnetic gear with different settings obtained in step 3 include the eddy current losses of the inner rotor permanent magnet and outer rotor permanent magnet obtained using the eddy current loss model and the core losses of the inner rotor magnetic ring, outer rotor magnetic ring, and magnetic ring stator obtained using the iron loss separation model.

[0020] Optionally, in step 3, when the inner rotor and outer rotor permanent magnets are working simultaneously, the magnetic field harmonic distribution of the inner and outer air gaps of the magnetic gears of the adjusting ring stator with different settings is obtained respectively; based on the magnetic field harmonic distribution of the inner and outer air gaps, the alternating frequency of each magnetic field harmonic and the corresponding magnetic induction intensity are obtained; based on the obtained alternating frequency of each magnetic field harmonic and the corresponding magnetic induction intensity, the eddy current loss of the inner rotor permanent magnet and the outer rotor permanent magnet is obtained.

[0021] Compared with the prior art, the present invention has at least the following beneficial effects:

[0022] (1) The loss characteristic analysis method of the present invention obtains the characteristics of the magnetic gear by analyzing the magnetic field harmonic distribution of the inner air gap and the outer air gap between the magnetic ring stator and the inner rotor and the outer rotor, so that the loss characteristic analysis results obtained are accurate and have strong applicability.

[0023] (2) The loss characteristic analysis method of the present invention can realize the loss analysis and evaluation of magnetic gears under different connecting bridge structure settings, thereby enhancing the universality of magnetic gear loss characteristic analysis. Attached Figure Description

[0024] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0025] Figure 1 This is a flowchart of the loss characteristic analysis method of the present invention;

[0026] Figures 2a-2d The present invention provides three configurations for the adjusting magnetic ring stator: a bridgeless configuration, an internally connected bridge configuration, an externally connected bridge configuration, and a double-connected bridge configuration.

[0027] Figure 3 The simulated magnetic field line distribution diagram is for the loss characteristic analysis method of the present invention;

[0028] Figure 4a The diagram shows the variation of radial and tangential magnetic induction intensity on the inner rotor, which is the method for analyzing the loss characteristics of the present invention.

[0029] Figure 4b The diagram shows the variation of radial and tangential magnetic induction intensity on the stator of the magnetic ring, which is the method for analyzing the loss characteristics of the present invention.

[0030] Figure 4c The graph shows the variation of radial and tangential magnetic induction intensity on the outer rotor of the loss characteristic analysis method of the present invention.

[0031] Figure 5a A comparison diagram showing the variation of eddy current loss of permanent magnet in magnetic gear outer rotor with rotational speed for different connecting bridge structures, as described in the analysis method of loss characteristics of this invention.

[0032] Figure 5b A comparison diagram showing the variation of the core loss of the magnetic gear outer rotor magnetic ring with the rotational speed of the different connecting bridge structures used in the loss characteristic analysis method of this invention.

[0033] Figure 5c This is a comparison chart showing the variation of core loss of the stator of the magnetic gear adjusting ring with the speed of the outer rotor for different connecting bridge structures, which is the method for analyzing the loss characteristics of the present invention.

[0034] Figure 5d This is a comparison chart showing the variation of eddy current loss of the permanent magnet in the inner rotor of the magnetic gear with the rotational speed of the outer rotor for different connecting bridge structures, which is the method for analyzing the loss characteristics of the present invention.

[0035] Figure 6 This is a comparison chart showing the variation of the overall loss of magnetic gears with the external rotor speed under different connecting bridge structures, which is the method for analyzing the loss characteristics of the present invention.

[0036] Figure 7 This is a comparison chart of the transmission efficiency of magnetic gears with different connecting bridge structures under full load, which is the basis for the loss characteristic analysis method of the present invention.

[0037] Figure 8 This is a cross-sectional schematic diagram of the overall structure of the air turbine starter of the present invention;

[0038] Figure 9 This is a schematic diagram of the overall structure of the air turbine starter of the present invention;

[0039] Figure 10 This is a cross-sectional structural diagram of the housing and guide assembly of the present invention;

[0040] Figure 11 This is a schematic diagram of the input rotor assembly of the air turbine starter of the present invention;

[0041] Figure 12 This is a cross-sectional schematic diagram of the input rotor assembly structure of the air turbine starter of the present invention;

[0042] Figure 13 This is a schematic diagram of the output rotor assembly of the present invention;

[0043] Figure 14 This is a cross-sectional schematic diagram of the output rotor assembly of the present invention;

[0044] Figure 15 This is a cross-sectional schematic diagram of the stator assembly of the air turbine starter of the present invention;

[0045] Figure 16 This is a schematic diagram of airflow inside the air turbine starter chamber of the present invention;

[0046] Figure 17 This is a schematic diagram of a single side of the magnetic gear rotor support structure of the present invention.

[0047] Figure label:

[0048] 1. Housing and guide assembly structure, 101 turbine guide, 102 guide cone, 103 bearing stator, 104 first stator cover, 105 second stator cover, 106 rear end cover, 107 shaft end seal ring, 108 output rotor positioning sleeve; 2. Input rotor assembly structure, 201 air turbine, 202 input rotor magnetic ring, 203 input rotor permanent magnet assembly, 204 input rotor sheath, 205 input rotor baffle, 206 high-speed angular contact ball bearing, 207 bearing retaining ring, 208 locking ring, 209 input rotor damper, 210 double-layer helical elastic retaining ring, 3. 301 Output rotor permanent magnet assembly, 302 Output rotor magnetic ring, 303 Output spindle, 304 Overrunning clutch, 305 Output shaft of output rotor assembly, 306 Output driven shaft, 307 Bearing spacer, 308 Angular contact ball bearing A, 309 Angular contact ball bearing B, 310 Double-layer helical elastic retaining ring for shaft, 311 Needle roller bearing A, 312 Needle roller bearing B, 4 Stator assembly, 401 Stator core, 402 Stator support frame, 403 Stator injection-molded filler, 404 Stator end plate, 5 Stator support, 6 Adjusting magnetic block, 7 Non-magnetic material. Detailed Implementation

[0049] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0050] The method of this invention analyzes the core loss of the adjusting magnetic ring stator and the inner and outer rotor magnetic guide rings, as well as the eddy current loss of the permanent magnets of the inner and outer rotors. Different arrangements of the adjusting magnetic ring stator affect the overall magnetic induction intensity and eddy current loop distribution of the magnetic gear, thus having different effects on different components of the magnetic gear.

[0051] A specific embodiment of the present invention, such as Figure 1-7 This paper discloses an analysis method for the loss characteristics of magnetic gears, particularly a method for analyzing the loss characteristics of magnetic gears in an air turbine starter, which includes the following steps:

[0052] Step 1: Determine the parameters and materials of the magnetic gear according to the design requirements; establish a finite element analysis model of the magnetic gear based on the determined magnetic gear parameters and materials;

[0053] Understandably, the design requirements include the starter's gear ratio, etc.

[0054] The structure of the magnetic gear is designed based on the determined magnetic gear parameters and materials. The magnetic gear includes an inner rotor, an outer rotor, an inner rotor permanent magnet, an outer rotor permanent magnet, and a magnetic ring stator. The magnetic ring stator can be configured as a non-connecting bridge type, an internally connected bridge type, an externally connected bridge type, or a double-connecting bridge type. The magnetic ring stator includes a magnetic adjustment block, which is a strip-shaped structure composed of stacked amorphous sheets of magnetically conductive material with high permeability and low loss. Figure 2a As shown, the non-connecting bridge type magnetic ring stator also includes a support frame and non-magnetic materials. The support frame has a strip-shaped structure, and the magnetic material is parallel to the axis of the support frame. Non-magnetic materials are arranged on the axial periphery of the support frame. The support frame is made of aluminum alloy, which has the advantages of being lightweight and non-magnetic. The support frame and the magnetic material are stacked alternately to form a circular cylindrical ring structure. The two ends of the support frame are filled with epoxy resin plastic to improve the mechanical strength of the stator laminations. Figure 2b As shown, the externally connected bridge type magnetic ring stator also includes an external connecting bridge. Multiple magnetically conductive materials are arranged in a circular cylindrical structure with a preset gap size. The external connecting bridge is set on the outside of the circular cylindrical structure, so that the multiple magnetically conductive materials are connected into a whole to enhance the mechanical strength of the magnetic ring stator and facilitate the positioning of stator laminations. Figure 2c As shown, the internally connected bridge type magnetic ring stator also includes an internally connected bridge. Multiple magnetically conductive materials are arranged in a circular annular columnar structure with preset gaps, and the internally connected bridge is located inside the circular annular columnar structure. For example... Figure 2d As shown, the double-connecting-bridge type magnetic ring stator also includes an inner connecting bridge and an outer connecting bridge. Multiple magnetic materials are arranged in a circular columnar structure with a preset gap size. The inner connecting bridge and the outer connecting bridge are respectively arranged on the inner and outer sides of the circular columnar structure.

