A method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology.

Abstract

A method for optimizing the natural frequencies of a paddy field grader structure based on dimensional linkage and response surface methodology is disclosed. The method comprises the following steps: S01: Establishing a simplified 3D model of the paddy field grader structure; S02: Parametrically configuring the model; S03: Linking SolidWorks and Workbench to establish dimensional relationships and a set of dimensional parameters; S04: Performing modal analysis to obtain the total deformation and the first six natural frequencies of the grader structure, setting some output results as output parameters and adding them to the dimensional parameter set; S05: Performing sensitivity analysis on the dimensional parameter set to select input parameters with higher overall sensitivity values; S06: Performing multi-objective response surface optimization to obtain the optimal design parameters; S07: Reconstructing the model based on the optimal parameters and performing modal analysis to confirm the optimization effect. This invention can accurately and efficiently optimize structural parameters using response surface methodology to improve their natural frequencies and reduce resonance risk, belonging to the field of agricultural machinery structure optimization technology.

Description

Technical Field

[0001] This invention relates to agricultural machinery structure optimization technology, specifically to a method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology. Background Technology

[0002] In modern agriculture, paddy field graders are important agricultural machinery. Their main function is to improve soil structure through loosening and leveling, thereby increasing the quality and efficiency of paddy field cultivation. With the expansion of agricultural production and the increasing demands for mechanization efficiency, higher requirements are placed on the design of paddy field graders, particularly in optimizing their natural frequencies to reduce resonance risks and improve operational stability and reliability. During operation, paddy field graders are primarily subjected to excitation from the road surface and engine vibration. When the grader's natural frequency approaches these excitation frequencies, resonance occurs. This resonance not only reduces work efficiency but also accelerates equipment wear and tear, increases maintenance costs, and can negatively impact the operator's health, leading to suboptimal leveling results and consequently affecting crop yields. Studies show that the excitation frequency range of paddy field surfaces is typically between 0.869 and 4.34 Hz, while the excitation frequency of the engine used in paddy field graders is approximately 18 Hz. This indicates that the main excitation frequencies from the external environment are concentrated in the lower frequency band. Therefore, in order to avoid resonance, the low-order natural frequencies of the paddy field grader should be increased as much as possible when designing and optimizing its structure.

[0003] However, previous optimization methods typically focused only on the dimensional impact of individual components of a paddy field grader, neglecting the complex interrelationships between dimensions throughout the entire assembly. Because of the lack of correlation between the characteristic parameters of the paddy field grader model, adjusting the dimensions of a particular feature cannot automatically update the parameters of related features simultaneously. This necessitates manually modifying multiple feature parameters to respond to design changes. This significantly reduces the flexibility and efficiency of optimizing the inherent frequency of the paddy field grader structure and makes it difficult to achieve a globally optimal design for the structure. Summary of the Invention

[0004] To address the technical problems existing in the prior art, the purpose of this invention is to provide a method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology. This method can accurately and efficiently optimize the structural parameters of the paddy field grader to improve its natural frequency and reduce the risk of resonance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology includes the following steps:

[0007] S01: Establish a simplified 3D model of the initial paddy field grader structure;

[0008] S02: Parametrically configure the 3D model of the paddy field grader created in step S01;

[0009] S03: Associate SolidWorks with Workbench, start Workbench directly from SolidWorks, import the 3D model of the paddy field grader from step S02 into Ansys Workbench and perform parametric design, establish dimension association and establish dimension parameter set;

[0010] S04: Perform modal analysis on the simplified model of the paddy field grader imported into Ansys Workbench in step S03 to obtain the total deformation of the paddy field grader structure and the first six natural frequencies in the initial state, and set some of the output results as output parameters to the size parameter set established in step S03.

[0011] S05: Associate the set of size parameters in step S04 with the parameter correlation module in Ansys Workbench to perform parameter sensitivity analysis and calculate the comprehensive sensitivity, thereby selecting input parameters with higher comprehensive sensitivity values.

[0012] S06: Import the parameterized paddy field grader structure model from step S04 into the response surface optimization module of Ansys Workbench for multi-objective response surface optimization to obtain the optimal design parameters.

[0013] S07. Reconstruct the paddy field grader structure model based on the optimal structural parameters obtained in step S06 and perform modal analysis to confirm the first six natural frequencies and mass of the optimized paddy field grader structure. Compare and analyze these parameters with the initial first six natural frequencies of the paddy field grader structure obtained in step S02 to confirm the optimization effect.

[0014] As a preferred embodiment, in step S04, the modal analysis specifically includes steps S41 to S45:

[0015] S41: New model modal analysis module, using parameter transfer, import the simplified model of the paddy field grader from step S3 into the modal analysis module;

[0016] S42: Define the material properties of the paddy field grader structural model;

[0017] S43: Mesh generation. Tetrahedral elements are used to mesh the simplified model of the paddy field grader. A 15mm mesh size is applied to the crossbeam and the left and right connecting rods, while a 20mm mesh size is used for the rest.

[0018] S44: Add connection pairs and constraints. Based on the working principle of the paddy field grader, add corresponding connection pairs and constraints to the model. Set the various hinge connections of the paddy field grader as slewing joints, set the connection between the elevation hydraulic rod and the elevation hydraulic cylinder as a sliding joint, and set the connection between the horizontal hydraulic rod and the horizontal hydraulic cylinder as a sliding joint. Apply cylindrical supports to the connection between the elevation hydraulic rod, the crossbeam, and the left and right connecting rods and the machine body.

