An analytical calculation method for air-gap flux density of unequal magnetization rotor poles

Abstract

This disclosure provides an analytical calculation method for the air gap magnetic flux density of unequally magnetized rotor poles. The method includes: determining the remanent magnetization distribution identifier of the permanent magnet in the unipolar permanent magnet based on the number of permanent magnets in the surface-mounted permanent magnet synchronous motor; determining the magnetic field distribution of the permanent magnet corresponding to the remanent magnetization distribution identifier; determining the magnetization intensity of the unipolar permanent magnet based on the magnetic field distribution and the shape of the permanent magnet; and determining the remanent magnetization density of the unipolar permanent magnet based on the magnetization intensity of the unipolar permanent magnet.

Description

Technical Field

[0001] This disclosure relates to the field of electric motors, and in particular to an analytical calculation method for the air gap magnetic flux density of unequally magnetized rotor poles. Background Technology

[0002] Existing surface-mounted permanent magnet synchronous motors for high-speed spindles typically employ rotor eccentricity or non-uniform magnetic pole shapes to improve the sinusoidal sine flux density in the no-load air gap. While these methods can reduce air gap magnetic flux density harmonics and improve torque stability to some extent, they still have significant drawbacks: rotor eccentricity leads to uneven stress on the sheath, easily causing localized stress concentrations, thus affecting rotor mechanical strength and high-speed operation stability; non-uniform magnetic poles or specially shaped permanent magnets increase processing complexity and assembly costs, and are prone to structural instability or insufficient mechanical strength under high-speed rotation conditions; furthermore, current technologies struggle to minimize overall harmonics while maintaining the effective value of air gap magnetic flux density, thus failing to adequately reduce torque ripple and spindle vibration, affecting processing accuracy and system response performance. Moreover, current parameter calculations for permanent magnet synchronous motors require the construction of complex finite element models, involving tedious mesh generation and large-scale numerical calculations, consuming significant computational resources, increasing calculation cycles and response times, resulting in low parameter calculation efficiency. Summary of the Invention

[0003] This disclosure proposes a surface-mounted permanent magnet synchronous motor and a method for calculating its parameters, in order to solve the above-mentioned technical problems to a certain extent.

[0004] In a first aspect, this disclosure provides a method for calculating the parameters of a surface-mounted permanent magnet synchronous motor, including: The remanent magnet distribution identifier of the permanent magnet in the unipolar permanent magnet is determined based on the number of permanent magnets in the surface-mounted permanent magnet synchronous motor. Determine the magnetic field distribution of the permanent magnet corresponding to the remanent magnetization distribution identifier; The magnetization intensity of the unipolar permanent magnet is determined based on the magnetic field distribution and the permanent magnet shape of the permanent magnet. The remanence density of the unipolar permanent magnet is determined based on its magnetization intensity.

[0005] In a first aspect, this disclosure provides a surface-mounted permanent magnet synchronous motor, wherein parameter calculation is performed based on the method described in the first aspect.

[0006] As described above, this disclosure provides a surface-mounted permanent magnet synchronous motor and its parameter calculation method. It determines the remanent magnetization distribution marker based on the number of permanent magnets in a single-pole permanent magnet, then determines the magnetic field distribution corresponding to this marker. Next, it combines the magnetic field distribution with the shape of the permanent magnet to determine the magnetization intensity of the single-pole permanent magnet, and finally determines the remanent magnetization density based on the magnetization intensity. Through step-by-step derivation and calculation, the key parameters of the single-pole permanent magnet in the surface-mounted permanent magnet synchronous motor can be accurately determined, providing accurate data support for motor performance analysis and optimization design, and helping to improve motor operating efficiency and stability. Compared to the finite element analysis method, it eliminates the need to construct complex finite element models, saving the tedious mesh generation and large-scale numerical calculation process, greatly shortening the calculation cycle, and quickly providing parameter results, significantly improving optimization efficiency. While ensuring consistent calculation results with the finite element analysis method, it lowers the threshold for high requirements on computing resources and professional software, reduces uncertainties caused by software operation and model errors, and makes the parameter optimization process more controllable and repeatable, providing an efficient and reliable approach for parameter calculation and optimization of surface-mounted permanent magnet synchronous motors. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in this disclosure or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 This is a schematic diagram of the structure of a surface-mounted permanent magnet synchronous motor for a high-speed spindle according to an embodiment of the present disclosure.

[0009] Figure 2 This is a schematic diagram of the first filling structure and the second filling structure according to an embodiment of the present disclosure.

[0010] Figure 3 This is a schematic diagram of parameters for parametric modeling during the modulation of the air gap magnetic field in an embodiment of this disclosure.

[0011] Figure 4 This is a schematic diagram of the radial component and tangential component of the magnetization vector in an embodiment of this disclosure.

[0012] Figure 5 This is a schematic diagram illustrating the optimized process of a surface-mounted permanent magnet synchronous motor for a high-speed spindle according to an embodiment of this disclosure.

[0013] Figure 6 This is a schematic diagram of the radial component and tangential component of the magnetization vector in an embodiment of this disclosure.

[0014] Figure 7This is a schematic diagram of the rotor and permanent magnet parameters according to an embodiment of the present disclosure.