[0055] Optionally, the sum of the number of pole pairs of permanent magnets on the inner and outer rotors is equal to the number of magnetic adjustment blocks in the stator of the magnetic adjustment ring, ensuring the stable operation of the magnetic reducer.

[0056] Two-dimensional finite element analysis was performed on the magnetic gears with the aforementioned structure, which were of the type without a connecting bridge, with an internal connecting bridge, with an external connecting bridge, and with a double connecting bridge, using electromagnetic analysis software (such as Ansoft Maxwell software), to obtain finite element analysis models of the magnetic gears with the type without a connecting bridge, with an internal connecting bridge, with an external connecting bridge, or with a double connecting bridge.

[0057] Step 2: Based on the finite element analysis model of the magnetic gear, obtain the simulated magnetic field line distribution and simulated magnetic field change frequency of the magnetic gear, and compare and verify them with the judgment conditions;

[0058] Specifically, when the inner rotor permanent magnet and the outer rotor permanent magnet work simultaneously, the magnetic gear finite element analysis model based on the four types of magnetic ring stators is used to simulate the corresponding magnetic gear magnetic field line distribution and simulated magnetic field change frequency using electromagnetic analysis software (such as Ansoft Maxwell software).

[0059] Optionally, the finite element analysis models of the magnetic gears based on the four types of magnetic ring stators are obtained, and electromagnetic analysis software is used to simulate the distribution of simulated magnetic field lines passing through the corresponding magnetic ring stator and the distribution of simulated magnetic field lines in the air surrounding the corresponding magnetic ring stator.

[0060] Optionally, the simulated magnetic field change period of the inner rotor, the adjusting ring stator, and the outer rotor can be obtained by using electromagnetic analysis software (such as Ansoft Maxwell software), and the corresponding simulated magnetic field change frequency of the inner rotor, the adjusting ring stator, and the outer rotor can be obtained by using the simulated magnetic field change period of the inner rotor, the adjusting ring stator, and the outer rotor.

[0061] The theoretical magnetic field variation frequencies of the inner rotor, adjusting ring stator, and outer rotor of the magnetic gear are obtained.

[0062] The theoretical expression for the frequency of magnetic field change of the inner rotor is:

[0063]

[0064] In the formula, p1 is the rotational speed of the inner rotor permanent magnet, and n3 is the number of tuning blocks.

[0065] The theoretical expression for the frequency of magnetic field change of the stator of the tuning ring is:

[0066]

[0067] In the formula, n1 is the number of pole pairs of the permanent magnets on the inner rotor.

[0068] The theoretical expression for the frequency of magnetic field change of the external rotor is:

[0069]

[0070] In the formula, p2 is the rotational speed of the outer rotor.

[0071] The magnetic field line distribution of the simulated magnetic gear is determined based on the magnetic field line distribution criteria. Specifically, if the ratio of the number of magnetic field lines passing through the stator of the magnetic ring to the number of magnetic field lines in the air surrounding the stator of the magnetic ring is greater than the magnetic field line number threshold, it is considered to meet the requirements; otherwise, it is not considered to meet the requirements.

[0072] To determine whether the simulated magnetic field change frequency of the magnetic gear meets the requirements based on the magnetic field change frequency condition, specifically, the simulated magnetic field change frequencies of the inner rotor, adjusting ring stator, and outer rotor are compared and verified with the theoretical magnetic field change frequencies of the inner rotor, adjusting ring stator, and outer rotor of the magnetic gear. If the difference between the two does not exceed the frequency change threshold, it means that it meets the requirements; otherwise, it does not meet the requirements.

[0073] If the simulated magnetic field line distribution and / or the simulated magnetic field change frequency meet the requirements, proceed to step 3. If the simulated magnetic field line distribution and / or the simulated magnetic field change frequency do not meet the requirements, return to step 1 to redetermine the parameters and materials of the magnetic gear and the finite element analysis model of the magnetic gear until the simulated magnetic field line distribution and / or the simulated magnetic field change frequency meet the requirements.

[0074] Step 3: Based on the eddy current loss model and the iron loss separation model, obtain the overall energy loss of the magnetic gear and its variation with the speed of the outer rotor;

[0075] Specifically, electromagnetic analysis software (such as Ansoft Maxwell software) was used to obtain the energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet and adjusting ring stator of magnetic gears with non-connecting bridge, internal connecting bridge, external connecting bridge and double connecting bridge. The energy losses include eddy current losses and iron core losses.

[0076] Furthermore, the eddy current loss distribution of the inner and outer rotor permanent magnets is analyzed using an eddy current loss model, as well as the variation law of eddy current loss with the outer rotor speed. The iron loss separation model is used to analyze the core loss distribution of the inner rotor magnetic ring, outer rotor magnetic ring, and adjusting ring stator, as well as the variation law of iron core loss with the outer rotor speed. The total energy loss of the magnetic gear is obtained by summing the energy losses of the eddy current loss and iron core loss of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and adjusting ring stator. The variation laws of eddy current loss and iron core loss reveal that the four connecting bridge configurations alter the magnetic field magnitude and eddy current loop of the magnetic gear, thus affecting the energy loss of the reducer. A comparative analysis is conducted on the variation laws of eddy current loss, iron core loss, and overall loss of each component of the magnetic gear corresponding to the adjusting ring stator in the four configurations, as well as the variation law of the losses with the outer rotor speed.

[0077] Optionally, the energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and magnetic ring stator using the simulated magnetic field change period of the inner rotor, adjusting ring stator, and outer rotor magnetic gears with non-connecting bridge, internally connected bridge, externally connected bridge, and double-connecting bridge types are obtained respectively.

[0078] The expression for the iron loss separation model is as follows:

[0079]

[0080] In the formula, p Fe For core loss, p h For hysteresis loss, p e For eddy current losses, K e and K h Here, denoted as the core loss coefficient, n as the magnetic field harmonic order, f as the alternating frequency of the magnetic field, ρ as the core density, V as the core volume, and B as the core volume. nr and B nt These are the radial and tangential components of the nth magnetic field harmonic, respectively.

[0081] The inner and outer rotor permanent magnets have extremely high electrical conductivity, while the magnetic gears generate many alternating magnetic field harmonics. When the reducer is working, these harmonics cut the permanent magnets, generating strong induced eddy currents, thus forming eddy current losses. The expression for the eddy current loss model is as follows:

[0082]

[0083] In the formula, p v ρ is the eddy current loss, b is the width of the permanent magnet, h is the height of the permanent magnet, and ρ is the eddy current loss. R V is the resistivity of the permanent magnet. PM Let f be the volume of the permanent magnet. n Let B be the alternating frequency of the nth magnetic field harmonic. n denoted as , where is the magnetic induction intensity of the alternating magnetic field of the nth harmonic.

[0084] The expression for the total energy loss of the magnetic gear is:

[0085] P loss =p Fe +p v .

[0086] Optionally, when the permanent magnets of the inner and outer rotors are working simultaneously, electromagnetic analysis software (such as Ansoft Maxwell software) is used to obtain the magnetic field harmonic distribution of the inner and outer air gaps of the magnetic gears with non-connecting bridge, internally connected bridge, externally connected bridge and double-connecting bridge respectively. Fourier series decomposition is performed on the magnetic field harmonic distribution of the inner and outer air gaps to obtain the alternating frequency of each magnetic field harmonic and the corresponding magnetic induction intensity (i.e. magnetic flux density amplitude).

[0087] Step 4: Analyze the transmission efficiency of the magnetic gear and its variation with the rotational speed of the outer rotor;

[0088] Comparative analysis of the transmission efficiency of magnetic gears under full load in four stator arrangement configurations with adjusting magnetic rings.

[0089] The transmission efficiency of magnetic gears under full load was analyzed using electromagnetic analysis software (such as Ansoft Maxwell software), including those with no connecting bridge, internal connecting bridge, external connecting bridge, and double connecting bridge, and the variation law of magnetic gear transmission efficiency with the speed of the outer rotor was obtained.

