Finite element-based performance optimization method and system

Abstract

The invention relates to the technical field of finite element optimization, in particular to a performance optimization method and system based on finite elements, and the method comprises the steps: obtaining a finite element model of a gear in a transplanting mechanism of a rice transplanter, and dividing the finite element model into a plurality of grids; corresponding loads are applied to the finite element model according to simulation data of gears when the rice transplanter works, simulation indexes of all the grids are obtained, the grid sizes of all the grids are optimized based on the simulation indexes, and optimized target grids are output; determining a performance index of each target grid, optimizing design parameters of the target grids according to the performance indexes, and updating the finite element model based on the optimized design parameters to serve as a final finite element model of the gear; according to the method, through deep coupling of grid optimization and parameter optimization, the analysis precision and optimization efficiency of the gear can be improved.

Description

Technical Field

[0001] This invention relates to the field of finite element optimization technology, and specifically to a performance optimization method and system based on finite element analysis. Background Technology

[0002] Traditional design processes often rely on empirical formulas and simplified models for gear structure design. This approach struggles to comprehensively consider the dynamic stress conditions and complex stress distributions of gears during actual operation, potentially leading to strength redundancy or localized weak points in the designed gears. This makes it impossible to achieve lightweight design while ensuring structural reliability. Furthermore, traditional optimization methods often focus on optimizing single performance indicators, neglecting the coupling relationships between different performance indicators, making it difficult to obtain a design scheme with excellent overall performance. Simultaneously, in finite element analysis, the quality of mesh generation directly affects the accuracy of simulation results and computational efficiency. Traditional manual or simple automatic mesh generation methods are prone to mesh distortion and uneven element quality, thus impacting the accuracy and efficiency of subsequent optimization analyses. These problems are particularly prominent in the design of the gears in the rice transplanter's separating mechanism. Because this mechanism operates in harsh environments, the gears must withstand cyclic impact loads and alternating stresses, placing extremely high demands on their structural strength, transmission efficiency, and service life. Traditional design methods are no longer sufficient to meet the design requirements of modern agricultural machinery for high-performance, high-reliability components. Summary of the Invention

[0003] The purpose of this invention is to provide a performance optimization method and system based on the finite element method, which aims to accurately model and optimize the gears in the rice transplanter's separating mechanism using finite element technology, in order to solve the problems of insufficient analysis accuracy and low optimization efficiency of traditional design methods under complex working conditions.

[0004] To achieve the above objectives, the present invention provides the following technical solution: In a first aspect, embodiments of the present invention provide a performance optimization method based on the finite element method, the method comprising the following steps: S100, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple meshes; S200: Based on the simulation data of the gears during the operation of the rice transplanter, corresponding loads are applied to the finite element model to obtain the simulation indices of each mesh. Based on these indices, the mesh size of each mesh is optimized, and the optimized target mesh is output. The simulation indices characterize the mesh's prediction accuracy and computational efficiency in response to the structural changes. S300, determine the performance index of each target mesh, optimize the design parameters of the target mesh according to the performance index, update the finite element model based on the optimized design parameters, and use it as the final finite element model of the gear; the design parameters include the gear module, number of teeth, tooth width, tooth tip height coefficient, pressure angle, and the elastic modulus and Poisson's ratio of the material.

[0005] Optionally, in S100, obtaining the finite element model of the gears in the rice transplanter's separating mechanism, and dividing the finite element model into multiple meshes, includes: S110, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple regions according to geometric features; S120, determine the corresponding mesh type according to the geometry of each region, and divide the corresponding region into multiple meshes according to the mesh type; the mesh type includes tetrahedral mesh and hexahedral mesh.

[0006] Optionally, in S200, the step of applying corresponding loads to the finite element model based on the simulation data of the gears of the rice transplanter during operation, obtaining simulation indices for each mesh, optimizing the mesh size of each mesh based on the simulation indices, and outputting the optimized mesh size includes: S210, determine the force parameters of the gears during the operation of the rice transplanter, and define the loads of each mesh in the finite element model according to the force parameters. The loads include load type, position and direction. The force parameters include transplanting resistance, periodic frequency, inertial force, impact load and gravity. S220, Set the constraints of the finite element model, apply corresponding loads to each mesh in the finite element model according to the simulation data, configure the finite element solver parameters and calculate the simulation values ​​of each mesh; The constraints include bearing housing constraints, gear shaft constraints and tooth surface contact constraints; The simulation values ​​include the stress value, strain value, displacement and element mass of the mesh; S230, Based on the simulation values ​​and the baseline values ​​of the reference grid, determine the simulation index of each grid, take maximizing the simulation index of each grid as the optimization objective, use an improved genetic algorithm to iteratively optimize the grid size of each grid, and output the optimized grid size.

[0007] Optionally, determining the simulation indices for each grid based on the simulation values ​​and the baseline values ​​of the reference grid includes: Obtain the reference values ​​of the reference mesh, which include the stress value, strain value, element mass, and displacement of the reference mesh; The stress index is obtained by dividing the stress value of the mesh by the stress value of the reference mesh; the strain index is obtained by dividing the strain value of the mesh by the strain value of the reference mesh; the mesh quality index is obtained by subtracting the ratio of the difference between the element mass and the minimum element mass to the difference between the maximum element mass and the minimum element mass from 1; and the displacement index is obtained by dividing the displacement of the mesh by the displacement of the reference mesh. The simulation parameters of the mesh are obtained by weighted fusion of stress parameters, strain parameters, mesh quality parameters, and displacement parameters.

