A multi-objective optimization design method for a harmonic elimination coil of a low-vibration induction motor

Abstract

The application discloses a harmonic-elimination coil multi-objective optimization design method for a low-vibration induction motor, and belongs to the technical field of motor optimization design. The method comprises the following steps: deducing the relationship between the induction voltage and the number of turns according to an air-gap magnetic field analytical model, determining key variables such as the harmonic-elimination coil wire diameter, the number of turns, the span, the number of parallel branches, the resistance value and temperature characteristics of the current-limiting resistor, the main winding slot fill rate and the stator slot type size fine-tuning amount; establishing an electromagnetic field simulation model to verify and correct the empirical coefficient, and determining a feasible optimization interval; establishing an electro-magnetic-thermal multi-physical field collaborative simulation system, using a multi-objective optimization algorithm to iteratively optimize to obtain a Pareto solution set, and using three-dimensional electromagnetic field time-step finite element refinement verification; and selecting a final scheme according to a service scene. The application balances the electromagnetic vibration suppression and the loss, torque and temperature rise indexes, and improves the design precision and safety through three-dimensional verification and process deviation evaluation.

Description

Technical Field

[0001] This invention relates to the field of motor optimization design technology, and in particular to a multi-objective optimization design method for harmonic suppression coils of low-vibration induction motors. Background Technology

[0002] Induction motors are crucial power sources in my country's industrial and agricultural production, high-end manufacturing, transportation, and other civilian sectors, as well as in defense industries such as aerospace, deep-sea submersibles, and ship propulsion. Their vibration and noise levels directly affect equipment reliability, working environment comfort, and the acoustic concealment of underwater equipment. However, with the widespread application of variable frequency drive (VFD) technology, the abundant current time harmonics introduced by the VFD establish a series of rotating magnetic fields in the motor's air gap, each with the same number of pole pairs as the fundamental frequency but different rotational speeds. These magnetic fields cross-couple with the inherent spatial harmonic magnetic fields within the motor, generating complex electromagnetic excitation forces covering both high and low frequency bands, thus deteriorating the motor's vibration and noise performance.

[0003] Currently, research on vibration and noise reduction in induction motors mainly focuses on three aspects: first, from the perspective of optimizing the electromagnetic field of the motor itself, suppressing specific orders of electromagnetic force waves by adjusting the winding arrangement or slot size; second, from the power supply side, reducing current harmonic content by optimizing filter design or improving PWM control strategies; and third, from the perspective of vibration transmission path, reducing vibration response amplitude by optimizing mechanical damping and structural stiffness. However, in terms of optimizing the electromagnetic field of the motor itself, existing research almost entirely focuses on adjusting the parameters of the stator main winding, or on adjusting the core structure and slot size, rarely involving novel designs at the magnetic circuit-circuit topology level, and therefore also neglecting optimization design methods for stator-side harmonic suppression coils. Taking the electromagnetic vibration and loss indices in the optimization design of harmonic suppression coils as an example, a harmonic suppression coil with a larger cross-sectional area is beneficial for reducing electromagnetic vibration, but it increases additional copper losses. Therefore, how to balance high efficiency and low vibration and noise has become a core challenge in the research and design of low-vibration induction motors with harmonic suppression coils. Summary of the Invention

[0004] For induction motors where low vibration is the primary performance indicator, especially those requiring inverter power supply, this invention provides a multi-objective optimization design method for harmonic suppression coils in low-vibration induction motors. This method can reduce electromagnetic vibration while balancing mechanical strength, manufacturing costs, additional losses, and temperature rise, and ensure that the design has sufficient margin under actual manufacturing and service conditions.