[0090] The expression for transmission efficiency is:

[0091]

[0092] In the formula, P in For the input rotor power, P out This is the output rotor power; optionally, the inner rotor is the input rotor and the outer rotor is the output rotor.

[0093] Step 5: Determine whether the overall energy loss of the magnetic gear obtained in Steps 3 and 4 and its variation with the outer rotor speed, as well as the transmission efficiency and its variation with the outer rotor speed, meet the optimal structural index. If the index is met, the process ends and the optimal magnetic gear structure is obtained. If the index is not met, return to Step 1 to redetermine the parameters, materials, and finite element analysis model of the magnetic gear until the index is met and the optimal magnetic gear structure is obtained.

[0094] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment. The specific implementation steps are as follows:

[0095] First, a finite element model of the magnetic gear was established, and simulation experiments were conducted based on the Ansoft Maxwell platform. The main simulation process is as follows:

[0096] (1) Determine the parameters and materials of the magnetic gear according to the design requirements, see Table 1-2;

[0097] Table 1 Parameters of Magnetic Gears

[0098]

[0099] Table 2 Materials of Magnetic Gears

[0100]

[0101]

[0102] Both the inner and outer rotor permanent magnets of the reducer are radially magnetized, with alternating N-stage and S-stage magnetization. Finite element analysis models of four types of magnetic gears are generated based on the determined parameters and materials of the magnetic gears. The mesh of the finite element analysis models is based on edge length, with a maximum mesh size of less than 1 mm. Parallel boundary conditions are used, set at the edges of the magnetic guide rings of the inner and outer rotors. Two rotational bands are set for the inner and outer rotors; during simulation, one rotational band is fixed while the other rotates.

[0103] (2) Results Analysis

[0104] Under the conditions given in Table 1-2, the analytical method for analyzing the loss characteristics of magnetic gears proposed in this invention is applied, and the following simulation results are obtained.

[0105] Analysis of the magnetic field distribution of magnetic gears:

[0106] Figure 3 This is a magnetic field line distribution diagram obtained from a finite element model simulation. It can be seen that the distribution of magnetic field lines and magnetic induction intensity changes entirely near the stator of the adjusting ring. There are many magnetic field lines passing through the stator of the adjusting ring, while very few pass through the surrounding air, thus altering the magnetic field distribution of the entire magnetic gear and proving the magnetic field modulation effect of the adjusting ring stator. Adding a connecting bridge will affect the magnetic field lines of the magnetic gear, such as... Figure 3 As shown, it can be seen that whether or not a connecting bridge is added affects the distribution of the magnetic field in the magnetic gear. (Comparison) Figure 3 The distribution of magnetic field lines reveals that the addition of a connecting bridge creates a magnetic field shielding effect, causing some magnetic field lines to accumulate near the connecting bridge and form a closed loop.

[0107] Figure 4 shows the changes in magnetic induction intensity of each component of a magnetic gear, taking a non-connecting bridge magnetic gear as an example. Figure 4a This graph shows the variation of radial and tangential magnetic induction intensity on the inner rotor. It can be seen that the frequency of the variation in radial and tangential magnetic induction intensity on the inner rotor is very high, but the amplitude of the variation is very small, almost negligible. When the inner rotor speed is 725 rpm, the frequency of its magnetic field variation, according to the formula, is 398.75 Hz, which translates to 23.95 cycles within 60 ms. Figure 4a The changes are consistent. Figure 4b This is a graph showing the changes in radial and tangential magnetic induction intensity on the stator of the adjusting magnetic ring. It can be seen that the frequency of the magnetic induction intensity change on the stator is low, but the amplitude of the change is very large, exhibiting an alternating trend of positive and negative values, but without a clear regularity. When the inner rotor speed reaches 725 rpm, the frequency of the magnetic field change on the stator of the adjusting magnetic ring, according to the formula, is 48.34 Hz, which translates to 2.9 cycles within 60 ms. Figure 4cThis is a graph showing the changes in radial and tangential magnetic induction intensity on the outer rotor. Similar to the trend in the stator with the same magnetic ring, the change in magnetic induction intensity on the outer rotor is also relatively large, but the frequency is low. When the outer rotor's speed reaches 100 rpm, its frequency, according to the formula, is 55 Hz, and the cycle within 60 ms is 3.3 cycles.

[0108] Loss characteristics analysis of magnetic gears:

[0109] Figure 5a and Figure 5b These are comparison charts showing the variation of eddy current losses in the permanent magnet of the outer rotor and the core loss in the outer rotor's magnetic guide ring with the rotational speed of the magnetic gear, respectively, for different connecting bridge structures. It can be seen that, regardless of whether it's a permanent magnet or an outer rotor magnetic guide ring, the structure without connecting bridges has the highest losses, followed by the external connecting bridge, then the internal connecting bridge, and the lowest losses are found in the double connecting bridge. This is because adding connecting bridges reduces the magnetic induction intensity of the reducer.

[0110] Figure 5c This is a comparison chart showing the variation of core loss in magnetic gear stators with different connecting bridge structures as a function of the outer rotor speed. The chart shows that the core loss of the stator with connecting bridges is greater than that without connecting bridges because the connecting bridges increase the eddy current loop within the magnetic ring, thus increasing eddy current losses. The double-connecting-bridge structure has slightly higher core losses than a single connecting bridge due to the presence of two bridges. Furthermore, the loss of the stator with an external connecting bridge is slightly greater than that with an internal connecting bridge. This is because the magnetic induction intensity and variation are greater in the external connecting bridge section of the stator, resulting in a slightly larger induced current, and the loop length of the external connecting bridge is slightly longer than that of the internal connecting bridge.

[0111] Figure 5d This chart compares the variation of eddy current losses in the permanent magnets of the inner rotor of magnetic gears with different connecting bridge structures as a function of the outer rotor speed. The losses are similar for the inner connecting bridge and the double connecting bridge, and similar for the no-connecting-bridge and the outer connecting bridge. The losses in the inner connecting bridge and the double connecting bridge are significantly lower than those in the inner connecting bridge and the outer connecting bridge. However, the losses in the permanent magnets of the inner rotor are much smaller than those in the outer rotor and the adjusting stator, so their impact on the overall loss is relatively small. The losses in the magnetic guide ring of the inner rotor are extremely small and can be largely ignored.

[0112] Figure 6This chart compares the overall energy loss of magnetic gears with different connecting bridge structures as a function of the external rotor speed. Since the mechanical friction loss of the magnetic gear reducer is very small, the sum of the losses of the five components is approximated as the overall energy loss of the magnetic gear. When the output rotor speed reaches approximately 6000 rpm, the overall energy loss of the magnetic gear is nearly 9 kW. However, for magnetic gears with different connecting bridge structures, although the energy losses of individual components differ somewhat, the overall energy loss is not significantly different, with a difference within 0.4 kW.

[0113] Transmission efficiency analysis of magnetic gears:

[0114] Figure 7 This chart compares the transmission efficiency of magnetic gears with different connecting bridge structures under full load. Although the arrangement of the adjusting ring stator has little impact on the total energy loss of the magnetic gears, the total power varies among magnetic gears with different connecting bridge structures. Therefore, the arrangement of the adjusting ring has a significant impact on the transmission efficiency of the magnetic gears. It can be seen that the transmission efficiency is higher with no connecting bridge and the internal connecting bridge, approximately 3% higher than that with the external connecting bridge and the double connecting bridge.

[0115] The conclusions drawn from this finite element model of the magnetic gear are as follows:

[0116] Although the losses of individual components of magnetic gears with different connecting bridge structures vary considerably, the overall losses are not significantly different. Under full load conditions, the overall efficiency of the bridgeless and internally connected bridge types is superior to that of the externally connected and double-connected bridge types, with an overall efficiency increase of approximately 3%. This method not only calculates the losses of individual components of magnetic gears but also provides a good unified quantification of the loss characteristics and transmission efficiency of magnetic gears with different connecting bridge structures. In this model case, the optimal choice is ultimately determined to be the bridgeless magnetic gear.

[0117] Another specific embodiment of the present invention is shown in the appendix. Figure 8-17 The analytical method described above is used to analyze the magnetic gears of an air turbine starter based on magnetic deceleration.

