Electromagnetic Performance Calculation Method and System for Hybrid Permanent Magnet Surface-Mounted Permanent Magnet Synchronous Motor

Abstract

This invention belongs to the field of electromagnetic performance calculation technology for electric motors, and particularly relates to a method and system for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor. The method includes: calculating the no-load slotless air gap magnetic flux density based on the remanent magnet distribution of the hybrid permanent magnet and the air gap magnetic field boundary conditions; correcting the slotless air gap magnetic flux density based on the difference in magnetic barrier width and magnet thickness; establishing a relationship between the relative permeability of the air gap and the slot opening based on the stator slot model of the motor to calculate the relative permeability of the slotted air gap; calculating the slotted air gap magnetic flux density under no-load conditions in a complex coordinate system; and calculating the cogging torque of the motor based on the slotted air gap magnetic flux density using the energy method. This invention establishes a suitable remanent magnet distribution model and air gap magnetic field boundary conditions, and uses the superposition theorem to calculate an accurate no-load slotless air gap magnetic flux density; it fully considers the characteristics of the hybrid permanent magnet motor where the left and right sides of the magnetic poles are permanent magnets with different materials, remanent magnet characteristics, and sizes, and where there is a magnetic barrier between them.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic performance calculation technology of electric motors, and particularly relates to a method and system for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Due to the increasing scarcity of rare earth resources and the continuous rise in rare earth prices, a hybrid permanent magnet surface-mount permanent magnet synchronous motor (PMSM) using non-rare earth and rare earth materials as a common excitation source has been proposed as an alternative to the traditional rare earth PMSM. Compared with the traditional rare earth PMSM, the hybrid PMSM not only has superior electromagnetic performance but also effectively reduces its dependence on rare earth materials.

[0004] However, because the rotor of a hybrid permanent magnet surface-mount permanent magnet synchronous motor uses different types of permanent magnet materials, and the magnetic field characteristics of the two types of permanent magnet materials are not the same, the analysis and modeling of this motor is quite difficult, and the electromagnetic characteristics are hard to predict accurately. If the traditional finite element method is used to analyze and calculate its magnetic field and torque, high-precision meshes and complex iterations are required, resulting in excessively long calculation times. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a method and system for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor. This method has low computational load, fast computation speed, and can reduce computational memory while ensuring computational accuracy.

[0006] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0007] The first aspect of this invention provides a method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor, comprising:

[0008] Based on the residual magnetism distribution of the hybrid permanent magnet in the motor and the boundary conditions of the air gap magnetic field, the slotless air gap magnetic flux density of the motor under no-load conditions is calculated, and the slotless air gap magnetic flux density is corrected according to the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet.

[0009] Based on the stator slot model of the motor, the relationship between the relative permeability of the air gap and the slot opening under no-load conditions is established, and the relative permeability of the slotted air gap is obtained by Fourier decomposition calculation.

[0010] In the complex coordinate system, the slotted air gap magnetic flux density under no-load conditions of the motor is calculated based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap.

[0011] Based on the slotted air gap magnetic flux density of the motor under no-load conditions, the cogging torque of the motor is calculated using the energy method.

[0012] The second aspect of the present invention provides an electromagnetic performance calculation system for a hybrid permanent magnet surface-mount permanent magnet synchronous motor, comprising: a slotless air gap magnetic flux density calculation module, configured to: calculate the slotless air gap magnetic flux density of the motor under no-load conditions based on the residual magnetism distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field, and correct the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet;

[0013] The slotted air gap relative permeability calculation module is configured to: establish the relationship between the air gap relative permeability and the slot opening under no-load conditions based on the stator slot model of the motor, and obtain the slotted air gap relative permeability through Fourier decomposition calculation.

[0014] The slotted air gap magnetic flux density calculation module is configured to: calculate the slotted air gap magnetic flux density under no-load conditions of the motor based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap in a complex coordinate system.

[0015] The motor cogging torque calculation module is configured to calculate the motor cogging torque based on the slotted air gap magnetic flux density under no-load conditions using the energy method.

[0016] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in the first aspect of the present invention.

