Axle gear lightweight design method and equipment based on dynamic response and topological optimization

Abstract

The invention provides an axle gear lightweight design method and equipment based on dynamic response and topological optimization, belongs to the technical field of axle gear design, and aims to establish an axle system-level dynamic model through MASTA, evaluate the system dynamic performance based on the established axle model, and ensure that the system has good NVH (Noise Vibration and Harshness) performance. And if the dynamic performance does not reach the standard, taking the dynamic meshing flexibility of the meshing pair as a target function, taking a gear lightweight design index into consideration, carrying out topological optimization on a gear spoke, and calculating the optimized gear statics and system dynamics response. And determining a final gear spoke structure. On the basis of system dynamic response, an optimization model about meshing flexibility is constructed, volume mass reduction serves as an optimization target, gear lightweight design is achieved in combination with mature finite element software and MASTA, and system NVH performance optimization is achieved while good static performance of the gear is guaranteed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of axle gear design, and particularly relates to a lightweight design method and device for an axle gear based on dynamic response and topological optimization. BACKGROUND

[0002] The gear of a new energy vehicle works under high-speed and high-torque conditions, causing medium and high frequency radiation noise in the shell. Topological optimization design of the gear is the most commonly used optimization method at present, which obtains the best performance and volume quality by changing the structural layout.

[0003] In the related art, the structural stiffness of the gear is reduced after weight reduction, which causes the dynamic meshing flexibility of the meshing pair to be equal in the frequency band of 5kHz-6kHz, and the phase difference is 180°. At this time, the dynamic meshing force will produce vibration superposition effect, causing the acceleration of the bridge shell measuring point to rise from 2.5g to >3g, exceeding the NVH performance threshold. This causes the cycle of weight reduction, vibration exceeding the standard, weight recovery, and lightweight failure, which cannot balance lightweight and performance.

[0004] The gear shaft has the dual functions of gear meshing and torque transmission. If the gear shaft spoke is directly optimized, such as opening and reducing weight, the bending stiffness of the shaft will be weakened. If the shaft diameter is reduced by 1mm, the stiffness will be reduced by 8%-10%, causing the shaft system to exceed the standard under maximum torque, causing bearing abnormal noise and gear uneven wear. The optimization result often appears that the included angle of the sharp corner profile is <30°, the width of the narrow gap structure is <2mm, and these structures cannot be realized through conventional machining processes. The sharp corner machining needs to be customized with a forming tool, the narrow gap is easy to cause the milling cutter to break, and the asymmetric hole will cause uneven stress on the spoke. SUMMARY

[0005] The application provides a lightweight design method for an axle gear based on dynamic response and topological optimization, which takes into account the lightweight design of the gear and the system dynamics response, and ensures the collaborative optimization of the statics performance and dynamics response of the gear.

[0006] The method comprises the following steps: S101: a parameterized model of an axle gear shaft system is established in system dynamics software, and a finite element condensed model is replaced for the shell, the shaft and the spoke to construct a system dynamics model; S102: based on the system dynamics model, the system dynamics response under the maximum torque condition is analyzed, the meshing pair to be optimized is determined through order analysis according to the frequency band in which the acceleration response of the measuring point is greater than 3g, and is recorded as gear G1 and gear G2, wherein G2 is located on the gear shaft; S103: the dynamic meshing force and the dynamic meshing flexibility of G1 and G2 are extracted respectively, and the dynamic meshing flexibility is taken as the topological optimization target; S104: Select the coaxial gear G3 of G2 as the optimization object, adjust the meshing pair stiffness matrix by changing the G3 spoke structure, and offset the frequency characteristics of G2 to optimize the vibration characteristics; S105: The spoke regions of G1 and the coaxial gear G3 are topologically optimized by using a variable density topology optimization method, a structural flexibility increase is taken as an objective function, and a material mass removal is taken as a constraint condition; S106: The fairing treatment is performed on the topologically optimized spoke to obtain an optimized gear model; S107: The optimized gear model is imported into a system model, finite element condensation is performed, and gear statics analysis is executed to verify gear strength and meshing performance as statics indexes; S108: The system dynamics response is analyzed under the same working condition to verify whether the optimized statics indexes and the dynamics response meet the requirements.

[0007] As can be seen from the above technical solutions, the present application has the following advantages: The axle gear lightweight design method based on dynamics response and topology optimization provided by the present application removes the redundant material of the gear G1 and the gear G2 precisely through variable density topology optimization and fairing treatment. The gear G1 and the gear G2 both achieve weight reduction without affecting the core meshing and assembly functions of the gears.

[0008] Through order analysis positioning the optimization object, taking meshing flexibility as the optimization target, and indirectly adjusting the frequency of G2, the vibration superposition problem caused by equal meshing flexibility and 180° phase difference is solved. After optimization, the bridge shell measurement point acceleration response is reduced from >3g to ≤3g in the 5.3kHz~5.7kHz frequency band, and the dynamic meshing force is reduced by more than 20%, effectively avoiding abnormal sound and resonance during axle operation, and meeting the NVH performance requirements of passenger cars and commercial vehicles.

[0009] Through stress verification under the maximum torque working condition, it is ensured that the key mechanical indexes of the optimized gear meet the requirements, the maximum bending stress of the gear G1 and the gear G3 is ≤180MPa, the meshing contact stress is ≤350MPa, and the maximum equivalent stress of the spoke is ≤245MPa, without stress concentration risk (the fairing treatment reduces the sharp corner stress concentration coefficient from 3.2 to 1.2). The purpose of lightweight and strength improvement is achieved.

[0010] The fairing treatment converts the irregular density cloud picture of the topology optimization into a waist-shaped hole and a smooth contoured machinable structure: the waist-shaped hole size is standardized, the edge is circularly transitioned, and can be machined through a conventional milling process without the need for custom-made tools. At the same time, it is verified that the minimum distance between the waist-shaped hole and the hub and the gear teeth is ≥3mm, avoiding assembly interference.