[0118] Furthermore, the air turbine starter based on magnetic deceleration includes a housing and guide assembly structure 1 and a magnetic gear;

[0119] The magnetic gear includes a rotor, a magnetic gear stator assembly structure 4, and a magnetic gear rotor support structure;

[0120] The rotor includes an output rotor assembly structure 3 and an input rotor assembly structure 2, which are separately disposed within the housing and guide assembly structure 1 of the magnetic gear. The output rotor assembly structure 3 has a hollow portion axially provided for housing the input rotor assembly structure 2.

[0121] The output rotor assembly structure 3, the magnetic gear stator assembly structure 4, and the input rotor assembly structure 2 are nested together and are all mounted on the housing and guide assembly structure 1.

[0122] The inner wall of the housing and guide assembly structure 1 and the outer wall of the output rotor assembly structure 3, the output rotor assembly structure 3 and the magnetic gear stator assembly structure 4, and the magnetic gear stator assembly structure 4 and the input rotor assembly structure 2 are all spaced apart to allow gas to flow through.

[0123] The support mechanism includes a support stator 5 with a ring-shaped fixing structure in the middle, and a three-point support positioning structure set at both the inner and outer ends of the support stator 5. The three-point support positioning structure includes two second support components and one third support component, which are not on a straight line, so that the first support component and the second support component form a stable triangular support structure at the same end, ensuring stable rotational support between the output shaft 305 of the output rotor assembly structure and the input rotor assembly structure during rotation.

[0124] Furthermore, a first annular cavity is formed between the outer side of the input rotor assembly structure 2 and the inner side of the output rotor assembly structure 3. The radial width of the first annular cavity is equal along the circumference of the input rotor assembly structure 2. A connecting portion is provided circumferentially at one end of the output rotor assembly structure 3 that protrudes axially from the input rotor assembly structure 2. An output shaft 305 coaxial with the input rotor assembly structure 2 is provided through the connecting portion. A second annular cavity is formed between the outer side of the output shaft 305 and the inner side of the input rotor assembly structure 2. A support mechanism is provided axially within the second annular cavity of the housing and guide assembly structure 1. The support mechanism is connected to the input rotor assembly structure 2 and the output shaft 305 respectively to provide support for the output rotor assembly structure 3 and the input rotor assembly structure 2.

[0125] Furthermore, by forming a first annular cavity for placing the stator assembly structure 4 between the input rotor assembly structure 2 and the output rotor assembly structure 3, on the one hand, a gap can be formed between the stator assembly structure 4 and the input rotor and the output rotor, and on the other hand, the stator assembly structure 4 can be independent of the output rotor except for the coupling effect of the magnetic field, thus reducing the complexity of the entire rotor structure.

[0126] Furthermore, by forming a first annular cavity with a radial width equal to that of the two circumferentially circumferentially oriented input rotor assembly structures, the inner and outer rotors do not directly contact each other during high-speed rotation, resulting in less vibration and noise. Simultaneously, it also features overload protection; under overload conditions, the magnetic gears can protect the structure from physical damage through out-of-step operation. When an overload occurs, the resultant torque on the low-speed rotor suddenly increases, causing its rotational speed to decrease rapidly, and the angular displacement difference between the two rotors increases rapidly. When the maximum transmitted torque is less than the load torque, the low-speed rotor continues to decelerate, and the rotor angular displacement difference continues to widen. Afterward, regardless of how the angular displacement difference changes, the transmitted torque remains less than the load torque, causing the low-speed rotor speed to decrease to zero. During this process, the transmitted torque on the high-speed rotor gradually increases, alternating between positive and negative maximum values. The above analysis shows that when an overload occurs, the low-speed rotor speed gradually decreases to 0, the high-speed rotor speed changes and begins to oscillate, and the angular displacement difference between the high-speed and low-speed rotors continuously expands. Even after the load is removed, it can still operate normally, demonstrating the advantages of automatic overload protection. It solves the instability during rotation caused by the large magnetic fields between the stator assembly structure 4, the input rotor assembly structure 2, and the output rotor assembly structure 3. Based on magnetic gear transmission, the air turbine starter has an output stator positioning sleeve installed in its housing and guide assembly. The inner cylindrical surface of the output rotor positioning sleeve has eight circumferentially evenly distributed rollers. The output rotor positioning sleeve fits onto the outer cylindrical surface of the output rotor's magnetic guide ring, effectively limiting the radial displacement of the output rotor and improving the stability during rotation. Simultaneously, a dovetail structure is designed on the inner surface of the output rotor's magnetic guide ring in the output rotor assembly to fix the output rotor's permanent magnet. The output main shaft and the output driven shaft welded together in the output rotor assembly transmit power through an overrunning clutch, preventing reverse drive of the air turbine starter and further improving stability.

[0127] Optionally, one end of the first annular cavity is connected to the hollow portion, and the other end is connected to the interior of the housing and guide assembly structure 1. A stator assembly structure 4 is disposed within the first annular cavity, and the connection between the stator assembly structure 4 and the housing and guide assembly structure 1 is located within the communication point between the first annular cavity and the interior of the housing and guide assembly structure 1. Thus, the first annular cavity can not only be used for the installation of the stator assembly structure 4, but also guide the internal airflow through the gap between the stator assembly structure 4 and the input and output rotors. Furthermore, by fixing the stator assembly structure 4 to the housing and guide assembly structure 1 at the connection point within the communication point between the first annular cavity and the interior of the housing and guide assembly structure 1, the connection point affecting the uniformity of the first annular cavity can be located at the end of the airflow guidance, ensuring the uniformity of the gap between the stator assembly structure 4 and the input and output rotors, further reducing interference with the airflow within the device, making the rotation of the input and output rotors more stable, while simultaneously reducing energy loss and machine wear.

[0128] Optionally, the stator 5 is supported, with one end away from the connecting part connected to the housing and guide assembly structure 1, and the other end disposed in the communication between the first annular cavity and the hollow part; at least two second support assemblies are provided for connecting the stator 5 and the input rotor assembly structure 2; and a third support assembly is provided for connecting the stator 5 and the output shaft 305, and is located between adjacent second support assemblies along the axial direction of the output shaft 305.

[0129] Optionally, each of the first and second support assemblies includes at least one angular contact bearing 206, and the third support assembly includes a needle roller bearing 312.

[0130] Optionally, the input rotor and the stator are supported by angular contact bearings to achieve stability at higher speeds and to withstand larger loads; the output rotor and the stator are supported by needle roller bearings 312, making the radial structure of the entire coaxial structure more compact and reducing the overall mass.

[0131] Optionally, the input rotor assembly structure 2 is circumferentially provided with a power unit that protrudes axially from one end of the output rotor assembly structure 3, and the power unit is located on the side of the connection that is away from the output rotor assembly structure 3.

[0132] Optionally, along the axial direction, the power unit is located at one end of the input rotor assembly structure 2 that protrudes from the output rotor assembly structure 3, and further located on the side of the connection away from the output rotor assembly structure 3. This can reduce the influence of external airflow on the rotation of the final output rotor assembly structure 3, and further reduce the interference of flowing air on the internal rotating structure.

[0133] Optionally, the radial distances between the rolling element centers of the needle roller bearing 312 and the angular contact bearings 206 of the first and second support assemblies and the axis of the output shaft 305 are not equal.

[0134] Optionally, bearing rolling centers at different positions relative to the output axis position in the radial direction can be set to avoid damage to the bearing structure caused by excessive axial force. At the same time, by setting bearings at multiple different radial positions, the stable rotation of the input rotor assembly, the output rotor assembly, and the output shaft 305 during rotation is ensured.

[0135] Optionally, when arranging the structure, the annular area of ​​the connecting part is considered in advance, and the projections of the clamping part, the input rotor assembly structure 2, the output rotor assembly structure 3, and the stator assembly structure 4 along the axis of the output shaft 305 of the second support component are all located on the connecting part in the axial direction. The annular area of ​​the connecting part is limited and reduced according to the specific size of each structure in use, so that the overall structure is more compact and the radial length can be effectively reduced. Furthermore, the steps of the input rotor, stator assembly structure 4, output rotor, support structure, and output shaft 305 corresponding to the support structure adopt a layered nesting structure, which can effectively reduce the defects of multi-section axial arrangement and reduce the overall axial dimension of the device.

[0136] Optionally, a magnetic gear stator assembly structure is disposed between the input rotor assembly structure and the output rotor assembly structure, the magnetic gear stator assembly structure comprising:

[0137] The stator support frame 402 includes multiple support plates arranged circumferentially at equal intervals and multiple mounting parts, with the mounting parts disposed between two adjacent support plates.