[0019] S45: Solve the first six modes to obtain their deformation cloud diagram, thereby obtaining the first six natural frequencies and corresponding mode shapes of the paddy field grader structure in the initial state;

[0020] S46: Output the results. Output the calculated natural frequencies and deformation contour maps, and set the first-order and second-order natural frequencies and structural mass as output parameters, adding them to the size parameter set established in step S03.

[0021] As a preferred option, step S06, multi-objective response surface optimization includes the following steps:

[0022] S61. Create a new response surface optimization module and use parameter passing to import the simplified model of the paddy field grader from step S04 into the response surface optimization module.

[0023] S62. In the response surface optimization module of Ansys Workbench, a Latin hypercube test design is performed on the four input parameters with high comprehensive sensitivity values ​​selected in step S05.

[0024] S63. Construct a response surface model based on the experimental results obtained from the Latin hypercube experimental design in step S62;

[0025] S64. Test the response surface model constructed in step S63 to determine whether the response surface model meets the goodness-of-fit requirements.

[0026] S65. Construct a multi-objective response surface optimization design mathematical model based on the response surface model generated in step S63, and perform multi-objective response surface optimization on the structure of the paddy field grader to obtain the optimal design parameters.

[0027] As a preferred option, in step S01, when creating a 3D model of the paddy field grader in SolidWorks, the assembly should be designed from top to bottom to establish linkage features and realize the linkage of related dimensions between the parts of the assembly. First, an assembly containing nine parts is created using SolidWorks Treehouse: a crossbeam, left connecting rod, right connecting rod, mounting frame, grader blade, elevation hydraulic rod, elevation hydraulic cylinder, horizontal hydraulic rod, and horizontal hydraulic cylinder. The parts are then arranged in the order of installation according to the actual installation sequence of the paddy field grader. The components are then drawn in the assembly according to the assembly relationship.

[0028] As a preferred approach, in step S02, when setting parameters for the dimensions to be optimized in the model, two types of dimensions need to be set: one is the dimension parameter setting in the sketch, where "DS_" is added before the name of the corresponding dimension parameter in sketch editing mode; the other is the dimension parameter setting for features, such as the depth of an extrusion feature. Since dimensions cannot be named when setting feature dimension parameters, making parameter modification impossible, a global variable is used to define this parameter to achieve linkage between parameter modification and dimension. First, add a global variable in the assembly model named "scraper". Go to Tools -> Equations from the menu bar, add a global variable, and name it in English with the prefix "DS_", such as "DS_Variable", and assign a value to the variable. Then, open the component containing the feature, select the corresponding feature for editing, and in the feature's dimension setting, first delete the dimension, then click the dimension input box and enter the expression = "DS_Variable@scraper.Assembly". This expression is used to reference the global variable "DS_Variable" in the assembly "scraper". In this way, it can be ensured that the size of the part feature can be automatically adjusted as the global variable "DS_Variable" in the assembly changes, thus achieving flexible linkage of dimensions.

[0029] As a preferred method, in step S03, starting Workbench from SolidWorks requires first installing the ANSYS plugin in SolidWorks. The command "ANSYS 2022R1" → "Ansys Workbench" in the "Tools" menu of the main interface creates a Geometry project. Double-clicking "Geometry" in column A2 of project A loads DesignModeler. In DM, update Attach1 to generate the model, thus completing the import of the paddy field grader model. When performing parametric design on the paddy field grader model, locate the variables defined in step S02 and check the boxes in front of them. Set all variables involved in optimization as input parameters to establish a set of dimensional parameters. In the generated set of dimensional parameters, set the parameter associations according to the relationships between the parameters. For example, if the relationship between the crossbeam length l1 and the left / right connecting rod length l2 is l1 = l2 + 30mm, then in the parameter l2 property interface, define the parameter value as the expression "l1 - 30".

[0030] As a preferred approach, in step S05, when performing correlation analysis on all input parameters in the size parameter set, only the first-order natural frequency and the second-order natural frequency are selected as key response variables for analysis. The correlation type is Spearman correlation, and the mean accuracy is set to 0.01 and the standard deviation accuracy is set to 0.02. The correlation analysis is then started, allowing the system to calculate the influence of each input parameter on the first-order and second-order natural frequencies of the selected output parameters. After the analysis is completed, the generated sensitivity histogram is viewed, and the four input parameters with higher overall sensitivity values ​​are selected.

[0031] As a preferred option, in step S62, when designing the experiment, only select the input parameters with higher comprehensive sensitivity values ​​selected in step S05, and set upper and lower limits for each input parameter. Then, set the "Experiment Type Design" and "Sample Type," and select the method as needed. Here, Latin hypercube sampling design and CCD sampling are selected. Update the "Experiment Design" to generate the experimental design points. Note that during the update of the "Experiment Design," do not close the paddy field grader model in SolidWorks associated with Ansys Workbench. After updating the "Experiment Design," double-click to enter the "Response Surface" and set the response surface type. Here, select the standard response surface, and update to generate the corresponding response surface results. Import the "Experiment Design Points" generated in step S62 into the software Design-Expert for multivariate regression fitting to obtain the prediction models of the first and second order natural frequencies and structural mass of the paddy field grader.