[0011] By analyzing the dynamic response, extracting the compliance, and expanding the optimization objects, G1, G2, and G3 were identified as the optimization objects, reducing the amount of simulation calculations and improving optimization efficiency. This approach satisfies the overall vehicle performance and safety requirements. Attached Figure Description

[0012] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 A flowchart of a lightweight design method for axle gears based on dynamic response and topology optimization; Figure 2 This is a schematic diagram of the electric drive bridge assembly model; Figure 3 A schematic diagram of the acceleration response at the measuring point of the target meshing pair; Figure 4 A schematic diagram of the dynamic meshing force and meshing compliance curves of the target meshing pair; Figure 5 A schematic diagram of the finite element model for optimizing the front meshing pair G1; Figure 6 A schematic diagram of the finite element model of the coaxial gear G3 before optimization; Figure 7 A schematic diagram of the optimized meshing pair G1 finite element model; Figure 8 A schematic diagram of the optimized coaxial gear G3 finite element model; Figure 9 A schematic diagram for optimizing the static response of the front gear; Figure 10 A schematic diagram showing the optimized static properties of the gear; Figure 11 This is a schematic diagram of the acceleration response of the target meshing pair measuring points after optimization. Figure 12 This is a schematic diagram of an electronic device. Detailed Implementation

[0014] This invention relates to a lightweight design method for axle gears based on dynamic response and topology optimization. A system-level model of the gear shaft is constructed using MASTA, and the system's dynamic response under high torque conditions is analyzed. Order analysis is used to determine the meshing pairs requiring optimization, and their dynamic meshing forces and meshing compliance are extracted. A finite element model of the optimized gear is established in finite element software, using gear meshing compliance as the objective function while also considering lightweight design parameters, and topology optimization is performed on the gear. The static and dynamic performance of the optimized gear is then evaluated to ensure coordinated optimization of multiple objectives.

[0015] The lightweight design method of axle gear based on dynamic response and topology optimization involved in the present application will be described in detail below. For the purpose of illustration but not for the purpose of limitation, specific details such as specific system structures, techniques, etc. are presented in order to thoroughly understand the embodiments of the present application. However, it should be clear to those skilled in the art that the present application can also be implemented in other embodiments without these specific details.

[0016] It should be understood that when used in the specification of the present application, the term includes indicates the presence of the described features, whole, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, whole, steps, operations, elements, components and / or their collection. The terms include, contain, have and their variants mean to include but not limited to, unless otherwise specifically emphasized otherwise.

[0017] The phrase one or some embodiments described in the present application means that the specific features, structures or characteristics described in the embodiment are included in one or more embodiments of the present application. Therefore, the phrases appearing in different places in the present application in one embodiment, in some embodiments, in other embodiments, in additional embodiments, etc. do not necessarily all refer to the same embodiment, but mean one or more but not all embodiments, unless otherwise specifically emphasized otherwise.

[0018] The technical solutions in the embodiments of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making creative efforts fall within the scope of protection of the present application.

[0019] Please refer to Figure 1 The flowchart of the lightweight design method of axle gear based on dynamic response and topology optimization in a specific embodiment is shown, and the method comprises: S101: A parameterized model of the axle gear system is established in the system dynamics software, and finite element condensed models of the shell, shaft and spoke are replaced to construct a system dynamics model.

[0020] In some embodiments, a parameterized model based on the pinion shaft system is established in MASTA, mainly including bearings, shafts, gears, etc. Tetrahedral meshing is performed on key parts such as the housing, shaft, spoke, etc. The full finite element model is imported into MASTA for running condensation. Bearings are selected according to the actual bearing type in the bearing library. REB3 coupling is used between the spoke and the bearing. RBE3 coupling is used for the shaft and bearing and spline connection. The shaft hub connection is established at the position of the axle housing spring seat. The axle housing is grounded to ensure the accuracy of the system model. The MASTA simulation model of the electric drive axle is as shown in Figure 2 An acceleration sensor is installed around the oil drain hole of the axle housing to measure the dynamic response of the system. In some specific embodiments, S101 specifically includes the following steps: S1011: Tetrahedral meshing is performed on key parts such as the housing, shaft, spoke, etc.

[0021] In some embodiments, the geometry of the housing, shaft, and spoke is discretized using tetrahedral elements. The grid size is determined according to the structural complexity and analysis accuracy requirements to ensure that the grid quality meets the finite element analysis standards.

[0022] S1012: The divided full finite element model is imported into the system dynamics software, and the finite element condensation is run.

[0023] In some embodiments, the full finite element model is imported into the system dynamics software. The bearing mounting nodes, shaft and gear connection nodes, etc. are selected. After setting the condensation algorithm parameters, the condensation process is executed.

[0024] In this way, by dividing the system degrees of freedom into main degrees of freedom as reserved and slave degrees of freedom as condensed, the influence of the slave degrees of freedom is condensed onto the main degrees of freedom, the model is reduced, and the calculation scale is greatly reduced under the premise of ensuring accuracy.

[0025] S1013: According to the actual bearing type, select the bearing in the software bearing library. RBE3 coupling is used between the spoke and the bearing, the shaft and the bearing, and the spline connection.

[0026] In some embodiments, the corresponding type of bearing is selected. The connection nodes of the spoke and the bearing are set as slave nodes, and the bearing reference nodes are set as master nodes. RBE3 coupling is established. Similarly, RBE3 coupling is established for the nodes of the shaft and the bearing and the spline connection. RBE3 coupling simulates the mechanical behavior of rigid or quasi-rigid connection, ensures the motion coordination and force transmission between the spoke and the bearing, the shaft and the bearing, and the spline, and accurately reflects the stiffness and motion relationship of the actual connection.

[0027] S1014: Establish the shaft hub connection at the position of the axle housing spring seat, and ground the axle housing.

[0028] In some embodiments, the constraint relationship of the shaft hub connection is established at the position of the axle housing plate spring seat, and the freedom degree of the axle housing in the grounding direction is limited; the grounding constraint is applied to the axle housing to simulate the actual connection of the axle with the ground. The shaft hub connection and the grounding provide a real boundary constraint condition for the system, so that the constraint state of the model in the dynamic analysis is consistent with the actual working condition.

[0029] S1015: An acceleration sensor is installed around the axle housing drain hole to measure the dynamic response of the system.

[0030] In some embodiments, the acceleration sensor is installed around the axle housing drain hole, and the measurement direction and sampling parameters are set to obtain the acceleration time history data at this position. The acceleration sensor reflects the dynamic response of the system by measuring the structural vibration acceleration, which is a key means for evaluating the NVH (Noise, Vibration and Harshness) performance. The software simulation can reproduce the dynamic response data of the actual test.

[0031] As can be seen, the parametric model can accurately reproduce the geometry and assembly relationship of the axle shaft system. The finite element condensation retains the key degrees of freedom and condenses the secondary degrees of freedom, thereby reducing the model calculation scale while ensuring the accuracy of the mechanical characteristics. The RBE3 coupling can simulate the force transmission characteristics of rigid or quasi-rigid connection, the grounding and the shaft hub connection provide boundary constraints consistent with the actual working condition, and the acceleration sensor provides a data acquisition interface for subsequent dynamic response measurement.

[0032] S102: Based on the system dynamic model, the system dynamic response under the maximum torque working condition is analyzed, the meshing pair to be optimized is determined through order analysis according to the frequency band with an acceleration response greater than 3g at the measurement point, and is recorded as gear G1 and gear G2, wherein G2 is located on the gear shaft.