[0005] To achieve the above objectives, the present invention provides a multi-objective optimization design method for harmonic suppression coils of low-vibration induction motors, comprising the following steps: S1. Based on the analytical model of the air gap magnetic field and the theoretical model of the damping strength of the harmonic suppression coil magnetic field, the mathematical relationship between the induced voltage generated by the harmonic suppression coil during the operation of the induction motor and the number of coil turns is derived. By analyzing the suppression effect of the induced voltage on the harmonic components of the air gap magnetic field, the target design variables affecting electromagnetic vibration are determined. The target design variables include the wire diameter, number of turns, span, number of parallel branches of the harmonic suppression coil, as well as the resistance value and temperature characteristics of the series current limiting resistor. At the same time, the fill factor of the main winding slot and the fine adjustment of the stator slot size are included in the variable set. S2. Establish a rapid electromagnetic field simulation model, numerically verify the calculated value of the induced voltage derived in S1, compare the simulation results with the analytical results to correct the empirical coefficients in the theoretical model, and determine the feasible optimization range of each parameter of the harmonic suppression coil by combining the actual process capabilities of motor manufacturing enterprises and the safe range of induced voltage. S3. Establish a multi-physics collaborative simulation and evaluation system for electromagnetic and thermal fields. Use modern multi-objective optimization algorithms to iteratively optimize within the feasible optimization range determined in S2 to obtain the Pareto solution set. Then, use three-dimensional electromagnetic field time-stepping finite element method to verify the Pareto solution set. S4. Based on the specific service scenario of the motor, select the target implementation scheme from the Pareto solution set verified in S3, and complete the multi-objective optimization design of the harmonic suppression coil.

[0006] Preferably, in S1, the total resistance of the harmonic suppression coil is The total cross-sectional area of ​​the conductive part is ; in, For the number of parallel branches, The number of turns in each parallel branch, For coil fill factor, The cross-sectional area per turn, Resistivity This is the total length of the conductor; Induced voltage Induced current Magnetic field damping strength ,in For coupled harmonic magnetic flux, For impedance, For leakage sensation, Angular frequency; When leakage is ignored, , This represents the average length per turn.

[0007] Preferably, in S2, the feasible optimization range for each parameter of the harmonic suppression coil includes: The wire diameter ranges from 0.5mm to 2.0mm, the number of turns ranges from 1 to 10 turns, the current limiting resistor ranges from 0.1Ω to 100Ω, and the span of the harmonic suppression coil is expressed as a multiple of the stator tooth width. The induced voltage calculated by the electromagnetic field simulation model is compared with the induced voltage derived analytically in S1. The empirical coefficients in the deviation correction theoretical model are used to ensure that the error between the corrected analytical model and the simulation model is within the preset threshold range.

[0008] Preferably, in S3, the optimization objectives include: The optimization measures include reducing specific order electromagnetic force, reducing total motor losses, maintaining or increasing average motor torque, controlling the temperature of the harmonic suppression coil and the current-limiting resistor; the optimization variables include the wire diameter, number of turns, number of parallel branches, and span of the harmonic suppression coil, the resistance value and temperature characteristics of the current-limiting resistor, the main winding slot fill factor, and the stator slot size fine-tuning amount.

[0009] Preferably, in S3, the electromagnetic field part of the multi-physics field co-simulation and evaluation system of electro-magnetism-thermal adopts a two-dimensional transient finite element model to solve the radial magnetic flux density of the air gap and calculate the radial electromagnetic force wave amplitude of each spatial order and frequency through Maxwell stress tensor method, while outputting the total motor loss and average torque.

[0010] Preferably, in S3, the temperature field part of the electro-magnetic-thermal multi-physics field collaborative simulation evaluation system adopts a three-dimensional steady-state thermal finite element model, which maps the loss density obtained from the electromagnetic field simulation to the three-dimensional model, solves the steady-state thermal balance equation, and outputs the hottest temperature of the harmonic elimination coil and the highest surface temperature of the current limiting resistor.

[0011] Preferably, in S3, the improved non-dominated sorting genetic algorithm NSGA-II is used for multi-objective iterative optimization. The initial population is randomly generated within the parameter range determined in S2, and the population size is set to 150. Multiphysics simulation is performed on each individual and four objective function values ​​are calculated. The population is stratified according to non-dominated sorting and crowding distance. A new generation of population is generated through tournament selection, crossover, and mutation operations. The crossover probability is set to 0.85 and the mutation probability is set to 0.08. The iteration continues until the average change rate of the Pareto front is less than 1% for 30 consecutive generations or the maximum number of generations of 200 is reached.

[0012] Preferably, in S3, when using the three-dimensional electromagnetic field time-stepping finite element method to refine the Pareto solution, the three-dimensional model includes the complete stator core, rotor, main winding end, harmonic suppression coil end connection part, and approximate geometry of the current limiting resistor. The mesh uses tetrahedral elements and is locally refined in multiple layers on the surface of the harmonic suppression coil conductor, air gap, and slot region. The ratio of the longest side to the shortest side does not exceed 10, and the total number of meshes is controlled between 2 million and 3 million. The solver step size is less than 1 / 20 of the PWM carrier period. If the deviation between the three-dimensional verification result and the two-dimensional result is less than 10%, the Pareto solution is retained; otherwise, it is discarded or iterated again.