[0008] Optionally, in S300, determining the performance indicators of each target mesh, optimizing the design parameters of the target mesh based on the performance indicators, and updating the finite element model based on the optimized design parameters as the final finite element model of the gear includes: S310, determine the performance optimization target of the gear and establish the mapping relationship between performance indicators and design parameters; the mapping relationship is a nonlinear regression model of performance indicators and design parameters, the performance indicators include tooth root bending strength, tooth surface contact strength, transmission efficiency and structural lightweighting indicators, and the design parameters include gear module, number of teeth, tooth width, tooth tip height coefficient, pressure angle and the elastic modulus and Poisson's ratio of the material; S320, by performing sensitivity analysis on the performance indicators and design parameters, key design parameters that have a significant impact on the performance indicators are identified; S330, establish a multi-objective optimization model, with the optimization objectives being the maximum tooth root bending strength, the maximum tooth surface contact strength, the highest transmission efficiency, and the minimum structural lightweight index, and set the constraints of the design parameters; S340 employs an improved non-dominated sorting genetic algorithm for multi-objective optimization. Through fast non-dominated sorting and crowding calculation, it generates a uniformly distributed Pareto optimal solution set in the objective space, with each solution corresponding to a set of design parameter combinations. S350: Select the scheme with the best overall performance from the Pareto optimal solution set as the optimized design parameters, and update the finite element model based on the optimized design parameters as the final finite element model of the gear.

[0009] Secondly, embodiments of the present invention provide a performance optimization system based on the finite element method, the system comprising: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any of the preceding statements.

[0010] The beneficial effects of this invention are as follows: This invention discloses a performance optimization method and system based on finite element method. First, an initial finite element model is constructed through region partitioning and mesh type matching. The model details are then refined by combining the functional characteristics of non-circular gears and eccentric gears, laying a precise geometric foundation for subsequent analysis. Next, dynamic loads are applied based on multi-source simulation data, and the mesh size is iteratively optimized using an improved genetic algorithm. This significantly improves computational efficiency while ensuring the accuracy of structural response prediction, solving the problems of strong subjectivity and difficulty in balancing accuracy and efficiency in traditional mesh partitioning. Finally, by establishing a nonlinear mapping relationship between performance indicators and design parameters, an improved non-dominated sorting genetic algorithm is used for multi-objective optimization. The optimal solution with the best overall performance is selected from the Pareto optimal solution set, achieving synergistic optimization of tooth root bending strength, tooth surface contact strength, transmission efficiency, and structural lightweighting. This invention, through deep coupling of mesh optimization and parameter optimization, enables the gear finite element model to accurately reflect the mechanical behavior under actual working conditions and significantly improve the operational stability and service life of the rice transplanting mechanism through the optimization of design parameters, providing a systematic technical path for the high-performance design of core components of rice transplanters. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the 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.

[0012] Figure 1 This is a flowchart illustrating a performance optimization method based on the finite element method in an embodiment of the present invention.

[0013] Figure 2 This is a structural block diagram of a performance optimization system based on the finite element method in an embodiment of the present invention. Detailed Implementation

[0014] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present invention can be combined with each other.

[0015] Addressing the design challenges of gears in the rice transplanter's separating mechanism, traditional methods suffer from insufficient accuracy in predicting structural strength under dynamic loads and struggle to balance the trade-offs between strength, efficiency, and lightweight design. This leads to premature gear failure or excessive energy consumption during actual operation, hindering the transplanter's operational stability and lifespan. Furthermore, the subjectivity of mesh generation and the limitations of optimizing single performance indicators further reduce the engineering practicality and overall performance of the design scheme.

[0016] To address the technical problems in related technologies, this invention provides a performance optimization method and system based on the finite element method. This invention combines multi-dimensional mesh optimization and parameter optimization to achieve accurate modeling and comprehensive performance improvement of gear structures. In the mesh optimization stage, an initial model is constructed through region partitioning and mesh type matching. Considering the actual working conditions of the gears in the rice transplanter's separating mechanism, dynamic loads including transplanting resistance, periodic frequency, inertial force, impact load, and gravity are applied. An improved genetic algorithm is used to iteratively optimize the mesh size, aiming to maximize simulation indicators and effectively balancing computational accuracy and efficiency. In the parameter optimization stage, a nonlinear regression model of performance indicators and design parameters is established. Sensitivity analysis identifies key design parameters, and a multi-objective optimization model is constructed with objectives such as tooth root bending strength, tooth surface contact strength, transmission efficiency, and structural lightweighting. An improved non-dominated sorting genetic algorithm is used to obtain the Pareto optimal solution set. Finally, the design parameter combination with the optimal comprehensive performance is selected to update the finite element model.

[0017] See Figure 1 The present invention provides a performance optimization method based on the finite element method, the method comprising the following steps:

[0018] S100, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple meshes;

[0019] Specifically, the first step is to obtain relevant parameters of the gears in the rice transplanter's separating mechanism, including but not limited to the number of teeth, module, tooth width, and material properties. These parameters are the foundational data for finite element analysis, and their accuracy directly affects the reliability of the subsequent analysis results. The authenticity and completeness of the parameters are ensured through precise measurement and acquisition from design drawings and other materials. Next, using professional finite element modeling software, an accurate finite element model is constructed based on the obtained gear parameters.