[0017] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the electromagnetic performance calculation method for a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in the first aspect of the present invention.

[0018] The above one or more technical solutions have the following beneficial effects:

[0019] (1) This invention studies the permanent magnet distribution characteristics of hybrid permanent magnet surface-mounted permanent magnet synchronous motors, builds a suitable remanent magnet distribution model and air gap magnetic field boundary conditions, and uses the superposition theorem to calculate the accurate no-load slotless air gap radial and tangential magnetic flux density; fully considers that the left and right sides of the magnetic poles of the hybrid permanent magnet motor are permanent magnets with different materials, remanent magnet characteristics and sizes, and there is a certain distance between them, and corrects the calculation results. The calculation results are universal for hybrid permanent magnet surface-mounted permanent magnet synchronous motors.

[0020] (2) In calculating the unloaded air gap magnetic flux density, the present invention innovatively calculates the accurate unloaded slotted air gap radial and tangential magnetic flux density by assuming that the radial component is a real component and the tangential component is an imaginary component in a complex coordinate system.

[0021] (3) In calculating the cogging torque, the present invention ignores the tangential component of the air gap magnetic flux density, assumes that the air gap magnetic flux density enters the stator slot vertically outside the stator slot, and reaches the side of the stator slot through a semi-circular path with the tooth angles on both sides of the stator slot as the center. Based on the energy method, the accurate cogging torque is calculated.

[0022] (4) When calculating the back electromotive force and electromagnetic torque, this invention takes into account that the hybrid permanent magnet motor adopts a fractional slot winding distribution, which cannot be solved by the traditional winding distribution coefficient. Therefore, the fractional slots of the motor are converted into integer slots to obtain the improved slot pitch electrical angle and the number of slots per phase per pole. The proposed method is universal for fractional slot motors.

[0023] (5) The electromagnetic performance calculation method based on analytical method proposed in this invention can more quickly solve for the unloaded slotted air gap magnetic flux density, cogging torque and back electromotive force of the hybrid permanent magnet surface-mount permanent magnet synchronous motor compared with the finite element simulation results.

[0024] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 A flowchart of a method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor according to the first embodiment;

[0027] Figure 2 The stator and rotor structure diagrams are for the first embodiment of the hybrid permanent magnet surface-mount permanent magnet synchronous motor;

[0028] Figure 3 A simplified structural diagram of the rotor hybrid permanent magnet of the motor in the first embodiment;

[0029] Figure 4 A schematic diagram showing the magnetization direction of the rotor hybrid permanent magnet of the motor in the first embodiment;

[0030] Figure 5 This is a schematic diagram showing the air gap region division of the motor in the first embodiment;

[0031] Figure 6 A comparison diagram of the radial and tangential magnetic flux densities of the unloaded slotless air gap obtained by the analytical method in the first embodiment and the results of the finite element method;

[0032] Figure 7 This is a structural diagram of the rotor of the motor in the first embodiment, where the hybrid permanent magnets have unequal thicknesses and magnetic barriers exist.

[0033] Figure 8 The diagram shows a comparison between the radial and tangential magnetic flux densities of the unloaded slotless air gap obtained by analytical method and the results of the finite element method, after corrections based on unequal thickness and magnetic barriers in the first embodiment.

[0034] Figure 9 A schematic diagram of the air gap structure of the motor in the first embodiment, considering the stator slots;

[0035] Figure 10 A comparison diagram of the radial and tangential magnetic flux densities of the unloaded slotted air gap obtained by the analytical method in the first embodiment and the results of the finite element method.

[0036] Figure 11 The slot model established when calculating the cogging torque of the motor in the first embodiment;

[0037] Figure 12 This is a comparison chart of the electromagnetic torque obtained by the analytical method in the first embodiment and the finite element results;

[0038] Figure 13 This is a winding distribution diagram of the motor in the first embodiment;

[0039] Figure 14 In the diagrams (a) and (b), respectively, the electromotive force star diagram and the electromotive force distribution diagram for each phase of the motor in the first embodiment are shown.

