Axial flux motor multi-subdomain magnetic field analytical modeling system and method

Abstract

The application discloses an axial flux motor multi-subdomain magnetic field analytical modeling system and method, relates to the technical field of motor and electromagnetic field modeling, and comprises the following steps: in the axial flux motor multi-subdomain magnetic field analytical modeling process, a time-frequency expansion mode associated with the rotating speed is introduced, the magnetic field analytical result is expanded, and based on the time-frequency expansion result, main magnetic field components and high-order perturbation magnetic field components are distinguished; meanwhile, a continuously traceable harmonic characteristic mark is established for each order magnetic field component obtained through expansion. Through the introduction of the time-frequency expansion and layered processing mechanism associated with the rotating speed, the high-order perturbation magnetic field components are identified, constrained and inhibited, so that the magnetic field analytical result remains physical consistency and stability under high-speed working conditions; meanwhile, the influence of abnormal magnetic field oscillation on torque and noise is reduced, and the modeling reliability and running smoothness of the axial flux motor under high-speed operation are improved through the combination of boundary interaction description, phase and amplitude collaborative processing and the combined action of time and space.

Description

Technical Field

[0001] This invention relates to the field of motor and electromagnetic field modeling technology, specifically to a multi-subdomain magnetic field analytical modeling system and method for axial flux motors. Background Technology

[0002] Multi-subdomain analytical modeling of the magnetic field in axial flux motors addresses the characteristics of energy-saving axial flux motors, such as the magnetic flux primarily closing along the motor axis, complex structural layers, and uneven material distribution. Based on the motor's actual physical structure and electromagnetic characteristics, the internal magnetic field space is divided into several interconnected sub-regions. Within each sub-region, an analytical expression with well-defined boundary conditions is established based on the fundamental laws of electromagnetic fields. Through the continuity and coupling relationships between sub-regions, a unified description of the overall magnetic field is achieved. This method, by analytically deriving physical quantities such as magnetomotive force and magnetic induction intensity within the sub-regions, accurately characterizes the magnetic field distribution patterns and their interactions in different regions such as the stator, rotor, permanent magnets, and air gap, without relying on extensive numerical discretization calculations. This provides a physically interpretable modeling approach for the electromagnetic performance analysis, structural parameter design, and operational characteristic prediction of energy-saving axial flux motors.

[0003] The existing technology has the following shortcomings: In existing technologies, when performing multi-subdomain magnetic field analytical modeling of axial flux motors under high-speed conditions, the magnetic field distribution is typically described using multi-order analytical terms. As the rotational speed continues to increase, higher-order terms related to the frequency of rotational angle changes are easily amplified abnormally, resulting in magnetic field oscillations with fixed periods in the analytical results. While these oscillations mathematically satisfy the analytical equations and subdomain boundary conditions, and are therefore considered valid results in calculations, they are difficult to realistically generate in actual operation due to limitations imposed by core hysteresis, eddy current losses, and structural damping. Existing technologies often fail to identify such non-physical oscillations. For example, in high-speed disc-type axial flux motors, analytical models may predict multiple rapid fluctuations in air gap magnetic flux density per revolution, leading the control system to frequently adjust the current accordingly. However, in actual operation, this can easily induce significant electromagnetic noise and torque pulsation, thus affecting motor stability.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this application and may therefore include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-subdomain magnetic field analytical modeling system and method for axial flux motors to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a multi-subdomain magnetic field analytical modeling method for axial flux motors, comprising the following steps: In the process of analytical modeling of the multi-subdomain magnetic field of the axial flux motor, a time-frequency expansion method related to the rotational speed is introduced to expand the analytical results of the magnetic field. Based on the time-frequency expansion results, the main magnetic field components and higher-order disturbance magnetic field components are distinguished. At the same time, harmonic feature markers that can be continuously tracked are established for each order of magnetic field components obtained by expansion. Based on the established harmonic feature markers, the higher-order perturbation magnetic field components that exhibit abnormal amplitude growth with rotational speed are located, and the phase-time trajectory of the located higher-order perturbation magnetic field components is extracted to form an oscillation feature set for characterizing magnetic field oscillation behavior. Based on the formed set of oscillation features, and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, the source of magnetic field oscillation corresponding to the set of oscillation features is determined, and at the same time, a boundary interaction description result reflecting the change of the multi-subdomain boundary relationship is generated. Based on the generated boundary interaction description results, during the magnetic field analytical modeling calculation process, phase constraints and amplitude limits are applied to the higher-order disturbance magnetic field components corresponding to the oscillation source, and a set of control instructions divided into time and space dimensions is generated based on the phase constraints and amplitude limits. Based on the generated set of control commands, the higher-order perturbation magnetic field components in the magnetic field analytical modeling process are processed. By introducing a reverse time back-off mechanism and a high-frequency oscillation slow-release section, and combining it with a zero-mean torque cancellation method, the abnormal magnetic field oscillations caused by the higher-order perturbation magnetic field components are suppressed online.

[0007] Preferably, the steps for obtaining harmonic feature markers are as follows: In the process of magnetic field analytical modeling, a correlation expression between rotational speed and angular displacement is established, and rotational speed is introduced into the time axis and rotational axis expression of the magnetic field analytical results. The multi-subdomain magnetic field analytical results are projected onto the time domain sequence and angular domain sequence labeled with rotational speed. After completing the rotational speed labeling, the magnetic field analysis results are subjected to time-frequency expansion in relation to the rotational speed. The magnetic field physical quantities are jointly expanded along the time dimension and the rotational angle dimension to form a set of magnetic field components with frequency and order indicators. Based on the magnetic field component set, the main magnetic field components and higher-order perturbation magnetic field components are distinguished according to energy proportion, component continuity and order stability, and the distinction results are written back to the magnetic field component set of each subdomain. After component differentiation is completed, harmonic characteristic markers containing rotational speed labeling information, frequency indication, order indication, subdomain identifier and phase reference are established for each order magnetic field component to achieve continuous tracking across subdomains.

[0008] Preferably, when establishing harmonic characteristic markings, the speed marking information and order indication constitute the basis for maintaining component identity, and the phase reference benchmark unifies the phase reference method of the same order magnetic field component in each subdomain, so that the magnetic field component maintains continuous identity during speed change, and a consistent correspondence is formed between the stator subdomain, air gap subdomain, permanent magnet subdomain and rotor subdomain.

[0009] Preferably, the steps for forming the oscillation feature set are as follows: Based on the harmonic characteristic marking, a following relationship oriented to the rotational speed change is established. The magnetic field components of each order are formed into a continuous following sequence according to the harmonic characteristic marking, and the amplitude evolution with the rotational speed is recorded. Based on the follow-up sequence and amplitude evolution record, the higher-order perturbation magnetic field components are located, and the location results are supplemented with rotational speed range indication and subdomain correlation indication. The trajectory of phase change over time is extracted from the high-order perturbation magnetic field components obtained by positioning, according to the harmonic characteristic markers, and a phase increment sequence and a phase loop point sequence are formed. Based on the positioning results and phase trajectory information, an oscillation feature set bound to the subdomain identifier is formed to characterize the magnetic field oscillation behavior.

[0010] Preferably, the steps for generating the boundary interaction description result are as follows: The oscillation feature set is structured and organized, the feature entries are merged according to harmonic feature marking, and the trajectory correlation of rotation speed labeling information, subdomain identification, amplitude evolution record, and phase change over time is established. At the same time, the subdomain boundary information index is supplemented. After the data processing is completed, a family of frequency-related dissipation curves is constructed by combining the material loss characteristics, and the amplitude evolution record is aligned with the family of dissipation curves to form a dissipation reference for the oscillation source. Based on the dissipative reference discrimination, the attenuation law of the end magnetic field is introduced, an axial attenuation path index is established, and a boundary phase transfer trajectory is formed to improve the spatial reference discrimination; The source of magnetic field oscillations is determined based on dissipative reference discrimination and spatial reference discrimination, and boundary interaction description results reflecting the changes in the relationship between multiple subdomains are generated simultaneously.

[0011] Preferably, the source of magnetic field oscillation is identified by using harmonic feature markers as a unified reference identifier, and the subdomain boundary information index is synchronously associated under the constraint of rotational speed labeling information. This ensures that the boundary interaction description results simultaneously include the boundary phase transfer state and the boundary amplitude transfer state, which are used to limit the phase constraint and amplitude limit input in subsequent magnetic field analytical modeling calculations.