[0013] Preferably, in S3, during the three-dimensional fine verification process, the influence of the deviation of the end length of the harmonic suppression coil during the manufacturing process on the end inductance and total resistance is evaluated, and the overheating risk coefficient of the current limiting resistor is calculated; when the surface temperature of the current limiting resistor exceeds 100°C, the scheme is judged as unacceptable and is rejected.

[0014] Preferably, in S4, the final solution is selected based on the specific service scenario of the motor, including: For electric vehicle drive motors, the Pareto solution with optimal electromagnetic vibration is preferred; for industrial motors that operate at full load for extended periods, the Pareto solution with optimal loss or temperature rise is preferred; for cost-sensitive household appliance motors, the Pareto solution with the simplest process and moderate slot fill factor is selected.

[0015] The advantages and beneficial effects of this invention compared to the prior art are: 1. Achieved a quantitative balance between electromagnetic vibration suppression and other engineering indicators: This invention incorporates electromagnetic vibration, loss, torque and temperature rise into a unified evaluation system through a multi-objective optimization framework, avoiding the design dilemma caused by the additional loss and temperature rise problems that may be brought about by the harmonic suppression coil.

[0016] 2. The improved NSGA-II algorithm is used to obtain the Pareto solution set: It provides designers with multiple alternative solutions. Designers can choose flexibly according to the specific application scenario of the motor (such as electric vehicles, industrial pumps, home appliances, etc.). For example, the vibration-optimal solution is selected in vibration-sensitive applications, and the temperature rise-optimal solution is selected in heat-load-sensitive applications.

[0017] 3. Verifying the two-dimensional simulation results using a three-dimensional electromagnetic field time-stepping finite element method significantly improves design accuracy. Two-dimensional models cannot accurately simulate end leakage flux and three-dimensional eddy current effects, and deviations in the end length of the harmonic suppression coil introduce approximately 5% uncertainty in the total resistance. Three-dimensional verification effectively corrects this error, preventing excessive performance deviations in the actual prototype.

[0018] 4. The physical risk of the current-limiting resistor overheating leading to resin glue failure and thus causing foreign objects to fall into the rotor is quantified: This invention uses this risk as a criterion for eliminating the solution, ensuring that any design that enters the final candidate solution has a safety margin of not less than 10°C on the resistor surface temperature.

[0019] 5. A complete collaborative simulation system for refined verification of two-dimensional electromagnetic-thermal-three-dimensional electromagnetic fields was established, avoiding the one-sidedness of previous methods that used a single electromagnetic field to evaluate the effect of harmonic suppression coils.

[0020] 6. This invention fully considers process feasibility and cost constraints: in S2, the optimization range is determined by process capability, and in S3, the tank fill rate is used as a constraint, so that the final design scheme can be successfully put into production.

[0021] 7. This invention is not only applicable to the optimization of harmonic suppression coils of induction motors, but its multi-parameter, multi-objective, and multi-constraint optimization framework can be extended to the structural design of other types of electromagnetic devices, and has good versatility and scalability.

[0022] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0023] Figure 1 This is a flowchart of a multi-objective optimization design method for a harmonic suppression coil of a low-vibration induction motor, as described in an embodiment of the present invention. Figure 2 This is an expanded flowchart of the optimized design process S3 according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the low-frequency band of the radial electromagnetic force spectrum of different embodiments of the present invention; Figure 4 This is a schematic diagram of the high-frequency band of the radial electromagnetic force spectrum in different embodiments of the present invention. Detailed Implementation

[0024] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0026] like Figures 1-2 As shown, the present invention provides a multi-objective optimization design method for harmonic suppression coils in low-vibration induction motors, employing the following technical solution: S1: Identify key design variables.