[0032] As a preferred option, in step S64, the absolute coefficient R is used. 2 Root mean square error E RMS Mean absolute error E RMA The accuracy of the fitted surface is evaluated. If the response surface model does not meet the goodness-of-fit requirement, the response surface model is rebuilt until it meets the goodness-of-fit requirement.

[0033] R 2 The calculation formula is:

[0034]

[0035] E RMS The calculation formula is:

[0036]

[0037] E RMA The calculation formula is:

[0038]

[0039] Among them, y i These are DOE test data values. The predicted values ​​are from the response surface similarity model. denoted as the mean of the DOE experimental data, where the DOE experimental data values ​​are sample data obtained after conducting DOE sampling experiments based on the predicted values ​​of the response surface similarity model.

[0040] As a preferred option, the mathematical model for multi-objective response surface optimization design in step S65 is as follows:

[0041]

[0042] Where F(X) is the objective function of the final output of the multi-objective response surface optimization calculation, and max F(X) is the output value of the objective function F(X) when the first and second natural frequencies are maximized and the mass is minimized; y1(X) is the first natural frequency of the optimized structure, y2(X) is the second natural frequency of the optimized structure, and y3(X) is the mass of the optimized structure; γ1 is the weighting coefficient of the first natural frequency, γ2 is the weighting coefficient of the second natural frequency, and γ3 is the weighting coefficient of the structural mass; the formula st is the constraint condition, and 36Hz is twice the frequency of the paddy field grader engine; X is the decision vector, representing the adjustable input parameters; x1, x2, x3, and x4 correspond to the design variables beam width w1, beam height h1, beam thickness d1, and beam length l1, respectively.

[0043] The first-order natural frequency model of the paddy field grader is:

[0044]

[0045] The second-order natural frequency model of the paddy field grader is:

[0046]

[0047] The mass model of the paddy field grader is as follows:

[0048]

[0049] When performing multi-objective response surface optimization on the structure of a paddy field grader, the optimization objectives are to maximize the first-order natural frequencies and minimize the structural mass. Constraints include ensuring that the first and second-order natural frequencies are more than twice the paddy field excitation frequency and engine frequency, and that the design variables fall within a certain range. A multi-objective genetic algorithm (MOGA) is used for optimization, with an initial population size of 10,000, each iteration generating 100 new populations, a maximum of 20 iterations, a permissible deviation of 2%, and a maximum permissible Pareto percentage of 70%. The first and second-order natural frequencies are given higher importance, while the structural mass is set to the default importance. After setting the optimization attributes, three candidate points satisfying the conditions are generated through the solution process. Finally, considering both primary and secondary objectives, one of these candidate points is selected as the optimal design point.

[0050] The present invention has the following advantages:

[0051] (1) The present invention realizes the linkage of related dimensions of parts in the assembly, ensuring that the dimensions of the parts can automatically coordinate and change when adjusted, thereby improving the flexibility and efficiency of the design.

[0052] (2) This invention establishes a real-time bidirectional association between SolidWorks and Ansys Workbench, realizing a seamless connection from modeling to analysis and optimization. It uses parameterized settings and global variables to manage dimensions and establishes a multi-objective response surface optimization based on the dimension parameters of the real-time bidirectional association. This allows the model to be easily adjusted during the optimization process, effectively shortening the reconstruction time of the optimized 3D model and improving the efficiency of optimizing the natural frequency of the paddy field grader structure.

[0053] (3) This invention employs Latin hypercube experimental design and multiple regression fitting methods, combined with the accuracy evaluation of response surface models (such as R²). 2 The root mean square error (RMSE) ensures the high reliability and accuracy of the fitted model.

[0054] (4) This invention uses a multi-objective genetic algorithm (MOGA) to seek the optimal solution, which ensures that the optimal parameter combination can be found even in a complex design space. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention.

[0056] Figure 2 This is a schematic diagram of the overall structure of the paddy field grader used in the experiment.

[0057] Figure 3 A schematic diagram of the structural connection when adding a connecting pair to a paddy field grader.

[0058] Figure 4This is a diagram showing the result of meshing a simplified 3D model.

[0059] Figure 5 This is a graph showing the results after sensitivity analysis of all input parameters.

[0060] Figure 6 This is a schematic diagram of the structural parameters with high overall sensitivity values ​​selected after parameter sensitivity analysis.

[0061] 1-Elevation hydraulic rod, 2-Elevation hydraulic cylinder, 3-Crossbeam, 4-Mounting bracket, 5-Horizontal hydraulic cylinder, 6-Horizontal hydraulic rod, 7-Leveling shovel, 8-Right connecting rod, 9-Left connecting rod. Detailed Implementation

[0062] The present invention will now be described in further detail with reference to specific embodiments.

[0063] Figure 1 As shown, a method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology includes the following steps:

[0064] S01: Establish a simplified 3D model of the initial paddy field grader structure;

[0065] S02: Parametrically configure the 3D model of the paddy field grader created in step S01;

[0066] S03: Associate SolidWorks with Workbench, start Workbench directly from SolidWorks, import the 3D model of the paddy field grader from step S02 into Ansys Workbench and perform parametric design, establish dimension association and establish dimension parameter set;

[0067] S04: Perform modal analysis on the simplified model of the paddy field grader imported into Ansys Workbench in step S03 to obtain the total deformation of the paddy field grader structure and the first six natural frequencies in the initial state, and set some of the output results as output parameters to the size parameter set established in step S03.

[0068] S05: Associate the set of size parameters in step S04 with the parameter correlation module in Ansys Workbench to perform parameter sensitivity analysis and calculate the comprehensive sensitivity, thereby selecting input parameters with higher comprehensive sensitivity values.