[0040] Figure 15 In the diagrams (a) and (b), respectively, it is a comparison diagram of the back electromotive force of the motor obtained by analytical method and the finite element result, and a Fourier harmonic analysis diagram obtained by Fourier harmonic analysis in the first embodiment. Detailed Implementation

[0041] The technical concept of this invention is as follows: Analyzing the magnetic field of a hybrid permanent magnet synchronous motor (PMSM) using analytical methods mainly involves solving two problems: first, how to model the hybrid permanent magnet on the rotor; and second, how to model the stator slots. The hybrid permanent magnet is the magnetic source of the PMSM, and modeling its magnetic field is a fundamental condition for analyzing the motor's electromagnetic field. The stator slots have a relatively small impact on the motor's magnetic field, mainly causing uneven distribution of air gap permeability, resulting in distortion of the air gap flux density. Analyzing the cogging torque of the hybrid permanent magnet PMSM using analytical methods requires modeling and analyzing the flux density on the stator slot sides. Analyzing the back electromotive force (EMF) and electromagnetic torque of the hybrid permanent magnet PMSM using analytical methods requires analyzing the winding structure and EMF distribution of each phase of the motor. Taking into full account the special structural characteristics of the hybrid permanent magnet on the rotor, the invention calculates the no-load air gap flux density model, the cogging torque model, and the output electromagnetic torque model of the hybrid permanent magnet surface-mounted PMSM.

[0042] Example 1

[0043] like Figure 1 As shown in the figure, this embodiment discloses a method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor, including:

[0044] Step 1: Calculate the slotless air gap magnetic flux density under no-load conditions based on the residual magnetism distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field in the motor. Correct the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet.

[0045] Step 2: Based on the stator slot model of the motor, establish the relationship between the relative permeability of the air gap and the slot opening under no-load conditions, and calculate the relative permeability of the slotted air gap through Fourier decomposition.

[0046] Step 3: In the complex coordinate system, calculate the slotted air gap magnetic flux density under no-load conditions based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap.

[0047] Step 4: Based on the slotted air gap magnetic flux density of the motor under no-load conditions, calculate the cogging torque of the motor using the energy method.

[0048] Step 1 includes: Step 101: Calculate the slotless air gap magnetic flux density of the motor under no-load conditions based on the residual magnetism distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field; specifically including:

[0049] Step 1011: Based on the structure of the hybrid permanent magnet and the magnetization direction of the hybrid permanent magnet, obtain the remanent magnetization distribution model that takes into account the distribution of the hybrid permanent magnet;

[0050] Based on the division of the air gap region of the motor, the relationship between magnetic flux density and magnetization intensity in the air gap region and the hybrid permanent magnet region under the case of no slotting is obtained:

[0051] air gap region

[0052] AlNiCo region

[0053] NdFeB region

[0054] In this diagram, region I is the air gap region outside AlNiCo, region II is the air gap region outside NdFeB, region III is the AlNiCo permanent magnet region, and region IV is the NdFeB permanent magnet region. μ0 is the free permeability, and μ... l and μ h These are the relative permeabilities of permanent magnets AlNiCo and NdFeB, respectively. and These are the magnetization vectors of AlNiCo and NdFeB, respectively. and These are the magnetic flux density vector and magnetic field strength vector for regions I and IV, respectively. and These are the magnetic flux density vector and magnetic field strength vector of region II, respectively. and These are the magnetic flux density vector and magnetic field strength vector for region III, respectively.

[0055] Step 1012: The radial and tangential components of magnetization are represented by the remanence of the permanent magnet:

[0056]

[0057]

[0058]

[0059] Where μ0 is the free permeability, θ is the rotor angle of the motor, p is the number of poles of the motor, and α l and α h The polar arc coefficients of AlNiCo and NdFeB are respectively, B l and B h The remanence of AlNiCo and NdFeB are respectively, M r and M θ These represent the radial and tangential components of the magnetization, respectively. Several conclusions can be drawn from this: the tangential component of the magnetization is always zero; the radial component is related to the remanence of the permanent magnet; and the magnetization is zero in regions without permanent magnets.