[0138] The stator core assembly 401 includes a plurality of stator cores axially arranged at equal intervals; the stator cores are inserted into the mounting section and are interference-fitted with two adjacent support plates that make up the mounting section.

[0139] The axis of the support plate is horizontal with the axis of the stator core; a groove is formed between two adjacent stator cores and the support plate;

[0140] Stator injection molding filler 403 is used to fill the grooves;

[0141] The stator end plate 404 is used to cooperate with the stator support frame 402 to fix the stator core assembly 401 between two adjacent support plates.

[0142] The magnetic gear stator assembly structure provided by this invention eliminates the connecting bridge structure in the stator core 401, using a stator support frame 402 for fixation. This results in better torque performance, allowing for the transmission of greater torque compared to structures with connecting bridges, improving torque performance by 5%-50%. Simultaneously, in terms of transmission efficiency, it improves efficiency by 3% compared to existing double connecting bridges, internal connecting bridges, and external connecting bridges. Furthermore, it reduces end magnetic leakage. Specifically, the stator is composed of the stator support frame 402, the core, and stator injection molding material. Permanent magnets are attached to the surfaces of both the inner and output rotors, and magnetically conductive and non-magnetically conductive material blocks are arranged alternately to form a magnetic adjustment ring. Considering the high frequency of the alternating magnetic field in the stator core, the core is constructed using stacked amorphous materials, resulting in relatively low losses at high frequencies. Simultaneously, the support frame is made of low-density, non-magnetically conductive 7075 aluminum alloy, reducing the weight of the reducer and not affecting the magnetic field of the inner rotor and the magnetic adjustment stator during their combined stroke. The spaced arrangement achieved through the support frame structure and the use of thermosetting materials for filling achieves both increased structural strength and weight reduction. There is a uniform, annular, air-filled gap between the inner and output rotors and the stator. Due to the low torque performance requirements and the misconception that a connecting bridge increases structural strength, the absence of a connecting bridge not only outperforms other structures in torque performance but can also improve structural strength and reduce weight by modifying the structure, using support frames and thermosetting materials to fill the gaps in the support frame. This significantly improves performance while maintaining the structural strength and cost requirements of a structure with a connecting bridge. In the air turbine starter of this invention, the magnetic gear stator assembly 4 is equipped with a stator support frame 402. This reduces the radial obstruction of the stator core along the stator support frame while ensuring the mechanical strength of the stator assembly 4, thus improving the magnetic field modulation performance of the stator core 401. Furthermore, this bridgeless gear stator structure provides a more significant torque transmission effect. Torque performance is also one of the important performance parameters of a magnetic reducer, directly reflecting its operating characteristics, maximum operating torque, and load-bearing capacity.

[0143] Optionally, the stator end plate 404 is fitted with a plurality of bolts, the support plate has holes along the axial direction of the stator assembly 4 that mate with the bolts, and the stator support bracket 402 has fixing holes on the side wall at the end away from the support plate; and / or

[0144] A positioning groove is provided on one end face of the stator end plate 404 near the stator support frame 402, and a positioning block is provided on the stator core 401 that is inserted into the positioning groove.

[0145] Optionally, the stator support frame 402 is connected to the outside by opening fixing holes, and the stator end plate 404 is assembled and fixed to the support plate by bolts. Specifically, the axes of the holes and the fixing holes are perpendicular to each other.

[0146] The stator end plate 404 has a positioning groove. After the stator core 401 is clamped, the positioning groove and the positioning block are inserted to achieve radial positioning of the stator core 401.

[0147] Optionally, the stator support frame 402 is a circumferential ring structure with an axis; multiple support plates are arranged circumferentially along the axis; the mounting part is connected to the interior of the stator support frame 402 and is arranged radially through the stator support frame 402.

[0148] Optionally, in order to interact with the output rotor and the input rotor, the stator support frame 402 is configured as a circumferential ring structure, so that it has a central axis; the mounting part is arranged to be radially through the stator support frame 402, so that the stator core 401 can be exposed in the radial direction of the stator support frame 402 after being clamped and fixed, thereby further improving the utilization efficiency of the core.

[0149] Optionally, the wall thickness of the support plate gradually increases from the inside to the outside along the radial direction of the stator support frame 402, so that the support plate forms two inclined sidewalls; the axis is located in the plane where all the inclined sidewalls of the support plate are located; the sidewall of the stator core 401 that mates with the support plate is parallel to the inclined sidewall, and / or the sidewall of the stator core 401 that mates with the support plate is provided with a mounting groove for accommodating the end of the support plate.

[0150] Optionally, the groove includes a first groove and a second groove arranged radially along the stator support frame 402; an outer air gap communicating with the first groove is formed between the stator assembly 4 and the output rotor; and an inner air gap communicating with the second groove is formed between the stator assembly 4 and the input rotor.

[0151] Optionally, by dividing the groove radially into a first groove and a second groove along the stator support frame 402 and filling them with stator injection filler 403 respectively, the smoothness of the inner and outer walls of the stator support frame 402 can be optimized after the stator core assembly is installed.

[0152] Optionally, the outer air gap and the inner air gap are coaxially arranged with the shaft; the thickness of the outer air gap and the inner air gap along the radial direction of the stator support frame 402 are equal, and the thickness of the inner air gap is calculated using the following formula:

[0153] h in =k*maxU total +Z;

[0154] Among them, h in Where is the thickness of the internal air gap, k is the safety margin factor, and maxU total Z represents the change in the thickness of the internal air gap of the input rotor during operation, and Z represents the thermal expansion of the input rotor.

[0155] The thickness of the internal air gap of the stator assembly 4, maxUtotal For diameters < 0.22 mm, Z = 0.15 mm, and k = 1.5, the following formula must be satisfied:

[0156] h in >0.22*1.5+0.15, considering manufacturing costs, for h in =0.5mm.

[0157] Optionally, firstly, in the structural design, since the design of the magnetic stator is always accompanied by core loss, in order to reduce its loss coefficient and thus reduce its core loss, the loss coefficient is reduced in material selection and size design; secondly, the thickness of the inner and outer air gaps of the magnetic gear reducer affects the magnetic field distribution of the system, and the change of the air gap will directly affect the performance of the entire magnetic reducer. Therefore, through the analysis of the following three cases (1) the loss change under only changing the inner air gap (2) the loss change under only changing the outer air gap (3) the loss change under changing both the inner and outer air gaps together, the relationship between magnetic loss and air gap thickness is determined, and load, vibration and other variables are added in Abaqus software to calculate the optimal air gap thickness as 0.5mm; in addition, when considering the influence of end leakage flux on torque performance, three-dimensional finite element analysis models of four different magnetic reducers with different structures are established, and the static torque change diagram of the output rotor of different magnetic reducers with different structures when considering the end leakage flux effect is shown. It was found that the bridgeless structure reduces the magnetic resistance between the internal output rotors, allowing more magnetic lines of force to reach the permanent magnet of the output rotor, thereby reducing the number of magnetic lines of force in the air domain and mitigating the end leakage magnetic effect.

[0158] Furthermore, regarding U total The change in the thickness of the internal air gap of the input rotor during operation is calculated using the following formula:

[0159] maxU total =u1+u2+u3;

[0160] Where u1 is the displacement change caused by centrifugal load and torque load, u2 is the displacement change caused by vibration, and u3 is the process tolerance of the reducer;

[0161] Specifically, u1, based on the finite element method (FEM) platform, observed a maximum displacement of 0.0803 mm caused by centrifugal force after applying a maximum load of 45,000 rpm. u2, also based on the FEM platform, performed harmonic response analysis on the input rotor. Since the input rotor speed of the reducer does not exceed 45,000 rpm and the highest frequency is less than 750 Hz, resonance will not occur in actual operation. Furthermore, the maximum value of the input rotor vibration displacement at 750 Hz is less than 0.0005 mm. With the stator tolerance of the magnetic ring set to 0.046 mm and the tolerance of the input rotor permanent magnet sheath set to 0.074 mm, the total tolerance u3 will not exceed 0.12 mm.

[0162] Optionally, on the same stator assembly structure, the circumferential angle of the magnetic material occupying the stator assembly structure is θ. sp The circumferential angle of the non-magnetic material in the stator assembly structure is τ. sp If the slotting ratio of the stator assembly structure is α, then the following formula is satisfied:

[0163]

[0164] Wherein, the value of α is [0, 1], and the slotting rate α is the opening rate of the mounting part along the circumferential direction of the stator assembly structure;

[0165] It is understandable that the stator core is made of magnetically conductive material, while the support plate and filler material are made of non-magnetically conductive material;

[0166] Under the same magnetic field strength of the stator core assembly, calculate the output torque of the stator assembly structure on the input rotor and output rotor under different slotting ratios, and obtain the slotting ratio corresponding to the maximum output torque, which is α=0.45.