[0020] During the modeling process, the geometry of the gear is meticulously depicted, taking into account the actual structural characteristics of the gear, such as the potential impact of keyways and chamfers on mechanical properties. Simultaneously, the boundary conditions of the model are appropriately set to simulate the installation and stress conditions of the gear in actual operation. For example, the shaft hole and shaft of the gear are appropriately constrained to simulate its fixing method in the transmission system.

[0021] It should be noted that gears include non-circular gears and eccentric gears. Non-circular gears are modified for speed change, while eccentric gears are eccentric for displacement. In the rice transplanter's separating mechanism, non-circular gears and eccentric gears are used to achieve different functions. Non-circular gears, through their special tooth profile and pitch curve, can change the transmission ratio to meet the different speed requirements during rice transplanting. For example, at different stages of transplanting, the speed change of non-circular gears can precisely control the movement speed of the seedling claws to meet agronomic requirements and improve the uniformity and accuracy of transplanting. Eccentric gears, on the other hand, utilize their eccentric characteristics to generate displacement changes. These displacement changes can be converted into specific movements of components such as the seedling claws in the vertical or horizontal directions, assisting in the grasping, conveying, and insertion of seedlings. By rationally utilizing these two types of special gears, combined with optimized parameters obtained based on finite element analysis, the overall performance of the rice transplanter's separating mechanism can be further improved.

[0022] S200: Based on the simulation data of the gears during the operation of the rice transplanter, corresponding loads are applied to the finite element model to obtain the simulation indices of each mesh. Based on these indices, the mesh size of each mesh is optimized, and the optimized target mesh is output. The simulation indices characterize the mesh's prediction accuracy and computational efficiency in response to the structural changes.

[0023] Specifically, firstly, based on the various loads borne by the gears during actual operation of the rice transplanter, the specific sources and acquisition methods of the simulation data are determined. This can be achieved through field testing, using sensors and other equipment to collect data on the stress, strain, displacement, and unit mass of the gears under different operating conditions; alternatively, it can be achieved through laboratory simulation experiments, simulating the operating scenario of the rice transplanter in a controlled environment to obtain corresponding simulation data. This simulation data is crucial for applying loads to the finite element model and conducting subsequent analysis, and its quality directly affects the effectiveness of the optimization results.

[0024] After acquiring the simulation data, it needs to be preprocessed to remove noise and outliers, ensuring the accuracy and reliability of the data. Then, based on the preprocessed simulation data, corresponding loads are applied to the finite element model. The applied loads need to accurately reflect the force conditions of the gears during actual operation, including the type, magnitude, location, and direction of the loads. For example, the resistance to transplanting rice will generate a certain force on the gear teeth; the specific value and distribution of this force need to be determined based on the simulation data and applied to the corresponding location in the finite element model. Periodic frequencies will cause the gears to vibrate periodically, requiring the setting of corresponding periodic loads in the model. Inertial forces, impact loads, and gravity also need to be applied according to actual conditions to comprehensively simulate the gears' stress conditions.

[0025] After applying the load, the mesh size of each mesh is optimized based on simulation metrics. Simulation metrics are crucial parameters for evaluating the accuracy and computational efficiency of mesh predictions of structural response; their calculation formulas have been previously provided. The simulation metric value for each mesh is calculated by substituting its simulation values ​​into the metric formula. Then, based on the magnitude of the metric values, the impact of different mesh sizes on prediction accuracy and computational efficiency is analyzed. For meshes with lower metric values, it indicates that their prediction accuracy or computational efficiency needs improvement, requiring adjustment of their mesh size. For example, if a mesh's low metric value is due to insufficient prediction accuracy caused by an excessively large mesh size, the mesh size can be appropriately reduced to improve prediction accuracy; conversely, if the low computational efficiency is due to an excessively small mesh size, the mesh size can be appropriately increased to improve computational efficiency while maintaining a certain level of prediction accuracy.

[0026] During the optimization process, the mesh size needs to be continuously adjusted and the simulation index values ​​recalculated until the simulation index values ​​of each mesh meet the preset requirements. At this point, the optimized mesh size is output. The optimized mesh size can improve computational efficiency as much as possible while ensuring prediction accuracy, laying a good foundation for subsequent finite element model solving operations.

[0027] S300, determine the performance index of each target mesh, optimize the design parameters of the target mesh according to the performance index, update the finite element model based on the optimized design parameters, and use it as the final finite element model of the gear; the design parameters include the gear module, number of teeth, tooth width, tooth tip height coefficient, pressure angle, and the elastic modulus and Poisson's ratio of the material.

[0028] In the embodiments provided by this invention, a progressive process of mesh generation, mesh size optimization, and design parameter optimization is achieved, realizing a complete optimization process from geometric modeling to performance improvement. First, an initial finite element model is constructed by region division and mesh type matching. The model details are then refined based on the functional characteristics of non-circular gears and eccentric gears, laying a precise geometric foundation for subsequent analysis. Next, dynamic loads are applied based on multi-source simulation data, and the mesh size is iteratively optimized using an improved genetic algorithm. This significantly improves computational efficiency while ensuring the accuracy of structural response prediction, solving the problems of strong subjectivity and difficulty in balancing accuracy and efficiency in traditional mesh generation. Finally, by establishing a nonlinear mapping relationship between performance indicators and design parameters, an improved non-dominated sorting genetic algorithm is used for multi-objective optimization. The optimal solution with the best overall performance is selected from the Pareto optimal solution set, achieving synergistic optimization of tooth root bending strength, tooth surface contact strength, transmission efficiency, and structural lightweighting. This method, through deep coupling of mesh optimization and parameter optimization, enables the gear finite element model to accurately reflect the mechanical behavior under actual working conditions, and significantly improves the operational stability and service life of the rice transplanting mechanism through the optimization of design parameters, providing a systematic technical path for the high-performance design of core components of rice transplanters.