[0060] Step 1013: Ignoring the mutual influence between permanent magnets, the Fourier series of the radial and tangential magnetization expressions of the slotless air gap motor under no-load conditions can be synthesized by superimposing the magnetization expressions of the two permanent magnets:

[0061]

[0062]

[0063] in,

[0064]

[0065] In the formula, μ0 is the free permeability, and B l and B h The remanence of AlNiCo and NdFeB are respectively, M r and M θ M represents the radial and tangential components of the magnetization, respectively. rnl and M rnh M represents the amplitudes of different harmonics corresponding to the radial components of the magnetization of AlNiCo and NdFeB, respectively. θnl and M θnh The amplitudes of different harmonics after Fourier decomposition of the tangential components of the magnetization of AlNiCo and NdFeB are respectively.

[0066] Step 1014: Establish the radial and tangential magnetic field strength and magnetic flux density boundary conditions for the air gap region and the hybrid permanent magnet region:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] In the formula, H θI，θIV (r, θ) represents the tangential components of the magnetic field intensity in regions I and IV, H θII，θIII (r, θ) represents the tangential components of the magnetic field intensity in regions II and III, B rI (r, θ), B rII (r, θ), B rIII (r, θ) and B rIV(r, θ) represent the radial components of the magnetic flux density in regions I, II, III, and IV, respectively, and H... θI (r, θ), H θII (r, θ), H θIII (r,θ) and H θIV (r, θ) represent the tangential components of the magnetic field intensity in regions I, II, III, and IV, respectively, where θ is the rotor angle of the motor, and r, R s R r R m , respectively, are the sampling point radius, stator inner diameter, rotor core outer diameter, and rotor permanent magnet outer diameter.

[0074] Step 1015: Combined with the magnetization expression, solve the boundary conditions to obtain the expressions for the radial and tangential magnetic flux density in the slotless air gap under no-load conditions:

[0075]

[0076]

[0077] In the formula, B r (r,θ) and B θ (r, θ) represent the radial and tangential magnetic flux densities in the slotless air gap under no-load conditions, respectively, and α l and α h The polar arc coefficients of AlNiCo and NdFeB are K, respectively. Bl (n), K Bh (n), f Bnl (r) and f Bnh (r) are respectively:

[0078]

[0079]

[0080]

[0081]

[0082] Among them, M rnl and M rnh The amplitudes, μ, of the different harmonics corresponding to the radial components of the magnetization of AlNiCo and NdFeB, respectively, are given by Fourier decomposition. l and μ h These are the relative permeabilities of permanent magnets AlNiCo and NdFeB, respectively, where r is the sampling radius and R is the relative permeability. s R m R r These are the stator inner diameter, permanent magnet outer diameter, and rotor outer diameter of the motor, respectively.

[0083] The comparison figure shows the radial and tangential magnetic flux densities of the unloaded slotless air gap obtained by analytical method and the results obtained by finite element method. Figure 6 As shown.

[0084] Step 102: Correct the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet;

[0085] like Figure 7 As shown, since the left and right sides of the magnetic poles of the hybrid permanent magnet motor are permanent magnets of different materials, remanence characteristics, and sizes, and there is a magnetic barrier between them at a certain distance, the formula in step 101 needs to be modified to account for these characteristics; specifically including:

[0086] Step 1021: Considering the magnetic barrier of width w between the two permanent magnets, the expressions for the radial and tangential magnetization of the slotless air gap and the Fourier series of the magnetic flux density under no-load conditions of the motor are corrected as follows:

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, w is the magnetic barrier width, μ0 is the free permeability, and B1 and B h The remanence of AlNiCo and NdFeB are respectively, M r and M θ M represents the radial and tangential components of the magnetization, respectively. rnl and M rnh M represents the amplitudes of different harmonics corresponding to the radial components of the magnetization of AlNiCo and NdFeB, respectively. θnl and M θnh The amplitudes of different harmonics corresponding to the tangential components of the magnetization of AlNiCo and NdFeB are given by Fourier decomposition. r (r,θ) and B θ (r, θ) represent the radial and tangential magnetic flux densities in the slotless air gap under no-load conditions, respectively, and α l and α h The polar arc coefficients are AlNiCo and NdFeB, respectively.