[0167] Optionally, the working condition of the gear stator can be improved through certain gear stator structure optimizations. The output torque under different magnetic ring slotting ratios was studied, and the optimal magnetic ring slotting ratio of 0.45 was selected, increasing the output torque by 4 Nm. The structural parameters of the magnetic stator were optimized using the surface response method and a genetic algorithm. Without reducing the peak torque of the coaxial magnetic gears, the optimal parameter combination was found, effectively improving the stability of the magnetic stator structure.

[0168] Optionally, the stator support frame 402 is made of 7075 aluminum alloy, the magnetic conductive part of the stator core 401 is composed of amorphous laminates stacked together, and the stator injection filler 403 is thermosetting plastic.

[0169] Optionally, the magnetic gear stator assembly 4 includes a stator core 4011, a stator support frame 402, a stator injection-molded filler 403, and a stator end plate 404. The stator core 401 is made of amorphous soft magnetic material, and the stator support frame 402 is made of 7075 aluminum alloy. The stator core 401 is installed in the middle of the partitions of the stator support frame 402 via an interference fit, achieving uniform circumferential distribution. The stator injection-molded filler 403 is made of thermosetting plastic and fills the inner and outer gaps of the stator support frame 402, making the stator assembly 4 a cylinder. The stator end plate 404 is connected to the stator support frame 402 by bolts.

[0170] Optionally, the magnetic gear output rotor assembly structure includes:

[0171] The first shaft is used to connect to the external driven end and output the power generated by the output rotor assembly structure;

[0172] The second shaft body has a through hole in the first shaft body that is axially inserted for fitting the second shaft body, and the first shaft body and the second shaft body are connected by a one-way transmission.

[0173] The magnetic part is used to connect to the second shaft and transmit torsional force. The magnetic part includes multiple output rotor permanent magnet assemblies 301 and an output rotor magnetic ring 302 for connecting the output rotor permanent magnet assemblies 301 to the second shaft.

[0174] The inner wall of the output rotor magnetic ring 302 is provided with multiple grooves for installing rotor permanent magnet components along the circumferential direction, and the groove width gradually decreases from the bottom to the opening.

[0175] Multiple output rotor permanent magnet assemblies 301 are inserted into each groove along the axial direction of the second shaft, and the output rotor permanent magnet assemblies 301 are composed of at least two permanent magnets spliced ​​together along the circumferential direction of the second shaft.

[0176] The magnetic gear output rotor assembly structure provided by the present invention has multiple dovetail-shaped grooves designed on the inner wall of the magnetic guide ring 302 of the output rotor, and epoxy resin is used to bond and fix the permanent magnet assembly 301 of the output rotor, which can effectively fix the permanent magnet assembly 301 of the output rotor.

[0177] By transmitting power to the first and second shafts through a unidirectional drive configuration, the structure can be simplified while preventing the second shaft from being driven by the first shaft rotating in the opposite direction.

[0178] Furthermore, the radially magnetized permanent magnets are evenly divided into multiple blocks, which are then installed and fixed. That is, based on the aforementioned permanent magnet assembly, each individual permanent magnet is evenly divided into multiple blocks, maintaining its original mounting position for installation and fixation. After being divided, the permanent magnets are assembled into a single integral magnetic pole for installation. This reduces the eddy current losses of the permanent magnets. The circumferentially divided permanent magnet assembly of the output rotor in the improved air turbine starter magnetic gear reducer effectively reduces the iron losses of the permanent magnets.

[0179] In some embodiments, the outer wall of the second shaft has an extended edge formed outward in the circumferential direction, and the inner wall of the output rotor magnetic ring 302 has an annular groove that is connected to the edge of the extended edge, and the annular groove is connected to the groove.

[0180] The sidewall edge of the extended side is formed with a positioning plate along the circumferential direction, and a rib plate is formed between adjacent grooves to abut against the positioning plate.

[0181] In this embodiment, when the second shaft and the output rotor magnetic ring 302 are installed, the outer wall of the second shaft is extended outward to form an extension edge, which increases the circumferential installation size of the second shaft. This is beneficial for installing and connecting output rotor magnetic rings 302 with larger diameters. The surface of the output rotor magnetic ring 302 for installing the output rotor permanent magnet assembly 301 is larger, so as to install more output rotor permanent magnet assemblies 301 and facilitate cooperation with the external stator. By forming a positioning plate circumferentially on the extension edge, the annular groove can be abutted to position the output rotor magnetic ring 302. After abutting, the positioning plate abuts against the rib, which can limit the output rotor permanent magnet assembly 301 placed in the groove on one side, which helps to stabilize the installation of the output rotor permanent magnet assembly 301.

[0182] Specifically, the end face of the output rotor magnetic ring 302 is provided with a notch that communicates with the annular groove, and the edge of the extended side is provided with a plug that can be inserted into the notch, so that the output rotor magnetic ring 302 and the second shaft with the extended side are engaged and fixed, and the plug and the notch are fixed in the axial direction of the output rotor magnetic ring 302 by a drilled bolt to form a fixed assembly in the axial and radial directions.

[0183] In some embodiments, the second shaft and the first shaft are connected by a transmission mechanism, which is used to make the first shaft follow the rotation of the second shaft rotating in a preset direction or to prevent the second shaft from following the rotation of the first shaft rotating in the opposite direction.

[0184] In this embodiment, the second shaft and the first shaft are connected by a transmission mechanism to achieve unidirectional transmission. This allows the transmission mechanism to make the first shaft follow the rotation of the second shaft rotating in a preset direction, or the second shaft not follow the rotation of the first shaft rotating in the opposite direction, thus preventing the second shaft from being driven to rotate by an external reverse torsional force.

[0185] Specifically, the transmission mechanism is an output clutch.

[0186] Specifically, the first shaft is the output driven shaft 306, the second shaft is the output main shaft 303, and the output shaft assembly includes the output main shaft 303, the output driven shaft 306, the output spline shaft 305, and the output clutch; the output driven shaft 306 and the output spline shaft 305 are welded to form the driven shaft weld assembly; the driven shaft weld assembly is connected to the output main shaft 303 through the output clutch; the output clutch is an overrunning clutch 304, which is a one-way clutch, thereby preventing the air turbine starter from being driven in the reverse direction.

[0187] In some embodiments, the end of the first shaft near the magnetic part extends radially outward to form a first extended edge communicating with the through hole, and the side of the extended edge near the second shaft extends axially toward the magnetic part along the second shaft to form a second extended edge.

[0188] The first extended edge, the second extended edge, and the outer wall of the second shaft together form an annular receiving cavity with an opening;

[0189] The transmission mechanism is installed at one end of the annular cavity near the second shaft.

[0190] In this embodiment, an L-shaped first extension edge is formed by extending the end of the first shaft near the magnetic part outward, thereby forming a circumferential annular inner platform in the central through hole of the first shaft. The extension edge extends towards the magnetic part near the edge of the second shaft, so that the extension edge is Z-shaped on one side after being cut along the axial direction of the first shaft. An annular recessed platform is formed near the edge of the second shaft, and the recessed platform and the annular inner platform are arranged opposite to each other, so that they cooperate with the outer wall of the second shaft to form an annular receiving cavity with an opening.

[0191] By placing the transmission mechanism at one end of the annular cavity near the second shaft, the transmission mechanism can be directly arranged between the second shaft and the first shaft in the radial direction.

[0192] In some embodiments, an angular contact ball bearing B309 for connecting the second shaft and the outer housing is disposed within the annular receiving cavity, and the outer wall of the first shaft is connected to the outer housing via an angular contact ball bearing A308, with the end face of the angular contact ball bearing A308 connected to the first extended edge; and / or

[0193] The outer wall of one end of the second shaft is connected to the central through hole through the needle roller bearing A311, and the other end of the second shaft is connected to the outer housing through the needle roller bearing B312. The transmission mechanism is located between the needle roller bearing A311 and the needle roller bearing B312.