[0029] In some embodiments, S100, obtaining the finite element model of the gears in the rice transplanter's separating mechanism and dividing the finite element model into multiple meshes includes: S110, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple regions according to geometric features; S120, determine the corresponding mesh type according to the geometry of each region, and divide the corresponding region into multiple meshes according to the mesh type; the mesh type includes tetrahedral mesh and hexahedral mesh.

[0030] Specifically, the appropriate mesh type is selected based on the complexity of different regions. Mesh types include tetrahedral meshes and hexahedral meshes. Tetrahedral meshing is relatively simple and suitable for models with complex shapes, but its accuracy may be slightly inferior. For critical regions with complex geometries, such as tooth roots and tooth tips, which are prone to stress concentration during operation, a more refined hexahedral mesh is used to improve the accuracy of capturing the structural response in these regions. For non-critical regions with relatively regular geometries and more uniform stress distribution, such as gear spokes and hubs, tetrahedral meshes, which have higher meshing efficiency, can be used to effectively reduce the number of elements and lower computational costs while ensuring that the required computational accuracy is met.

[0031] Meanwhile, at the transition points between different regions, a reasonable mesh density gradient is set to avoid calculation errors caused by abrupt changes in mesh size, ensuring that the mesh quality of the entire finite element model is uniform and meets the calculation requirements.

[0032] In some embodiments, S200, the step of applying corresponding loads to the finite element model based on simulation data of the gears of the rice transplanter during operation, obtaining simulation indices for each mesh, optimizing the mesh size of each mesh based on the simulation indices, and outputting the optimized mesh size includes:

[0033] S210, determine the force parameters of the gears during the operation of the rice transplanter, and define the loads of each mesh in the finite element model according to the force parameters. The loads include load type, position and direction. The force parameters include transplanting resistance, periodic frequency, inertial force, impact load and gravity.

[0034] Specifically, based on field trials or machine design specifications, typical operating parameters of the transplanting mechanism gears are obtained: transplanting resistance - the interaction force between the seedling and the soil during transplanting, with a measured range of 50~200N (single seedling), and a periodic frequency f=0.5~2Hz (corresponding to a travel speed of 1~3m / s); inertial force is the centrifugal force when the gear rotates with the transplanting mechanism; impact load is the instantaneous collision force between the seedling claw and the seedling during seedling picking; gravity is the distributed load caused by the weight of the gear itself, with the direction vertically downward.

[0035] Based on the load characteristics, the load type is selected as concentrated force (F) or distributed force (q). The transplanting resistance acts on the connection point between the seedling claw and the gear (such as the tooth groove contact area). The concentrated force is the static load average value, and the sine function simulates the periodic fluctuation. The inertial force acts on the center of mass of the gear, and the body load is used. The impact load acts on the tooth surface contact area, and the step load is used. The gravity acts on the gear as a whole, and the distributed force is used.

[0036] The transplanting resistance is located by coordinates at the contact point between the tooth groove and the seedling claw (e.g., the midpoint of the tooth width, z=0.5b), and its direction is along the direction of seedling insertion (vertically downward, with an angle θ=30°~45° with the horizontal plane); the inertial force is radial along the gear shaft (perpendicular to the plane of rotation); the impact load is along the normal direction of the tooth surface (perpendicular to the tangent at the contact point); and the gravity is along the vertically downward direction (-Z axis).

[0037] S220, Set the constraints of the finite element model, apply corresponding loads to each mesh in the finite element model according to the simulation data, configure the finite element solver parameters and calculate the simulation values ​​of each mesh; The constraints include bearing housing constraints, gear shaft constraints and tooth surface contact constraints; The simulation values ​​include the stress value, strain value, displacement and element mass of the mesh;

[0038] The generated mesh undergoes quality checks. Inspect parameters such as aspect ratio and Jacobian determinant to ensure the mesh quality meets the requirements of finite element analysis. For poor-quality meshes, such as those with excessively large aspect ratios or Jacobian determinants exceeding reasonable ranges, make local adjustments or re-mesh the mesh to improve computational stability and result accuracy. Rigorous mesh quality control lays the foundation for accurate subsequent finite element analysis.

[0039] It should be noted that the simulation data was obtained through simulation experiments of the actual working state of a rice transplanter. The simulation data includes the maximum stress at the root of the mesh (unit: MPa), the root mean square displacement (unit: mm), and the element mass (unit: kg). The simulation values ​​include the stress value (unit: MPa), strain value (dimensionless), displacement (unit: mm), and element mass (unit: kg) of the mesh. The simulation indicators characterize the prediction accuracy and computational efficiency of the mesh for the structural response.

[0040] Specifically, for bearing housing constraints, the gear is mounted on the insertion mechanism housing via bearings. The bearing housing restricts the translational degree of freedom of the gear, but allows the rotational degree of freedom around the axis of rotation. For gear shaft constraints, if the gear and shaft are interference fit, binding constraints need to be applied in the contact area between the shaft and the gear's inner hole to simulate the force transmission of the interference fit. For tooth surface contact constraints, contact pairs are set in the meshing area of ​​the gear pair, and normal contact behavior (hard contact, no separation) and tangential friction behavior (friction coefficient μ=0.1~0.15, simulating friction under mud and sand lubrication) are defined.