[0012] Preferably, the steps for generating the control instruction set are as follows: The boundary interaction description results are subjected to constraint object mapping, and the boundary continuity characterization, boundary coupling strength characterization, boundary phase offset characterization are bound to the harmonic feature markers, and the corresponding subdomain boundary positions are clarified. After completing the mapping of the constrained objects, phase constraints are applied to the higher-order perturbation magnetic field components corresponding to the oscillation source based on the reference sequence of the boundary phase offset evolving over time, while maintaining consistency between the harmonic feature marker and the subdomain identifier. Based on phase constraints, amplitude constraints are applied to the same higher-order perturbation magnetic field components by combining amplitude evolution records and boundary coupling strength characterization quantities. Based on phase constraints and amplitude limitations, a set of control commands is generated, which is divided into time and space dimensions and bound to subdomain identifiers.

[0013] Preferably, when generating the set of control instructions, the interval division of the time dimension is kept consistent with the trajectory of phase change over time, and the subdomain identifier of the spatial dimension is matched with the subdomain boundary position, so that the phase constraint and amplitude limit remain continuous and consistent at the boundary of each subdomain, thereby giving the set of control instructions a unified constraint reference caliber in the multi-subdomain structure.

[0014] Preferably, based on the generated set of control commands, the higher-order perturbation magnetic field components in the analytical modeling process of the magnetic field are processed. By introducing a reverse time back-off mechanism, a high-frequency oscillation slow-release section, and a zero-mean torque cancellation method, the higher-order perturbation magnetic field components are constrained in the following steps: The set of control commands is expanded to include an execution entry point. Command entries are grouped according to harmonic characteristics and a binding relationship is established between time dimension interval identifiers and spatial dimension subdomain identifiers. After binding is completed, a reverse time back-off mechanism is introduced to back-off the phase and amplitude expressions of higher-order perturbation magnetic field components along the time axis, and to maintain phase reference consistency at the subdomain boundary. Based on the reverse time back-off mechanism, a high-frequency oscillation slow-release section is introduced to continuously slow-release the amplitude and phase expressions of the higher-order perturbation magnetic field components within the corresponding time interval. By combining zero-mean torque cancellation with the slow-release processing path, the torque contribution of higher-order perturbation magnetic field components is symmetrically configured, thereby achieving online suppression of abnormal magnetic field oscillations.

[0015] An analytical modeling system for multi-subdomain magnetic fields of axial flux motors, comprising a harmonic annotation module, an oscillation feature extraction module, an oscillation discrimination module, a constraint generation module, and an oscillation suppression module: The harmonic annotation module introduces a time-frequency expansion method related to rotational speed during the analytical modeling of the multi-subdomain magnetic field of the axial flux motor. It expands the analytical results of the magnetic field and distinguishes the main magnetic field components from the higher-order perturbation magnetic field components based on the time-frequency expansion results. At the same time, it establishes continuously traceable harmonic feature markers for each order of magnetic field components obtained by expansion. The oscillation feature extraction module, based on the established harmonic feature markers, locates the high-order perturbation magnetic field components that exhibit abnormal amplitude growth with changing rotation speed, and extracts the trajectory of phase change over time around the located high-order perturbation magnetic field components to form an oscillation feature set for characterizing the magnetic field oscillation behavior. The oscillation discrimination module, based on the formed oscillation feature set and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, discriminates the source of magnetic field oscillation corresponding to the oscillation feature set, and generates boundary interaction description results that reflect the changes in the multi-subdomain boundary relationship. The constraint generation module, based on the generated boundary interaction description results, applies phase constraints and amplitude limits to the higher-order disturbance magnetic field components corresponding to the oscillation source during the magnetic field analytical modeling calculation process, and generates a set of control instructions divided by time and space dimensions based on the phase constraints and amplitude limits. The oscillation suppression module, based on the generated set of control instructions, processes the high-order perturbation magnetic field components during the analytical modeling of the magnetic field. By introducing a reverse time back-off mechanism and a high-frequency oscillation mitigation section, and combining it with a zero-mean torque cancellation method, it suppresses the abnormal magnetic field oscillations caused by the high-order perturbation magnetic field components online.

[0016] The technical effects and advantages provided by the present invention in the above technical solution are as follows: This invention introduces a hierarchical processing mechanism involving time-frequency expansion, harmonic feature marking, and oscillation feature sets related to rotational speed during the analytical modeling of the multi-subdomain magnetic field of an axial flux motor. This mechanism ensures that the analytical magnetic field results maintain stable physical consistency under high-speed operating conditions. By locating, identifying, and constraining higher-order perturbation magnetic field components, the invention avoids the continuous amplification of mathematically valid but physically unrealizable magnetic field oscillations in the analytical results. Consequently, the modeling results more closely approximate the actual operating conditions when describing the magnetic field distribution in regions such as the stator, rotor, permanent magnets, and air gap. This enhances the reliability and usability of the analytical magnetic field model under high-speed conditions, providing a more reliable foundation for subsequent electromagnetic performance analysis and parameter design.

[0017] This invention introduces phase constraints, amplitude limitations, and time-space co-processing methods based on boundary interaction description results during the analytical modeling and calculation of the magnetic field. This enables continuous and controllable suppression of higher-order perturbation magnetic field components during the modeling process. Through the combined effects of a reverse time back-off mechanism, a high-frequency oscillation mitigation section, and a zero-mean torque cancellation method, the influence of abnormal magnetic field oscillations on the analytical results and torque expression can be effectively weakened, reducing the risk of electromagnetic noise and torque fluctuations caused by the analytical model. This improves the overall stability and smoothness of the axial flux motor under high-speed operating conditions. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0019] Figure 1 This is a flowchart of the analytical modeling method for the multi-subdomain magnetic field of the axial flux motor of the present invention.

[0020] Figure 2 This is a schematic diagram of the modules of the multi-subdomain magnetic field analytical modeling system for the axial flux motor of the present invention. Detailed Implementation

[0021] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description disclosed herein will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art.

[0022] This invention provides, for example Figure 1 The analytical modeling method for the multi-subdomain magnetic field of the axial flux motor shown includes the following steps: In the process of analytical modeling of the multi-subdomain magnetic field of the axial flux motor, a time-frequency expansion method related to the rotational speed is introduced to expand the analytical results of the magnetic field. Based on the time-frequency expansion results, the main magnetic field components and higher-order disturbance magnetic field components are distinguished. At the same time, harmonic feature markers that can be continuously tracked are established for each order of magnetic field components obtained by expansion. To maintain the physical usability and consistency of the analytical results of the multi-subdomain magnetic field under high-speed conditions, the magnetic field analytical results are subjected to time-frequency expansion with speed correlation, and harmonic feature markers that can be continuously tracked are established. The specific implementation steps are as follows: A correlation between rotational speed and angular displacement is established, and the rotational speed of the axial flux motor is introduced as a constant throughout the magnetic field analytical modeling process. Based on the angular velocity corresponding to the rotational speed, the evolution relationship of the rotational angle over time is determined, and this evolution relationship is embedded in the expression of the magnetic field analytical results, so that the magnetic field analytical results form a one-to-one mapping between the time axis and the rotational axis. On this basis, the multi-subdomain magnetic field analytical results are uniformly projected onto the time domain sequence and angular domain sequence labeled with rotational speed, thereby providing a consistent independent variable system for subsequent time-frequency expansion and avoiding the expression differences of inconsistent parameter calibers of the same magnetic field analytical results at different rotational speeds.

[0023] After completing the rotational speed labeling and unifying the independent variables, the magnetic field analysis results are subjected to a time-frequency expansion method related to rotational speed. During time-frequency expansion, the time variable of the rotational speed label is used as the expansion driving quantity, and the rotation angle variable is used as the synchronization reference quantity. The magnetic field physical quantities such as magnetomotive force and magnetic induction intensity are jointly expanded along the time dimension and the rotation angle dimension within each subdomain. During the expansion process, the continuous change of the same physical quantity is decomposed into a set of expansion components with frequency indication in the time dimension and order indication in the rotation angle dimension, so that each expansion component carries both "frequency information of rotational speed labeling" and "spatial order information". After the expansion is completed, all expansion components are merged according to frequency and order to obtain a set of magnetic field components with clear time-frequency positions. The expression format of this set is kept consistent in different subdomains such as stator, rotor, permanent magnet, and air gap, so that the magnetic field analysis results still maintain an isomorphic expansion aperture when cross-subdomain docking.

[0024] The time-frequency expansion method adopts a time-rotation angle dual-domain joint expansion structure driven by rotation speed annotation information. The specific implementation process is as follows: In the process of magnetic field analytical modeling, magnetomotive force or air gap magnetic flux density is selected as the expansion object. The magnetic field analytical results are expressed as a function of time variable and rotation angle variable. The rotation angle variable is obtained by integrating the rotation speed annotation information. That is, a mapping relationship between rotation angle and time is established based on the relationship between angular velocity and time, so that a one-to-one correspondence is formed between the time axis and the rotation angle axis. After the mapping relationship is established, the magnetic field analytical results are resampled in the angular domain, so that the original time series is rearranged under a uniform rotation angle interval, thereby obtaining the angular domain sequence with rotation angle as the independent variable.