[0033] In some embodiments, according to the actual running load spectrum of the axle, the dynamic response of the system is evaluated when the input torque under the maximum torque working condition is 250Nm in a wide working speed range. The acceleration at the axle housing measurement point is extracted as shown in Figure 3 The acceleration response at the measurement point is taken as the evaluation index (>3g), and the frequency band (5.3kHz~5.7kHz) with a larger acceleration response is determined. According to the response order, it is determined that the meshing pairs to be optimized are G1 and G2.

[0034] It should be noted that the frequency band with an acceleration response greater than 3g in the identification spectrum is analyzed in terms of order, and the gear meshing order is associated, i.e. order = number of teeth × speed / 60, and finally the meshing pairs causing the excessive response are determined as G1 and G2.

[0035] In some specific embodiments, S102 specifically includes the following steps: S1021: Apply the maximum torque working condition load in the system dynamics model, set the input shaft speed range to 1000-6000 rpm, apply a 250 Nm constant torque at the input shaft end, define the simulation step size to be 0.1 ms, and the total simulation time to be 2 s.

[0036] In some embodiments, the actual working conditions are accurately reproduced on the established system dynamics model. The input shaft speed range of 1000-6000 rpm covers the typical working interval of the axle, and the 250 Nm torque corresponds to the maximum load working condition. The simulation step size of 0.1 ms ensures that dynamic responses up to 5 kHz or more can be captured, and the time length of 2 s ensures that the system reaches a steady state. In the MASTA software, the speed-torque relationship is set through the load spectrum definition module, and the transient dynamics solver is selected for simulation.

[0037] S1022: Perform system dynamics solving, extract three-directional acceleration time domain response data at pre-set measurement points around the axle housing drain hole, and save the acceleration data.

[0038] In some embodiments, through multi-point and multi-directional vibration monitoring, the dynamic behavior of the system under excitation is comprehensively mastered, and original data is provided for frequency domain and order analysis.

[0039] S1023: Perform fast Fourier transform on the acceleration time domain data, convert to the frequency domain, set the frequency resolution to 10 Hz, identify the peak points with acceleration amplitude exceeding 3g in the frequency band of 5.3 kHz-5.7 kHz, and record the frequencies and amplitudes corresponding to these peak points.

[0040] In some embodiments, the fast Fourier transform FFT decomposes the time domain acceleration signal into frequency domain components, and the frequency resolution of 10 Hz can clearly distinguish between dense modes. The frequency band of 5.3 kHz-5.7 kHz is focused on because this frequency band exhibits abnormal vibration in actual testing. Through the spectral peak detection algorithm, resonance peaks exceeding the 3g threshold are identified, and their exact frequencies and amplitudes are recorded.

[0041] S1024: Based on the system speed parameters and the gear tooth number, calculate the meshing order of each meshing pair, match the identified acceleration peak frequencies with the order frequencies of each meshing pair, and determine that the meshing pairs causing the peaks exceeding the threshold in the frequency band of 5.3 kHz-5.7 kHz are G1 and G2.

[0042] In some embodiments, order analysis is a key technology for rotating machinery vibration diagnosis, and by calculating the rotational frequencies of each shaft and their harmonics, as well as the gear meshing frequencies (shaft frequency x tooth number), a complete order spectrum is established. In S1023, the peak frequencies identified are matched with the meshing orders of G1 and G2, and the matching tolerance is set to ±20 Hz. When the peak frequency coincides with the order frequency of a certain meshing pair, it is determined that this meshing pair is the vibration source.

[0043] S1025: Quantify the contribution of the G1 and G2 meshing pairs to the excessive vibration, calculate the ratio of the peak acceleration caused by them in the 5.3kHz-5.7kHz frequency band to the total acceleration response, and confirm that these two meshing pairs are the main optimization objects.

[0044] In some embodiments, the vibration contribution of the G1 and G2 meshing pairs in the problem frequency band is calculated, and the impact degree is expressed in percentage form. The specific calculation is: the ratio of the square sum of the peak acceleration amplitude caused by G1 (or G2) to the square sum of all peak amplitudes of the total acceleration response in the 5.3kHz-5.7kHz frequency band. When the contribution of a certain meshing pair exceeds the set threshold, it is confirmed as the main optimization object, ensuring that optimization resources are invested in the most critical parts and improving optimization efficiency.

[0045] S103: Extract the dynamic meshing force and dynamic meshing flexibility of G1 and G2 respectively, and take the dynamic meshing flexibility as the topology optimization target.

[0046] In some embodiments, the dynamic meshing force of the meshing pairs G1 and G2 and their dynamic meshing flexibility are extracted, as shown in Figure 4 for the frequency band with large vibration acceleration response (5.3kHz~5.7kHz), the peak acceleration caused by the equal flexibility and 180-degree phase difference of the target meshing pairs G1 and G2 is focused on. Changing the flexibility of G1 and G2 can change the meshing peak.

[0047] This embodiment targets the peak value of this frequency band, combines the lightweight constraint condition, and increases the flexibility of G1 as the optimization target, thereby reducing the excitation source of the meshing pair and optimizing the dynamic response of the system; considering that G2 is a gear shaft structure, the flexibility of G3 can be changed to make the frequency of G2 shift forward, avoid the equal flexibility of the meshing pair when the phase difference is 180 degrees, thereby reducing the excitation source of the meshing pair and optimizing the dynamic response of the system.

[0048] S104: According to the gear shaft structure of the meshing pair G2, select the coaxial gear G3 as the optimization object, adjust the meshing pair stiffness matrix by changing the G3 spoke structure, and make the frequency characteristics of G2 shift to optimize the vibration characteristics.

[0049] In some embodiments, since G2 is a gear shaft structure, directly optimizing its spokes can affect the strength and stiffness of the shaft, so G3 coaxial with G2 is selected as an indirect optimization object; a coupled mechanical model of the G2-G3 coaxial system is established by using finite element software, hexahedral mesh is divided and bearing support constraints are applied, and the system coupling stiffness matrix is calculated; by changing the thickness of the G3 spoke, the position of the opening and other structural parameters through parametric analysis, the change of the elements related to G2 in the coupling stiffness matrix is observed, the key adjustment area of the G3 spoke is determined, and finally the structure of the area is changed to make the frequency characteristics of G2 deviate from 5.3kHz~5.7kHz.

[0050] The regular grid division of the helical gear geometric model in the embodiment: in order to quickly generate a regular finite element grid model, first, the helical gear is regionally divided, the entire tooth region is divided into an involute tooth profile part, a dedendum circle part and a gear wheel body part, the gear end face mesh is stretched, and a regular hexahedral mesh model is divided. Thus, the division of the single-tooth finite element grid model is completed.

[0051] Generation of the multi-tooth model in the embodiment: the rotational amplitude of the lightweight gear spoke is changed according to the corresponding number of teeth, and the nodes are processed together to generate G1 and G3 models, and the obtained gear model is as shown in Figure 5 and Figure 6 .