[0092] Step 1022: Considering the thickness difference Δh between the two permanent magnets, the coefficients of the radial and tangential magnetic flux density in the slotless air gap under no-load conditions of the motor are corrected:

[0093]

[0094]

[0095] The comparison diagram, based on the results of the unequal thickness and magnetic barrier corrections, shows the radial and tangential magnetic flux densities of the unloaded slotless air gap obtained analytically, compared with the results obtained by the finite element method. Figure 8 As shown.

[0096] Step 2: Based on the stator slot model of the motor, establish the relationship between the relative permeability of the air gap and the slot opening under no-load conditions, and calculate the relative permeability of the slotted air gap through Fourier decomposition.

[0097] like Figure 9 The diagram shows the air gap structure of the motor considering the stator slots. The stator slot model is simplified to a straight slot model with infinite depth. The Fourier series expressions for the relative permeability of the air gap in the radial and tangential directions can be expressed as:

[0098]

[0099]

[0100] Where, ρ r (θ,r) and ρ t (θ, r) represent the radial and tangential relative permeabilities of the air gap, respectively, and ρ0 is the relative permeability of ρ. r (θ,r) represents the DC component after Fourier decomposition, ρ nr (r) and ρ nt (r) represents ρ r (θ,r) and ρ t (θ,r) represents the amplitudes of different harmonic orders after Fourier decomposition, N s θ is the number of motor slots. sa This refers to the winding spacing;

[0101] The amplitudes of the DC component and different harmonics can be expressed as:

[0102]

[0103]

[0104]

[0105] Among them, b s α is the width of the slot. t For the slot spacing, k a and k b The coefficient used to correct the relative permeability, g' is the effective length of the air gap, and η is a transition coefficient with no practical significance. η can be expressed as a solution to the equation:

[0106]

[0107] Then g' can be represented as:

[0108] g′=g+h m / μ ave

[0109] In the formula, g is the air gap width, and h m For the thickness of the permanent magnet, μ ave The average relative permeability of AlNiCo and NdFeB is given.

[0110] Step 3: In the complex coordinate system, calculate the slotted air gap magnetic flux density under no-load conditions based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap; specifically including:

[0111] Step 301: Assuming the radial component is the real component and the tangential component is the imaginary component, we obtain the conjugate forms of the slotless air gap magnetic flux density and the relative permeability of the slotted air gap in complex coordinates:

[0112] B(r, θ) = B r (r, θ) + jB θ (r, θ)

[0113] ρ(θ, r) = ρ r (θ,r)-jρ θ (θ, r)

[0114] In the formula, B(r, θ) is the slotless air gap magnetic flux density, B r (r, θ) and B θ (r, θ) are the radial and tangential components of B(r, θ), respectively, and ρ(θ, r) is the relative permeability of the slotted air gap. r (θ, r) and ρ θ (θ, r) are the radial and tangential components of ρ(θ, r), respectively.

[0115] Step 302: In the complex coordinate system, calculate the radial and tangential magnetic flux densities of the unloaded slotted air gap based on the product of the magnetic flux density of the slotless air gap and the relative permeability of the slotted air gap:

[0116] B slotted (r, θ)=B(r, θ)*ρ(θ, r)

[0117] = (B r (r, θ)*ρ r (θ,r)+B θ (r, θ)*ρ θ (θ,r))

[0118] +j(B θ (r, θ)*ρr (θ,r)-B r (r, θ)*ρ θ (θ,r))

[0119] =B slotted-r (r, θ) + jB slotted-θ (r, θ)

[0120] In the formula, B slotted (r, θ) represents the unloaded slotted air gap magnetic flux density, B slotted-r (r, θ) and B slotted-θ (r, θ) represent B slotted The radial and tangential components of (r, θ).

[0121] The comparison figure shows the radial and tangential magnetic flux densities of the unloaded slotted air gap obtained by analytical method and the results obtained by finite element method. Figure 10 As shown.