[0025] After completing the angular domain resampling, the angular domain sequence is expanded by order, and the magnetic field physical quantity is decomposed into several order components with clear order indications along the angular dimension. Each order component corresponds to the spatial harmonic structure. At the same time, the original time variable is retained, and the frequency of each order component is marked along the time dimension, so that each component carries both order indication and frequency indication information, thus forming a set of magnetic field components with "frequency-order" dual identification.

[0026] After forming the set of magnetic field components, the energy ratio, order stability, and phase continuity are used as the component classification criteria. Components that maintain a constant order and stable energy ratio during continuous rotational speed changes are identified as the main magnetic field components. Components with higher order and densely distributed frequency drift or phase abrupt changes with rotational speed changes are identified as higher-order perturbation magnetic field components. The above classification process uses frequency indication and order indication as unified discrimination coordinates to ensure that the classification results have a consistent comparison caliber under different rotational speed labeling conditions.

[0027] After the components are distinguished, a harmonic feature mark is established for each magnetic field component. The harmonic feature mark includes at least speed marking information, order indication, frequency indication, subdomain identifier, and a unified phase reference. The speed marking information and order indication constitute the basis for maintaining the component identity, so that the same order component maintains its identity continuity during speed changes. The phase reference is used to unify the phase reference method of each subdomain for the same order component, thereby ensuring that a consistent component correspondence can be established between the stator subdomain, air gap subdomain, permanent magnet subdomain, and rotor subdomain.

[0028] Based on the magnetic field component set obtained from time-frequency expansion, the main magnetic field components and higher-order perturbation magnetic field components are distinguished. The determination of the main magnetic field components is based on a comprehensive criterion of energy proportion, component continuity, and order stability during rotational speed changes: components that maintain stable order indication with rotational speed changes, have continuous phase evolution, and have a dominant contribution in the component set are classified as main magnetic field components, while components that exhibit higher order indication, rapid frequency shift with rotational speed changes, or dense phase evolution are classified as higher-order perturbation magnetic field components. To ensure that the distinction process is closely connected with the time-frequency expansion results of the previous sub-step, when distinguishing between the main magnetic field components and higher-order perturbation magnetic field components, the frequency indication and order indication formed by time-frequency expansion are directly used as the unified coordinates for component discrimination. The distinction results are written back to the magnetic field component set of each subdomain using the same coordinate system, so that the main magnetic field components and higher-order perturbation magnetic field components can maintain consistent component numbering logic and phase reference caliber at the boundary of each subdomain, thus laying the foundation for subsequent continuous tracking across subdomains.

[0029] After distinguishing between the main magnetic field components and higher-order perturbation magnetic field components, continuously trackable harmonic feature markers are established for each order of magnetic field component obtained from the expansion. These harmonic feature markers consist of rotational speed annotation information, frequency indication, order indication, subdomain identifier, and a phase reference benchmark. The rotational speed annotation information is written into the harmonic feature marker to indicate the angular velocity environment corresponding to the component; the frequency and order indications are written into the harmonic feature marker to indicate the position of the component in the time-frequency expansion coordinate system; the subdomain identifier is written into the harmonic feature marker to indicate the component's affiliation in the multi-subdomain structure; and a unified phase reference benchmark is set to constrain the phase reference method of different subdomains for the same component. During the establishment of the harmonic feature markers, a combination of "rotational speed annotation information + order indication" is used to address the potential frequency drift of the same order component during rotational speed changes. The key maintains the continuity of component identity and locks the phase expression caliber of the component with a phase reference benchmark, so that the harmonic feature marker can maintain a stable tracking link even when the rotational speed changes continuously. When splicing cross-subdomain field quantities, components with the same order indication and consistent phase reference benchmark in each subdomain are assigned consistent harmonic feature markers. This allows the analytical expression of the same harmonic component on the stator side, air gap side, permanent magnet side, and rotor side to achieve a consistent correspondence through the harmonic feature markers. Thus, without changing the basic structure of multi-subdomain magnetic field analytical modeling, the magnetic field analysis results, the distinction results between the main magnetic field components and the higher-order disturbance magnetic field components, and the continuous tracking information of each order magnetic field component are unified into the same annotation system. This provides a consistent analytical basis and reference caliber for subsequent positioning, phase trajectory extraction, and constraint processing of higher-order disturbance magnetic field components.

[0030] Based on the established harmonic feature markers, the higher-order perturbation magnetic field components that exhibit abnormal amplitude growth with rotational speed are located, and the phase-time trajectory of the located higher-order perturbation magnetic field components is extracted to form an oscillation feature set for characterizing magnetic field oscillation behavior. To ensure that higher-order perturbation magnetic field components under high-speed operating conditions can be stably identified in the multi-subdomain magnetic field analysis results and form an oscillation characterization basis for subsequent processing, the location and phase trajectory extraction of higher-order perturbation magnetic field components are carried out around harmonic feature markers. The specific implementation steps are as follows: Based on continuously traceable harmonic feature markers, a tracking relationship oriented towards speed variation is established. The correspondence of each order magnetic field component under different speed marking conditions is concatenated according to the harmonic feature markers, so that the magnetic field components indicated by the same order form a continuous tracking sequence as the speed changes from low to high. When forming the tracking sequence, the amplitude of the magnetic field component under each speed marking condition is uniformly converted into the same reference aperture. The reference aperture is jointly defined by the speed marking information and the subdomain identifier, so that the amplitude representation of the same magnetic field component in different subdomains maintains a consistent physical meaning, thereby establishing subsequent amplitude comparisons with speed variation on a unified scale. After the tracking sequence is completed, the amplitude evolution of the set of higher-order perturbation magnetic field components is recorded one by one along the speed variation direction. The sequence of amplitude variation with speed is written into the auxiliary field of the harmonic feature marker consistent with that component, so that the harmonic feature marker simultaneously carries "identity continuity" and "amplitude evolution continuity".

[0031] Based on the follow-up sequence and amplitude evolution record, the high-order perturbation magnetic field components exhibiting abnormal amplitude growth with rotational speed are located. The location process uses harmonic feature markers as the index entry point. First, components whose order indicators reach a preset range are screened from the set of high-order perturbation magnetic field components. Then, components exhibiting "nonlinear amplification quantization characteristics within the rotational speed growth range" are identified from the screened components based on the amplitude evolution record. To avoid location offset caused by differences in amplitude dimensions between different subdomains, an amplitude standard bound to the subdomain identifier is used for location. Components corresponding to the same harmonic feature marker are located in the stator, air gap, and permanent magnet. The amplitude evolution in subdomains such as rotor is compared in parallel, and components that meet the "cross-subdomain synchronous amplification" characteristic are given priority in the positioning results. When the positioning results are output, the positioning results are given in the form of a set of harmonic feature markers, and each located harmonic feature marker is given a speed range indicator and a subdomain association indicator. The speed range indicator is used to describe the speed range in which the abnormal amplitude growth occurs, and the subdomain association indicator is used to describe the distribution location of the abnormal amplitude growth in the multi-subdomain structure. Thus, the positioning results can be traced back to the identity of the magnetic field component and the operating condition location where the abnormal amplitude growth occurs.

[0032] The phase-time trajectory of the higher-order perturbation magnetic field components obtained from the localization is extracted. The phase trajectory extraction uses harmonic feature markers from the localization results as unique reference keys. The expanded components corresponding to the same harmonic feature marker in the magnetic field analysis results are stitched together on a continuous time axis. A phase reference benchmark is used to unify the phase expression at each moment, ensuring that the phase trajectory does not experience reference frame drift when crossing speed rating segments and subdomain segments. During the phase trajectory construction process, the time axis adopts a time variable consistent with the speed rating information, maintaining consistency between the description of phase-time changes and the aforementioned time-frequency expansion speed rating system. Furthermore, the rotation angle mapping relationship is synchronously introduced into the phase trajectory expression, enabling the phase trajectory to possess both temporal and rotation angle continuity. To enhance the ability of the phase trajectory to characterize oscillation behavior, a phase increment sequence and a phase loop point sequence are further introduced into the trajectory where the phase changes over time. The phase increment sequence is used to describe the continuous trend of phase change at adjacent time points, while the phase loop point sequence is used to describe the distribution of loop events when the phase crosses the reference benchmark. Both types of sequences are bound and stored with harmonic feature markers, so that the phase evolution characteristics of the same higher-order perturbation magnetic field component under different rotation speed labeling conditions can be continuously tracked and kept comparable.