[0052] S105: A variable density topology optimization method is used to perform topology optimization on the spoke regions of the meshing pair G1 and the coaxial gear G3, with the increase of structural flexibility as the objective function and the removal of material mass as the constraint condition.

[0053] In some embodiments, the Optimization module in the finite element software is used to perform topology optimization on the driving gear and the driven gear. The optimization region grid type is hexahedral grid, and the grid needs to be refined. The variable density topology optimization method is used, and the maximum allowed number of iterations is 500 times. The relative density of the spoke region grid element is used as the design variable, and its value is 0-1. The increase of the structural flexibility of G1 and G3 is used as the objective function, and the removal of material mass is used as the constraint condition. The topology optimization is performed on the gear spoke part. The spoke is the topology optimization region, and the main reason is that this part of the material is under smaller load and has larger redundancy.

[0054] It needs to be further explained that as the removal of material continuously increases, the flexibility of G1 also increases, the weight of the gear decreases, the corresponding flexibility curve gradually decreases, and the strength of the gear also decreases, so subsequent static force school needs to be performed to ensure that the safety use requirements are met. As the removal of material continuously increases, the flexibility of G3 increases, the stiffness of the G1 gear shaft system decreases, and the corresponding frequency moves forward. At the same time, the strength of G3 also decreases, and it needs to be subjected to static force school to ensure that the safety use requirements are met.

[0055] It can be seen that the flexibility of G1 and G3 is precisely improved under the lightweight constraint, which not only meets the demand of dynamic optimization, but also realizes material weight reduction. The refined hexahedral mesh combined with the SIMP model makes the optimization result have both accuracy and manufacturability.

[0056] S106: fairing processing is performed on the spoke after topological optimization to obtain an optimized gear model.

[0057] In some embodiments, in the post-processing module of the finite element software, a relative density threshold is set to divide the entity reserved area and the hole removed area of the spoke; the irregular boundary is fitted to the initial profile of the waist-shaped hole by sampling the boundary of the hole removed area; the center coordinates, length and width of the hole are determined; the Bezier curve is used to fit the edge of the waist-shaped hole, and the control points are adjusted to make the two ends of the hole transition with circular arcs and eliminate sharp corners and broken lines. The fairing profile is imported into the CAD software to check the minimum distance (≥3mm) between the waist-shaped hole and the hub and the gear, verify that the material removal rate meets the constraint, and finally export the optimized G1 and G3 gear models in STEP / IGES format.

[0058] It should be noted that the objective function converges after multiple iterations and finally tends to be stable. The gear model after fairing processing of the size obtained after optimization is shown in Figure 7 and Figure 8 The mass of G1 before optimization is 4.825kg, and the mass after optimization is 4.465kg. The mass of G3 before optimization is 2.9kg, and the mass after optimization is 2.576kg. The weight reduction holes are all waist-shaped holes, and the overall mass is reduced by about 91.15%. Through the distance check and the material removal rate verification, it is ensured that the model meets the assembly requirements and meets the lightweight constraint.

[0059] S107: The optimized gear model is imported into the system model, and finite element condensation is performed, and statics analysis of the gear is performed to verify the gear strength and meshing performance as statics indicators.

[0060] In some embodiments, the STEP model of the optimized G1 and G3 is imported into MASTA, and the corresponding components in the original system model are replaced, and the coaxiality of the gear and the shaft is ensured to be ≤0.02mm through coordinate alignment; the tetrahedral mesh of the G1 and G3 spokes is re-divided, the Guyan condensation algorithm is used to run finite element condensation, and the RBE3 coupling relationship is kept consistent with the original model; a maximum torque load of 250Nm is applied to the power input shaft, and a radial+axial constraint is applied to the bridge shell plate spring seat, the statics solver is started, the gear root stress, spoke stress and meshing contact stress are calculated, and the results are compared with the material allowable stress.

[0061] It should be noted that, under the same working condition, the statics analysis of the gear, combined with Table 1 and Table 2, the gear strength and meshing performance before and after optimization are respectively shown in Figure 9 and Figure 10 After the structure is optimized, the statics performance of the gear is improved, which proves that the original gear design has a great redundancy.

[0062] Table 1: Gear strength and meshing performance before optimization

[0063] Table 2: Gear strength and meshing performance after optimization

[0064] S108: Analyze the system dynamics response under the same working condition, and verify whether the statics indicators and dynamics response after optimization meet the standards.

[0065] In some embodiments, based on the system model after S107 condensation, the maximum torque of 250Nm, the axle housing constraint, and the acceleration sensor parameters are consistent with S102, and the dynamics simulation is run; the axle housing measurement point acceleration data is extracted and converted into a frequency response spectrum, and it is checked whether the acceleration peak value in the frequency band of 5.3kHz~5.7kHz is ≤3g; at the same time, the dynamic meshing flexibility of G1 and G2 in the frequency band is extracted, and it is judged whether there is a phase difference of 180° and an amplitude deviation of ≤10%; combined with the statics indicators (stress ≤ allowable stress) of S107, it is comprehensively judged whether the optimization scheme meets the standards, and if any indicator does not meet the standards, it returns to S105 to adjust the topology optimization parameters.

[0066] It should be noted that, under the same working condition, the dynamics response of the system mainly focuses on the acceleration response peak value at the axle housing measurement point, to ensure that the peak value is lower than (3g), so as to realize good NVH performance on the basis of lightweight. The corresponding dynamics response is shown in Figure 11 After optimization, the system dynamics performance is significantly improved, and the system vibration acceleration response caused by the target meshing pair is lower than 3g. When the concerned frequency band (5.3kHz~5.3kHz) avoids the phase difference of 180° between the mutually meshing gears, the flexibility values are equal, thereby reducing the dynamic meshing force and improving the system NVH performance.

[0067] In an embodiment of the present application, based on step S103, a possible embodiment will be given below to non-limitingly illustrate the specific implementation scheme. S103 specifically includes the following steps: S1031: Extract the dynamic meshing force time domain data of the meshing pair G1 and G2 from the system dynamics simulation results, and construct the meshing force time sequence.

[0068] S1032: Establish a contact analysis model of the gear pair in the finite element software, apply a unit load on the tooth surface, calculate the dynamic displacement response of the tooth surface on the meshing line, and obtain displacement-time data.

[0069] S1033: Perform synchronous Fourier transform on the dynamic meshing force and dynamic displacement data, calculate the ratio of the two in the frequency domain, and obtain the meshing flexibility frequency response function, formula:

[0070] Where C(f) is the meshing flexibility, X(f) is the dynamic displacement frequency domain response, and F(f) is the dynamic meshing force frequency domain response.

[0071] S1034: In the problem frequency band of 5.3 kHz-5.7 kHz, analyze the amplitude and phase characteristics of the meshing flexibility of G1 and G2, and identify the frequency points where the flexibility amplitudes are equal and the phases are close to 180°.