[0015] Figure 8 This is a schematic diagram illustrating the effects of different methods in the embodiments of this disclosure. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0017] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this disclosure should have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms "first," "second," and similar terms used in the embodiments of this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0018] Against the backdrop of rapid development in modern industry and intelligent manufacturing, high-speed spindle motors have become indispensable core components in CNC machine tools, robots, high-speed machining centers, and aerospace precision machining. These applications place extremely high demands on the motor's torque output capability, torque smoothness, high-speed operation reliability, and mechanical structural strength. With the continuous increase in motor speed and power density, the centrifugal force and mechanical stress experienced by the rotor and its sheath during high-speed rotation increase significantly. Ensuring the reliability of the rotor structure under high-speed operation has become a key technical issue.

[0019] Furthermore, to meet the demands of high-precision machining and rapid response, the motor must possess a high effective value of air gap magnetic flux density to ensure sufficient output torque and system dynamic performance. Simultaneously, the harmonic content in the motor's air gap magnetic flux density must be controlled at a low level to reduce torque fluctuations and rotor vibration, ensuring spindle stability and machining accuracy during high-speed rotation. In high-speed machining scenarios, even small instantaneous torque fluctuations can cause tool fretting or machining errors, affecting part surface quality and machining accuracy. Therefore, achieving high sinusoidal strength and low harmonicity in the air gap magnetic flux density while ensuring its effective value is a crucial technical indicator that must be considered in the design of high-speed spindle motors.

[0020] Therefore, the field of high-speed spindle motors urgently needs to optimize rotor structure design and address technical challenges such as localized stress concentration in the sheath and the stability of permanent magnets, while ensuring output performance and high-speed operational reliability. This is of great significance for improving the processing efficiency and accuracy of intelligent manufacturing equipment, as well as the operational reliability of high-end equipment such as aerospace equipment.

[0021] Currently, to improve the sinusoidal nature of the air gap magnetic flux density waveform in surface-mounted permanent magnet synchronous motors for high-speed spindles, existing technologies mainly employ methods such as rotor eccentric arrangement or non-uniform magnetic pole design. By eccentrically arranging the rotor, specific harmonic components in the air gap magnetic flux density can be reduced to a certain extent, thereby improving the smoothness of torque output; by changing the shape of the magnetic poles or using arc-shaped or fan-shaped permanent magnets, the air gap magnetic flux density waveform can also be adjusted to make it closer to the ideal sinusoidal shape.

[0022] However, these existing methods still have significant limitations. Eccentric rotor arrangement leads to uneven stress on the sheath, causing localized stress concentrations and increasing the risk of rotor deformation or damage, thus affecting the reliability of high-speed operation. Non-uniform magnetic poles or special pole shapes increase processing and assembly difficulties, resulting in high manufacturing costs, and are prone to insufficient mechanical strength or structural instability under high-speed rotation conditions. Furthermore, while ensuring the effective value of the air gap magnetic flux density, these methods still struggle to minimize overall air gap magnetic flux density harmonics, failing to adequately reduce torque ripple and spindle vibration, thereby limiting the motor's performance in high-speed precision machining.

[0023] Therefore, existing technologies have not yet been able to simultaneously ensure the sinusoidal and effective values ​​of the air gap magnetic flux density while also taking into account the mechanical strength, structural reliability, ease of manufacturing, and torque stability of the sheath. There is still room for further optimization.

[0024] Existing surface-mounted permanent magnet synchronous motors for high-speed spindles typically employ rotor eccentricity or non-uniform magnetic pole shapes to improve the sinusoidal sine flux density in the no-load air gap. While these methods can reduce air gap magnetic flux density harmonics and improve torque stability to some extent, they still have significant drawbacks: rotor eccentricity leads to uneven stress on the sheath, easily causing localized stress concentrations, thus affecting rotor mechanical strength and high-speed operation stability; non-uniform magnetic poles or specially shaped permanent magnets increase processing complexity and assembly costs, and are prone to structural instability or insufficient mechanical strength under high-speed rotation conditions; furthermore, existing technologies struggle to minimize overall harmonics while ensuring the effective value of the air gap magnetic flux density, thus failing to adequately reduce torque ripple and spindle vibration, affecting machining accuracy and system response performance.

[0025] This disclosure provides a surface-mount permanent magnet synchronous motor for a high-speed spindle, comprising: The stator is used to provide the rotating magnetic field for the stator. The rotor includes a rotor core, a plurality of permanent magnet arrays attached to the outer surface of the rotor core, and a sheath fitted over the permanent magnet arrays; wherein, the permanent magnet arrays include a plurality of permanent magnets arranged in a polar arc direction, and the permanent magnets have different magnetization intensities; a first filling structure is provided between the permanent magnet arrays to isolate the permanent magnet arrays, and the permanent magnets are fixed to each other and / or to the first filling structure based on a second filling structure; The rotor is used to provide a permanent magnet magnetic field, and the stator rotating magnetic field cuts the permanent magnet magnetic field to generate electromagnetic torque to drive the rotor to move.

[0026] The rotor employs a surface-mount structure, with multiple arrays of permanent magnets attached to the outer surface of the rotor core. Each array contains permanent magnets with varying magnetization intensities, arranged along their pole arcs. A first filling structure isolates the permanent magnet arrays, while a second filling structure fixes the relative positions of the permanent magnets and between them and the filling structure. This design, by optimizing the distribution of permanent magnet magnetization intensity, effectively improves the air gap magnetic field waveform, reduces harmonic content, thereby decreasing motor vibration and noise, improving operational stability, enhancing rotor structural strength, meeting high-speed rotation requirements, and improving motor efficiency and reliability.

[0027] In some embodiments, the stator includes a stator core and a stator winding; wherein, the inner circumference of the stator core is provided with a plurality of slots for mounting the stator winding, the stator generates a stator rotating magnetic field through current, and the stator rotating magnetic field interacts with the permanent magnet magnetic field to generate torque.