[0041] The solver used is the TransientStructural solver in ANSYS Workbench, which is suitable for dynamic response analysis under periodic loads. The time step is set to Δt = 0.001s based on the working frequency f = 1Hz (to ensure sampling of at least one complete cycle). The energy convergence tolerance is set to 1e-5 (to ensure calculation accuracy), and the maximum number of iterations is 50 (to avoid divergence). Mesh with a distortion rate > 0.8 is filtered by element distortion rate (Jacobian determinant) (marked as "bad elements" and re-meshed).

[0042] Taking a cylindrical spur gear (m=4mm, z=20) used in a rice transplanter as an example, a periodic transplanting resistance F(t)=100(1+sin(2πt))N is applied, with an inertial force of 20N (angular velocity 10rad / s) and a peak impact load of 250N (impact duration 0.02s). After solving using TransientStructural, the peak equivalent stress of the mesh at the tooth root transition fillet is 1180MPa (close to the allowable contact stress of 1500MPa), the combined deformation is 0.03mm (not exceeding the allowable deformation), and the contact pressure is uniformly distributed, verifying the accuracy of the load application and solution.

[0043] By following the steps above, the mechanical response data of the gear model in each grid can be accurately obtained, providing reliable data support for the subsequent construction of grid performance index formulas.

[0044] S230, Based on the simulation values ​​and the baseline values ​​of the reference grid, determine the simulation index of each grid, take maximizing the simulation index of each grid as the optimization objective, use an improved genetic algorithm to iteratively optimize the grid size of each grid, and output the optimized grid size.

[0045] It should be noted that the stress value must be controlled within the allowable stress range of the material, the strain value and displacement must meet the gear transmission accuracy requirements, and the element mass should be minimized as much as possible while ensuring structural strength to reduce the inertial force during gear operation. The optimization variables are set as mesh size parameters, including the mesh refinement coefficient for critical regions and the mesh coarsening coefficient for non-critical regions, and the value range of each variable is set. By initializing the population, the fitness value of each individual is calculated, and selection, crossover, and mutation operations are performed based on the fitness value. The population is iteratively updated until the preset convergence condition is met, such as the objective function value changing less than a threshold for multiple consecutive generations or reaching the maximum number of iterations. Finally, the optimized mesh size is output, realizing differentiated configuration of mesh size in critical and non-critical regions. This ensures the calculation accuracy of stress concentration areas such as the tooth root and tooth tip (mesh size refined to 0.1~0.5mm), while reducing the overall computational load by reasonably enlarging the mesh size in non-critical regions (1~3mm), achieving an optimal balance between accuracy and efficiency in the finite element model.

[0046] In some embodiments, determining the simulation metrics for each grid based on the simulation values ​​and the baseline values ​​of the reference grid includes: Obtain the reference values ​​of the reference mesh, which include the stress value, strain value, element mass, and displacement of the reference mesh; The stress index is obtained by dividing the stress value of the mesh by the stress value of the reference mesh; the strain index is obtained by dividing the strain value of the mesh by the strain value of the reference mesh; the mesh quality index is obtained by subtracting the ratio of the difference between the element mass and the minimum element mass to the difference between the maximum element mass and the minimum element mass from 1; and the displacement index is obtained by dividing the displacement of the mesh by the displacement of the reference mesh. The simulation parameters of the mesh are obtained by weighted fusion of stress parameters, strain parameters, mesh quality parameters, and displacement parameters.

[0047] This multi-dimensional weighted calculation method comprehensively considers the mesh's performance in terms of stress accuracy, strain accuracy, element mass, and displacement accuracy. This allows the simulation metrics to fully reflect the mesh's overall performance, providing a quantitative basis for subsequent optimization of mesh design parameters. For example, if a mesh has stress values ​​close to the reference mesh, strain values ​​relatively small, element mass within a reasonable range, and displacement as expected, its simulation metric values ​​will be high, indicating that the mesh achieves good computational efficiency while maintaining computational accuracy.

[0048] Specifically, the simulation index formula is as follows:

[0049] in, The simulation metrics representing the mesh, Indicates the stress value of the mesh; This represents the stress value of the reference mesh (0.1mm fine mesh). This represents the strain value of the mesh; This represents the strain value of the reference mesh; Indicates the unit mass (Jacobi determinant normalized value, range [0,1]); , These are the minimum and maximum values ​​of the unit mass, respectively; This represents the displacement of the mesh. This indicates the displacement of the reference mesh; For the weighting coefficients, satisfying For example, ω1=0.4 (stress accuracy), ω2=0.2 (displacement accuracy), ω3=0.3 (mesh quality), and ω4=0.1 (displacement). By adjusting the weighting coefficients, the mesh model can be flexibly optimized according to actual needs, ensuring the best simulation results under different working conditions, and further improving the reliability and practicality of finite element analysis.