[0072] S1035: As the target of eliminating or reducing the meshing flexibility resonance peak value of G1 and G2 in the problem frequency band, the specific target value of topology optimization is determined to be more than 30% reduction of the flexibility amplitude, and this is used as the quantitative index for subsequent optimization.

[0073] In some embodiments, the gear pair G1 and G2 is selected by the gear pair analysis tool, and the output parameter is set as the dynamic meshing force. Based on the contact mechanics principle of finite element method, the deformation response of the structure under load is obtained by numerical solving of the elastic mechanics equation. The time-domain meshing force and displacement data are imported into MATLAB or Python processing environment, and the fast Fourier transform algorithm is applied to convert them into frequency domain data. The Hanning window function is used to reduce spectral leakage. The flexibility value is calculated at each frequency point in the frequency domain, which is the complex ratio of displacement frequency response to force frequency response. Finally, the complex function of flexibility varying with frequency is obtained, which contains amplitude and phase information. Based on vibration theory, when the flexibility amplitudes of two coupled systems are similar and the phases are opposite, strong resonance response will occur, and the specific frequency points that cause vibration amplification can be accurately located. Based on the resonance frequency points identified in S1034, the average flexibility amplitude of these frequency points is calculated as the reference. The optimization target is set to reduce the flexibility amplitude of these frequency points by 30%, while ensuring that the flexibility change in other frequency bands does not exceed 10%. The target value is specified as the constraint condition of the optimization problem, including the upper limit of the flexibility amplitude and the range limit. The complex vibration problem is converted into a clear optimization index, making the topology optimization have a clear direction, improving the optimization efficiency and effect.

[0074] In one embodiment of the present application, based on step S104, a possible embodiment will be given below to specifically illustrate the specific implementation scheme. S104 specifically includes the following steps: S1041: Confirm the shafting assembly relationship of the meshing pair G2 and the coaxial gear G3 in the system dynamics model, and determine the connection mode and support constraint conditions of the two.

[0075] S1042: Extract the shaft diameter, length, and tooth width of the G2 gear shaft, the thickness, hub diameter, and rim thickness of the G3 gear, and the elastic modulus and Poisson's ratio of the shafting material shared by the two.

[0076] S1043: Establish a coupled mechanical model of the G2-G3 coaxial system using finite element software, divide the mesh and apply bearing support constraints consistent with the actual working conditions, and calculate the coupled stiffness matrix of the system.

[0077] S1044: Through parameterized analysis, change the spoke thickness and hole position of G3, observe the changes of the elements related to G2 in the coupled stiffness matrix, and identify the key areas of G3 spoke that affect the stiffness of G2.

[0078] S1045: According to the identification results of the key areas, formulate the key area thinning and weight reduction hole of G3 spoke structure, and determine the thickness adjustment amount and hole size range of structural adjustment.

[0079] In some embodiments, the coaxial gear forms a mechanical coupling relationship through the shared shafting, and the structural deformation of the G3 spoke will be transmitted to the G2 gear shaft through the shafting, thereby changing the overall stiffness characteristics of G2; the bearing constraint condition determines the stiffness transmission path of the shafting, directly affecting the degree of stiffness influence of G3 on G2. The shaft diameter and spoke thickness determine the cross-sectional moment of inertia and bending stiffness of the component, and the material properties determine the deformation ability of the material, which together constitute the basic input for calculating the stiffness matrix, and are the quantitative G2 and G3 stiffness correlation data. In the finite element software, import the geometric models of G2 and G3, divide the hexahedral mesh for the shafting, G2 gear, and G3 gear respectively; apply radial and axial constraints at the bearing installation position to establish the overall mechanical model of the G2-G3 coaxial system; calculate the coupled stiffness matrix of the system through the static analysis module, and output the elements related to the radial and circumferential stiffness of the G2 gear shaft. Considering that the structure of different areas of the spoke has different contributions to the overall stiffness, the near-hub area is closer to the shafting, and its stiffness change is more easily transmitted to G2 through the shafting; the near-rim area is far from the shafting, and the stiffness change has a weaker impact on G2, so by comparing the influence amplitude of different areas, the key action area can be locked, and the efficiency and pertinence of subsequent topology optimization can be improved. For the identified near-hub area of G3 spoke, specific adjustment schemes are formulated based on the lightweight demand: if it is necessary to reduce the stiffness of G2 to achieve frequency shift, a waist-shaped hole or a thinning amount not exceeding 20% of the initial thickness can be designed in the key area; for non-key areas, only small amplitude thickness adjustment is performed to assist lightweight.

[0080] In one embodiment of the present application, based on step S105, a possible embodiment will be given below to specifically illustrate the non-limiting embodiment. S105 specifically includes the following steps: S1051: In the finite element software, define the spoke area of gears G1 and G3 as the design space, and the tooth profile area and mounting hole area as the non-design space, and set all the hexahedral mesh elements in the spoke area as the optimizable elements.

[0081] S1052: Set the relative density of each hexahedral mesh element as the design variable, with the value range of 0 to 1, wherein 0 represents material removal and 1 represents material retention, and the initial value is uniformly set to 0.5.

[0082] S1053: Take the increase of structural compliance of the gear spoke area as the objective function, and establish the mathematical expression of the optimization problem, while setting the mass reduction of 35% as the constraint condition.

[0083] S1054: Perform iterative calculation by using the material interpolation model in the variable density method, set the penalty factor to 3, the maximum number of iterations to 500, and the convergence tolerance to 0.001.

[0084] S1055: Start the optimization solver to perform iterative calculation, output the intermediate result every 10 iterations, monitor the convergence of the objective function and the constraint condition, and stop the calculation when the convergence standard or the maximum number of iterations is reached.

[0085] It can be seen that based on the space definition principle of topology optimization, the structural integrity of the tooth surface and the mounting interface is ensured not to be affected by optimization by limiting the optimization area, while the best distribution of material in the non-key area is sought. Based on the continuum topology optimization theory, the distribution state of material in the design domain is described by introducing continuous design variables, the discrete 0-1 optimization problem is converted into a continuous optimization problem, and the stability and convergence efficiency of the optimization process are improved. The objective function is defined as the minimization of structural compliance, i.e. , wherein U(ρ) is the displacement vector and K(ρ) is the stiffness matrix. Through the graphical interface of the optimization module, set compliance as the objective function, select mass as the constraint type, and input the target mass fraction as 0.65. At the same time, set the response constraint to ensure that the maximum stress does not exceed the allowable value. Based on the material interpolation and penalty optimization principle, the design variables are driven to the two poles of 0 or 1 by penalizing the intermediate density value, and finally the clear topology structure is obtained.