[0028] The stator consists of a stator core and stator windings. Multiple slots are formed on the inner circumference of the stator core to properly house the stator windings. When current is applied to the stator windings, a rotating magnetic field is generated. This magnetic field interacts with the permanent magnet field provided by the permanent magnets on the rotor, thereby generating the torque that drives the motor. This ensures the stable and efficient generation of the stator rotating magnetic field, which works well with the permanent magnet field, effectively improving the motor's torque output performance and operating efficiency, and guaranteeing the stable and reliable operation of the high-speed spindle permanent magnet synchronous motor.

[0029] Specifically, see Figure 1 , Figure 1 A schematic diagram of a surface-mounted permanent magnet synchronous motor for a high-speed spindle according to an embodiment of the present disclosure is shown. Figure 1In this design, the stator can be a cylindrical hollow structure, comprising a stator core 1 and stator windings. The stator core 1 can be made of laminated silicon steel sheets, exhibiting high permeability and low loss characteristics. The inner circumference of the stator core 1 has multiple stator slots for mounting the stator windings, reducing eddy current losses. Stator slots can be open slots, with their openings fully open for easy winding insertion, but this increases cogging effect (torque ripple). Stator slots can also be semi-open / closed slots: the slot openings are partially or completely closed, reducing cogging effect. The number of poles (2p) and the number of slots (Q) must be matched, for example, 6 poles with 36 slots or 8 poles with 48 slots, to optimize magnetic field distribution and reduce harmonics. The stator windings can be three-phase windings, connected in a star (Y-shape) or delta (Δ-shape) configuration, embedded in the slots in a distributed or concentrated manner to form a symmetrical rotating magnetic field. The stator windings generate a rotating magnetic field through current, which interacts with the rotor magnetic field to produce torque. The winding ends are arc-shaped or stepped to reduce copper loss and space occupation, while also facilitating heat dissipation.

[0030] The rotor includes a rotor core 6, a permanent magnet array 3 attached to its outer surface, and a sheath 2 covering the permanent magnets. The rectangular permanent magnet array consists of multiple rectangular or tile-shaped permanent magnets arranged along the pole arc direction to form continuous magnetic poles. Each magnetic pole is composed of several rectangular permanent magnets with different magnetization intensities, forming a magnetic field modulation rotor structure. The outer periphery of the rotor is quasi-polygonal in shape, meaning it is not strictly circular but close to a polygonal shape to fix the rectangular permanent magnets, forming a non-uniform geometric structure, thereby optimizing the air gap magnetic flux density distribution and reducing sheath stress concentration. Each rectangular permanent magnet is attached to the edge of the quasi-polygon. A first filling structure 4, similar to an acrylic sheet, is present between the magnet poles to fix the magnets and eliminate stress concentration in the sheath caused by geometric discontinuities (sheath stress refers to the mechanical stress borne by the sheath covering the rotor permanent magnets under high-speed rotation, centrifugal force, and the constraint of the permanent magnet filling structure). A second filling structure 5 fills the spaces between the magnets. The second filling structure 5 can be made of potting material, such as epoxy resin, polyurethane, or other high-strength filling materials suitable for high-speed rotation conditions. Through potting, the load distribution on the rotor's outer periphery is uniform, and the stress concentration of the sheath under high-speed rotation conditions is significantly reduced.

[0031] In some embodiments, the magnetization intensity of the permanent magnets in the permanent magnet array is symmetrically distributed and gradually decreases from the middle along both sides.

[0032] Specifically, the magnetization intensity of the permanent magnets in the permanent magnet array is set to be symmetrically distributed and gradually decrease from the center to both sides. This makes the air gap magnetic field distribution more reasonable, effectively optimizes the symmetry and sinusoidal nature of the magnetic field, reduces magnetic field harmonic components, and reduces torque pulsation and motor vibration noise caused by harmonics. At the same time, it can improve the power density and efficiency of the motor, making the motor run more smoothly and reliably in high-speed spindle applications, and significantly optimizing its performance.

[0033] In some embodiments, the permanent magnet may be rectangular or tile-shaped.

[0034] The size, material, and magnetization intensity of each rectangular permanent magnet can be independently adjusted to ensure anti-demagnetization capability under high-speed operating conditions and optimize the sinusoidal nature of the air gap magnetic flux density. The central magnet has the highest magnetization intensity, while the side magnets have lower magnetization intensity. This gradient distribution achieves smooth air gap magnetic flux density and improves torque output stability. Specifically, rectangular permanent magnets are relatively simple to manufacture, have lower costs, and are suitable for mass production; tile-shaped permanent magnets, on the other hand, can better fit the outer surface of the rotor core and are more compatible with the air gap magnetic field distribution. The choice between these two shapes can be flexibly determined according to specific needs, which helps to optimize the rotor structure, improve the magnetic field distribution, enhance the electromagnetic performance of the motor, and enable the motor to have better operating stability and efficiency in high-speed spindle applications.

[0035] In some embodiments, the shape of the first filling structure matches the permanent magnet, and the number of the first filling structures is at least one.

[0036] The first filling structure is designed to match the shape of the permanent magnet, and at least one such structure is provided. The matching shape allows for a tight fit with the permanent magnet, effectively isolating the permanent magnet array and avoiding magnetic circuit interference. The number of structures is flexible and can be adjusted according to actual needs, enhancing the overall integrity of the rotor structure while helping to optimize the magnetic field distribution, reduce magnetic leakage, improve the utilization efficiency of the motor's magnetic field, and thus improve motor performance, ensuring stable and efficient operation of the high-speed spindle permanent magnet synchronous motor.