[0069] S06: Import the parameterized paddy field grader structure model from step S04 into the response surface optimization module of Ansys Workbench for multi-objective response surface optimization to obtain the optimal design parameters.

[0070] S07. Reconstruct the paddy field grader structure model based on the optimal structural parameters obtained in step S06 and perform modal analysis to confirm the first six natural frequencies and mass of the optimized paddy field grader structure. Compare and analyze these parameters with the initial first six natural frequencies of the paddy field grader structure obtained in step S02 to confirm the optimization effect.

[0071] Specifically, in step S01, when creating a 3D model of the paddy field grader in SolidWorks, the assembly should be designed from top to bottom to establish linkage features and realize the linkage of related dimensions between the parts of the assembly. First, use SolidWorks Treehouse to create an assembly containing 9 parts: crossbeam, left connecting rod, right connecting rod, mounting frame, grader blade, elevation hydraulic rod, elevation hydraulic cylinder, horizontal hydraulic rod, and horizontal hydraulic cylinder. Then, arrange the order of parts according to the actual installation sequence of the paddy field grader and draw the components in the assembly according to the assembly relationship.

[0072] Specifically, in step S02, when setting parameters for the dimensions that need optimization in the model, two types of dimensions need to be set: one is the dimension parameter setting in the sketch, where "DS_" is added before the name of the corresponding dimension parameter in sketch editing mode; the other is the dimension parameter setting for features, such as the depth of an extrusion feature. Since dimensions cannot be named when setting feature dimension parameters, making parameter modification impossible, a global variable is used to define this parameter to achieve linkage between parameter modification and dimension. First, add a global variable in the assembly model named "scraper". From the menu bar, go to: Tools -> Equations, add a global variable, and the variable name should be in English with the prefix "DS_", such as "DS_Variable", and assign a value to the variable. Then, open the component containing the feature, select the corresponding feature for editing, and when setting the feature's dimensions, first delete the dimension, then click the dimension input box and enter the expression = "DS_Variable@scraper.Assembly". The purpose of this expression is to reference the global variable "DS_Variable" in the assembly "scraper". In this way, it can be ensured that the size of the part feature can be automatically adjusted as the global variable "DS_Variable" in the assembly changes, thus achieving flexible linkage of dimensions.

[0073] Specifically, in step S03, starting Workbench from SolidWorks requires first installing the ANSYS plugin in SolidWorks. The main interface uses the command "ANSYS2022R1" → "Ansys Workbench" under "Tools" to create a Geometry project. Double-clicking "Geometry" in column A2 of project A loads DesignModeler. In DM, update Attach1 to generate the model, thus completing the import of the paddy field grader model. When performing parametric design on the paddy field grader model, locate the variables defined in step S02 and check the boxes in front of them. Set all variables involved in optimization as input parameters to establish a set of dimensional parameters. In the generated set of dimensional parameters, set the parameter associations according to the relationships between the parameters. For example, if the relationship between the crossbeam length l1 and the left / right connecting rod length l2 is l1 = l2 + 30mm, then in the parameter l2 property interface, define the parameter value as the expression "l1 - 30".

[0074] Specifically, in step S04, the modal analysis includes steps S41 to S45:

[0075] S41: New model modal analysis module, using parameter transfer, import the simplified model of the paddy field grader from step S3 into the modal analysis module;

[0076] S42: Define the material properties of the paddy field grader structural model;

[0077] S43: Mesh generation. Tetrahedral elements are used to mesh the simplified model of the paddy field grader. A 15mm mesh size is applied to the crossbeam and the left and right connecting rods, while a 20mm mesh size is used for the rest.

[0078] S44: Add connection pairs and constraints. Based on the working principle of the paddy field grader, add corresponding connection pairs and constraints to the model. Set the various hinge connections of the paddy field grader as slewing joints, set the connection between the elevation hydraulic rod and the elevation hydraulic cylinder as a sliding joint, and set the connection between the horizontal hydraulic rod and the horizontal hydraulic cylinder as a sliding joint. Apply cylindrical supports to the connection between the elevation hydraulic rod, the crossbeam, and the left and right connecting rods and the machine body.

[0079] S45: Solve the first six modes to obtain their deformation cloud diagram, thereby obtaining the first six natural frequencies and corresponding mode shapes of the paddy field grader structure in the initial state;

[0080] S46: Output the results. Output the calculated natural frequencies and deformation contour maps, and set the first-order and second-order natural frequencies and structural mass as output parameters, adding them to the size parameter set established in step S03.

[0081] Specifically, in step S05, when performing correlation analysis on all input parameters in the size parameter set, only the first-order natural frequency and the second-order natural frequency are selected as key response variables for analysis. The correlation type is Spearman correlation, and the mean accuracy is set to 0.01 and the standard deviation accuracy is set to 0.02. The correlation analysis is started, allowing the system to calculate the influence of each input parameter on the first-order and second-order natural frequencies of the selected output parameters. After the analysis is completed, the generated sensitivity histogram is viewed, and the four input parameters with higher overall sensitivity values ​​are selected.

[0082] Specifically, in step S06, multi-objective response surface optimization includes the following steps:

[0083] S61. Create a new response surface optimization module and use parameter passing to import the simplified model of the paddy field grader from step S04 into the response surface optimization module.