[0033] Based on the positioning results and phase trajectory extraction results, an oscillation feature set is formed to characterize the magnetic field oscillation behavior. The oscillation feature set uses harmonic feature markers as the primary key and aggregates amplitude evolution records, speed range indicators, subdomain association indicators, phase change trajectories over time, phase increment sequences, and phase loop point sequences. The aggregated information is then organized into feature entries for oscillation behavior characterization. Each feature entry corresponds to a higher-order perturbation magnetic field component, and its abnormal amplitude growth pattern, temporal continuity of phase trajectory, fluctuation distribution of phase increment, and dense distribution of phase loop events are recorded in a unified field structure. This allows the oscillation feature set to provide evidence of the temporal evolution of magnetic field oscillation behavior while maintaining the continuous tracking advantage of harmonic feature markers. After the oscillation feature set is formed, it is bound to the subdomain identifiers of the multi-subdomain structure. This allows subsequent processing to simultaneously obtain the identity information, operating condition information, and cross-subdomain distribution information of the higher-order perturbation magnetic field component when referencing the oscillation feature set. This provides a unified and directly applicable characterization basis for the subsequent identification of abnormal oscillation sources and the generation of boundary interaction description results.

[0034] Based on the formed set of oscillation features, and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, the source of magnetic field oscillation corresponding to the set of oscillation features is determined, and at the same time, a boundary interaction description result reflecting the change of the multi-subdomain boundary relationship is generated. To establish a referable correspondence between the oscillation feature set and the actual material dissipation behavior and end three-dimensional leakage effect of the axial flux motor, thereby enabling interpretable discrimination of the source of magnetic field oscillation and synchronous output of boundary interaction description results of changes in multi-subdomain boundary relationships, the specific implementation steps are as follows: The previously formed oscillation feature set is structured and aligned. Each feature entry in the oscillation feature set is merged according to harmonic feature markers. Based on the merging, a four-element correlation link is established: speed labeling information, subdomain identifier, amplitude evolution record, and phase change trajectory over time. This ensures that each feature entry forms a continuous operating condition sequence under different speed labeling conditions, while maintaining consistent correspondences between stator subdomains, air gap subdomains, permanent magnet subdomains, and rotor subdomains. After establishing the correlation link, subdomain boundary information indexes are added to each feature entry. These indexes use the adjacency relationship of subdomain identifiers as clues to bind the boundary positions of stator and air gap, air gap and permanent magnet, and permanent magnet and rotor to the feature entries. This allows the oscillation feature set to directly point to the phase continuity and amplitude transmission state of the oscillation components at the boundaries of multiple subdomains during subsequent discrimination processes, and to connect the speed labeling information and the subdomain boundary positions with the same reference caliber.

[0035] After completing the structured alignment of the oscillation feature set, a dissipation reference quantity for oscillation source discrimination is established by combining the material loss characteristics of the axial flux motor. The hysteresis dissipation characteristics of the core material, the eddy current dissipation characteristics of the core material, the conductivity dissipation characteristics of the permanent magnet material, and the eddy current dissipation characteristics of the winding conductor are uniformly organized into a family of frequency-related dissipation curves. The frequency indication range corresponding to each feature item is obtained by mapping the rotational speed labeling information, thereby aligning the feature items in the oscillation feature set with the material loss characteristics within the same frequency coordinate. Based on the alignment, the amplitude growth slope sequence and amplitude growth interval boundary are extracted along the amplitude evolution record in the oscillation feature set. By comparing the amplitude growth slope sequence with the frequency-related dissipation curve family, the dissipation curve family provides amplitude growth attainability constraints within the corresponding frequency indication range. The amplitude growth attainability constraints are used to limit the energy compensation level that the magnetic field component can maintain during continuous rotational speed increase under the action of material loss. When the amplitude evolution record shows a growth pattern that exceeds the amplitude growth attainability constraints, the corresponding feature entry is marked as dissipation mismatch oscillation, while the harmonic feature mark and subdomain identifier remain unchanged, so that the dissipation mismatch oscillation can still be continuously tracked in the multi-subdomain structure. At the same time, it provides a discrimination entry consistent with material loss for the subsequent introduction of the end magnetic field attenuation law.

[0036] After obtaining the dissipative mismatch oscillation markers, the spatial reference for identifying the source of magnetic field oscillations is further improved by combining the end magnetic field attenuation law. The end magnetic field attenuation law is expressed with axial distance as the independent variable, and an axial attenuation path index is established based on the axial path from the end boundary to each subdomain position. The axial attenuation path index is linked with the subdomain boundary information index, so that the distribution state of each feature entry near the stator end, permanent magnet end, and rotor end can be uniformly described. After the end magnetic field attenuation law is introduced, the phase advancement consistency sequence and phase change point distribution are extracted from the phase change trajectory of the oscillation feature set over time. The phase advancement consistency sequence is then projected along the axial attenuation path index to the subdomain boundary position to form the boundary phase transfer track. The attenuation law of the end magnetic field is manifested in the phase transmission trajectory at the boundary as a smoothing trend of phase transmission and an attenuation trend of amplitude transmission near the end. When the feature items in the oscillation feature set still maintain a dense distribution of high-frequency phase change points near the end and are accompanied by a continuous amplification of amplitude evolution record, the corresponding feature items are classified into end attenuation inconsistent oscillation. When the feature items show a natural attenuation of amplitude evolution record with increasing axial distance on the end attenuation path and are accompanied by a continuous phase advancement consistency sequence, the corresponding feature items are classified into end attenuation consistent oscillation. Thus, under the joint constraints of material loss characteristics and end magnetic field attenuation law, a discrimination basis with both frequency and spatial dimensions is formed for the oscillation source discrimination.

[0037] The source of magnetic field oscillations is determined based on three classification results: dissipative mismatch oscillations, inconsistent end-damping oscillations, and consistent end-damping oscillations. Simultaneously, boundary interaction descriptions reflecting changes in multi-subdomain boundary relationships are generated. The source determination uses harmonic feature markers as the primary key output. The determination content includes at least the determination interval corresponding to the rotational speed annotation information, the distribution location corresponding to the subdomain identifier, the growth pattern category corresponding to the amplitude evolution record, and the phase transfer pattern category corresponding to the phase-time trajectory. This ensures that each higher-order perturbation magnetic field component has a consistent determination output format under different rotational speed annotation conditions. The boundary interaction description results further characterize the changes in multi-subdomain boundary relationships based on the above determination outputs. Using the subdomain boundary information index as a framework, the boundary interaction description results provide a continuity representation of the boundary based on the boundary phase transfer trajectory and the boundary amplitude transfer state. The system includes three characterization parameters: boundary coupling strength and boundary phase offset. Boundary continuity is represented by the length of continuous segments in the phase-advancing consistency sequence and the sparsity of phase abrupt change points. Boundary coupling strength is represented by the transmission ratio of amplitude evolution records on both sides of the boundary and the energy compensation level. Boundary phase offset is represented by the relative offset of the boundary phase transmission trajectory under a reference phase benchmark. By using harmonic characteristic markers to connect the oscillation characteristic set, material loss characteristics, and end magnetic field attenuation laws, and by using subdomain boundary information indexes to connect the boundary phase transmission trajectory and boundary amplitude transmission state, the results of magnetic field oscillation source discrimination and boundary interaction description are simultaneously generated within the same characterization system. This provides a reference basis with working condition orientation, subdomain orientation, and boundary relationship orientation for implementing phase constraints and amplitude limitations in subsequent magnetic field analytical modeling calculations.

[0038] To further clarify the specific implementation path for oscillation source identification and boundary interaction description result generation, enabling those skilled in the art to directly complete the identification process based on the oscillation feature set, material loss characteristics, and end magnetic field attenuation law, the following supplementary explanation is provided regarding the identification process and the construction method of the boundary interaction description result: After the oscillation feature set is structured, for each harmonic feature mark, a frequency mapping function is first constructed. The rotational speed marking information and order indication are substituted into the rotational speed-frequency conversion relationship to obtain the frequency indication sequence of the feature item under each rotational speed marking condition. The frequency indication sequence is used as a unified input variable for subsequent alignment with the frequency-related dissipation curve family, so that the material loss characteristics participate in the discrimination under the same frequency coordinate.

[0039] After completing the frequency mapping, the frequency-related dissipation curve family is discretized into dissipation reference intervals corresponding to the frequency indication sequence, and the upper limit interval of energy compensation corresponding to material dissipation is calculated in each dissipation reference interval. At the same time, the amplitude evolution record of the corresponding feature item is read from the oscillation feature set, and the amplitude growth slope and amplitude growth interval length are calculated in the same frequency indication interval. By comparing the amplitude growth slope with the upper limit interval of energy compensation, a "growth slope - dissipation reference" matching matrix is ​​established. When the growth slope exceeds the upper limit of energy compensation allowed by the dissipation reference interval in a continuous frequency interval, it is determined that the feature item forms a dissipation mismatch oscillation in the corresponding speed marking interval, and the determination result is written into the oscillation source discrimination field.