[0027] First, based on the analytical model of the air gap magnetic field and the theoretical model of the damping strength of the harmonic suppression coil, the mathematical relationship between the induced voltage generated by the harmonic suppression coil during the operation of the induction motor and the number of coil turns is derived. By analyzing the suppression effect of the induced voltage on the harmonic components of the air gap magnetic field, key design variables that have a significant impact on electromagnetic vibration are determined. These variables include the wire diameter, number of turns, span, and number of parallel circuits of the harmonic suppression coil, as well as the resistance value and temperature characteristics of the series current-limiting resistor. Simultaneously, the fill factor of the main winding and the fine-tuning of the stator slot dimensions are included in the variable set to coordinate the spatial competition between the harmonic suppression coil and the main winding during the optimization process. The damping strength theoretical model and the induced voltage mathematical model are as follows: From the enameled wire resistance formula and the harmonic suppression coil structure, we can know that: ; ; in, For the number of parallel branches, The number of turns of the harmonic suppression coil in each parallel branch. For coil fill factor, This represents the total cross-sectional area of ​​the conductive portion of the harmonic suppression coil. Let be the cross-sectional area per turn of the harmonic suppression coil. When the harmonic suppression coil is directly short-circuited without a series resistor, the total resistance of the harmonic suppression coil is . The above formula can be used to calculate it. The resistivity of the corresponding material. This represents the total length of the harmonic suppression coil conductor.

[0028] The induced voltage, induced current, and magnetic field damping strength of the harmonic suppression coil can be expressed as: ; ; ; in, The harmonic flux coupled by a certain harmonic suppression coil. For the impedance of the harmonic suppression coil, To eliminate leakage inductance in the harmonic suppression coil, Angular frequency, It is the magnetomotive force generated by the harmonic suppression coil, and it can be regarded as an indicator of the strength of magnetic field damping.

[0029] When the leakage inductance of the harmonic suppression coil is ignored, the following can be further obtained from the above formula: ; in, This is the average length of each turn of the harmonic suppression coil. Therefore, under the condition of a direct short circuit in the harmonic suppression coil, when the fill factor... and average length per turn When all dimensions remain constant, the damping strength of the magnetic field is only related to the total cross-sectional area. The number of parallel branches is relevant, but not to the number of parallel branches or the wire diameter. However, in actual design, due to the significant difference in wire diameter between motors of different capacities, the number of parallel branches can be used to balance the contradiction between the technological difficulty of wire arrangement and current density.

[0030] When a resistor is connected in series at the end of the harmonic suppression coil, its damping strength on the magnetic field is calculated using the above formula. For a specific motor, the above formula can be simplified to empirical coefficients for quick calculation.

[0031] S2: Determine the range of parameter optimization.

[0032] A rapid electromagnetic field simulation model was established to numerically verify the calculated induced voltage values ​​derived in S1. The simulation results were compared with analytical results to correct the empirical coefficients in the theoretical model. Then, considering the actual technological capabilities of motor manufacturing enterprises, such as minimum wire diameter limits, slot insulation thickness, slot fill factor limits, and the safe range of induced voltage, the feasible optimization ranges for each parameter of the harmonic suppression coil were determined. Specifically, this included: wire diameter range of 0.5mm to 2.0mm, upper and lower limits of the number of turns from 1 to 10 turns, current-limiting resistor value range of 0.1Ω to 100Ω, and the harmonic suppression coil span expressed as a multiple of the stator tooth width. This ensured that the subsequently optimized scheme was manufacturable and operable in engineering.

[0033] S3: Establish a high-precision multi-physics field collaborative simulation and evaluation system, and use modern optimization algorithms to obtain the Pareto solution set.

[0034] This step is the core of the entire optimization method. The performance evaluation of the harmonic suppression coil cannot rely solely on electromagnetic vibration; it must simultaneously consider its comprehensive impact on motor losses, temperature rise, output torque, and its own thermal stability. This step establishes a multi-physics co-simulation process involving electro-magnetism and heat, and employs a multi-objective optimization algorithm for iterative optimization.

[0035] S3.1 Define the optimization objective and optimization variables.

[0036] There are four optimization objectives, which are in competition with each other: The first objective is to reduce electromagnetic forces of a specific order. The core function of the harmonic suppression coil is to suppress radial force waves of a specific spatial order that cause electromagnetic vibrations, usually expressed as a percentage reduction in the amplitude of the force waves.

[0037] The second objective is to reduce the total motor loss. The introduction of the harmonic suppression coil will introduce additional copper losses and may also affect iron losses, altering the saturation level of the main magnetic circuit and thus affecting the main winding losses. Therefore, the total motor loss needs to be controlled as an optimization objective.