[0084] S62. In the response surface optimization module of Ansys Workbench, a Latin hypercube test design is performed on the four input parameters with high comprehensive sensitivity values ​​selected in step S05.

[0085] S63. Construct a response surface model based on the experimental results obtained from the Latin hypercube experimental design in step S62;

[0086] S64. Test the response surface model constructed in step S63 to determine whether the response surface model meets the goodness-of-fit requirements.

[0087] S65. Construct a multi-objective response surface optimization design mathematical model based on the response surface model generated in step S63, and perform multi-objective response surface optimization on the structure of the paddy field grader to obtain the optimal design parameters.

[0088] Specifically, in step S62, when designing the experiment, only select the input parameters with higher comprehensive sensitivity values ​​selected in step S05, and set upper and lower limits for each input parameter. Then, set the "Experiment Type Design" and "Sample Type," and select the method as needed. Here, Latin hypercube sampling design and CCD sampling are selected. Update the "Experiment Design" to generate the experimental design points. Note that during the update of the "Experiment Design," do not close the paddy field grader model in SolidWorks associated with Ansys Workbench. After updating the "Experiment Design," double-click to enter the "Response Surface" and set the type of response surface. Here, select the standard response surface, and update to generate the corresponding response surface results. Import the "Experiment Design Points" generated in step S62 into the software Design-Expert for multivariate regression fitting to obtain the prediction models of the first and second order natural frequencies and structural mass of the paddy field grader.

[0089] Specifically, in step S64, the absolute coefficient R is used. 2 Root mean square error E RMS Mean absolute error E RMA The accuracy of the fitted surface is evaluated. If the response surface model does not meet the goodness-of-fit requirement, the response surface model is rebuilt until it meets the goodness-of-fit requirement.

[0090] R 2 The calculation formula is:

[0091]

[0092] E RMS The calculation formula is:

[0093]

[0094] E RMA The calculation formula is:

[0095]

[0096] Among them, y i These are DOE test data values. The predicted values ​​are from the response surface similarity model. denoted as the mean of the DOE experimental data, where the DOE experimental data values ​​are sample data obtained after conducting DOE sampling experiments based on the predicted values ​​of the response surface similarity model.

[0097] Specifically, in step S65, the mathematical model for multi-objective response surface optimization design is as follows:

[0098]

[0099] Where F(X) is the objective function of the final output of the multi-objective response surface optimization calculation, and max F(X) is the output value of the objective function F(X) when the first and second natural frequencies are maximized and the mass is minimized; y1(X) is the first natural frequency of the optimized structure, y2(X) is the second natural frequency of the optimized structure, and y3(X) is the mass of the optimized structure; γ1 is the weighting coefficient of the first natural frequency, γ2 is the weighting coefficient of the second natural frequency, and γ3 is the weighting coefficient of the structural mass; the formula st is the constraint condition, and 36Hz is twice the frequency of the paddy field grader engine; X is the decision vector, representing the adjustable input parameters; x1, x2, x3, and x4 correspond to the design variables beam width w1, beam height h1, beam thickness d1, and beam length l1, respectively.

[0100] The first-order natural frequency model of the paddy field grader is:

[0101]

[0102] The second-order natural frequency model of the paddy field grader is:

[0103]

[0104] The mass model of the paddy field grader is as follows:

[0105]

[0106] When performing multi-objective response surface optimization on the structure of a paddy field grader, the optimization objectives are to maximize the first-order natural frequencies and minimize the structural mass. Constraints include ensuring that the first and second-order natural frequencies are more than twice the paddy field excitation frequency and engine frequency, and that the design variables fall within a certain range. A multi-objective genetic algorithm (MOGA) is used for optimization, with an initial population size of 10,000, each iteration generating 100 new populations, a maximum of 20 iterations, a permissible deviation of 2%, and a maximum permissible Pareto percentage of 70%. The first and second-order natural frequencies are given higher importance, while the structural mass is set to the default importance. After setting the optimization attributes, three candidate points satisfying the conditions are generated through the solution process. Finally, considering both primary and secondary objectives, one of these candidate points is selected as the optimal design point.

[0107] This embodiment uses Figure 2The simplified 3D model of the paddy field grader shown is used as the initial model for subsequent optimization. The structure of this grader consists of an elevation hydraulic rod 1, an elevation hydraulic cylinder 2, a crossbeam 3, a mounting frame 4, a horizontal hydraulic cylinder 5, a horizontal hydraulic rod 6, a grader shovel 7, a right connecting rod 8, and a left connecting rod 9. This simplifies local features of the grader that do not affect the simulation analysis. The right and left connecting rods are the same component and will be referred to as "connecting rods" below. Next, step S02 is executed, and the simplified 3D model is parameterized according to Table 1. Specifically, parameters in the table that are of sketch parameter type are parameterized by adding "DS_" before the name of the corresponding dimension parameter in sketch editing mode. Parameters in the table that are of feature parameter type are parameterized by adding a global variable to the assembly model and referencing this variable when editing feature dimensions. Taking the parameterization of the crossbeam length as an example, a global variable "DS_l1" is added to the assembly model named "scraper," and its value is given as 820. Then open the component containing the feature, select the corresponding feature for editing, and in the feature's dimension settings, first delete the dimension, then click the dimension input box and enter the expression = "DS_l1@scraper.Assembly". Following the parameter setting method described above, set the beam width w1, beam height h1, beam thickness d1, beam length l1, connecting rod width w2, connecting rod height h2, connecting rod thickness d2, and connecting rod length l2 respectively, with variable names as "DS_w1", "DS_h1", "DS_d1", "DS_l1", "DS_w2", "DS_h2", "DS_d2", and "DS_l2".