[0037] In some embodiments, the first filling structure is made of a low magnetic permeability material, and the second filling structure is made of a high strength filling material.

[0038] The first filling structure is made of a low-permeability magnetic material, which effectively avoids magnetic flux short circuits, reduces magnetic leakage, and ensures that the magnetic flux generated by the permanent magnet can efficiently participate in electromagnetic conversion. The second filling structure uses a high-strength filling material, which enhances the mechanical strength and stability of the rotor structure and can withstand the centrifugal force generated by high-speed rotation. This optimizes the magnetic circuit performance of the motor and improves the reliability of the rotor, making the motor operate more efficiently and stably in high-speed spindle applications.

[0039] Specifically, such as Figure 2As shown, the rectangular permanent magnet array 3 consists of multiple rectangular permanent magnets arranged closely along the sides of a quasi-polygon in the direction of the pole arc, forming a continuous magnetic pole. The direction of the pole arc can refer to the alignment of the length direction of the permanent magnet with the tangent direction of the rotor circumference, maximizing magnetic flux utilization. Each magnetic pole consists of several rectangular permanent magnets with different magnetization intensities; the middle block has the highest magnetization intensity, gradually decreasing towards the sides, forming a gradient distribution. This gradient in magnetization modulates the air gap magnetic flux density waveform, making it closer to a sine wave, thereby reducing torque ripple and improving output stability.

[0040] The sheath, made of non-magnetic material (such as stainless steel or carbon fiber), is fitted over the permanent magnet to secure it, preventing it from falling off due to centrifugal force during high-speed rotation; it also isolates the permanent magnet from the external environment, providing mechanical protection. The first filling structure can use low-permeability materials such as acrylic sheets to further isolate the magnetic poles and reduce magnetic leakage. The second filling structure fills the gaps between adjacent permanent magnets and between the permanent magnet and the sheath. It can be made of high-strength, high-temperature resistant materials such as epoxy resin or polyurethane to adapt to high-speed rotation conditions. The second filling structure secures the permanent magnet, eliminates stress concentration in the sheath caused by geometric discontinuities, and ensures uniform load distribution, thus improving the rotor's structural strength.

[0041] The permanent magnet synchronous motor according to embodiments of this disclosure employs a gradient-magnetized permanent magnet and a quasi-polygonal rotor shape in synergy to optimize the air gap magnetic flux density waveform, reduce harmonic content, thereby reducing torque pulsation and iron loss, and improving the magnetic field modulation effect. The combination design of the potting layer and the sheath effectively disperses the centrifugal force during high-speed rotation, preventing permanent magnet detachment or sheath breakage, making it suitable for high-speed applications. Furthermore, the size, material, and magnetization intensity of each permanent magnet can be independently adjusted to ensure magnetic stability during high-speed operation and improve demagnetization resistance.

[0042] In some embodiments, the magnetization method of the permanent magnet includes parallel magnetization or radial magnetization.

[0043] Parallel magnetization refers to the magnetization direction of the permanent magnet being parallel to the rotor axis (i.e., the magnetic pole direction is along the axial direction), while radial magnetization refers to the magnetization direction of the permanent magnet being along the rotor radius (i.e., the magnetic pole direction is towards the center). Similar magnetic field modulation effects can be achieved through optimization. Parallel magnetization produces a better sinusoidal air gap magnetic field than radial magnetization. Specifically, parallel magnetization is relatively simple and low-cost, and it results in a more uniform magnetic field distribution on the surface of the permanent magnet, making it suitable for scenarios where magnetic field uniformity requirements are not high but cost-effectiveness is prioritized. Radial magnetization, on the other hand, allows the magnetic field generated by the permanent magnet to better match the actual needs of the motor's air gap magnetic field, effectively improving the air gap magnetic field waveform, reducing harmonic content, and enhancing the motor's torque output capability and operating efficiency. Flexible selection of the magnetization method based on the specific performance requirements and application scenarios of the motor can optimize the overall performance of the motor.

[0044] In some embodiments, the magnetization intensity of the permanent magnet is determined based on a target remanent magnetization density that minimizes the total harmonic distortion function corresponding to the permanent magnet array within a constraint range; the constraint range includes the remanent magnetization range and the range of the number of permanent magnets corresponding to the permanent magnet array determined based on preset performance indicators.

[0045] The optimization objective can be set as the remanent magnetization density that minimizes the total harmonic distortion (THD) function of the permanent magnet array within a specific constraint range. The constraint range can be determined based on preset performance indicators, including the remanent magnetization range and the range of the number of permanent magnets. This optimizes the magnetization intensity of the permanent magnets, effectively reducing THD and thus improving the magnetic field quality of the permanent magnet array, better meeting the performance requirements of equipment such as motors for magnetic field stability and efficiency. Specifically, based on preset performance indicators, such as the efficiency and output torque fluctuation requirements of electromagnetic equipment, the reasonable range of remanent magnetization and the selectable range of the number of permanent magnets can be precisely determined. Within the given constraints, mathematical optimization algorithms, such as finite element analysis, are used to solve for the THD function of the permanent magnet array. During the solution process, the remanent magnetization density is continuously adjusted, and the corresponding THD value is calculated. Through multiple iterations, the target remanent magnetization density that minimizes THD is found. Finally, the magnetization intensity of the permanent magnets is determined based on the obtained target remanent magnetization density.