[0040] After completing the dissipation reference discrimination, spatial reference discrimination is performed by introducing the end magnetic field attenuation law for both labeled and unlabeled feature entries. First, an axial distance sequence is constructed based on the subdomain boundary information index. The end boundary position is taken as the starting point of the axial distance. The positions of the stator subdomain, air gap subdomain, permanent magnet subdomain, and rotor subdomain in the axial direction are sequentially encoded as path nodes to form an axial attenuation path index. Then, the amplitude evolution records in the oscillation feature set are mapped along the axial attenuation path index, the amplitude attenuation gradient at each path node is calculated, and the attenuation gradient is compared with the attenuation reference curve given by the end magnetic field attenuation law.

[0041] Simultaneously, the phase advancement consistency sequence and phase abrupt change point distribution are extracted from the phase-time trajectory, and the phase advancement consistency sequence is projected onto the boundary positions of each subdomain corresponding to the axial decay path index to form the boundary phase transfer trajectory. The phase continuity segment length and phase offset distribution are calculated on the boundary phase transfer trajectory and compared with the phase smoothing reference trend corresponding to the end magnetic field decay law. When the amplitude decay gradient on the axial decay path does not match the reference curve and is accompanied by a dense distribution of phase abrupt change points in the boundary phase transfer trajectory, it is determined to be an end decay inconsistent oscillation. When the amplitude decay gradient on the axial decay path is consistent with the reference curve and the boundary phase transfer trajectory maintains a continuous advancement pattern, it is determined to be an end decay consistent oscillation.

[0042] After completing the material dissipation reference discrimination and the end space reference discrimination, the judgment results of dissipation mismatch oscillation, end attenuation inconsistent oscillation and end attenuation consistent oscillation are summarized according to harmonic characteristic labels, and a unified oscillation source discrimination result entry is established. Each oscillation source discrimination result entry includes at least the rotation speed labeling range, frequency indication range, subdomain distribution location, amplitude growth pattern type and phase transfer pattern type, thus forming a discrimination data structure that can be directly referenced later.

[0043] After the oscillation source discrimination results are formed, each discrimination entry is expanded at the boundary level based on the subdomain boundary information index. The oscillation source discrimination results are projected onto the boundary positions of each subdomain, and the boundary continuity characterization, boundary coupling strength characterization, and boundary phase shift characterization are calculated at the boundary level, where: The continuity characterization of the boundary is composed of the length of the continuous segment in the boundary phase transmission trajectory and the density of phase abrupt change points; The intensity of the interface coupling is characterized by the ratio of amplitude transfer recorded by the amplitude evolution on both sides of the interface and the energy compensation level within the material dissipation reference interval. The boundary phase offset characterization quantity consists of the offset sequence of the boundary phase transfer trajectory under the phase reference datum; The above three types of characterization quantities form boundary data entries bound to harmonic feature markers within each rotational speed marking interval, and are classified according to the boundary position of the subdomain, forming a data set of boundary interaction description results. The boundary interaction description results also retain the reference relationship with the oscillation source discrimination results, so that in the subsequent magnetic field analytical modeling calculation process, the corresponding boundary continuity characterization quantity, boundary coupling strength characterization quantity, and boundary phase offset characterization quantity can be directly called as the input basis for phase constraints and amplitude limits based on the harmonic feature markers.

[0044] Based on the generated boundary interaction description results, during the magnetic field analytical modeling calculation process, phase constraints and amplitude limits are applied to the higher-order disturbance magnetic field components corresponding to the oscillation source, and a set of control instructions divided into time and space dimensions is generated based on the phase constraints and amplitude limits. To enable the boundary interaction description results obtained in the preceding steps to directly affect the analytical modeling and calculation process of the magnetic field and to form executable constraint inputs for specific higher-order perturbation magnetic field components, thereby forming an instruction expression that can be organized in terms of time and space dimensions, the specific implementation steps are as follows: The boundary interaction description results are subjected to constraint object mapping. The boundary continuity characterization, boundary coupling strength characterization, and boundary phase offset characterization in the boundary interaction description results are bound one by one with the harmonic feature markers. The boundary position, subdomain identifiers on both sides of the boundary, and the set of higher-order perturbation magnetic field components related to the boundary are clearly defined by the subdomain boundary information index for each boundary interaction description result. After the binding is completed, the oscillation source discrimination output is concatenated along the harmonic feature markers so that each higher-order perturbation magnetic field component has a consistent boundary position reference method in the discrimination interval corresponding to the rotation speed label information. The boundary phase offset characterization is projected onto the time axis of the phase change trajectory over time to form a reference sequence of boundary phase offset evolution over time. This allows subsequent phase constraints to directly reference the reference sequence of boundary phase offset evolution over time in the continuous time expression, and allows subsequent amplitude constraints to directly reference the subdomain identifiers on both sides of the boundary corresponding to the boundary coupling strength characterization in spatial positioning.

[0045] After completing the mapping of the constraint objects, phase constraints are applied to the higher-order perturbation magnetic field components corresponding to the oscillation source during the analytical modeling calculation of the magnetic field. The phase constraints use a phase reference benchmark as a unified benchmark and the reference sequence of the boundary phase offset evolving over time as the constraint input. The phase expression of each higher-order perturbation magnetic field component in the subdomains on both sides of the boundary is consistent. The implementation of the phase constraints includes introducing a phase offset compensation amount and a phase advancement consistency window into the trajectory of phase change over time. The phase offset compensation amount is given by the boundary phase offset characterization amount under the corresponding rotational speed annotation information, which is used to make the phase expression of each higher-order perturbation magnetic field component consistent with the phase shift over time. The phase representation of the subdomains maintains the same reference aperture under the phase reference datum. The phase advancement consistency window is given by the boundary continuity characterization quantity under the corresponding rotational speed label information, which is used to limit the trajectory of phase change over time to maintain a continuous advancement pattern within the window interval. During the application of phase constraints, the harmonic feature markers are kept unchanged, so that the higher-order perturbation magnetic field components after phase constraints can still be continuously tracked along the harmonic feature markers during rotational speed changes. Furthermore, the subdomain identifier and subdomain boundary information index are kept unchanged, so that the phase representation after phase constraints can be directly used for subsequent boundary continuity representation at the multi-subdomain boundary position.

[0046] After applying phase constraints, amplitude limits are imposed on higher-order perturbation magnetic field components corresponding to the same oscillation source during the analytical modeling calculation of the magnetic field. The amplitude limits are spatially allocated based on amplitude evolution records and combined with the boundary coupling strength characterization. First, the upper bound of the amplitude and the upper bound of the amplitude change rate of the higher-order perturbation magnetic field component are determined within the time interval corresponding to each rotational speed label. Then, the upper bound of the amplitude and the upper bound of the amplitude change rate are allocated to the subdomains on both sides of the boundary according to the subdomain identifier. The upper bound of the amplitude is jointly limited by the energy compensation level given by the family of frequency-related dissipation curves corresponding to the material loss characteristics within the frequency indication range of this component and the transfer ratio corresponding to the boundary coupling strength characterization, ensuring that the boundary... The weaker the coupling strength characterization quantity at the boundary position, the stricter the upper bound constraint is obtained in the amplitude constraint. The upper bound of the amplitude change rate is given by the growth pattern category of the amplitude evolution record within the corresponding rotation speed label information interval, which is used to limit the excessive amplitude fluctuations that appear on the time axis. During the application of amplitude constraint, the phase expression after phase constraint remains unchanged, so that the amplitude constraint acts on the amplitude expression corresponding to the amplitude evolution record without changing the phase advancement consistency window. Thus, the higher-order perturbation magnetic field component is simultaneously constrained by phase constraint and amplitude constraint in the time dimension, and simultaneously constrained by subdomain identifier and boundary coupling strength characterization quantity in the spatial dimension.