[0050] In some embodiments, in S300, determining the performance index of each target mesh, optimizing the design parameters of the target mesh based on the performance index, and updating the finite element model based on the optimized design parameters as the final finite element model of the gear includes:

[0051] S310, determine the performance optimization target of the gear and establish the mapping relationship between performance indicators and design parameters; the mapping relationship is a nonlinear regression model of performance indicators and design parameters, the performance indicators include tooth root bending strength, tooth surface contact strength, transmission efficiency and structural lightweighting indicators, and the design parameters include gear module, number of teeth, tooth width, tooth tip height coefficient, pressure angle and the elastic modulus and Poisson's ratio of the material;

[0052] The mapping relationship is a nonlinear regression model constructed based on gear design theory and finite element simulation data. The root bending strength (σ_F) is positively correlated with the module (m) and tooth width (b), and negatively correlated with the number of teeth (z) (m²b / z). The tooth surface contact strength (σ_H) is proportional to the square root of the module (m) and the number of teeth (z) (m√z), and positively correlated with the material's elastic modulus (E). The transmission efficiency (η) is significantly affected by the pressure angle (α), with the meshing loss being minimal at α=20°, and is also related to the addendum coefficient (h_a). Related (h_a) =1 indicates optimal overlap ratio); the structural lightweight index (M) is defined as the ratio of gear mass (ρV, where ρ is material density and V is volume) to rated load, which is positively correlated with module and tooth width, and needs to be minimized under strength constraints.

[0053] S320, by performing sensitivity analysis on the performance indicators and design parameters, key design parameters that have a significant impact on the performance indicators are identified;

[0054] The Sobol global sensitivity analysis method was used to calculate the sensitivity index of each design parameter on tooth root bending strength, tooth surface contact strength, transmission efficiency, and structural lightweighting indicators. For example, the sensitivity index of module (m) on tooth root bending strength was 0.65, and that of tooth width (b) was 0.25, indicating that module is the most critical parameter affecting tooth root bending strength; the sensitivity index of pressure angle (α) on transmission efficiency reached 0.7, making it a core parameter for transmission efficiency optimization. Based on the sensitivity analysis results, design parameters with a sensitivity index greater than 0.3 were selected as optimization variables, such as module, tooth width, and pressure angle, to reduce the dimensionality of the optimization problem and improve optimization efficiency.

[0055] S330, establish a multi-objective optimization model, with the optimization objectives being the maximum tooth root bending strength, the maximum tooth surface contact strength, the highest transmission efficiency, and the minimum structural lightweight index, and set the constraints of the design parameters;

[0056] The constraints include: module m∈[3mm,5mm] (to meet the spatial installation requirements of the rice transplanter's dividing mechanism), number of teeth z=20 (to match the transmission ratio), tooth width b∈[20mm,40mm] (to avoid material waste and bulky mechanism caused by excessive width), pressure angle α∈[15°,25°] (standard value range), material elastic modulus E=206GPa (45# steel), Poisson's ratio μ=0.3 (conventional value for metallic materials).

[0057] S340 employs an improved non-dominated sorting genetic algorithm for multi-objective optimization. Through fast non-dominated sorting and crowding calculation, it generates a uniformly distributed Pareto optimal solution set in the objective space, with each solution corresponding to a set of design parameter combinations.

[0058] An improved non-dominated sorting genetic algorithm (NSGA-III) is used to solve the multi-objective optimization problem. The initial population size is 100, the crossover probability is 0.8, the mutation probability is 0.1, and the number of iterations is 200. Through fast non-dominated sorting and crowding calculation, a uniformly distributed Pareto optimal solution set is generated in the objective space, and each solution corresponds to a set of design parameter combinations.

[0059] S350: Select the scheme with the best overall performance from the Pareto optimal solution set as the optimized design parameters, and update the finite element model based on the optimized design parameters as the final finite element model of the gear.

[0060] Using the ideal point method, after normalizing the performance indicators of each objective, the Euclidean distance between each Pareto solution and the ideal point (the point formed by the optimal values ​​of each objective) is calculated. The solution with the smallest distance is the optimal solution. Taking a certain optimization result as an example, the optimal design parameters are: m=4.2mm, b=32mm, α=22°. Substituting these parameters into the finite element model, re-meshing, and performing simulation verification, the results show that the tooth root bending strength is improved by 12% (from 1180MPa to 1038MPa), the tooth surface contact strength is improved by 8%, the transmission efficiency is improved by 2.5%, and the structural lightweight index is reduced by 5%, all meeting the design requirements. Based on this, the finite element model is updated, and the final finite element model of the gear is completed.

[0061] This invention combines finite element simulation with multi-objective optimization algorithms to construct a complete solution from mesh accuracy optimization to design parameter optimization. Below is a specific embodiment provided by this invention:

[0062] In the meshing stage, the 3D gear model is first geometrically cleaned, removing fine features such as rounded corners and chamfers to simplify the model. Then, different mesh partitions are created based on the gear's structural characteristics (e.g., teeth, hub, spokes, etc.). For stress concentration areas such as the tooth meshing region, hexahedral meshes are used for fine meshing, with mesh sizes controlled between 0.5-1 mm. For relatively simple structures such as the hub and spokes, tetrahedral meshes are used, with mesh sizes set to 2-3 mm, to reduce computational load while maintaining calculation accuracy. After meshing, mesh quality checking tools are used to verify parameters such as element distortion rate and aspect ratio, ensuring that the distortion rate of all meshes is less than 0.1 and the aspect ratio is less than 5, avoiding simulation distortion due to mesh quality issues.