[0046] In some embodiments, determining the total harmonic distortion function based on the air gap magnetic flux density harmonic content includes: Where THD is the total harmonic distortion function, is the air gap magnetic flux density of the nth harmonic, and is the air gap magnetic flux density of the fundamental wave.

[0047] Among them, using the harmonic content of air gap magnetic flux density to construct the total harmonic distortion function can scientifically and quantitatively assess the overall distortion degree of harmonics in air gap magnetic flux density, providing a key basis for optimizing permanent magnet design and adjusting magnetic circuit structure, thereby effectively reducing the negative impact of magnetic field harmonics and improving the performance stability and operating efficiency of electromagnetic equipment.

[0048] In some embodiments, the magnetization intensity of the permanent magnet is determined based on a target remanent magnetization density that minimizes the total harmonic distortion function corresponding to the permanent magnet array within a constrained range, including: Based on the candidate remanent magnets within the remanent magnet range and the candidate permanent magnets within the permanent magnet quantity range, the air gap magnetic flux density distribution corresponding to the permanent magnet array is calculated. The total harmonic distortion function is determined based on the air gap magnetic flux density distribution. The minimum value of the total harmonic distortion function corresponds to the number of candidate permanent magnets and the candidate remanent magnetization density, which are then used as the target number of permanent magnets and the target remanent magnetization density. The magnetization intensity of the permanent magnet is determined based on the target remanent magnetization density, and the number of permanent magnets is determined based on the number of target permanent magnets.

[0049] The process involves selecting candidate remanence and the number of candidate permanent magnets based on preset remanence and permanent magnet quantity ranges, and calculating the air gap magnetic flux density distribution of the permanent magnet array accordingly. Then, based on this distribution, the total harmonic distortion (THD) function is determined, and the candidate permanent magnet quantity and candidate remanence density corresponding to its minimum value are identified as target values. Finally, the magnetization intensity is determined based on the target remanence density, and the number of permanent magnets is determined based on the target number of permanent magnets. This method effectively reduces the THD of the air gap magnetic flux density, improves the magnetic field quality, and enhances the performance of the permanent magnet array, meeting the requirements of electromagnetic equipment for a stable and efficient magnetic field.

[0050] Specifically, such as Figure 3 As shown, Figure 3 A schematic diagram of the optimization process for a surface-mounted permanent magnet synchronous motor for a high-speed spindle according to an embodiment of this disclosure is shown. It involves the design and optimization of the air gap magnetic field of electromagnetic devices (which may involve motors or transformers, etc.). Its core is to achieve effective control of the air gap magnetic flux density and reduce total harmonic distortion (THD) through parameterization, electromagnetic field solving, and optimization algorithms. Figure 3 As shown, firstly, the minimum limit for the effective value of the air gap magnetic flux density (B_rms) can be determined. Specifically, the minimum requirement for the effective value of the air gap magnetic flux density (B_rms) can be clearly defined to ensure that the electromagnetic equipment can meet basic performance requirements during operation, such as output torque or induced voltage. Specifically, the minimum limit for the effective value of the air gap magnetic flux density (B_rms) can be determined through theoretical calculations based on the working principle and performance requirements of the electromagnetic equipment. This typically involves parameters such as the equipment's rated power, speed, and efficiency. Alternatively, empirical data from similar equipment or industry standards can be referenced to determine a reasonable B_rms value; or, electromagnetic simulation software can be used to simulate the initially designed equipment to verify whether the B_rms value meets the performance requirements.

[0051] Secondly, the number N of monopole magnets and the corresponding remanence density variable B_n are parameterized. The number N of monopole magnets is parameterized, and a corresponding remanence density variable B_n is assigned to each magnet. This allows for flexible adjustment of the magnet configuration and remanence density during subsequent optimization to explore different design schemes. Specifically, a parameterized model of the magnets can be established in electromagnetic simulation software. This can include defining the number N of magnets and the remanence density B_n of each magnet as adjustable parameters. Reasonable value ranges and step sizes are set for N and B_n to facilitate traversal or search during subsequent optimization. Simulations are used to verify the accuracy of the parameterized model, ensuring that the model reflects the magnetic properties of the actual magnets.

[0052] Next, the calculation is performed using an electromagnetic field analysis tool. The parameterized model is solved using this tool. This is to obtain the distribution and characteristics of the air gap magnetic field under given parameters, including the magnetic flux density waveform and harmonic content. Specifically, parameters such as the solver type, accuracy, and boundary conditions can be set in the electromagnetic field analysis tool. The simulation is then run to calculate the air gap magnetic field distribution under given magnet parameters, which can include information such as the amplitude, phase, and harmonic content of the magnetic flux density. The simulation results can be analyzed to evaluate whether the performance of the air gap magnetic flux density meets the requirements. If not, the magnet parameters need to be adjusted and the simulation repeated.

[0053] Then, optimization is performed using software algorithms. Specifically, the magnet parameters can be optimized using optimization software algorithms. A constraint is set that the effective magnetic flux density (B_eff) is greater than the minimum limit value (B_rms) to ensure that the optimized solution meets basic performance requirements. The optimization objective is set to minimize the total harmonic distortion (THD) to improve the waveform quality of the air gap magnetic field and reduce the impact of harmonics on equipment performance. Specifically, an optimization problem can be defined. This includes setting constraints (B_eff > B_rms) and an optimization objective (minimize THD). A suitable optimization algorithm, such as a genetic algorithm or particle swarm optimization algorithm, is selected to search for the optimal solution within the given parameter space. The optimization algorithm is run to iteratively adjust the magnet parameters until the optimal solution that satisfies the constraints and minimizes THD is found. The optimized magnet parameters are then substituted into electromagnetic simulation software for verification to ensure the accuracy and reliability of the optimization results.