[0108] Table 1 Structural Parameter Settings for Paddy Field Graders

[0109] Design parameters Parameter type variable name initial value Beam width / mm Sketch parameters <![CDATA[DS_w1]]> 40 Beam height / mm Sketch parameters <![CDATA[DS_h1]]> 60 Beam thickness / mm Sketch parameters <![CDATA[DS_d1]]> 5 Beam length / mm Feature parameters <![CDATA[DS_l1]]> 820 Linkage width / mm Sketch parameters <![CDATA[DS_w2]]> 40 Linkage height / mm Sketch parameters <![CDATA[DS_h2]]> 60 Connecting rod thickness / mm Sketch parameters <![CDATA[DS_d2]]> 5 Linkage length / mm Feature parameters <![CDATA[DS_l2]]> 790

[0110] In step S03, when performing parametric design on the simplified 3D model of the paddy field grader imported into Ansys Workbench, locate the variables defined in step S02 and check the small squares in front of them. Set all variables involved in the optimization as input parameters to establish a set of dimensional parameters. In the generated parameter set, associate the connecting rod length l2 with the crossbeam length l1. In the parameter l2 property interface, define the parameter value as the expression "l1-30". Associate the mounting frame width w3 with the crossbeam length w1. In the parameter w2 property interface, define the parameter value as the expression "w1+10".

[0111] Next, step S04 is executed to perform modal analysis on the simplified 3D model of the paddy field grader imported into Ansys Workbench in S03. This yields the total deformation and the first six natural frequencies of the paddy field grader structure in its initial state, and some of the output results are set as output parameters. Specifically, the material properties are first defined: the paddy field grader structure material is Q235, with a density of 7.85 g / cm³. 3 The Young's modulus is 200 GPa, and the Poisson's ratio is 0.3. Then, according to... Figure 3 Table 2 shows the connection pairs set at various joints of the simplified model of the paddy field grader, and cylindrical supports are applied at the connection points of the elevation hydraulic rod, crossbeam, and left / right connecting rods with the machine body. Tetrahedral elements are used to mesh the simplified model of the paddy field grader, with a 15mm mesh size applied to the crossbeam and left / right connecting rods, and a 20mm mesh size used for the remaining parts. The meshed model is shown below. Figure 3 As shown in the figure. Finally, the first six modes were solved, and the results are shown in Table 3.

[0112] Table 2. Structural Connection Relationships of Paddy Field Graders

[0113]

[0114]

[0115] Table 3. Modal analysis results of the initial paddy field grader structure

[0116] order Natural frequency / Hz Mode shape 1 4.00 The grader swings along the Y-axis. 2 7.35 The mounting bracket oscillates around the X-axis. 3 9.54 The oscillation of the leveling shovel around the Y-axis 4 15.23 The grader swings along the Z-axis. 5 18.16 The screed and mounting frame swing along the Z-axis. 6 44.22 The shovel swings along the Y-axis.

[0117] After step S04, the modal analysis results are obtained. The first and second natural frequencies and structural mass are set as output parameters and added to the size parameter set, and represented by the symbols ω1, ω2 and m, respectively.

[0118] After step S05, the sensitivity analysis results for the seven input parameters are obtained, as shown in the figure. Figure 5 As shown in the figure, the comprehensive sensitivity values ​​of the seven input parameters were calculated, and the results are shown in Table 4. The four input parameters with the highest comprehensive sensitivity values ​​were then selected: beam width w1, beam height h1, beam thickness d1, and beam length l1. Figure 6 As indicated by the label.

[0119] Table 4. Overall sensitivity values ​​for each input parameter

[0120] Input parameters <![CDATA[w1]]> <![CDATA[h1]]> <![CDATA[d1]]> <![CDATA[l1]]> <![CDATA[w2]]> <![CDATA[h2]]> <![CDATA[d2]]> Overall sensitivity / % 22.52 15.81 21.11 35.39 1.95 1.84 1.38

[0121] In step S06, when performing multi-objective response surface optimization on the structure of the paddy field grader, the constructed response surface model is tested, and the results are shown in Table 5. The determination coefficients R of each output parameter are as follows: 2 Approaching 1, the root mean square error ERMS and the relative maximum absolute error E RMA All values ​​approaching 0 indicate that the response surface model has high accuracy and can be further optimized. The optimization objectives are to maximize the first and second natural frequencies of the paddy field grader structure and minimize its mass. Constraints include the first and second natural frequencies being greater than twice the paddy field excitation frequency and the engine excitation frequency, as well as the range of design variable values, as shown in Tables 6 and 7. Finally, a multi-objective optimization genetic algorithm (MOGA) is used to optimize and solve the objective function, configured as shown in Table 8. The initial population size is set to 10,000, the number of new populations generated in each generation is 100, the maximum number of iterations is 20, the permissible deviation is set to 2%, and the maximum permissible Pareto percentage is set to 70%.