[0047] Based on phase constraints and amplitude limits, a set of control commands is generated, divided into time and spatial dimensions. The control command set uses harmonic characteristic markers as the primary key, speed marking information as the operating condition index, and interval identifiers (divided by time dimension) and subdomain identifiers (divided by spatial dimension) as dual indexes. Phase offset compensation, phase advance consistency window, upper bound of amplitude, and upper bound of amplitude change rate are written into the command entries. The time dimension division uses a time axis consistent with the phase change trajectory over time, further subdividing the discrimination interval corresponding to each speed marking information into continuous segments of initial interval, transition interval, and stable interval, allowing phase constraints and amplitude limits to have different constraint strengths in different segments. The spatial dimension division uses a spatial dimension consistent with the subdomain identifier. The instructions specify that command entries should be provided separately for stator subdomains, air gap subdomains, permanent magnet subdomains, and rotor subdomains. Each subdomain entry should include a boundary position identifier corresponding to the subdomain boundary information index, ensuring that the constraint input for the same higher-order perturbation magnetic field component remains consistent across different subdomains. The resulting set of control commands simultaneously incorporates time-dimension interval constraint information and spatial subdomain constraint information, and uses harmonic characteristics to identify the objects that pass through phase constraints and amplitude limitations. This allows the magnetic field analytical modeling calculation process to directly adjust the phase expression and limit the amplitude expression of higher-order perturbation magnetic field components according to the command entries in subsequent processing stages, thus providing a directly referable constraint execution basis for suppressing abnormal magnetic field oscillations.

[0048] Based on the generated set of control commands, the high-order perturbation magnetic field components in the magnetic field analytical modeling process are processed. By introducing a reverse time back-off mechanism and a high-frequency oscillation slow-release section, and combining it with a zero-mean torque cancellation method, the abnormal magnetic field oscillations caused by the high-order perturbation magnetic field components are suppressed online. To ensure that the previously generated set of control commands can form a continuous, executable processing path consistent with the multi-subdomain boundary constraints for higher-order perturbation magnetic field components during the analytical modeling of the magnetic field, and to suppress abnormal magnetic field oscillations caused by higher-order perturbation magnetic field components under high-speed operating conditions, the specific implementation steps are as follows: The set of control commands is expanded and bound to objects through execution entry. Each command entry in the control command set is merged according to harmonic characteristic marking, and a "range-subdomain-component" ternary binding relationship is established using time-dimensional interval identifiers and spatial-dimensional subdomain identifiers. This ensures that each higher-order perturbation magnetic field component has a unique corresponding phase offset compensation amount, phase advancement consistency window, upper bound of amplitude, and upper bound of amplitude change rate in each subdomain and time interval. After completing the ternary binding, the expressions of higher-order perturbation magnetic field components in the magnetic field analytical modeling process are split according to subdomain identifiers and connected with the corresponding command entries. During connection, the boundary position identifiers in the phase reference benchmark and boundary interaction description results are kept consistent, so that subsequent processing uses the same reference caliber for the phase and amplitude expressions of higher-order perturbation magnetic field components in each subdomain. At the same time, the time-dimensional interval identifiers are mapped to the time axis corresponding to the rotation speed label information, so that the start and end positions of each command entry on the time axis are consistent with the trajectory of phase change over time. This provides a directly referenceable interval interface for the subsequent introduction of a reverse time back-off mechanism and a high-frequency oscillation slow-release segment.

[0049] After completing the object binding of the control command set, a reverse time backoff mechanism is introduced to handle the accumulation of abnormal oscillations within the time dimension interval. The reverse time backoff mechanism establishes a backoff trigger window and a backoff recovery window around the interval markers of the time dimension. The backoff trigger window is taken from the boundary of the phase-advancing consistency window and is linked to the upper bound of the amplitude change rate. The backoff recovery window is taken from the internal continuous segment of the phase-advancing consistency window and is linked to the upper bound of the amplitude. When executing the reverse time backoff mechanism in each subdomain, the phase and amplitude expressions of the higher-order perturbation magnetic field components are reset along the time axis. The backoff segment reset uses the phase offset compensation amount as a reference to backoff the phase expression to the backoff recovery window. The reference phase position is used, and the amplitude expression is backed up to the reference amplitude position of the back-up recovery window based on the upper limit of the amplitude. This ensures that the higher-order perturbation magnetic field components after the back-up segment reset return to the continuous advancement pattern that matches the phase advancement consistency window on the time axis. To maintain the continuity at the boundary of multiple subdomains, the back-up segment reset is performed synchronously at the boundary position mark. This ensures that the subdomains on both sides of the boundary adopt the same back-up segment reset starting point and the same reference phase position in the same time interval. This avoids the accumulation of new boundary phase shifts after the introduction of the reverse time back-up mechanism, and makes the reverse time back-up mechanism a time dimension processing method to suppress the accumulation of abnormal oscillation self-excitation during the magnetic field analytical modeling calculation.

[0050] Based on the reverse time backtracking mechanism, a high-frequency oscillation buffer zone is introduced to handle the concentrated area of ​​high-frequency fluctuations caused by the interweaving of spatial and temporal dimensions. The high-frequency oscillation buffer zone is jointly defined by the time dimension interval identifier and the spatial dimension subdomain identifier in the control command set, and the corresponding higher-order perturbation magnetic field component is locked by the harmonic characteristic marker. The setting of the high-frequency oscillation buffer zone is constrained by the upper bound of the amplitude change rate. Time segments with amplitude change rates close to the upper bound are connected on the time axis to form a buffer zone. Within the buffer zone, the amplitude expression of the higher-order perturbation magnetic field component is subjected to segmented buffer processing. The segmented buffer processing adopts the same upper bound as the amplitude upper bound, and maintains the same amplitude continuity at the entrance of the buffer zone as outside the buffer zone. Inside the buffer zone, the amplitude change rate is kept below the upper bound of the amplitude change rate. At the exit of the slow-release section, the amplitude is maintained to be continuous with the subsequent time interval. At the same time, within the slow-release section, phase slow-release processing is performed on the phase expression under the constraint of the phase advancement consistency window. The phase slow-release processing limits the continuous direction of phase advancement with the phase advancement consistency window, and the tendency of phase change is distributed through the length of the slow-release section, so that the trajectory of phase change with time maintains a continuous advancement form within the slow-release section. At the boundary of multiple subdomains, the entrance, interior and exit of the slow-release section are synchronously aligned according to the boundary position mark, so that the subdomains on both sides of the boundary adopt the same slow-release section boundary for the same high-order perturbation magnetic field component. Thus, the high-frequency oscillation slow-release section becomes a means of releasing the high-frequency fluctuation density under the dual constraints of time and space dimensions, and together with the reverse time back-off mechanism, it suppresses the expansion of abnormal magnetic field oscillation.

[0051] By combining the reverse time back-off mechanism with the high-frequency oscillation slow-release section in the processing path, a zero-mean torque cancellation method is used to reduce the coupling output of higher-order disturbance magnetic field components in the torque response and maintain the stable expression of the overall electromagnetic output. The zero-mean torque cancellation method uses the torque expression in the magnetic field analytical modeling process as a reference, and symmetrically configures the contribution of the higher-order disturbance magnetic field components corresponding to the harmonic characteristic markers to the torque within a time interval, ensuring that the torque addition introduced by the higher-order disturbance magnetic field components within this time interval remains zero-mean in the interval integral sense. In specific implementation, the time dimension interval identifier in the control command set is used as the cancellation interval, and the spatial dimension subdomain identifier is used as the distribution boundary of the cancellation effect. Paired cancellation constraints are applied to the amplitude expression of the higher-order disturbance magnetic field components within the cancellation interval. The paired cancellation constraints are applied to the positive and negative additional segments with the upper bound of the amplitude as the boundary. Amplitude symmetry configuration is adopted, and the positive and negative additional segments are phase symmetry configuration is adopted based on the phase offset compensation amount, so that the torque additional amount in the cancellation interval forms a positive and negative symmetrical cancellation relationship on the time axis. At the boundary position mark, the zero-mean torque cancellation method is consistent with the phase advancement consistency window, so that the cancellation constraint does not destroy the phase continuity and amplitude transmission continuity of the subdomains on both sides of the boundary. By integrating the set of control commands into the entire process of ternary binding, reverse time back-off mechanism, high-frequency oscillation slow release segment and zero-mean torque cancellation method, the phase expression and amplitude expression of the higher-order perturbation magnetic field component in the magnetic field analytical modeling process are continuously constrained and segmented in the time and space dimensions at the same time. This forms an online suppression effect on the abnormal magnetic field oscillation caused by the higher-order perturbation magnetic field component, and keeps the boundary reference caliber consistent with the multi-subdomain boundary interaction description results of the suppression process.