[0054] By parametrically configuring magnets and controlling remanence density, combined with electromagnetic field simulation and optimization algorithms, precise control and optimization of the air gap magnetic field are achieved. This not only ensures that electromagnetic equipment meets basic performance requirements but also improves operating efficiency and stability by reducing total harmonic distortion. It has broad application prospects in electromagnetic equipment fields such as motor design and transformer optimization.

[0055] As can be seen, this disclosure optimizes the remanent magnetization distribution of multiple permanent magnets through parametric modeling and simulation, enabling the rotor to have lower local stress in the sheath, smaller rotor inertia, and higher air gap magnetic field concentration effect under high-speed rotation conditions. This achieves comprehensive optimization of the surface-mounted permanent magnet synchronous motor for high-speed spindles in terms of torque output capability, torque fluctuation suppression, and anti-demagnetization performance.

[0056] In the manufacturing process, rectangular permanent magnets are first attached to the outer periphery of the quasi-polygonal rotor core according to the designed magnetization strength and arrangement order. Then, potting and curing are performed, and finally, the entire assembly is installed into the sheath. This structure ensures the quasi-concentric arrangement of the rotor and sheath, avoids the local stress concentration problem caused by the eccentricity of traditional rotors, and simplifies the assembly process. This disclosure achieves a comprehensive technology for high-speed spindle surface-mount permanent magnet synchronous motor rotors in terms of air gap magnetic flux density sinusoidal optimization, sheath stress uniformity, and mechanical strength improvement through rectangular magnets, quasi-polygonal rotors, potting, and combinations of multiple magnetization strengths. To avoid local stress concentration in the sheath, improve rotor mechanical strength and high-speed operation stability, and simplify structural design and assembly processes, this disclosure proposes designing each magnetic pole of the rotor as composed of multiple rectangular permanent magnets. By rationally distributing the magnetization strength of each permanent magnet, the air gap magnetic flux density waveform can be optimized without rotor eccentricity, thereby improving torque stability, reducing harmonic content, and ensuring that the effective value of the air gap magnetic flux density meets the motor output performance requirements.

[0057] This disclosure also provides a method for calculating the parameters of a surface-mounted permanent magnet synchronous motor, including: The remanent magnet distribution identifier of the permanent magnet in the unipolar permanent magnet is determined based on the number of permanent magnets in the surface-mounted permanent magnet synchronous motor. Determine the magnetic field distribution of the permanent magnet corresponding to the remanent magnetization distribution identifier; The magnetization intensity of the unipolar permanent magnet is determined based on the magnetic field distribution and the permanent magnet shape of the permanent magnet. The remanence density of the unipolar permanent magnet is determined based on its magnetization intensity.

[0058] For surface-mounted permanent magnet synchronous motors, the remanence distribution is first identified based on the number of unipolar permanent magnets, thus clarifying the distribution characteristics of the remanence. Next, the magnetic field distribution corresponding to this identification is determined, and the magnetization intensity is then determined in conjunction with the shape of the permanent magnets. Finally, the remanence density is derived based on the magnetization intensity. By progressively deriving and correlating various parameters, the relevant parameters of the permanent magnets can be accurately calculated, providing reliable data support for the optimized design of the motor and helping to improve its performance and operating efficiency. Compared to traditional finite element analysis methods, this parameter calculation method for surface-mounted permanent magnet synchronous motors ensures accuracy while avoiding complex mesh generation and large-scale numerical calculations. It can quickly derive parameters such as the remanence density of the permanent magnets, significantly saving time and computational resources. It also reduces reliance on software and allows for flexible parameter adjustment based on different design requirements and conditions to adapt to various design scenarios.

[0059] In some embodiments, determining the remanent magnetization distribution identifier of the permanent magnets in a single-pole permanent magnet synchronous motor based on the number of permanent magnets in the single-pole permanent magnet includes: When the number of permanent magnets q is even, the remanent magnetization distribution identifier of the permanent magnets includes, ; When the number of permanent magnets q is odd, the remanent magnetization distribution identifier of the permanent magnets includes, .

[0060] Specifically, such as Figure 1 As shown, the number of magnet blocks in a unipolar permanent magnet can be defined as q, with symmetrical magnetization on both sides. If q is odd, there are (q+1) / 2 variables; if q is even, there are n variables, such as... Figure 4 As shown, Figure 4 A schematic diagram of the distribution of a unipolar magnet is shown when q is 10. At this time, each segment of the unipolar permanent magnet can be denoted as... .

[0061] The magnetic field distribution of each permanent magnet can include:

[0062] Among them, such as Figure 6 As shown, The radial component of the magnetization vector of the permanent magnet is given. Let be the tangential component of the magnetization vector of the permanent magnet. The angle between the radial component and the tangential component of the magnetization vector. Where is the vacuum permeability, and p is the number of pole pairs of the motor. is the pole arc coefficient. n is the harmonic order of the Fourier decomposition, and p is the number of pole pairs of the motor.

[0063] The above formula can be written in Fourier series form as follows:

[0064] Where n is the harmonic order. Let n be the nth harmonic component of the radial component of the magnetization vector of the j-th permanent magnet. It is the nth harmonic component of the radial component of the magnetization intensity vector of the j-th permanent magnet.