[0194] Furthermore, bearing spacers 307 are respectively provided between the two angular contact ball bearings A308 and the two angular contact ball bearings B309 to maintain the axial distance between the two bearings;

[0195] Furthermore, a double-layer helical elastic retaining ring 310 is provided at the end of the spline shaft near the output end of the angular contact ball bearing A308 for axial positioning of the angular contact ball bearing A308;

[0196] Furthermore, the needle roller bearing A311 located between the first shaft and the second shaft is provided with a double-layer helical elastic retaining ring 313 for axial positioning of the needle roller bearing A311.

[0197] In some embodiments, the height and length of the permanent magnet are the same as the height and length of the output rotor permanent magnet assembly 301 to which it is composed, and the width of the permanent magnet is smaller than the width of the output rotor permanent magnet assembly 301 to which it is composed.

[0198] In this embodiment, when multiple permanent magnets are assembled into an output rotor permanent magnet assembly 301, the rotor permanent magnet assembly is arranged and combined in a transverse circumferential docking manner, so that the size of the rotor permanent magnet assembly increases in the width direction while the size remains unchanged in the length and height directions, so as to install it in the groove and to continuously dock and install multiple output rotor permanent magnet assemblies 301 in the same groove.

[0199] In some embodiments, each of the permanent magnets consists of two circumferentially joined individual permanent magnets to reduce iron loss without changing the volume of a single permanent magnet.

[0200] In this embodiment, the number of magnetic pole pairs on the inner rotor is 4, the number of magnetic pole pairs on the outer rotor is 29, the number of magnetic adjustment stator blocks is 33, and the specific data are shown in Table 1 when the core size, permanent magnet size and other parameters are fixed.

[0201] Table 1 shows the variation of iron loss in the permanent magnet of the external rotor, considering the circumferential segmentation of the permanent magnet.

[0202]

[0203] Table 1 shows that, under the same conditions, dividing the permanent magnet of the output rotor into circumferential blocks can effectively reduce the iron loss of the permanent magnet under different working environments.

[0204] In some embodiments, the inner diameter of the output rotor magnetic ring 302 is greater than the radial distance between the connection point where the second shaft and the first shaft are sleeved and the axis of the second shaft.

[0205] In this embodiment, by making the inner diameter of the output rotor magnetic ring 302 larger than the radial distance between the connection point where the second shaft and the first shaft are sleeved and the axis of the second shaft, the rotation of the first shaft and the second shaft located in the middle is more stable, and at the same time, increasing the lever arm is beneficial to the driving of the first shaft and the second shaft.

[0206] Optionally, the magnetic gear input rotor assembly structure includes:

[0207] The rotor shaft has a hollow section extending axially through it for the external shaft to pass through. A guide assembly is disposed on the inner wall of the hollow section and is used to restrict the axial movement between the external shaft and the rotor shaft when they rotate circumferentially relative to each other. A magnetic section is disposed circumferentially on the outer wall of the rotor shaft and is used to generate magnetic force with the external stator to drive the rotor shaft to rotate circumferentially. An input rotor sleeve 204 is disposed outside the magnetic section, and the distance between any point on the outer wall of the input rotor sleeve 204 and the axis of the rotor shaft along the radial direction is a fixed value. The distance between each pair of corresponding points on the opposite surface of the external stator and the input rotor sleeve 204 along the radial direction of the rotor shaft is equal.

[0208] The magnetic gear input rotor assembly structure provided by the present invention can fix the magnetic part by providing an input rotor sleeve 204, effectively preventing it from falling off during high-speed rotation.

[0209] When setting the distance between various surfaces, the distance between any point on the outer wall of the input rotor sleeve 204 along the radial direction of the rotor shaft and the axis of the rotor shaft is a fixed value, and the distance between each pair of corresponding points on the opposite surface of the external stator and the input rotor sleeve 204 along the radial direction of the rotor shaft is equal. This ensures that the air gap between the input rotor and the external magnetic adjustment stator has good uniformity, and further enables the air turbine 201 starter of the aero-engine to have good reliability, stability and working performance.

[0210] Specifically, the air turbine 201 is integrally formed on the rotor shaft.

[0211] In some embodiments, an annular groove is coaxially formed on the outer wall of the rotor shaft, and at least one is formed along the axial direction of the rotor shaft. Annular ribs protruding from the bottom of the annular groove are formed at both ends of the annular groove along the axial direction of the rotor shaft. The magnetic part includes an input rotor magnetic ring 202 that abuts against the annular ribs. A strain cavity is formed between the input rotor magnetic ring 202, the annular ribs, and the annular groove.

[0212] In this embodiment, an annular rib is formed radially outward on the annular groove and abuts against the input rotor magnetic ring 202 to achieve overall support for the magnetic part. By forming a strain cavity, the volume can be accommodated when the rotor shaft is subjected to force and undergoes radial deformation or radial thermal expansion during high-speed rotation, so as to avoid direct action on the input rotor magnetic ring 202 and further action on the input rotor sheath 204 through the input rotor permanent magnet assembly, causing unevenness on the working surface.

[0213] In some embodiments, the guide assembly includes a plurality of high-speed angular contact ball bearings 206 disposed at the end of the hollow portion, the inner end faces of adjacent high-speed angular contact ball bearings 206 being connected by bearing retaining rings 207 to form a cover over the middle of the inner wall of the hollow portion; wherein, the plurality of high-speed angular contact ball bearings 206 are respectively radially opposite to the input rotor sleeve 204 and the air turbine 201 on the rotor shaft.

[0214] In this embodiment, multiple high-speed angular contact ball bearings 206 are used to assemble the rotor shaft and the shaft of the external output rotor, and connect the two during relative rotation. The multiple high-speed angular contact ball bearings 206 correspond to the input rotor sleeve 204 and the air turbine 201 on the rotor shaft, respectively. This allows the air turbine 201 and the corresponding position of the rotor shaft corresponding to the magnetic part that generates torsional force corresponding to the input rotor sleeve 204 to provide guiding support, ensuring the stability of the rotor shaft during rotation, and further enhancing the uniformity of the gap between the input rotor sleeve 204 and the external stator during relative rotation.

[0215] Furthermore, an input rotor damper 209 is installed on the inner wall of the hollow part and the outer end face of the high-speed angular contact ball bearing 206 to suppress the vibration of the high-speed angular contact ball bearing 206 and reduce its rubbing; a locking ring 208 for limiting the high-speed angular contact ball bearing 206 is assembled on the inner wall of the rotor shaft.

[0216] In some embodiments, the magnetic part further includes an input rotor permanent magnet assembly 203, which is disposed between the input rotor sheath 204 and the input rotor magnetic ring 202; the input rotor permanent magnet assembly 203 includes multiple pairs of permanent magnets arranged circumferentially along the input rotor magnetic ring 202 assembly; wherein, along the circumferential and axial directions of the input rotor magnetic ring 202, the magnetic poles of adjacent permanent magnets are different.

[0217] In this embodiment, by placing the input rotor permanent magnet between the input rotor sleeve 204 and the input rotor magnetic ring 202, the permanent magnet is clamped and limited by the complete inner walls of the input rotor sleeve 204 and the input rotor magnetic ring 202, which further ensures the stability of the rotor permanent magnet during rotation, so as to make the structure stable during long-term use.

[0218] In some embodiments, when the high-speed angular contact ball bearing 206 corresponds radially to the input rotor sleeve 204 along the rotor shaft, the high-speed angular contact ball bearing 206 corresponds to the strain chamber; and / or the mating gap between the same pair of permanent magnets and the annular rib are staggered along the axial direction of the rotor shaft; and / or a receiving portion connected to the end face of the input rotor magnetic ring 202 is provided on the rotor shaft.

[0219] In this embodiment, for the high-speed angular contact ball bearing 206 installed in the radial direction of the rotor shaft corresponding to the input rotor sleeve 204, by further aligning the high-speed angular contact ball bearing 206 with the strain chamber in the radial direction of the rotor shaft, the rotor shaft can be subjected to the eccentric force of the high-speed angular contact ball bearing 206, and the vibration and outward absorption can be achieved through the strain chamber. Moreover, the annular ribs are kept away from deformation, ensuring uniform clearance during high-speed operation. This further suppresses the problem that the peak torque of the coaxial magnetic gear will decrease significantly, while the amplitude of the pulsating torque, the start-up response time, and the iron loss will increase to a certain extent.

[0220] When two or more annular slots are set, the mating gaps of the two mating permanent magnets and the annular ribs are staggered along the axial direction of the rotor shaft, so that the mating gaps of the annular ribs on the adjacent annular slots are staggered with the mating gaps of the permanent magnets, ensuring that the gap between the stator and the input rotor sleeve 204 remains stable and unchanged when the rotor shaft is impacted.