[0038] The third objective is to maintain or increase the average torque of the motor. The damping effect of the harmonic suppression coil may weaken some of the fundamental torque while suppressing harmonics, therefore the optimized average torque must be no less than 95% of the original solution.

[0039] The fourth objective is to control the temperature of the harmonic suppression coil itself and the temperature of the current-limiting resistor. The harmonic suppression coil is located in the stator slot or at the end, where heat dissipation is limited, and its steady-state temperature rise must not exceed the allowable value of the insulation class; when connected in series with a resistor, the current-limiting resistor will generate a large amount of Joule heat during operation, and its surface temperature must not exceed the tolerance limit of the resistive material and the encapsulating resin.

[0040] There are eight optimization variables, including: the wire diameter, number of turns, number of parallel circuits, and span of the harmonic suppression coil; the resistance value of the current-limiting resistor connected in series with the harmonic suppression coil; the fill factor of the main winding slots; and the fine-tuning amount of the stator slot dimensions. These variables are interdependent. For example, increasing the number of turns will improve the induced voltage and magnetic field damping effect, but at the same time, it will increase the coil resistance and copper losses, and may also encroach on slot space, forcing a decrease in the fill factor of the main winding slots.

[0041] S3.2 Establish a multi-physics field collaborative finite element simulation model.

[0042] For each given combination of optimization variables, a co-simulation model including electromagnetic and temperature fields is established.

[0043] The electromagnetic field section employs a high-precision two-dimensional transient finite element model. The motor geometry model is established based on the actual stator and rotor lamination dimensions, and material properties include the nonlinear BH curve of silicon steel sheets and iron loss curves at different frequencies. The stator main winding and harmonic suppression coil are assigned their respective number of turns, wire diameter, and number of parallel branches, with the ends of the harmonic suppression coil represented by equivalent resistance and inductance. The applied excitation is a typical grid sinusoidal voltage or a typical inverter output PWM voltage waveform, containing harmonic components near the fundamental and carrier frequencies. The solution domain encompasses the entire motor cross-section, and the boundary condition is set to zero magnetic vector potential. The mesh is locally refined in the air gap and slot regions, with the element size not exceeding one-sixth of the shortest magnetic field spatial wavelength. After solving, the radial magnetic flux density in the air gap is extracted, and the radial electromagnetic force wave amplitude for each spatial order and frequency is calculated using the Maxwell stress tensor method. Simultaneously, the total motor losses are output, including main winding copper losses, harmonic suppression coil copper losses, and stator and rotor iron losses, and the average torque is calculated.

[0044] The temperature field section employs a three-dimensional steady-state thermal finite element model. The loss density calculated in the two-dimensional electromagnetic field simulation is mapped to the corresponding regions of the three-dimensional model according to volume: the copper losses of the stator main winding and the harmonic suppression coil are applied as volume heat sources to the coil conductor region; iron losses are applied to the stator teeth and stator yoke regions; and the Joule losses of the current-limiting resistor are applied as concentrated heat sources to the surface of the resistor model. The three-dimensional geometric model includes the stator core, the ends of the main winding, the ends of the harmonic suppression coil, the current-limiting resistor and its encapsulating resin, the housing, and the cooling air domain. For self-fan-cooled motors, the convective heat transfer coefficient applied to the housing surface is determined using empirical formulas; for forced air cooling, the inlet air velocity and air duct are set. The steady-state thermal balance equation is solved, outputting the hottest spot temperature of the harmonic suppression coil and the highest surface temperature of the current-limiting resistor.

[0045] S3.3 employs a multi-objective optimization algorithm for iterative optimization.

[0046] Since the four optimization objectives conflict with each other and there is no single mathematically optimal solution, this method preferably uses the improved non-dominated sorting genetic algorithm NSGA-II for multi-objective iterative optimization.

[0047] The specific process is as follows: First, an initial population is randomly generated within the parameter range determined by S2. Each individual represents a set of harmonic elimination coil parameter combinations, and the population size is preferably set to 150.

[0048] Then, S3.2 multiphysics simulation was performed on each individual to calculate four objective function values: electromagnetic force amplitude of a specific order, total motor loss, the ratio of average torque to the original value, and the hottest spot temperature of the harmonic suppression coil. Simultaneously, constraints were checked: the temperature rise of the harmonic suppression coil did not exceed the upper limit of 155°C for Class F insulation, the surface temperature of the current-limiting resistor did not exceed the glass transition temperature of its resin encapsulation material (110°C), and the slot fill factor of the main winding did not exceed 78% of the process upper limit.