[0065] Based on the analysis of the radial and tangential components of the magnetization vector within different angular intervals, the radial component of the magnetization vector is determined in each range. Mr and tangential components Mθ This study comprehensively considers motor parameters such as the number of pole pairs and pole arc coefficient, as well as factors such as the harmonic order of Fourier decomposition. Simultaneously, it transforms the magnetic field distribution formula using Fourier series form, converting it from a spatial function expression into a series summation form based on harmonic orders. This allows for a deeper analysis of the intrinsic laws governing the magnetic field distribution and improves the accuracy of parameter calculations.

[0066] Furthermore, we can obtain:

[0067] in, These are the calculated coefficients for each magnetization vector.

[0068] In some embodiments, the permanent magnet is tile-shaped, wherein...

[0069] When j is even or not odd (k) ; When j is odd and j=k .

[0070] Based on the known Fourier series form of the magnetic field distribution of a permanent magnet, the specific expressions for the magnetization vector components in the Fourier series are further derived. By introducing intermediate coefficients and considering different conditions such as the shape of the permanent magnet (e.g., tile-shaped and rectangular) and the parity or cardinality of the number of magnets, formulas for calculating these intermediate coefficients are given. The coefficient values ​​for each harmonic order are accurately calculated using trigonometric relationships, thus obtaining the Fourier series expression for the magnetization vector components. Corresponding formulas are given for different shapes of permanent magnets and different numbers of magnets q, enabling a more accurate simulation of the magnetic field characteristics of actual permanent magnets. Accurate calculation of the intermediate coefficients and the expressions for the magnetization vector components helps in the in-depth analysis of harmonic components in the magnetic field, providing a theoretical basis for optimizing permanent magnet design and reducing magnetic field harmonic distortion rate, thereby improving motor performance, such as increasing efficiency and reducing vibration and noise.

[0071] In some embodiments, the permanent magnet is rectangular in shape, wherein...

[0072] When j is even or not odd (k):

[0073] When j is odd and j=k

[0074] Wherein, is the air gap angle difference between the tile-shaped permanent magnet and the rectangular permanent magnet.

[0075] When the permanent magnet is rectangular, considering the air gap angle difference A between tile-shaped and rectangular permanent magnets, specific calculation formulas for the intermediate coefficient are given for different cases to meet the calculation requirements of the magnetic field distribution of rectangular permanent magnets. By incorporating key factors such as the air gap angle difference, the magnetic field distribution characteristics of rectangular permanent magnets can be reflected more realistically and accurately. This is beneficial for accurately deriving the magnetization vector components and for in-depth analysis of the magnetic field harmonics of rectangular permanent magnet motors. Furthermore, it provides strong theoretical support for optimizing motor design and improving motor performance, such as increasing electromagnetic conversion efficiency and reducing electromagnetic interference.

[0076] In some embodiments,

[0077] in, This is the polar arc coefficient. The thickness of the permanent magnet. This refers to the rotor outer diameter excluding the permanent magnet. Specifically, see [link to documentation]. Figure 7 , Figure 7 A schematic diagram of rotor and permanent magnet parameters according to an embodiment of the present disclosure is shown. For the rectangular permanent magnet, the phase angle tile-shaped segments on both sides are reduced. The angle of reduction on both sides is... .

[0078] In some embodiments, determining the magnetization of the monopole permanent magnet based on the magnetic field distribution and the permanent magnet shape includes: ;in, The magnetization intensity of the unipolar permanent magnet is given.

[0079] Based on the acquired magnetic field distribution information and the specific shape characteristics of the permanent magnet, the magnetization intensity is decomposed into radial component correlation terms and tangential component correlation terms. To calculate the sum of the first i Magnetization of each permanent magnet Mn This method comprehensively considers the effects of the magnetic field in different directions and the influence of its shape on the calculation of magnetization. It can more accurately determine the magnetization of permanent magnets, providing key parameter basis for in-depth analysis of the magnetic field characteristics of permanent magnets, optimization of permanent magnet design, and improvement of the performance of related motors and other equipment. It also helps to reduce magnetic field harmonics and improve energy conversion efficiency.

[0080] In some embodiments, determining the remanence density of the unipolar permanent magnet based on its magnetization includes:

[0081] in, The permeability of free space, Where n is the relative permeability, n is the harmonic order, and p is the number of pole pairs of the motor. The rotor outer diameter excluding the permanent magnet. The outer diameter of the rotor containing the permanent magnet. The inner diameter of the rotor. The angle between the radial component and the tangential component of the magnetization vector is denoted by r, and r is the distance from the calculated position to the center of the rotor.

[0082] The remanence density is determined based on the magnetization of the permanent magnet, and is calculated by decomposing it into radial and tangential components using Fourier series. Parameters such as vacuum permeability, relative permeability, harmonic order, number of motor pole pairs, and rotor inner and outer diameters are comprehensively considered. Among these, coefficients... The calculation incorporates the magnetization component of the permanent magnet and also introduces a position-dependent function and These functions take into account the distance from the calculation position to the rotor center, thus accurately describing the distribution of remanent magnetization at different positions and under different harmonics. This allows for a very precise determination of the remanent magnetization of the permanent magnet, fully considering the influence of various factors on it. Through Fourier series decomposition and comprehensive calculation of various parameters, the distribution characteristics of remanent magnetization in the spatial and harmonic domains can be clearly understood. This provides detailed and accurate data support for permanent magnet performance evaluation and motor design optimization, helping to improve motor efficiency, reduce losses, and minimize electromagnetic interference.