[0063] During the application of loads and constraints, force data on the gears during operation were collected through field tests based on the actual working conditions of the rice transplanter's separating mechanism. Specifically, torque and acceleration sensors were installed on the gear shaft to monitor torque changes and vibration frequencies in real time during transplanting. Combined with kinematic analysis of the separating mechanism, the transplanting resistance on the gears was calculated to be approximately 800-1200 N, with a periodic frequency consistent with the swing frequency of the transplanting arm, approximately 1.5 Hz. These force parameters were then transformed into load conditions in the finite element model: a contact force varying with time was applied to the tooth surface contact area, the magnitude of which was calculated based on the torque and the gear pitch circle radius; a torque load corresponding to the transplanting resistance was applied to the gear shaft; and the gear's own gravity load (material density taken as 7.85 g / cm³) and the inertial force generated by rotation (rotation speed converted to 300 r / min based on the rice transplanter's working speed) were also considered. Regarding constraints, a full degree of freedom constraint is applied to the bearing housing position, restricting its translation and rotation; a cylindrical surface constraint is applied to the mating surface between the gear shaft and the bearing, allowing only the rotational degree of freedom around the axis, in order to simulate actual installation conditions.

[0064] The numerical simulation was performed using Abaqus finite element analysis software, with the following solver parameters configured: an explicit dynamic analysis step was selected, the analysis time was set to two planting cycles (approximately 1.33 s), and the time step was 1e-5 s to capture the transient response under dynamic loads. After the solution was completed, the simulation values ​​of stress, strain, displacement, and element mass for each mesh element were extracted. The simulation results of the reference mesh (a standard model with a 0.2 mm fine mesh) were used as a benchmark to calculate the simulation indices for each mesh. For example, if the stress value of a certain gear tooth mesh is 350 MPa and the stress value of the reference mesh is 380 MPa, then the stress index of this mesh is 350 / 380≈0.92. If the element mass of this mesh is 1.2e-5 kg, with a minimum element mass of 0.8e-5 kg ​​and a maximum element mass of 2.0e-5 kg, then the mesh quality index is 1-[(1.2e-5-0.8e-5) / (2.0e-5-0.8e-5)]=1-(0.4e-5 / 1.2e-5)=1-1 / 3≈0.67. Assigning weights of 0.3, 0.3, 0.2, and 0.2 to the stress index, strain index, mesh quality index, and displacement index respectively, and then weighting and fusing them, the comprehensive simulation index of this mesh is 0.92×0.3+0.88×0.3+0.67×0.2+0.90×0.2=0.87. With the goal of maximizing the simulation indicators of each grid, an improved genetic algorithm was used to iteratively optimize the grid size. The population size of the algorithm was set to 50, the crossover probability was 0.8, the mutation probability was 0.1, and the number of iterations was 50 generations. The final optimized grid size was output: the grid size of the tooth region was optimized to 0.6 mm, which is 0.4 mm smaller than the initial value, and the simulation accuracy of the stress concentration region was improved by about 12%; the grid size of the spoke region was adjusted to 2.5 mm, which reduced the number of elements by 15% and improved the computational efficiency by about 20% while ensuring the accuracy of the overall structural stiffness calculation.

[0065] In the performance index and design parameter optimization phase, sensitivity analysis was first conducted using the controlled variable method. Four key design parameters were selected: module (2-4mm), number of teeth (18-24), tooth width (20-40mm), and pressure angle (20°-25°). Five levels were set for each parameter, resulting in a total of five... 4 =625 sets of simulation tests. For each set of tests, the tooth root bending strength, tooth surface contact strength, transmission efficiency, and structural lightweight index (expressed as gear mass) were calculated. A nonlinear regression model between performance indexes and design parameters was established using stepwise regression analysis. The results show that the sensitivity coefficient of module to tooth root bending strength is 0.78, and the sensitivity coefficient to tooth surface contact strength is 0.65; the sensitivity coefficient of tooth width to transmission efficiency is 0.52; and the sensitivity coefficient of pressure angle to lightweight index is -0.43 (the negative sign indicates a negative correlation). These four parameters were identified as key design parameters.

[0066] Based on the sensitivity analysis results, a multi-objective optimization model was established. The design parameters were constrained as follows: module ≥ 2.5 mm, number of teeth ≤ 22, tooth width ≥ 25 mm, and pressure angle within the range of 20°-22°. An improved non-dominated sorting genetic algorithm (NSGA-III) was used for solving the model. The algorithm parameters were set as follows: population size 100, number of generations 200, simulated binary crossover operator, and polynomial mutation operator. Through fast non-dominated sorting, individuals in the population were divided into different non-dominated levels. The crowding distance of each individual was calculated, and individuals with higher crowding were retained to maintain population diversity. After 200 generations of evolution, a Pareto optimal solution set containing 50 solutions was generated in the objective space. From the solution set, the optimal solution with the best overall performance was selected using the ideal point method: the tooth root bending strength reached 520MPa, the tooth surface contact strength was 1250MPa, the transmission efficiency was increased to 98.5%, and the gear mass was reduced to 1.8kg. Compared with the solution before optimization (tooth root bending strength 450MPa, tooth surface contact strength 1100MPa, transmission efficiency 97%, mass 2.2kg), all performance indicators were significantly improved.

[0067] The optimized design parameters (module 3mm, number of teeth 20, tooth width 30mm, pressure angle 20°) were updated in the finite element model, and the mesh was re-generated and the simulation was verified. The results show that the maximum stress of the optimized gear under rated operating conditions occurs at the tooth root transition fillet, with a stress value of 320MPa, which is less than the allowable stress of the material (400MPa), meeting the strength requirements. The tooth surface contact stress is 950MPa, lower than the contact fatigue limit (1100MPa). Power loss during transmission is reduced by approximately 15%, and structural mass is reduced by 18%, achieving multi-objective optimization of strength, efficiency, and lightweighting. This optimized scheme has been verified through prototype manufacturing and field trials. After 50 hours of continuous operation, the gear showed no significant wear or fatigue cracks, and the operational stability and service life of the insertion mechanism were effectively improved.