[0049] Next, individuals in the population are stratified according to the non-dominated sorting principle. The first stratum consists of non-dominated solutions, forming the current Pareto front. Within the same stratum, the diversity of solutions is maintained based on the crowding distance, which is calculated using Euclidean distance in the target space.

[0050] Then, selection, crossover, and mutation operations are performed to generate a new generation of population. The selection operation uses tournament selection with a tournament size of 2. The crossover probability can be set to 0.85, and the mutation probability to 0.08.

[0051] Repeat the above iterative process until the average rate of change of the Pareto front is less than 1% for 30 consecutive generations or the preset maximum number of generations, 200, is reached. Finally, a Pareto solution set is obtained, where each solution is non-dominated.

[0052] S3.4 uses three-dimensional electromagnetic field time-stepping finite element method to perform a refined verification of the Pareto solution.

[0053] Since the electromagnetic field simulation in S3.2 uses a two-dimensional model that ignores the end leakage flux and three-dimensional eddy current effect, and the end structure of the harmonic suppression coil has a certain influence on its own inductance, induced voltage and the loss of adjacent components, it is necessary to perform high-precision three-dimensional electromagnetic field time-stepping finite element verification on each candidate scheme in the Pareto solution set obtained in S3.3.

[0054] The geometry of the three-dimensional electromagnetic field model includes the complete stator core, rotor, main winding ends, end connections of the harmonic suppression coil, and the approximate geometry of the current-limiting resistor. Tetrahedral elements are used for mesh generation, with multi-layer local refinement applied to the conductor surface of the harmonic suppression coil, the air gap, and the slot region. To ensure computational accuracy, mesh quality criteria are set: the ratio of the longest side to the shortest side should not exceed 10, and the total number of meshes is controlled between 2 million and 3 million, depending on the computer hardware capabilities. The solver uses the time-stepped finite element method, with a step size required to be less than 1 / 20 of the PWM carrier period.

[0055] After the high-precision three-dimensional electromagnetic field time-stepping finite element simulation is completed, the following key indicators are extracted and compared with the two-dimensional results: the amplitude variation of the radial electromagnetic force wave of a specific order, the amplitude and phase of the induced voltage of the harmonic suppression coil, and the redistribution of copper losses in the main winding and the harmonic suppression coil, especially the additional copper losses caused by end leakage flux. If the deviation between the three-dimensional verification result and the two-dimensional result is less than 10%, the Pareto solution is considered valid and retained in the final candidate set; if the deviation exceeds 10%, the solution is marked as needing to be re-iterated using the three-dimensional model in S3.3, or it is directly discarded.

[0056] Furthermore, the engineering risks arising from manufacturing errors must be assessed in the 3D simulation: deviations in the length of the harmonic suppression coil end during manufacturing. In actual winding, the end protrusion length typically varies randomly from ±2mm to ±5mm, leading to changes in end inductance and consequently introducing approximately 5% uncertainty in the total resistance of the harmonic suppression coil. When the current-limiting resistor overheats, the surrounding epoxy resin adhesive used for fixing it softens or even carbonizes, causing resin failure. Upon failure, the current-limiting resistor may detach from the stator end and fall into the air gap between the rotor and stator inside the motor, potentially causing serious malfunctions such as rotor rubbing, winding insulation damage, or even complete machine jamming. Therefore, in the 3D simulation, an additional "resistor overheating risk factor" is calculated for each Pareto solution: when the surface temperature of the current-limiting resistor exceeds 100°C, the solution is directly deemed unacceptable.

[0057] After three-dimensional verification and risk screening, the remaining Pareto solutions constitute the final candidate set.

[0058] S4: Select the final solution based on the working environment and cyclical working conditions of the research subjects.

[0059] Different application scenarios have varying tolerances for vibration, losses, and temperature rise. For example, for electric vehicle drive motors, noise caused by low-frequency electromagnetic vibration has a significant impact on the driving experience, and the Pareto solution with optimal electromagnetic vibration should be prioritized. For industrial motors that operate at full load for extended periods, total losses and temperature rise are more critical, and the solution with optimal losses or optimal temperature rise should be prioritized. For cost-sensitive household appliance motors, vibration performance can be appropriately sacrificed, and the solution with the simplest process and moderate slot fill factor can be selected.