[0083] This disclosure also provides a surface-mounted permanent magnet synchronous motor (SPMSM), which performs parameter calculations or optimizations based on the methods described in the embodiments of this disclosure. For example, in the parameter optimization of the SPMSM, the remanence (Brj) of each permanent magnet in the unipolar permanent magnet is used as the optimization variable to improve motor performance. The optimization direction can be clearly defined (such as increasing torque density, reducing torque ripple, or improving efficiency), and constraints such as magnet size, air gap magnetic flux density, temperature limits, and cost can be set. Subsequently, Brj is decomposed into radial / tangential components (if segmented magnetization is used) through parametric modeling, and its correlation with performance such as air gap magnetic flux density and torque is established using the parameter calculation method described in the embodiments of this disclosure. On this basis, a global search and iterative optimization of the initial range of Brj is performed using a fitness function (such as a weighted combination of torque and ripple) as the evaluation criterion. The electromagnetic performance of each set of parameters can be verified by fast magnetic circuit calculation or FEA, and finally, the optimal solution that meets the constraints is selected through multiple rounds of iteration. Figure 8The parameter optimization method described in this disclosure achieves the same results as the parameter optimization method using finite element analysis. Compared to finite element analysis, it eliminates the need for complex finite element models, avoids tedious mesh generation and large-scale numerical calculations, significantly shortens the calculation cycle, and provides parameter results quickly, thus significantly improving optimization efficiency. While maintaining the same calculation results as finite element analysis, it lowers the barrier to entry for high-requirement computing resources and specialized software, reduces uncertainties caused by software operation and model errors, and makes the parameter optimization process more controllable and repeatable. This provides an efficient and reliable approach for parameter calculation and optimization of surface-mounted permanent magnet synchronous motors.

[0084] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this disclosure (including the claims) is limited to these examples; within the framework of this disclosure, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this disclosure as described above, which are not provided in detail for the sake of brevity.

[0085] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this disclosure, the provided drawings may or may not show well-known power / ground connections to integrated circuit (IC) chips and other components. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this disclosure, and this also takes into account the fact that the details of implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this disclosure will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this disclosure, it will be apparent to those skilled in the art that the embodiments of this disclosure can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0086] Although this disclosure has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0087] This disclosure is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for analytically calculating the air gap magnetic flux density of unequally magnetized rotor poles, characterized in that, include: The remanent magnet distribution identifier of the permanent magnet in the unipolar permanent magnet is determined based on the number of permanent magnets in the surface-mounted permanent magnet synchronous motor. Determine the magnetic field distribution of the permanent magnet corresponding to the remanent magnetization distribution identifier; The magnetization intensity of the unipolar permanent magnet is determined based on the magnetic field distribution and the permanent magnet shape of the permanent magnet. The remanence density of the unipolar permanent magnet is determined based on its magnetization intensity.

2. The method according to claim 1, characterized in that, The remanent magnet distribution identifier of the permanent magnets in the unipolar permanent magnet synchronous motor is determined based on the number of permanent magnets in the unipolar permanent magnet, including: When the number of permanent magnets q is even, the remanent magnetization distribution identifier of the permanent magnets includes , , ; When the number of permanent magnets q is odd, the remanent magnetization distribution identifier of the permanent magnets includes , , .

3. The method according to claim 1, characterized in that, Determining the magnetic field distribution of the permanent magnet corresponding to the remanent magnetization distribution identifier includes: ； in, The radial component of the magnetization vector of the unipolar permanent magnet is... Let be the tangential component of the magnetization vector of the unipolar permanent magnet. The angle between the radial component and the tangential component of the magnetization vector. Where is the vacuum permeability, and p is the number of pole pairs of the motor. This represents the polar arc coefficient.

4. The method according to claim 2, characterized in that, Also includes: Performing a Fourier transform on the magnetic field distribution of the permanent magnet yields: ； ； Where n is the harmonic order. Let n be the nth harmonic component of the radial component of the magnetization vector of the j-th permanent magnet. Let n be the nth harmonic component of the radial component of the magnetization intensity vector of the j-th permanent magnet; ； ； in, , , , These are the calculated coefficients for each magnetization vector.

5. The method according to claim 4, characterized in that, The permanent magnet is tile-shaped, wherein... ； ； When j is even or not odd (k) ； ； When j is odd and j=k ； 。 6. The method according to claim 4, characterized in that, The permanent magnet is rectangular in shape, wherein... ； ； When j is even or not odd (k) ； ； When j is odd and j=k ； ； in, This represents the air gap angle difference between the tile-shaped permanent magnet and the rectangular permanent magnet.

7. The method according to claim 6, characterized in that, include: ； ； ； ； ； in, This is the polar arc coefficient. The thickness of the permanent magnet. The outer diameter of the rotor excluding the permanent magnet.

8. The method according to claim 4, characterized in that, Determining the magnetization of the monopole permanent magnet based on the magnetic field distribution and the permanent magnet shape includes: ;in, The magnetization intensity of the unipolar permanent magnet is given.

9. The method according to claim 8, characterized in that, Determining the remanence density of the unipolar permanent magnet based on the magnetization of the permanent magnet includes: ； ； ； ； ； ； in, The permeability of free space, Where n is the relative permeability, n is the harmonic order, and p is the number of pole pairs of the motor. The rotor outer diameter excluding the permanent magnet. The outer diameter of the rotor containing the permanent magnet. The inner diameter of the rotor. The angle between the radial component and the tangential component of the magnetization vector is denoted by r, and r is the distance from the calculated position to the center of the rotor.

10. A surface-mounted permanent magnet synchronous motor, characterized in that, The parameters of the surface-mounted permanent magnet synchronous motor are calculated based on the method described in any one of claims 1-9.

Images