[0068] and Figure 1 The corresponding method is referenced. Figure 2 This invention provides a performance optimization system based on the finite element method, comprising: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method described above.

[0069] It is evident that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0070] Furthermore, embodiments of the present invention also disclose a computer program product or computer program stored in a computer-readable storage medium. A processor of a computer device can read the computer program from the computer-readable storage medium, and the processor executes the computer program, causing the computer device to perform the described method. Similarly, the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0071] It will be understood by those skilled in the art that all or some of the methods and systems disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0072] The above is a detailed description of the preferred embodiments of this disclosure. However, this disclosure is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this disclosure. All such equivalent modifications or substitutions are included within the scope defined by the claims of this disclosure.

Claims

1. A performance optimization method based on the finite element method, characterized in that, The method includes the following steps: S100, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple meshes; S200: Based on the simulation data of the gears during the operation of the rice transplanter, corresponding loads are applied to the finite element model to obtain the simulation indices of each mesh. Based on these indices, the mesh size of each mesh is optimized, and the optimized target mesh is output. The simulation indices characterize the mesh's prediction accuracy and computational efficiency in response to the structural changes. S300, determine the performance index of each target mesh, optimize the design parameters of the target mesh according to the performance index, update the finite element model based on the optimized design parameters, and use it as the final finite element model of the gear.

2. The method according to claim 1, characterized in that, In S100, the step of obtaining the finite element model of the gears in the rice transplanter's separating mechanism, and dividing the finite element model into multiple meshes, includes: S110, Obtain the finite element model of the gears in the rice transplanter's separating mechanism, and divide the finite element model into multiple regions according to geometric features; S120, determine the corresponding mesh type according to the geometry of each region, and divide the corresponding region into multiple meshes according to the mesh type; the mesh type includes tetrahedral mesh and hexahedral mesh.

3. The method according to claim 1, characterized in that, In S200, the step of applying corresponding loads to the finite element model based on simulation data of the gears during rice transplanter operation to obtain simulation indices for each mesh, optimizing the mesh size of each mesh based on the simulation indices, and outputting the optimized mesh size includes: S210, determine the force parameters of the gears during the operation of the rice transplanter, and define the loads of each mesh in the finite element model according to the force parameters. The loads include load type, position and direction. The force parameters include transplanting resistance, periodic frequency, inertial force, impact load and gravity. S220, Set the constraints of the finite element model, apply corresponding loads to each mesh in the finite element model according to the simulation data, configure the finite element solver parameters and calculate the simulation values ​​of each mesh; The constraints include bearing housing constraints, gear shaft constraints and tooth surface contact constraints; The simulation values ​​include the stress value, strain value, displacement and element mass of the mesh; S230, Based on the simulation values ​​and the baseline values ​​of the reference grid, determine the simulation index of each grid, take maximizing the simulation index of each grid as the optimization objective, use an improved genetic algorithm to iteratively optimize the grid size of each grid, and output the optimized grid size.

4. The method according to claim 3, characterized in that, The determination of simulation indices for each grid based on the simulation values ​​and the baseline values ​​of the reference grid includes: Obtain the reference values ​​of the reference mesh, which include the stress value, strain value, element mass, and displacement of the reference mesh; The stress index is obtained by dividing the stress value of the mesh by the stress value of the reference mesh; the strain index is obtained by dividing the strain value of the mesh by the strain value of the reference mesh; the mesh quality index is obtained by subtracting the ratio of the difference between the element mass and the minimum element mass to the difference between the maximum element mass and the minimum element mass from 1; and the displacement index is obtained by dividing the displacement of the mesh by the displacement of the reference mesh. The simulation parameters of the mesh are obtained by weighted fusion of stress parameters, strain parameters, mesh quality parameters, and displacement parameters.

5. The method according to claim 1, characterized in that, In S300, determining the performance indicators of each target mesh, optimizing the design parameters of the target mesh based on the performance indicators, and updating the finite element model based on the optimized design parameters to serve as the final finite element model of the gear includes: S310, determine the performance optimization target of the gear and establish the mapping relationship between performance indicators and design parameters; the mapping relationship is a nonlinear regression model of performance indicators and design parameters, the performance indicators include tooth root bending strength, tooth surface contact strength, transmission efficiency and structural lightweighting indicators, and the design parameters include gear module, number of teeth, tooth width, tooth tip height coefficient, pressure angle and the elastic modulus and Poisson's ratio of the material; S320, by performing sensitivity analysis on the performance indicators and design parameters, key design parameters that have a significant impact on the performance indicators are identified; S330, establish a multi-objective optimization model, with the optimization objectives being the maximum tooth root bending strength, the maximum tooth surface contact strength, the highest transmission efficiency, and the minimum structural lightweight index, and set the constraints of the design parameters; S340 employs an improved non-dominated sorting genetic algorithm for multi-objective optimization. Through fast non-dominated sorting and crowding calculation, it generates a uniformly distributed Pareto optimal solution set in the objective space, with each solution corresponding to a set of design parameter combinations. S350: Select the scheme with the best overall performance from the Pareto optimal solution set as the optimized design parameters, and update the finite element model based on the optimized design parameters as the final finite element model of the gear.

6. A performance optimization system based on the finite element method, characterized in that, The system includes: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 5.

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