[0060] Therefore, based on the robust Pareto solution set selected in S3.4, the final implementation scheme is chosen according to the specific service scenario of the motor. The multi-parameter optimization design of the harmonic suppression coil is then completed.

[0061] The following verification is based on a specific embodiment.

[0062] For a certain model of 5.5kW induction motor, the optimization effects of several harmonic suppression coil designs are compared. The induction motor parameters are shown in Table 1. Table 1. Parameters of a 5.5kW induction motor and parameters of the harmonic suppression coil used.

[0063] Table 2 compares the high-precision electromagnetic field simulation results of various parameter harmonic suppression coils. Some parameters in the optimization process are listed, and these parameter combinations produce drastically different electromagnetic vibration suppression effects or increased losses.

[0064] Table 2 shows the effects of different parameter combinations on the harmonic suppression coil of a 5.5kW induction motor.

[0065] For example, in N =10, With a parameter combination of 0.2, the harmonic suppression coil has 10 turns and is directly short-circuited. Compared to the original design, this scheme increases total losses by 942W and reduces total iron losses by 9.7W when the load speed remains constant. Although iron losses are reduced, the stator copper losses and harmonic suppression coil copper losses increase significantly, easily leading to coil overheating. Furthermore, the larger diameter enameled wire used in this parameter combination causes a decrease in the fill factor of the stator main winding slots. Therefore, even though this parameter combination has a good electromagnetic vibration suppression effect, it cannot be considered the final solution set for the Pareto front. Therefore, some schemes with excessive losses and poor electromagnetic force suppression effects can be initially eliminated.

[0066] To further observe the characteristics of radial electromagnetic force, Fourier analysis was performed on the radial electromagnetic force of the five operating conditions after the initial screening. The resulting spectra are as follows: Figure 3 and Figure 4 As shown. From the spectrum, it can be seen that... N =1, The parameter combination scheme of 0.02 has a certain effect in suppressing radial electromagnetic force in the mid-to-high frequency range and does not increase radial electromagnetic force in the low frequency range. Combined with the above loss data, this parameter combination has low loss and occupies a small slot area. After subsequent verification by high-precision three-dimensional electromagnetic field time-stepping finite element analysis, and verification considering the uncertainty of total resistance, the final selection was... N =1, =0.02 parameter combination as the harmonic suppression coil scheme.

[0067] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multi-objective optimization design method for harmonic suppression coils in low-vibration induction motors, characterized in that, Includes the following steps: S1. Based on the analytical model of the air gap magnetic field and the theoretical model of the damping strength of the harmonic suppression coil magnetic field, the mathematical relationship between the induced voltage generated by the harmonic suppression coil during the operation of the induction motor and the number of coil turns is derived. By analyzing the suppression effect of the induced voltage on the harmonic components of the air gap magnetic field, the target design variables affecting electromagnetic vibration are determined. The target design variables include the wire diameter, number of turns, span, number of parallel branches of the harmonic suppression coil, as well as the resistance value and temperature characteristics of the series current limiting resistor. At the same time, the fill factor of the main winding slot and the fine adjustment of the stator slot size are included in the variable set. S2. Establish a rapid electromagnetic field simulation model, numerically verify the calculated value of the induced voltage derived in S1, compare the simulation results with the analytical results to correct the empirical coefficients in the theoretical model, and determine the feasible optimization range of each parameter of the harmonic suppression coil by combining the actual process capabilities of motor manufacturing enterprises and the safe range of induced voltage. S3. Establish a multi-physics collaborative simulation and evaluation system for electromagnetic and thermal fields. Use modern multi-objective optimization algorithms to iteratively optimize within the feasible optimization range determined in S2 to obtain the Pareto solution set. Then, use three-dimensional electromagnetic field time-stepping finite element method to verify the Pareto solution set. S4. Based on the specific service scenario of the motor, select the target implementation scheme from the Pareto solution set verified in S3, and complete the multi-objective optimization design of the harmonic suppression coil.

2. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 1, characterized in that, In S1, the total resistance of the harmonic suppression coil is The total cross-sectional area of ​​the conductive part is ; in, For the number of parallel branches, The number of turns in each parallel branch, For coil fill factor, The cross-sectional area per turn, Resistivity This is the total length of the conductor; Induced voltage Induced current Magnetic field damping strength ; in For coupled harmonic magnetic flux, For impedance, For leakage sensation, Angular frequency; When leakage is ignored, , This represents the average length per turn.

3. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 1, characterized in that, In S2, the feasible optimization range for each parameter of the harmonic suppression coil includes: The wire diameter ranges from 0.5mm to 2.0mm, the number of turns ranges from 1 to 10 turns, the current limiting resistor ranges from 0.1Ω to 100Ω, and the span of the harmonic suppression coil is expressed as a multiple of the stator tooth width. The induced voltage calculated by the electromagnetic field simulation model is compared with the induced voltage derived analytically in S1. The empirical coefficients in the deviation correction theoretical model are used to ensure that the error between the corrected analytical model and the simulation model is within the preset threshold range.

4. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 1, characterized in that, In S3, the optimization objectives include: The optimization measures include reducing specific order electromagnetic force, reducing total motor losses, maintaining or increasing average motor torque, controlling the temperature of the harmonic suppression coil and the current-limiting resistor; the optimization variables include the wire diameter, number of turns, number of parallel branches, and span of the harmonic suppression coil, the resistance value and temperature characteristics of the current-limiting resistor, the main winding slot fill factor, and the stator slot size fine-tuning amount.

5. A multi-objective optimization design method for harmonic suppression coils in a low-vibration induction motor according to claim 4, characterized in that, In S3, the electromagnetic field part of the multi-physics field co-simulation and evaluation system of electro-magnetism-thermal adopts a two-dimensional transient finite element model to solve the radial magnetic flux density of the air gap and calculate the radial electromagnetic force wave amplitude of each spatial order and frequency through Maxwell stress tensor method. At the same time, the total motor loss and average torque are output.

6. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 4, characterized in that, In S3, the temperature field part of the electro-magnetic-thermal multi-physics field co-simulation evaluation system adopts a three-dimensional steady-state thermal finite element model. The loss density obtained from the electromagnetic field simulation is mapped to the three-dimensional model, the steady-state thermal balance equation is solved, and the hottest temperature of the harmonic elimination coil and the highest surface temperature of the current limiting resistor are output.

7. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 4, characterized in that, In S3, the improved non-dominated sorting genetic algorithm NSGA-II is used for multi-objective iterative optimization. The initial population is randomly generated within the parameter range determined in S2, and the population size is set to 150. Multiphysics simulation is performed on each individual and four objective function values ​​are calculated. The population is stratified according to non-dominated sorting and crowding distance. A new generation of population is generated through tournament selection, crossover, and mutation operations. The crossover probability is set to 0.85 and the mutation probability is set to 0.

08. The iteration continues until the average change rate of the Pareto front is less than 1% for 30 consecutive generations or the maximum number of generations of 200 is reached.

8. The multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 7, characterized in that, In S3, when using the three-dimensional electromagnetic field time-stepping finite element method to refine the Pareto solution, the three-dimensional model includes the complete stator core, rotor, main winding end, harmonic suppression coil end connection part, and approximate geometry of the current limiting resistor. The mesh uses tetrahedral elements and is locally refined in multiple layers on the surface of the harmonic suppression coil conductor, air gap, and slot region. The ratio of the longest side to the shortest side does not exceed 10, and the total number of meshes is controlled between 2 million and 3 million. The solver step size is less than 1 / 20 of the PWM carrier period. If the deviation between the three-dimensional verification result and the two-dimensional result is less than 10%, the Pareto solution is retained; otherwise, it is discarded or iterated again.

9. A multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 8, characterized in that, In S3, during the three-dimensional fine verification process, the impact of the deviation in the length of the harmonic suppression coil end during the manufacturing process on the end inductance and total resistance is evaluated, and the overheating risk factor of the current limiting resistor is calculated. When the surface temperature of the current limiting resistor exceeds 100°C, the scheme is deemed unacceptable and is eliminated.

10. A multi-objective optimization design method for harmonic suppression coils of a low-vibration induction motor according to claim 1, characterized in that, In S4, the final solution is selected based on the specific service scenario of the motor, including: For electric vehicle drive motors, the Pareto solution with optimal electromagnetic vibration is preferred; for industrial motors that operate at full load for extended periods, the Pareto solution with optimal loss or temperature rise is preferred; for cost-sensitive household appliance motors, the Pareto solution with the simplest process and moderate slot fill factor is selected.

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