[0221] By setting up a receiving part, the input rotor magnetic ring 202 can be limited and fixed, avoiding the impact of vibration generated during high-speed rotation on the position of the input rotor magnetic ring 202, thus stabilizing the radial relative position of the permanent magnet and the stator.

[0222] Specifically, the strain cavity is a ring-shaped body that gradually narrows outward along the radial direction of the ring, such that the face of the strain cavity opposite to the input rotor magnetic ring 202 is smaller than the end face of the strain cavity that is far away from the input rotor magnetic ring 202, thereby reducing the force applied to the input rotor magnetic ring 202.

[0223] In some embodiments, an input rotor baffle 205 is fitted at one end of the outer wall of the input rotor magnetic ring 202. The input rotor baffle 205 is used to support the permanent magnet along the axial direction of the input rotor magnetic ring 202. The permanent magnet is disposed in the receiving cavity formed by the input rotor magnetic ring 202, the input rotor baffle 205 and the input rotor sheath 204.

[0224] In this embodiment, the permanent magnet can be axially supported at one end by setting the input rotor baffle 205, so that the position of the permanent magnet is limited in the axial direction to avoid movement caused by vibration during operation. Furthermore, the permanent magnet is installed and fixed by the receiving cavity formed by the input rotor magnetic ring 202, the input rotor baffle 205 and the input rotor sheath 204. When there are multiple pairs of permanent magnets, it is easy to ensure that the distance between them is equal.

[0225] In some embodiments, the permanent magnet and the input rotor magnetic ring are bonded and fixed together with epoxy resin adhesive; and / or the input rotor sheath is fixed and covered on the outside of the permanent magnet by gap filler.

[0226] In this embodiment, the structural strength is guaranteed during high-speed rotation; the carbon fiber material does not affect the distribution of the air gap magnetic field; the uniformity of the air gap is guaranteed, and the negative impact of air gap non-uniformity on the working performance of the coaxial magnetic gear is reduced, specifically, the peak torque decreases, the amplitude of pulsating torque, the start-up response time increases, and the iron loss increases.

[0227] In this embodiment, the carbon fiber sheath is lightweight, has high tensile strength, and does not generate eddy current losses during operation. It has good temperature resistance, fast thermal conductivity, and is non-magnetic, resulting in strong dynamic balance during high-speed rotation. The permanent magnet material has high compressive strength but very low tensile strength, specifically ≤80MPa. Considering that the permanent magnet cannot withstand the enormous centrifugal force when the centrifugal force of the high-speed rotor becomes the main load, protective measures must be taken for the permanent magnet. Furthermore, the material has a certain degree of machinability, and the smooth surface quality ensures uniform air gap.

[0228] In some embodiments, the logarithm of the permanent magnet satisfies the following relationship: p in +p out =n s ; where n s The number of adjusting ring core blocks in the rotor permanent magnet assembly is the number of permanent magnets, P. in P is the logarithm of the permanent magnet. out This represents the number of permanent magnet pairs on the output rotor where the external shaft is located.

[0229] In this embodiment, the speed ratio of the input and output rotors can be changed by altering the number of pole pairs to achieve the desired technical specifications.

[0230] In some embodiments, the magnetization angle of adjacent circumferential permanent magnets is set to a preset angle; wherein, the preset angle is 60°, and the permanent magnets are arranged in a Halbach array to magnetize them.

[0231] In this embodiment, the air gap magnetic field of the magnetic gear is effectively improved, reducing pulsating torque; the permanent magnet Halbach array can mitigate the negative effects of non-uniform air gap while improving basic torque performance and reducing initial start-up response time.

[0232] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An analytical method for the loss characteristics of magnetic gears, characterized in that, Specifically, the following steps are included: Step 1: Determine the parameters and materials of the magnetic gear according to the design requirements; establish a finite element analysis model of the magnetic gear based on the determined magnetic gear parameters and materials; Step 2: Based on the finite element analysis model of the magnetic gear, obtain the simulated magnetic field line distribution and simulated magnetic field change frequency of the magnetic gear, and compare and verify them with the judgment conditions; Step 3: Based on the eddy current loss model and the iron loss separation model, obtain the overall energy loss of the magnetic gear and its variation with the speed of the outer rotor; Specifically, the simulation magnetic field change periods of the inner rotor, the adjusting magnetic ring stator, and the outer rotor are obtained through simulation. Using these simulated magnetic field change periods, the energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and adjusting magnetic ring stator of the magnetic gears in different configurations of the adjusting magnetic ring stator are obtained. The total energy loss of the magnetic gears is then obtained from the energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and adjusting magnetic ring stator of the magnetic gears in the different configurations of the adjusting magnetic ring stator. The energy losses of the inner rotor magnetic ring, outer rotor magnetic ring, inner rotor permanent magnet, outer rotor permanent magnet, and magnetic ring stator of the magnetic gear of the magnetic ring stator with different settings are obtained, including the eddy current loss of the inner rotor permanent magnet and outer rotor permanent magnet obtained by using the eddy current loss model and the iron core loss of the inner rotor magnetic ring, outer rotor magnetic ring, and magnetic ring stator obtained by using the iron loss separation model. When the inner and outer rotor permanent magnets are working simultaneously, the magnetic field harmonic distribution of the inner and outer air gaps of the magnetic gears of the adjusting ring stator with different settings is obtained respectively; based on the magnetic field harmonic distribution of the inner and outer air gaps, the alternating frequency and corresponding magnetic induction intensity of each magnetic field harmonic are obtained; based on the obtained alternating frequency and corresponding magnetic induction intensity of each magnetic field harmonic, the eddy current loss of the inner and outer rotor permanent magnets is obtained. Step 4: Analyze the transmission efficiency of the magnetic gear and its variation with the rotational speed of the outer rotor; Step 5: Determine whether the overall energy loss of the magnetic gears obtained in Steps 3 and 4 and its variation with the speed of the outer rotor, as well as the transmission efficiency and its variation with the speed of the outer rotor, meet the optimal structural index. If they meet the optimal structural index, obtain the magnetic gear with the optimal structure.

2. The analytical method according to claim 1, characterized in that, The design requirement is the gear ratio of the air turbine starter.

3. The analytical method according to claim 1, characterized in that, The magnetic gear includes an inner rotor, an outer rotor, an inner rotor permanent magnet, an outer rotor permanent magnet, and a stator with an adjusting magnetic ring. The stator with an adjusting magnetic ring can be configured as a non-connecting bridge type, an internally connected bridge type, an externally connected bridge type, or a double-connecting bridge type. Finite element analysis is performed on the magnetic gear with an adjusting magnetic ring stator of the non-connecting bridge type, internally connected bridge type, externally connected bridge type, or double-connecting bridge type to obtain the finite element analysis model of the magnetic gear.

4. The analytical method according to claim 3, characterized in that, The specific steps of step 2 are as follows: when the inner rotor permanent magnet and the outer rotor permanent magnet work simultaneously, the magnetic gear finite element analysis model of the magnetic ring stator based on the different setting methods is used to simulate and obtain the simulated magnetic field line distribution and simulated magnetic field change frequency of the corresponding magnetic gear. Determine whether the simulated magnetic field line distribution of the magnetic gear meets the requirements based on the magnetic field line distribution criteria. Determine whether the simulated magnetic field change frequency of the magnetic gear meets the requirements based on the magnetic field change frequency condition.

5. The analytical method according to claim 4, characterized in that, The simulated magnetic field line distribution of the corresponding magnetic gear obtained in step 2 is as follows: based on the finite element analysis model of the magnetic gear of the magnetic ring stator with different settings, the simulated magnetic field line distribution of the magnetic ring stator with the corresponding settings and the simulated magnetic field line distribution in the air around the magnetic ring stator are obtained respectively.

6. The analytical method according to claim 4, characterized in that, The simulated magnetic field change frequency of the corresponding magnetic gear obtained in step 2 is as follows: the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator and the outer rotor is obtained by simulation, and the simulated magnetic field change frequency of the inner rotor, the adjusting magnetic ring stator and the outer rotor is obtained by the simulated magnetic field change period of the inner rotor, the adjusting magnetic ring stator and the outer rotor.

7. The analytical method according to any one of claims 1-6, characterized in that, Magnetic gears used to analyze air turbine starters based on magnetic reduction.

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