[0122] Step 4: Based on the slotted air gap magnetic flux density of the motor under no-load conditions, calculate the motor cogging torque using the energy method; specifically including:

[0123] Step 401: Calculate the electromagnetic torque using the energy method:

[0124]

[0125]

[0126] In the formula, α is the angle of rotor rotation, θ is the relative angle between the rotor magnetic pole and the stator slot, and T is the angle between the rotor magnetic pole and the stator slot. cog (α) represents the cogging torque generated when the rotor rotates, W(α) represents the energy stored in the motor's magnetic field, μ0 represents the free permeability, G(α) represents the relative permeability of the air gap in the motor when the rotor rotates, and B unslotted-r (θ,α) represents the slotless air gap radial magnetic flux density of the motor when the rotor is rotating.

[0127] Step 402: Ignore the tangential component of the air gap flux density. Assume that the air gap flux density enters the stator slot perpendicularly from the outside of the stator slot and reaches the side of the stator slot through a semi-circular path centered on the tooth angles on both sides of the stator slot. The stator slot model is as follows: Figure 11 As shown, G(α) can be expressed as:

[0128]

[0129] Where, α s N is the slot width expressed in angles. s R is the number of motor slots, g' is the effective length of the air gap, and R is the number of slots in the motor. s This is the inner diameter of the motor stator.

[0130] Step 403: When calculating the cogging torque expression of the motor according to the energy method, it is necessary to perform Fourier decomposition on the air gap magnetic flux density on the side of the motor stator slot and the unloaded slotted air gap magnetic flux density. Since the number of slots and poles of the motor are not equal, the least common multiple of the number of slots and poles and its multiples need to be selected as the order of the Fourier decomposition.

[0131]

[0132]

[0133]

[0134]

[0135] Where μ0 is the free permeability, R m B is the outer diameter of the rotor permanent magnet body. l and B h The remanence of AlNiCo and NdFeB are respectively. The amplitudes of the different harmonics after the Fourier decomposition of G(α) are given. and The amplitudes of different harmonics after Fourier decomposition of the slotless air-gap radial magnetic flux density of AlNiCo and NdFeB are given, where Δh is the thickness difference between the two permanent magnets, and α is the amplitude of the two harmonics. l and α h The polar arc coefficients of AlNiCo and NdFeB are h, respectively. m For the thickness of the permanent magnet, μ ave The average relative permeability of AlNiCo and NdFeB is given by , and g is the air gap width. b represents the amplitude of different harmonics after Fourier decomposition of the relative permeability of the slotted air gap. s N is the slot width. L The number of slots N s With the extreme number N p Least common multiple of L ef It is the axial length of the motor rotor core.

[0136] The comparison figure between the electromagnetic torque obtained by analytical method and the finite element results is shown in the figure below. Figure 12 As shown.

[0137] As a further embodiment, it also includes: Step 5: Calculate the back electromotive force of the motor based on the slotted air gap magnetic flux density under no-load conditions;

[0138] Hybrid permanent magnet motor winding distribution diagram as shown in the figure Figure 13As shown, the motor uses a fractional slot winding distribution, which cannot be solved using the traditional winding distribution coefficient. Therefore, the fractional slots of the motor are converted into integer slots to obtain the improved slot pitch electrical angle (the slot pitch electrical angle refers to the value of the distance between slots after being converted into electrical angle) and the number of slots per phase per pole. The expression for the back electromotive force generated by a single winding of the motor is then derived.

[0139]

[0140] Where e is the back electromotive force of a single winding, and B slotted-rn R represents the amplitudes of different harmonics after Fourier decomposition of the radial flux density in the slotted air gap. s L is the inner diameter of the motor stator. ef It is the axial length of the motor rotor core, ω r K is the mechanical angular velocity of the motor. dn K is the winding distribution factor. pn θ is the short-pitch factor of the winding, p is the number of pole pairs, t is time, and θ0 is the initial position angle of the rotor.

[0141] Among them, K dn and K pn It can be represented as:

[0142]

[0143]

[0144] Where α' is the improved slot pitch electrical angle, and q' is the improved number of slots per phase per pole, it can be expressed as:

[0145]

[0146] Where m is the number of phases of the motor.