[0086] S1055 of the embodiment is to perform a complete optimization solving process. The optimization solver starts from the initial design, and sequentially performs finite element analysis, sensitivity analysis, and design variable updating. In each iteration, the displacement field is obtained by solving the equilibrium equation K(p)U=F, and then the objective function and constraint function values are calculated, followed by the calculation of sensitivity by the adjoint method, and the updating of the design variables by the mathematical programming algorithm. During the optimization process, the trends of the key indicators such as the mass fraction, the objective function value, and the maximum displacement are monitored in real time, and when the relative change of the objective function of the last 5 iterations is less than 0.001, it is determined to be converged. In this way, based on the numerical optimization algorithm, through the finite element analysis, sensitivity analysis, and design updating in the iteration process, the optimal material distribution mode is gradually approached, and the gradual improvement of the structure performance is realized.

[0087] In an embodiment of the present application, based on step S106, a possible embodiment will be given below to specifically and non-limitingly illustrate the specific implementation thereof. S106 specifically includes the following steps: S1061: In the finite element software, set the relative density threshold value, divide the entity reserved area and the hole removed area of the G1 and G3 spokes, and generate the initial boundary profile.

[0088] S1062: Sample the boundary points of the hole removed area using a geometric profile extraction tool, fit the irregular boundary to the initial geometric profile of the waist-shaped hole, and determine the center coordinates, length and width parameters of the hole.

[0089] S1063: Fit the profile edge of the waist-shaped hole using a Bezier curve, adjust the curve control points to make the two ends of the hole transition with circular arcs, and eliminate the profile sharp corners and broken lines.

[0090] S1064: Import the smoothed profile into the CAD software, check the minimum distance between the waist-shaped hole and the hub and the gear teeth, verify whether the spoke thickness uniformity and the material removal rate meet the constraints.

[0091] S1065: Export the smoothed G1 and G3 gear three-dimensional models in STEP / IGES format, save the model geometric parameters, and form the optimized gear model.

[0092] The S1061 topology optimization of this embodiment outputs a continuous relative density distribution. The continuous distribution is discretized by setting a threshold to convert the abstract optimization result into a geometric boundary that can be subsequently processed. The hole boundary generated by the S1062 topology optimization is mostly an irregular polyline, which does not conform to the actual manufacturing process. The waist-shaped hole has the characteristics of high weight reduction efficiency and low stress concentration. By fitting and converting into a regular shape, the lightweight demand and manufacturing feasibility can be met at the same time. The S1063 considers that the sharp corners and polylines on the contour will cause local stress concentration when the gear is working, which greatly reduces the fatigue life of the spoke. The Bezier curve has the characteristics of continuous and adjustable curvature, which can realize the smooth transition of the contour, reduce the stress concentration, and facilitate processing. The S1064 measures the minimum straight line distance of the waist-shaped hole and the inner hole of the hub, the root of the gear tooth, respectively, to ensure that the distance is greater than or equal to 3 mm, so as to avoid weakening the hub assembly strength or the gear meshing strength. The mass of the spoke before and after optimization is compared, the actual material removal rate is calculated, and it is confirmed that it is less than or equal to 10%, which meets the constraint condition of S105. In S1065, the G1 and G3 gear models after fairing are deleted, the redundant lines are merged, the coincident surfaces are combined, and the gap between the surfaces is repaired. The model is exported. The G1 spoke thickness (such as 15 mm), the number of waist-shaped holes (4), the size of a single waist-shaped hole (20 mm long x 8 mm wide), the G3 spoke thickness (such as 12 mm), the number of waist-shaped holes (3), and the size of a single waist-shaped hole (18 mm long x 6 mm wide) are configured. Finally, the geometric parameters are saved. It is ensured that the statics analysis of S107 and the system dynamics verification of S108 are successfully performed.

[0093] In an embodiment of the present application, based on step S107, a possible embodiment will be given below to specifically and non-limitingly illustrate the specific implementation thereof. S107 specifically comprises the following steps: S1071: Import the optimized G1 and G3 gear STEP / IGES format models output by S1065 into MASTA software, replace the G1 and G3 gear geometric models in the original system model, and check the model geometric tolerance to ensure assembly compatibility.

[0094] S1072: Re-divide the tetrahedral mesh at the key positions of the replaced G1 and G3 spokes, and run the finite element condensation by using the Guyan condensation algorithm, while keeping the RBE3 coupling relationship consistent with the original model.

[0095] S1073: In the MASTA statics analysis module, apply the maximum torque load to the power input shaft consistent with S1021, apply radial and axial constraints to the position of the axle housing plate spring seat, and reproduce the actual working boundary conditions.

[0096] S1074: Start the statics solver to calculate the stress distribution, strain distribution and meshing contact stress of the optimized G1 and G3 gears, and set the solution accuracy level to high precision to ensure the reliability of the results.

[0097] S1075: Extract the static analysis results, record the maximum equivalent stress, tooth root maximum bending stress, meshing contact stress values of G1, G3 gears, and compare them with the material allowable stress.

[0098] The S1071 of the embodiment optimizes the gear model after the shaft diameter, bearing matching size of the original system model; the geometric tolerance and defect check can avoid the virtual interference caused by model error during assembly, and ensure that the simulation results can reflect the real structure state. In S1072, the spoke structure of the optimized gear is different from the original model, and the mesh is re-divided to accurately reflect the structure form. The finite element condensation converts the detailed finite element model into a low-order system model by retaining the key main degrees of freedom and condensing the secondary degrees of freedom, which can ensure the accuracy of the mechanical properties of the key parts and reduce the calculation amount of subsequent system analysis. In S1073, the actual support restriction of the simulated axle is constrained, and the stress state under the maximum torque is simulated, which can reproduce the stress environment of the gear under the limit working condition and ensure that the analysis results can reflect the actual bearing capacity of the gear. In S1074, the mechanical property data of the optimized gear under the limit working condition is obtained, and the linear solver and high-precision setting balance the calculation efficiency and result accuracy, which can avoid excessive calculation and waste resources, and ensure the accuracy of the analysis results in the stress concentration area. In S1075, the spoke hole edge, tooth root position, tooth root maximum bending stress, and meshing contact stress of G1 and G3 gears are obtained, the allowable stress value of the gear material is queried, and the actual stress value and the allowable value are compared one by one to record the stress ratio. The static mechanical properties of the optimized gear are quantitatively verified to meet the standard, and the comparison standard with the material allowable stress is unified to ensure that the verification results have engineering persuasiveness.

[0099] In an embodiment of the present application, based on step S108, a possible embodiment will be given below to specifically and non-limitingly illustrate the specific implementation thereof. S108 specifically includes the following steps: S1081: In the integrated and optimized complete system dynamics model of the gear, 250Nm input torque and 1000-6000rpm speed range are applied, and transient dynamics analysis is performed.

[0100] S1082: Extract the three-direction acceleration response data of the same measuring point at the oil drain hole of the axle housing, keep the sampling frequency at 20kHz, and perform fast Fourier transform on the acceleration time domain data to obtain the frequency domain response of the concerned frequency band of 5.3kHz-5.7kHz.