[0052] To further clarify the specific execution logic of the reverse time rollback mechanism and the high-frequency oscillation slow-release section, and to enable those skilled in the art to directly implement the corresponding processing steps based on the control instruction set, the input parameters, triggering conditions, execution flow, and result write-back method of the above processing mechanism are supplemented as follows: The execution of the reverse time rollback mechanism takes the phase advance consistency window, the upper bound of the amplitude change rate, and the time dimension interval identifier in the control instruction set as input parameters. Its specific implementation process includes the following steps: Within each time dimension interval, the phase increment sequence and amplitude change rate sequence of the higher-order perturbation magnetic field component are scanned in real time along the time axis. When the phase increment in a continuous time segment exceeds the allowable advance range of the phase advance consistency window, and the corresponding amplitude change rate approaches or reaches the upper limit of the amplitude change rate, the time segment is marked as the back-off trigger segment, and the back-off trigger time is determined. Based on the rollback trigger time, search forward along the time axis for the nearest time point in a continuous segment within the phase advance consistency window. Determine this time point as the rollback recovery reference point, and read the phase expression value and amplitude expression value at this reference point as the reference phase position and reference amplitude position, respectively. Within the rollback triggering section, the phase and amplitude expressions of the higher-order disturbance magnetic field components are reset in a rollback segment. The phase expression is corrected according to the phase offset compensation amount and then rolled back to the reference phase position, while maintaining the phase advancement direction of subsequent time points consistent with the phase advancement consistency window. The amplitude expression is truncated according to the upper limit of the amplitude and rolled back to the reference amplitude position. At the same time, the amplitude change rate of adjacent time segments after rollback is limited to not exceeding the upper limit of the amplitude change rate. The phase and amplitude expressions after the backtracking segment is reset are written back into the magnetic field component expressions of the corresponding subdomains in the magnetic field analytical modeling process. At the subdomain boundary, the phase references of the subdomains on both sides of the boundary are updated synchronously according to the boundary position identifier, so that the backtracking process maintains a consistent phase reference caliber in the multi-subdomain structure.

[0053] Through the above steps, the reverse time rollback mechanism forms a time-dimensional processing flow with the structure of "trigger judgment - reference point determination - intra-segment reset - result writeback", which restores the higher-order perturbation magnetic field components to the continuous advancement state defined by the phase advancement consistency window on the time axis.

[0054] The establishment of the high-frequency oscillation slow-release zone also takes the time dimension interval identifier, spatial dimension subdomain identifier, upper bound of amplitude change rate, and phase advance consistency window in the control command set as inputs. Its specific implementation process includes the following steps: Within each time dimension interval, the amplitude change rate sequence of the higher-order perturbation magnetic field component is calculated. Continuous time segments whose amplitude change rate reaches or approaches the upper limit of the amplitude change rate are marked, and marked segments with adjacent time segments with an interval less than the preset time resolution are merged to form several candidate slow-release segments. For each candidate sustained-release segment, the segment inlet time and segment outlet time are determined, and the inlet amplitude and inlet phase are recorded at the segment inlet as a reference for the continuity of sustained-release treatment; Within the slow-release section, the amplitude expression is processed in segments. The segmented slow-release process adopts the amplitude gradual change constraint method to ensure that the amplitude change rate at any time point within the segment does not exceed the upper limit of the amplitude change rate, while ensuring that the amplitude at the segment exit is continuously connected with the amplitude at the first point of the subsequent time interval. Within the slow-release section, phase expression is subjected to phase slow-release processing. The phase slow-release processing is constrained by the phase advancement consistency window. Under the premise of keeping the phase advancement direction unchanged, the phase mutation amount is distributed according to the section length, so that the trajectory of phase change over time presents a continuous advancement pattern within the section. At the boundary of multiple subdomains, the entry and exit times of the slow-release segment are aligned according to the boundary location identifier, so that the subdomains on both sides of the boundary adopt the same slow-release segment boundary in the same time interval, and the boundary phase reference and boundary amplitude transfer status are updated synchronously.

[0055] Through the above steps, the high-frequency oscillation slow-release segment forms a time and space collaborative processing flow with the structure of "segment identification - segment boundary determination - segment internal gradual change processing - cross-subdomain alignment".

[0056] After completing the reverse time back-off mechanism and high-frequency oscillation slow-release section processing, the torque contribution of the higher-order disturbance magnetic field component is calculated, and the torque expression is divided into several offset intervals according to the time dimension interval identifier in the control command set. Within each cancellation interval, the torque addition corresponding to the higher-order disturbance magnetic field component is paired with the positive addition segment and the negative addition segment according to the time axis, so that the positive addition segment and the negative addition segment satisfy the upper limit constraint of amplitude expression and the symmetrical configuration corresponding to the phase offset compensation amount in phase expression, so that the torque addition within the cancellation interval is zero in the sense of time integration. The canceled torque expression is written back into the overall torque expression in the analytical modeling process of the magnetic field, and is kept consistent with the phase advance consistency window at the subdomain boundary.

[0057] This invention introduces a hierarchical processing mechanism involving time-frequency expansion, harmonic feature marking, and oscillation feature sets related to rotational speed during the analytical modeling of the multi-subdomain magnetic field of an axial flux motor. This mechanism ensures that the analytical magnetic field results maintain stable physical consistency under high-speed operating conditions. By locating, identifying, and constraining higher-order perturbation magnetic field components, the invention avoids the continuous amplification of mathematically valid but physically unrealizable magnetic field oscillations in the analytical results. Consequently, the modeling results more closely approximate the actual operating conditions when describing the magnetic field distribution in regions such as the stator, rotor, permanent magnets, and air gap. This enhances the reliability and usability of the analytical magnetic field model under high-speed conditions, providing a more reliable foundation for subsequent electromagnetic performance analysis and parameter design.

[0058] This invention introduces phase constraints, amplitude limitations, and time-space co-processing methods based on boundary interaction description results during the analytical modeling and calculation of the magnetic field. This enables continuous and controllable suppression of higher-order perturbation magnetic field components during the modeling process. Through the combined effects of a reverse time back-off mechanism, a high-frequency oscillation mitigation section, and a zero-mean torque cancellation method, the influence of abnormal magnetic field oscillations on the analytical results and torque expression can be effectively weakened, reducing the risk of electromagnetic noise and torque fluctuations caused by the analytical model. This improves the overall stability and smoothness of the axial flux motor under high-speed operating conditions.

[0059] This invention provides, for example Figure 2 The multi-subdomain magnetic field analytical modeling system for the axial flux motor shown includes a harmonic annotation module, an oscillation feature extraction module, an oscillation discrimination module, a constraint generation module, and an oscillation suppression module. The harmonic annotation module introduces a time-frequency expansion method related to rotational speed during the analytical modeling of the multi-subdomain magnetic field of the axial flux motor. It expands the analytical results of the magnetic field and distinguishes the main magnetic field components from the higher-order perturbation magnetic field components based on the time-frequency expansion results. At the same time, it establishes continuously traceable harmonic feature markers for each order of magnetic field components obtained by expansion. The oscillation feature extraction module, based on the established harmonic feature markers, locates the high-order perturbation magnetic field components that exhibit abnormal amplitude growth with changing rotation speed, and extracts the trajectory of phase change over time around the located high-order perturbation magnetic field components to form an oscillation feature set for characterizing the magnetic field oscillation behavior. The oscillation discrimination module, based on the formed oscillation feature set and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, discriminates the source of magnetic field oscillation corresponding to the oscillation feature set, and generates boundary interaction description results that reflect the changes in the multi-subdomain boundary relationship. The constraint generation module, based on the generated boundary interaction description results, applies phase constraints and amplitude limits to the higher-order disturbance magnetic field components corresponding to the oscillation source during the magnetic field analytical modeling calculation process, and generates a set of control instructions divided by time and space dimensions based on the phase constraints and amplitude limits. The oscillation suppression module, based on the generated set of control instructions, processes the high-order perturbation magnetic field components during the analytical modeling of the magnetic field. By introducing a reverse time back-off mechanism and a high-frequency oscillation mitigation section, and combining it with a zero-mean torque cancellation method, it suppresses the abnormal magnetic field oscillations caused by the high-order perturbation magnetic field components online.

[0060] The analytical modeling method for multi-subdomain magnetic fields of axial flux motors provided in this embodiment of the invention is implemented through the aforementioned analytical modeling system for multi-subdomain magnetic fields of axial flux motors. For details of the specific methods and processes of the analytical modeling system for multi-subdomain magnetic fields of axial flux motors, please refer to the embodiments of the analytical modeling method for multi-subdomain magnetic fields of axial flux motors described above, which will not be repeated here.