[0147] The electromotive force distribution diagram of the motor is as follows Figure 14 As shown in (a) and (b), based on the electromotive force distribution of the single-phase winding of the motor, the back electromotive force generated by all single-phase windings is calculated by superposition to obtain the single-phase back electromotive force, which is then multiplied by the three-phase symmetrical rated sinusoidal current to obtain the electromagnetic torque of the motor. A comparison diagram and Fourier analysis diagram of the motor back electromotive force obtained by the analytical method and the finite element results are shown in the figure. Figure 15 As shown in (a) and (b) in the figure.

[0148] Example 2

[0149] This embodiment discloses an electromagnetic performance calculation system for a hybrid permanent magnet surface-mount permanent magnet synchronous motor, including: a slotless air gap magnetic flux density calculation module, configured to: calculate the slotless air gap magnetic flux density of the motor under no-load conditions based on the residual magnetism distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field, and correct the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet;

[0150] The slotted air gap relative permeability calculation module is configured to: establish the relationship between the air gap relative permeability and the slot opening under no-load conditions based on the stator slot model of the motor, and obtain the slotted air gap relative permeability through Fourier decomposition calculation.

[0151] The slotted air gap magnetic flux density calculation module is configured to: calculate the slotted air gap magnetic flux density under no-load conditions of the motor based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap in a complex coordinate system.

[0152] The motor cogging torque calculation module is configured to calculate the motor cogging torque based on the slotted air gap magnetic flux density under no-load conditions using the energy method.

[0153] Example 3

[0154] The purpose of this embodiment is to provide a computer-readable storage medium.

[0155] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the electromagnetic performance calculation method for a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in Embodiment 1 of this disclosure.

[0156] Example 4

[0157] The purpose of this embodiment is to provide an electronic device.

[0158] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the electromagnetic performance calculation method for a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in Embodiment 1 of this disclosure.

[0159] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0160] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0161] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor, characterized in that, include: Based on the remanent magnetization distribution of the hybrid permanent magnet in the motor and the boundary conditions of the air gap magnetic field, the slotless air gap magnetic flux density of the motor under no-load conditions is calculated. The slotless air gap magnetic flux density is corrected based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet. The hybrid permanent magnet uses non-rare earth and rare earth materials as a common excitation source. Based on the stator slot model of the motor, the relationship between the relative permeability of the air gap and the slot opening under no-load conditions is established, and the relative permeability of the slotted air gap is obtained by Fourier decomposition calculation. In the complex coordinate system, the slotted air gap magnetic flux density under no-load conditions of the motor is calculated based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap. Based on the slotted air gap magnetic flux density of the motor under no-load conditions, the cogging torque of the motor is calculated according to the energy method, including: calculating the electromagnetic torque according to the energy method; ignoring the tangential component of the air gap magnetic flux density, assuming that the air gap magnetic flux density enters the stator slot perpendicularly outside the stator slot and reaches the side of the stator slot through a semi-circular path with the tooth angles on both sides of the stator slot as the center, performing Fourier decomposition on the air gap magnetic flux density on the side of the motor stator slot and the slotted air gap magnetic flux density under no-load conditions, selecting the common multiple of the number of motor slots and the number of poles as the order of the Fourier decomposition, and obtaining the expression for the motor cogging torque; The calculation of the back electromotive force (EMF) of a motor based on the slotted air gap flux density under no-load conditions includes: converting fractional slots of the motor into integer slots, obtaining the electrical angle of the slot spacing and the number of slots per phase and per pole; calculating the expression for the back EMF generated by a single winding of the motor; and obtaining the single-phase back EMF by superimposing the back EMF generated by all windings of a single phase according to the distribution of the EMF of the single-phase winding of the motor.