[0122] Table 5 Response Surface Accuracy Verification

[0123] Error type <![CDATA[ω1]]> <![CDATA[ω2]]> m <![CDATA[R 2 ]]> 0.99961 0.99928 0.99941 <![CDATA[E RMS ]]> <![CDATA[3.98×10 -7 ]]> <![CDATA[8.27×10 -6 ]]> <![CDATA[7.14×10 -6 ]]> <![CDATA[E RMA ]]> <![CDATA[4.85×10 -6 ]]> <![CDATA[5.19×10 -5 ]]> <![CDATA[4.71×10 -5 ]]>

[0124] Table 6 Optimization Objectives and Constraint Settings

[0125] objective function Optimization Objective constraint Weight First-order natural frequency maximize >36Hz High importance Second natural frequency maximize >36Hz High importance quality minimize none Default importance

[0126] Table 7 Range of Design Variable Values

[0127] symbol variable initial value lower limit upper limit <![CDATA[w1]]> Beam width 40 20 60 <![CDATA[h1]]> Beam height 60 40 120 <![CDATA[d1]]> Beam thickness 5 2 8 <![CDATA[l1]]> beam length 820 620 1020

[0128] Table 8 Configuration of Multi-Objective Optimization Algorithm

[0129]

[0130]

[0131] After S06, we get Figure 6 The optimized values ​​of each structural parameter were rounded to facilitate processing. Modal analysis was performed on the three-dimensional model of the optimized paddy field grader structure, and the results were compared with the initial values. The specific comparison results are shown in Tables 8 and 9.

[0132] Table 9 Comparison of results before and after optimization

[0133] Parameter name symbol Before optimization After optimization contrast Liang Kuan <![CDATA[w1 / mm]]> 40 20.7 -48.25％ Liang Gao <![CDATA[h1 / mm]]> 60 41.4 -31％ Liang Hou <![CDATA[d1 / mm]]> 5 8 +60％ Liang Chang <![CDATA[l1 / mm]]> 820 621 -24.27％ First-order natural frequency <![CDATA[ω1 / Hz]]> 4 40.523 +913.08％ Second-order natural frequency <![CDATA[ω2 / Hz]]> 7.35 50.12 +581.9％ Grader quality m / Kg 119.58 114.26 -4.45％

[0134] Table 10 Comparison of Modal Analysis Results Before and After Optimization

[0135] order Results before optimization / Hz Optimized result / Hz contrast 1 4.00 40.523 +913.08％ 2 7.35 50.12 +581.9％ 3 9.54 67.17 +604.09％ 4 15.23 96.18 +531.52％ 5 18.16 101.4 +458.37％ 6 44.22 161.55 +265.33％

[0136] As can be seen from the comparison table, the first six natural frequencies are significantly improved after optimization. This improvement expands the dynamic stability range of the system, enabling it to operate more stably and withstand higher frequency dynamic loads. Furthermore, the first and second natural frequencies are far from the external excitation frequency, greatly reducing the risk of resonance and significantly improving the system's vibration resistance. The grader's weight has also decreased slightly, achieving a balance between overall efficiency and cost.

[0137] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology, characterized in that, Includes the following steps: S01: Establish a simplified 3D model of the initial paddy field grader structure; S02: Parametrically configure the 3D model of the paddy field grader created in step S01; S03: Associate SolidWorks with Workbench, start Workbench directly from SolidWorks, import the 3D model of the paddy field grader from step S02 into Ansys Workbench and perform parametric design, establish dimension association and establish dimension parameter set; S04: Perform modal analysis on the simplified model of the paddy field grader imported into Ansys Workbench in step S03 to obtain the total deformation of the paddy field grader structure and the first six natural frequencies in the initial state, and set some of the output results as output parameters to the size parameter set established in step S03. S05: Associate the set of size parameters in step S04 with the parameter correlation module in Ansys Workbench to perform parameter sensitivity analysis and calculate the comprehensive sensitivity, thereby selecting input parameters with higher comprehensive sensitivity values. S06: Import the parameterized paddy field grader structure model from step S04 into the response surface optimization module of Ansys Workbench for multi-objective response surface optimization to obtain the optimal design parameters. S07. Reconstruct the structural model of the paddy field grader based on the optimal structural parameters obtained in step S06 and perform modal analysis to confirm the first six natural frequencies and mass of the optimized paddy field grader structure. Compare and analyze the first six natural frequencies of the initial paddy field grader structure obtained in step S02 to confirm the optimization effect. In step S06, multi-objective response surface optimization includes the following steps: S61. Create a new response surface optimization module and use parameter passing to import the simplified model of the paddy field grader from step S04 into the response surface optimization module. S62. In the response surface optimization module of Ansys Workbench, a Latin hypercube test design is performed on the four input parameters with high comprehensive sensitivity values ​​selected in step S05. S63. Construct a response surface model based on the experimental results obtained from the Latin hypercube experimental design in step S62; S64. Test the response surface model constructed in step S63 to determine whether the response surface model meets the goodness-of-fit requirements. S65. Construct a multi-objective response surface optimization design mathematical model based on the response surface model generated in step S63, and perform multi-objective response surface optimization on the structure of the paddy field grader to obtain the optimal design parameters. In step S65, the mathematical model for multi-objective response surface optimization design is as follows: Where F(X) is the objective function of the final output of the multi-objective response surface optimization calculation, and max F(X) is the output value of the objective function F(X) when the first and second natural frequencies are maximized and the mass is minimized; y1(X) is the first natural frequency of the optimized structure, y2(X) is the second natural frequency of the optimized structure, and y3(X) is the mass of the optimized structure; γ1 is the weighting coefficient of the first natural frequency, γ2 is the weighting coefficient of the second natural frequency, and γ3 is the weighting coefficient of the structural mass; the formula st is the constraint condition, and 36Hz is twice the frequency of the paddy field grader engine; X is the decision vector, representing the adjustable input parameters; x1, x2, x3, and x4 correspond to the design variables beam width w1, beam height h1, beam thickness d1, and beam length l1, respectively. The first-order natural frequency model of the paddy field grader is: The second-order natural frequency model of the paddy field grader is: The mass model of the paddy field grader is as follows: When performing multi-objective response surface optimization on the structure of the paddy field grader, the optimization objectives are to maximize the first-order and second-order natural frequencies of the paddy field grader structure and minimize the structural mass. The first-order and second-order natural frequencies are more than twice the excitation frequency of the paddy field ground and the engine frequency, and the range of design variable values ​​are used as constraints. A multi-objective genetic algorithm is used for optimization.

2. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S04, the modal analysis specifically includes steps S41 to S45: S41: New model modal analysis module, using parameter transfer, import the simplified model of the paddy field grader from step S3 into the modal analysis module; S42: Define the material properties of the paddy field grader structural model; S43: Mesh generation. Tetrahedral elements are used to mesh the simplified model of the paddy field grader. A 15mm mesh size is applied to the crossbeam and the left and right connecting rods, while a 20mm mesh size is used for the rest. S44: Add connection pairs and constraints. Based on the working principle of the paddy field grader, add corresponding connection pairs and constraints to the model. Set the various hinge connections of the paddy field grader as slewing joints, set the connection between the elevation hydraulic rod and the elevation hydraulic cylinder as a sliding joint, and set the connection between the horizontal hydraulic rod and the horizontal hydraulic cylinder as a sliding joint. Apply cylindrical supports to the connection between the elevation hydraulic rod, the crossbeam, and the left and right connecting rods and the machine body. S45: Solve the first six modes to obtain their deformation cloud diagram, thereby obtaining the first six natural frequencies and corresponding mode shapes of the paddy field grader structure in the initial state; S46: Output the results. Output the calculated natural frequencies and deformation contour maps, and set the first-order and second-order natural frequencies and structural mass as output parameters, adding them to the size parameter set established in step S03.

3. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S01, when creating a 3D model of the paddy field grader in SolidWorks, the assembly should be designed from top to bottom to establish linkage features and realize the linkage of related dimensions between the parts of the assembly. First, an assembly is created using SolidWorks Treehouse, which contains 9 parts: crossbeam, left connecting rod, right connecting rod, mounting frame, grader blade, elevation hydraulic rod, elevation hydraulic cylinder, horizontal hydraulic rod, and horizontal hydraulic cylinder. The parts are then arranged in the order of installation according to the actual installation sequence of the paddy field grader. The components are then drawn in the assembly according to the assembly relationship.

4. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S02, when setting parameters for the dimensions that need to be optimized in the model, two types of dimensions need to be set: one is the dimension parameter setting in the sketch, which is done by adding "DS_" before the name of the corresponding dimension parameter in sketch editing mode; the other is the dimension parameter setting for the feature, which is defined as a global variable to achieve the linkage between parameter modification and dimension.

5. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S03, when performing parametric design on the paddy field grader model, the variables defined in step S02 are found and checked, and all variables involved in the optimization are set as input parameters to establish a set of size parameters. In the generated set of size parameters, parameter association settings are performed according to the relationship between each parameter.

6. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S05, when performing correlation analysis on all input parameters in the size parameter set, only the first-order natural frequency and the second-order natural frequency are selected as key response variables for analysis. The correlation type is Spearman correlation, and the mean accuracy is set to 0.01 and the standard deviation accuracy is set to 0.

02. The correlation analysis is started, and the system calculates the influence of each input parameter on the first-order and second-order natural frequencies of the selected output parameters. After the analysis is completed, the generated sensitivity histogram is viewed, and the four input parameters with higher overall sensitivity values ​​are selected.

7. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, In step S62, when designing the experiment, only select the input parameters with higher overall sensitivity values ​​selected in step S05, and set upper and lower limits for each input parameter. Then, set the "Experiment Type Design" and "Sample Type," and select the method as needed. Here, Latin hypercube sampling design and CCD sampling are selected. Update the "Experiment Design" to generate the experimental design points. During the update of the "Experiment Design," do not close the paddy field grader model in SolidWorks associated with Ansys Workbench. After updating the "Experiment Design," double-click to enter the "Response Surface" and set the type of response surface. Here, select the standard response surface, and update to generate the corresponding response surface results. The "experimental design points" generated in step S62 are then imported into the software Design-Expert for multivariate regression fitting to obtain prediction models for the first and second order natural frequencies and structural mass of the paddy field grader.

8. The method for optimizing the natural frequency of a paddy field grader structure based on size linkage and response surface methodology as described in claim 1, characterized in that, Step S64, using the absolute coefficient R 2 Root mean square error E RMS Mean absolute error E RMA The accuracy of the fitted surface is evaluated. If the response surface model does not meet the goodness-of-fit requirement, the response surface model is rebuilt until it meets the goodness-of-fit requirement. R 2 The calculation formula is: E RMS The calculation formula is: E RMA The calculation formula is: Among them, y i These are DOE test data values. The predicted values ​​are from the response surface similarity model. denoted as the mean of the DOE experimental data, where the DOE experimental data values ​​are sample data obtained after conducting DOE sampling experiments based on the predicted values ​​of the response surface similarity model.

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