[0061] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method for analytical modeling of multi-subdomain magnetic fields in an axial flux motor, characterized in that, Includes the following steps: In the process of analytical modeling of the multi-subdomain magnetic field of the axial flux motor, a time-frequency expansion method related to the rotational speed is introduced to expand the analytical results of the magnetic field. Based on the time-frequency expansion results, the main magnetic field components and higher-order disturbance magnetic field components are distinguished. At the same time, harmonic feature markers that can be continuously tracked are established for each order of magnetic field components obtained by expansion. Based on the established harmonic feature markers, the higher-order disturbance magnetic field components that exhibit abnormal amplitude growth with rotational speed are located, and the phase-time trajectory of the located higher-order disturbance magnetic field components is extracted to form an oscillation feature set. Based on the formed set of oscillation features, and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, the source of magnetic field oscillation corresponding to the set of oscillation features is determined, and at the same time, a boundary interaction description result reflecting the change of the multi-subdomain boundary relationship is generated. Based on the generated boundary interaction description results, during the magnetic field analytical modeling calculation process, phase constraints and amplitude limits are applied to the higher-order disturbance magnetic field components corresponding to the oscillation source, and a set of control instructions divided into time and space dimensions is generated based on the phase constraints and amplitude limits. Based on the generated set of control commands, the higher-order perturbation magnetic field components in the magnetic field analytical modeling process are processed. By introducing a reverse time back-off mechanism and a high-frequency oscillation slow-release section, and combining it with a zero-mean torque cancellation method, the abnormal magnetic field oscillations caused by the higher-order perturbation magnetic field components are suppressed online.

2. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 1, characterized in that, The steps for obtaining harmonic feature markers are as follows: In the process of magnetic field analytical modeling, a correlation expression between rotational speed and angular displacement is established, and rotational speed is introduced into the time axis and rotational axis expression of the magnetic field analytical results. The multi-subdomain magnetic field analytical results are projected onto the time domain sequence and angular domain sequence labeled with rotational speed. After completing the rotational speed labeling, the magnetic field analysis results are subjected to time-frequency expansion in relation to the rotational speed. The magnetic field physical quantities are jointly expanded along the time dimension and the rotational angle dimension to form a set of magnetic field components with frequency and order indicators. Based on the magnetic field component set, the main magnetic field components and higher-order perturbation magnetic field components are distinguished according to energy proportion, component continuity and order stability, and the distinction results are written back to the magnetic field component set of each subdomain. After the components are distinguished, harmonic characteristic labels are established for each order of magnetic field component.

3. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 2, characterized in that, When establishing harmonic characteristic markings, the speed marking information and order indication constitute the basis for maintaining the component identity, and the phase reference benchmark unifies the phase reference method of the same order magnetic field component in each subdomain, so that the magnetic field component maintains continuous identity during speed change, and a consistent correspondence is formed between the stator subdomain, air gap subdomain, permanent magnet subdomain and rotor subdomain.

4. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 2, characterized in that, The steps for forming the oscillation feature set are as follows: Based on the harmonic characteristic marking, a following relationship oriented to the rotational speed change is established. The magnetic field components of each order are formed into a continuous following sequence according to the harmonic characteristic marking, and the amplitude evolution with the rotational speed is recorded. Based on the follow-up sequence and amplitude evolution record, the higher-order perturbation magnetic field components are located, and the location results are supplemented with rotational speed range indication and subdomain correlation indication. The trajectory of phase change over time is extracted from the high-order perturbation magnetic field components obtained by positioning, according to the harmonic characteristic markers, and a phase increment sequence and a phase loop point sequence are formed. Based on the positioning results and phase trajectory information, an oscillation feature set bound to the subdomain identifier is formed.

5. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 4, characterized in that, The steps for generating the boundary interaction description result are as follows: The oscillation feature set is structured and organized, the feature entries are merged according to harmonic feature marking, and the trajectory correlation of rotation speed labeling information, subdomain identification, amplitude evolution record, and phase change over time is established. At the same time, the subdomain boundary information index is supplemented. After the data processing is completed, a family of frequency-related dissipation curves is constructed by combining the material loss characteristics, and the amplitude evolution record is aligned with the family of dissipation curves to form a dissipation reference for the oscillation source. Based on the dissipative reference discrimination, the attenuation law of the end magnetic field is introduced, an axial attenuation path index is established, and a boundary phase transfer trajectory is formed to improve the spatial reference discrimination; The source of magnetic field oscillations is determined based on dissipative reference discrimination and spatial reference discrimination, and boundary interaction description results reflecting the changes in the relationship between multiple subdomains are generated simultaneously.

6. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 5, characterized in that, The source of magnetic field oscillation is identified by using harmonic feature markers as a unified reference identifier, and the subdomain boundary information index is synchronously associated under the constraint of rotation speed labeling information, so that the boundary interaction description results simultaneously include the boundary phase transmission state and the boundary amplitude transmission state.

7. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 5, characterized in that, The steps for generating the control instruction set are as follows: The boundary interaction description results are subjected to constraint object mapping, and the boundary continuity characterization, boundary coupling strength characterization, boundary phase offset characterization are bound to the harmonic feature markers, and the corresponding subdomain boundary positions are clarified. After completing the mapping of the constrained objects, phase constraints are applied to the higher-order perturbation magnetic field components corresponding to the oscillation source based on the reference sequence of the boundary phase offset evolving over time, while maintaining consistency between the harmonic feature marker and the subdomain identifier. Based on phase constraints, amplitude constraints are applied to the same higher-order perturbation magnetic field components by combining amplitude evolution records and boundary coupling strength characterization quantities. Based on phase constraints and amplitude limitations, a set of control commands is generated, which is divided into time and space dimensions and bound to subdomain identifiers.

8. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 7, characterized in that, When generating the set of control instructions, the interval division of the time dimension is kept consistent with the trajectory of phase change over time, and the subdomain identifier of the spatial dimension is matched with the subdomain boundary position. This ensures that the phase constraint and amplitude limit remain continuous and consistent at the boundaries of each subdomain, so that the set of control instructions has a unified constraint reference caliber in the multi-subdomain structure.

9. The analytical modeling method for multi-subdomain magnetic fields of an axial flux motor according to claim 7, characterized in that, Based on the generated set of control commands, the higher-order perturbation magnetic field components in the analytical modeling process of the magnetic field are processed. By introducing a reverse time back-off mechanism, a high-frequency oscillation slow-release section, and a zero-mean torque cancellation method, the higher-order perturbation magnetic field components are constrained in the following steps: The set of control commands is expanded to include an execution entry point. Command entries are grouped according to harmonic characteristics and a binding relationship is established between time dimension interval identifiers and spatial dimension subdomain identifiers. After binding is completed, a reverse time back-off mechanism is introduced to back-off the phase and amplitude expressions of higher-order perturbation magnetic field components along the time axis, and to maintain phase reference consistency at the subdomain boundary. Based on the reverse time back-off mechanism, a high-frequency oscillation slow-release section is introduced to continuously slow-release the amplitude and phase expressions of the higher-order perturbation magnetic field components within the corresponding time interval. By combining zero-mean torque cancellation with the slow-release processing path, the torque contribution of higher-order perturbation magnetic field components is symmetrically configured.

10. A multi-subdomain magnetic field analytical modeling system for an axial flux motor, used to implement the multi-subdomain magnetic field analytical modeling method for an axial flux motor as described in any one of claims 1-9, characterized in that, It includes a harmonic annotation module, an oscillation feature extraction module, an oscillation discrimination module, a constraint generation module, and an oscillation suppression module. The harmonic annotation module introduces a time-frequency expansion method related to rotational speed during the analytical modeling of the multi-subdomain magnetic field of the axial flux motor. It expands the analytical results of the magnetic field and distinguishes the main magnetic field components from the higher-order perturbation magnetic field components based on the time-frequency expansion results. At the same time, it establishes continuously traceable harmonic feature markers for each order of magnetic field components obtained by expansion. The oscillation feature extraction module, based on the established harmonic feature markers, locates the high-order disturbance magnetic field components that exhibit abnormal amplitude growth with changing rotational speed, and extracts the trajectory of phase change over time around the located high-order disturbance magnetic field components to form an oscillation feature set. The oscillation discrimination module, based on the formed oscillation feature set and combined with the material loss characteristics of the axial flux motor and the attenuation law of the end magnetic field, discriminates the source of magnetic field oscillation corresponding to the oscillation feature set, and generates boundary interaction description results that reflect the changes in the multi-subdomain boundary relationship. The constraint generation module, based on the generated boundary interaction description results, applies phase constraints and amplitude limits to the higher-order disturbance magnetic field components corresponding to the oscillation source during the magnetic field analytical modeling calculation process, and generates a set of control instructions divided by time and space dimensions based on the phase constraints and amplitude limits. The oscillation suppression module, based on the generated set of control instructions, processes the high-order perturbation magnetic field components during the analytical modeling of the magnetic field. By introducing a reverse time back-off mechanism and a high-frequency oscillation mitigation section, and combining it with a zero-mean torque cancellation method, it suppresses the abnormal magnetic field oscillations caused by the high-order perturbation magnetic field components online.

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