2. The method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in claim 1, characterized in that, The calculation of the slotless air gap magnetic flux density of the motor under no-load conditions, based on the remanent magnetization distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field, includes: Based on the structure of the hybrid permanent magnet and the magnetization direction of the hybrid permanent magnet, a remanence distribution model considering the distribution of the hybrid permanent magnet is obtained; The radial and tangential components of the magnetization intensity are calculated based on the remanence distribution model. Based on the division of the air gap region of the motor, the relationship between magnetic flux density and magnetization intensity in the air gap region and the hybrid permanent magnet region under the condition of no slotting is established; Calculate the Fourier series of the expression for the slotless air gap magnetization under no-load conditions based on the magnetization intensity of the hybrid permanent magnet; Establish boundary conditions for magnetic field strength and magnetic flux density in the air gap region and the hybrid permanent magnet region; The radial and tangential magnetic flux densities of the slotless air gap under no-load conditions are obtained by solving the boundary conditions.

3. The method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in claim 2, characterized in that, The correction of the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet includes: Based on the magnetic barrier width of the hybrid permanent magnet, the slotless air gap magnetization and slotless air gap magnetic flux density of the motor under no-load conditions are corrected. Based on the thickness difference of the hybrid permanent magnet, the coefficient of the slotless air gap magnetic flux density under no-load conditions of the motor is corrected.

4. The method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in claim 1, characterized in that, The stator slot model of the motor is a straight slot model with infinite slot depth.

5. The method for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in claim 1, characterized in that, The calculation of the slotted air gap magnetic flux density under no-load conditions in the complex coordinate system, based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap, includes: Assuming that the radial components of magnetic flux density and relative permeability are real components and the tangential components are imaginary components, we obtain the conjugate forms of slotless air gap magnetic flux density and slotted air gap relative permeability in complex coordinates. The radial and tangential magnetic flux densities of the unloaded slotted air gap are calculated by multiplying the magnetic flux density of the slotless air gap by the relative permeability of the slotted air gap.

6. A system for calculating the electromagnetic performance of a hybrid permanent magnet surface-mount permanent magnet synchronous motor, characterized in that, include: The slotless air gap magnetic flux density calculation module is configured to: calculate the slotless air gap magnetic flux density of the motor under no-load conditions based on the residual magnetism distribution of the hybrid permanent magnet and the boundary conditions of the air gap magnetic field; and correct the slotless air gap magnetic flux density based on the difference between the magnetic barrier width and the magnet thickness in the hybrid permanent magnet; wherein the hybrid permanent magnet uses non-rare earth and rare earth materials as a common excitation source. The slotted air gap relative permeability calculation module is configured to: establish the relationship between the air gap relative permeability and the slot opening under no-load conditions based on the stator slot model of the motor, and obtain the slotted air gap relative permeability through Fourier decomposition calculation. The slotted air gap magnetic flux density calculation module is configured to: calculate the slotted air gap magnetic flux density under no-load conditions in a complex coordinate system based on the slotless air gap magnetic flux density and the relative permeability of the slotted air gap, including: assuming the radial component is the real component and the tangential component is the imaginary component, obtaining the conjugate form of the slotless air gap magnetic flux density and the relative permeability of the slotted air gap in a complex coordinate system; and calculate the no-load radial and tangential magnetic flux densities of the slotted air gap based on the product of the slotless air gap magnetic flux density and the relative permeability of the slotted air gap in a complex coordinate system. The motor cogging torque calculation module is configured to: calculate the motor cogging torque based on the slotted air gap magnetic flux density under no-load conditions using the energy method, including: calculating the electromagnetic torque using the energy method; ignoring the tangential component of the air gap magnetic flux density, assuming that the air gap magnetic flux density enters the stator slot perpendicularly from the outside of the stator slot and reaches the side of the stator slot through a semi-circular path centered on the tooth angles on both sides of the stator slot, performing Fourier decomposition on the air gap magnetic flux density on the side of the motor stator slot and the slotted air gap magnetic flux density under no-load conditions, selecting the common multiple of the number of motor slots and poles as the order of the Fourier decomposition, and obtaining the expression for the motor cogging torque.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the electromagnetic performance calculation method for a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in any one of claims 1-5.

8. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the electromagnetic performance calculation method for a hybrid permanent magnet surface-mount permanent magnet synchronous motor as described in any one of claims 1-5.

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