[0101] S1083: Compare the acceleration peak values in the concerned frequency band before and after optimization, check whether the acceleration amplitude of any frequency point exceeds the threshold value of 3g, and record the number of frequency points exceeding the threshold value and the maximum exceeding amplitude.

[0102] S1084: Re-extract the dynamic meshing flexibility of the optimized G1 and G2 meshing pairs, and analyze whether the condition that the flexibility of the two meshing pairs is equal and the phase is close to 180° in the frequency band of 5.3 kHz-5.7 kHz is eliminated or improved.

[0103] S1085: Integrate the static performance index and the dynamic response index to determine whether the optimized gear meets the strength requirement and the NVH requirement at the same time, and form a final verification conclusion.

[0104] The embodiment is based on the consistency principle of dynamic simulation, and ensures that the difference between the system responses before and after optimization is completely caused by the modification of the gear structure through the same load and boundary conditions. Step S1082 locates the pre-set acceleration measuring point at the oil drain hole of the axle housing after the system dynamics analysis is completed, and outputs the acceleration time history data in X, Y and Z directions. The same post-processing method as before optimization is adopted, the spectral characteristics in the problem frequency band of 5.3 kHz-5.7 kHz are focused on, and the detailed spectrum graph in the frequency band is generated. The acceleration data in the whole frequency band is saved for further analysis. Step S1083 scans the whole spectrum in the frequency band of 5.3 kHz-5.7 kHz, and identifies all local peak points. The acceleration amplitude of each peak point is measured and compared with the threshold of 3g. The number, frequency position and over-standard amplitude of the over-standard points are counted. The overall level of acceleration in the frequency band is calculated, including the RMS value and the peak factor. The improvement degree of each index is calculated by comparing the corresponding data before optimization. The evaluation of the optimization effect is objectified and dataized, and clear basis is provided for design decision. Step S1084 extracts the dynamic meshing force and the dynamic displacement of the G1 and G2 meshing pairs from the system dynamics results after optimization, and calculates the meshing flexibility frequency response function according to the method of step S1033. In the frequency band of 5.3 kHz-5.7 kHz, the amplitude ratio and the phase difference distribution of the G1 and G2 flexibility are analyzed. Whether there is still the condition that the flexibility amplitude difference is not more than 10% and the phase difference is in the range of 170°-190° is checked. The occurrence frequency of such adverse conditions is recorded and compared with that before optimization. Step S1085 establishes a comprehensive evaluation matrix including static and dynamic indexes: the static indexes include the tooth root bending safety factor and the tooth surface contact safety factor; the dynamic indexes include the maximum acceleration amplitude, the number of over-standard frequency points and the overall vibration level. A weight factor and a qualified threshold are set for each index. The comprehensive score of the system after optimization is calculated and compared with the score before optimization. According to the evaluation result, a clear conclusion is given: complete compliance, partial compliance requiring further optimization or non-compliance requiring re-design. A complete verification report is formed, including all key data and comparison charts.

[0105] It should be understood that the size of the serial number of each step in the above embodiment does not mean the order of execution, and the execution order of each process should be determined according to its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0106] like Figure 12 As shown, this application also provides an electronic device, including a display module 103, a memory 102, a processor 101, a communication module 104, and a computer program stored in the memory and executable on the processor 101. When the processor 101 executes the program, it implements the steps of a lightweight design method for axle gears based on dynamic response and topology optimization.

[0107] In embodiments of the present invention, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments described and / or claimed herein.

[0108] In this embodiment, processor 101 may be implemented using at least one of an application-specific integrated circuit, a programmable logic device, a field-programmable gate array, a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such an implementation may be implemented within a controller. For software implementation, implementations such as processes or functions may be implemented with separate software modules that allow the performance of at least one function or operation. Software code may be implemented by a software application (or program) written in any suitable programming language, and the software code may be stored in memory and executed by the controller.

[0109] The display module 103 is used to display information input by the user or information provided to the user. The display module 103 may include a display panel, which may be configured in the form of a liquid crystal display, an organic light-emitting diode, or the like.

[0110] The memory 102 can be used to store software programs and various data. The memory 102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0111] The communication module 104 transmits radio signals to and / or receives radio signals from at least one of a base station, an external terminal, and a server. Such radio signals may include voice call signals, video call signals, or various types of data sent and / or received according to text and / or multimedia messages.

[0112] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A lightweight design method for axle gears based on dynamic response and topology optimization, characterized in that, The methods include: S101: Establish a parametric model of the axle gear system in the system dynamics software, and replace the housing, shaft and spokes with finite element condensation models to construct the system dynamics model; S102: Based on the system dynamics model, analyze the system dynamics response under the maximum torque condition. According to the frequency range where the acceleration response at the measuring point is greater than 3g, determine the meshing pair to be optimized through order analysis, denoted as gear G1 and gear G2, where G2 is located on the gear shaft. S103: Extract the dynamic meshing force and dynamic meshing compliance of G1 and G2 respectively, and use dynamic meshing compliance as the topology optimization target; S104: Select the coaxial gear G3 of G2 as the optimization object. Adjust the meshing stiffness matrix by changing the spoke structure of G3 to shift the frequency characteristics of G2 and optimize the vibration characteristics. S105: The topology of the spoke regions of G1 and coaxial gear G3 is optimized using the variable density topology optimization method, with the objective function being the increase of structural flexibility and the constraint being the removal of material mass. S106: Smooth the spokes after topology optimization to obtain the optimized gear model; S107: Import the optimized gear model into the system model, perform finite element reduction, and execute gear static analysis to verify gear strength and meshing performance as static indicators. S108: Analyze the dynamic response of the system under the same working conditions to verify whether the optimized static and dynamic indicators meet the standards.

2. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S101 specifically includes the following steps: Tetrahedral meshes were created for key components such as the shell, shaft, and spokes. Import the divided full finite element model into the system dynamics software and run the finite element condensation. Select the bearing from the software bearing library according to the actual bearing type, and use RBE3 coupling for the connection between the spokes and the bearing, the connection between the shaft and the bearing, and the spline connection. Establish a hub connection at the axle housing leaf spring seat location and ground the axle housing; An accelerometer is installed around the oil drain hole in the axle housing to measure the system's dynamic response.

3. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S102 specifically includes the following steps: The maximum torque load is applied in the system dynamics model, the input shaft speed range is set to 1000-6000 rpm, a constant torque of 250 Nm is applied at the input shaft end, the simulation step size is defined as 0.1 ms, and the total simulation time is 2 s. Perform system dynamics solution, extract triaxial acceleration time-domain response data at preset measuring points around the axle housing drain hole, and save the acceleration data; Perform a fast Fourier transform on the acceleration time-domain data to convert it to the frequency domain. Set the frequency resolution to 10Hz and identify the peak points in the frequency band of 5.3kHz-5.7kHz where the acceleration amplitude exceeds 3g. Record the frequency and amplitude corresponding to these peaks. Based on the system rotation speed parameters and the number of gear teeth, the meshing order of each meshing pair is calculated. The identified acceleration peak frequency is matched with the order frequency of each meshing pair to determine the meshing pair that causes the excessive peak in the 5.3kHz-5.7kHz frequency band, denoted as gear G1 and gear G2. The contribution of the G1 and G2 meshing pairs to the excessive vibration was quantified, and the ratio of the peak acceleration caused by them in the 5.3kHz-5.7kHz frequency band to the total acceleration response was calculated to confirm that these two meshing pairs are the main optimization targets.

4. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S103 specifically includes the following steps: The dynamic meshing force time-domain data of meshing pairs G1 and G2 are extracted from the system dynamics simulation results to construct the meshing force time series; A contact analysis model of the gear pair is established in finite element software. A unit load is applied to the tooth surface, and the dynamic displacement response of the tooth surface on the meshing line is calculated to obtain displacement-time data. Perform a synchronous Fourier transform on the dynamic meshing force and dynamic displacement data, calculate the ratio between the two in the frequency domain, and obtain the meshing compliance frequency response function, as shown in the formula: Where C(f) is the meshing compliance, X(f) is the dynamic displacement frequency domain response, and F(f) is the dynamic meshing force frequency domain response; Within the problem frequency band of 5.3kHz-5.7kHz, analyze the amplitude and phase characteristics of the meshing compliance of G1 and G2, and identify the frequency points where the compliance amplitudes are equal and the phases are close to 180°. With the goal of eliminating or reducing the meshing compliance resonance peak of G1 and G2 in the problem frequency band, the specific target value for topology optimization is to reduce the compliance amplitude by more than 30%, which is used as the quantitative indicator for optimization.

5. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S104 specifically includes the following steps: In the system dynamics model, confirm the shaft assembly relationship between meshing pair G2 and coaxial gear G3, and clarify the connection method and support constraints between the two. Extract the shaft diameter, length, and tooth width of gear G2, the thickness, hub diameter, and rim thickness of gear G3, as well as the elastic modulus and Poisson's ratio of the shared shaft material; A coupled mechanical model of the G2-G3 coaxial system was established using finite element software. The model was meshed and bearing support constraints consistent with actual working conditions were applied. The coupled stiffness matrix of the system was then calculated. By parametric analysis, the spoke thickness and opening position of G3 spokes were changed, and the changes of elements related to G2 in the coupled stiffness matrix were observed to identify the key areas of G3 spokes that affect the stiffness of G2. Based on the identification results of key areas, the key areas of the G3 wheel spoke structure were thinned and weight-reducing holes were opened, and the thickness adjustment amount and hole size range of the structural adjustment were clarified.

6. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S105 specifically includes the following steps: In the finite element software, the spoke regions of gears G1 and G3 are defined as the design space, while the tooth profile region and mounting hole region are defined as the non-design space. All hexahedral mesh elements in the spoke region are set as optimizable elements. Set the relative density of each hexahedral mesh element as a design variable, with a value ranging from 0 to 1; A mathematical expression for the optimization problem is established with the objective function of increasing the structural flexibility of the gear spoke region, while a 35% reduction in mass is set as a constraint. Iterative calculations were performed using the material interpolation model in the variable density method, with a penalty factor of 3, a maximum number of iterations of 500, and a convergence tolerance of 0.

001. Start the optimization solver to perform iterative calculations, outputting intermediate results every 10 iterations, monitoring the convergence of the objective function and constraints, and stopping the calculation when the convergence criterion or the maximum number of iterations is reached.

7. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S106 specifically includes the following steps: In the finite element software, a relative density threshold is set, and the solid retention area and hole removal area of ​​the G1 and G3 spokes are divided to generate the initial boundary profile. The boundary points of the hole removal area are sampled using a geometric contour extraction tool. The irregular boundary is fitted to the initial geometric contour of the waist-shaped hole, and the center coordinates, length and width parameters of the hole are determined. The contour edge of the waist-shaped hole is fitted using Bézier curves, and the curve control points are adjusted to make the two ends of the hole rounded, eliminating sharp corners and broken lines in the contour. Import the smoothed contour into CAD software, check the minimum distance between the waist-shaped hole and the hub and teeth, and verify whether the uniformity of the spoke thickness and the material removal rate meet the constraints. Export the smoothed 3D models of G1 and G3 gears in STEP / IGES format, save the model's geometric parameters, and form the optimized gear model.

8. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 7, characterized in that, S107 specifically includes the following steps: Import the optimized gear model into MASTA software, replace the G1 and G3 gear geometric models in the original system model, and check the geometric tolerances of the model to ensure assembly compatibility. The key parts of the replaced G1 and G3 wheel spokes were re-tetrahedralized, and the Guyan condensation algorithm was used to run the finite element condensation, while retaining the RBE3 coupling relationship consistent with the original model. In the MASTA static analysis module, the maximum torque load is applied to the power input shaft, and radial and axial constraints are applied to the position of the axle housing leaf spring seat to reproduce the actual working condition boundary conditions. Start the statics solver to calculate the stress distribution, strain distribution, and meshing contact stress of the optimized G1 and G3 gears; Extract the static analysis results, record the maximum equivalent stress, maximum bending stress at the tooth root, and meshing contact stress values ​​of gears G1 and G3, and compare them with the allowable stress of the material.

9. The lightweight design method for axle gears based on dynamic response and topology optimization according to claim 1, characterized in that, S108 specifically includes the following steps: In the complete system dynamics model of the integrated and optimized gear, a transient dynamics analysis is performed by applying an input torque of 250 Nm and a speed range of 1000-6000 rpm. Extract the triaxial acceleration response data from the same measuring point at the oil drain hole of the axle housing, keep the sampling frequency at 20kHz, and perform a fast Fourier transform on the acceleration time domain data to obtain the frequency domain response of the frequency band of interest from 5.3kHz to 5.7kHz. Compare the peak acceleration values ​​in the frequency band under interest before and after optimization, check if any frequency point has an acceleration amplitude exceeding the 3g threshold, and record the number of frequency points exceeding the standard and the maximum exceeding amplitude. The dynamic meshing compliance of the optimized G1 and G2 meshing pairs was re-extracted, and it was analyzed whether the situation in the 5.3kHz-5.7kHz frequency band where the compliance of the two meshing pairs is equal and the phase is close to 180° was eliminated or improved. By combining static performance indicators and dynamic response indicators, it is determined whether the optimized gear simultaneously meets the strength requirements and NVH requirements, thus forming the final verification conclusion.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the lightweight design method for axle gears based on dynamic response and topology optimization as described in any one of claims 1 to 9.

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