Reducer gear box lightweight design method based on topological optimization

Abstract

The invention discloses a speed reducer gear box lightweight design method based on topological optimization, and relates to the technical field of gear box optimization. A processing end establishes a three-dimensional parameterized geometric model, performs finite element mesh generation on the geometric model, optimizes material distribution of the geometric model based on a topological optimization algorithm, and optimizes the material distribution of the geometric model; a topological optimization result is parameterized into geometric features, a random generation tool is used for generating a plurality of initial variable sets, a genetic algorithm is used for outputting an optimal variable set, a geometric model is reconstructed according to the topological optimization result and a genetic algorithm result, and after dynamic-static simulation is conducted on the reconstructed geometric model, the optimal variable set is obtained. And evaluating whether the performance of the reconstructed geometric model reaches the standard or not, and if not, optimizing genetic algorithm parameters according to an evaluation result and then cyclically reconstructing the geometric model until the performance of the reconstructed geometric model reaches the standard. The design system intelligently optimizes a local high-stress area, so that the lightweight requirement is met, and meanwhile, the strength and rigidity balance of the structure is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of gearbox optimization, and particularly to a lightweight design method for a reducer gearbox based on topology optimization. Background Art

[0002] A reducer gearbox is a transmission device used to reduce the rotational speed and increase the torque, and is widely applied in the fields of machinery manufacturing, automobiles, wind power generation, aerospace, robotics, etc. The gearbox plays a key role in the entire power transmission system. Its design not only affects the transmission efficiency and reliability of the system, but also directly relates to the energy consumption, service life and manufacturing cost of the equipment. With the development of industrial equipment towards high efficiency, energy conservation and environmental protection, the demand for lightweight design of gearboxes has become increasingly prominent.

[0003] The existing technologies have the following defects:

[0004] 1. In traditional topology optimization design, the optimization algorithm often focuses on minimizing the overall mass, but does not fully consider the stiffness requirements of local regions (such as gear meshing areas, bearing seats, fixed connection areas). This may lead to: excessive deformation due to insufficient stiffness at key parts (such as gear support points), affecting the gear meshing accuracy, thereby reducing the transmission efficiency and service life of the gearbox, and aggravating the stress concentration problem, resulting in fatigue failure or microcrack propagation of the gearbox during long-term operation, shortening the service life.

[0005] 2. Traditional topology optimization algorithms (such as the SIMP method, the BESO method) optimize the material distribution through mathematical methods, but their optimization results are usually grid-like and irregular shapes. For example, there are irregular overhanging structures, isolated material units or sharp protrusions, resulting in difficulty in directly converting the optimized geometric model into a manufacturable CAD model. At the same time, the optimization results often lack clear geometric features (such as regular stiffeners, wall thickness gradients), making it difficult to perform secondary design and actual processing based on the optimization results subsequently.

[0006] Based on this, the present invention proposes a lightweight design method for a reducer gearbox based on topology optimization, which intelligently optimizes local high-stress regions to ensure the balance of structural strength and stiffness while meeting the lightweight requirements. Summary of the Invention

[0007] The purpose of the present invention is to provide a lightweight design method for a reducer gearbox based on topology optimization to solve the deficiencies in the background art.

[0008] To achieve the above purpose, the present invention provides the following technical solution: A lightweight design method for a reducer gearbox based on topology optimization, the design method comprising the following steps:

[0009] S1: The processing end establishes a three-dimensional parametric geometric model according to the functional requirements of the reduction gearbox.

[0010] S2: Conduct finite element mesh division on the geometric model, and optimize the material distribution of the geometric model based on the topology optimization algorithm.

[0011] S3: Parameterize the topology optimization results into geometric features, use a random generation tool to generate several initial variable sets, and use the genetic algorithm to output the optimal variable set.

[0012] S4: Reconstruct the geometric model according to the topology optimization results and the genetic algorithm results. After performing dynamic-static simulation on the reconstructed geometric model, evaluate whether the performance of the reconstructed geometric model meets the standards.

[0013] S5: If not up to standard, optimize the genetic algorithm parameters according to the evaluation results and then loop to reconstruct the geometric model until the performance of the reconstructed geometric model meets the standards.

[0014] In a preferred embodiment, reconstructing the geometric model according to the topology optimization results and the genetic algorithm results includes the following steps:

[0015] Generate a preliminary geometric contour from the density field generated by topology optimization through isosurface extraction technology, and retain the high-density material distribution in the key area through the threshold screening method.

[0016] Use a parametric geometry engine to convert the density field into manufacturable geometric features, including rib reinforcements, hole distributions, and wall thickness gradients.

[0017] Map the optimal variable set output by the genetic algorithm into the parametric geometric model, encode the distribution pattern of the holes using a parameter matrix, and meet the minimum hole diameter constraint of the casting process through a variable screening mechanism.

[0018] Import the optimized wall thickness gradient function into 3D software to generate a parametric shell structure, convert the discrete optimization results into a continuous geometric body based on the Voronoi diagram or mesh merging algorithm, eliminate irregular structures, and apply the curvature continuity algorithm to optimize the geometric boundary of the geometric model.

[0019] In a preferred embodiment, after performing dynamic-static simulation on the reconstructed geometric model, evaluating whether the performance of the reconstructed geometric model meets the standards includes the following steps:

[0020] Obtain the stress distribution, modal frequency, and fatigue life through dynamic-static simulation, and extract the parameters in the simulation results.

[0021] Quantify and normalize the simulation parameters, and perform weighted calculation on the processed simulation parameters to obtain the performance score of the reconstructed geometric model.

[0022] Compare the obtained performance score with a preset performance threshold. If the performance score is less than or equal to the performance threshold, it is analyzed that the performance of the reconstructed geometric model meets the standard. If the performance score is greater than the performance threshold, it is analyzed that the performance of the reconstructed geometric model does not meet the standard.

[0023] In a preferred embodiment, if it does not meet the standard, after optimizing the genetic algorithm parameters according to the evaluation results, the geometric model is cyclically reconstructed until it is analyzed that the performance of the reconstructed geometric model meets the standard, including the following steps:

[0024] If it is analyzed that the performance of the reconstructed geometric model does not meet the standard, dynamically correct the fitness threshold in the genetic algorithm according to the obtained performance score. The expression is: Zsnew = Zsold(1 + P), where Zsnew is the corrected fitness threshold, Zsold is the preset fitness threshold, and P is the performance score;

[0025] After inputting the corrected fitness threshold into the genetic algorithm, re-perform the global optimization of the variable set until it is analyzed that the performance of the geometric model meets the standard for any time, then judge that the condition is satisfied and output the final geometric model.

[0026] In a preferred embodiment, parameterize the topology optimization result into geometric features, including the following steps:

[0027] According to the high-density area distribution, define the axis coordinates, width, and height gradient of the rib, describe the weight reduction area with the hole center coordinates, radius, and distribution density matrix, fit the thickness change law through radial basis function or polynomial, and embed the manufacturing constraints through variable boundaries or penalty functions.

[0028] In a preferred embodiment, use a random generation tool to generate several initial variable sets, and use the genetic algorithm to output the optimal variable set, including the following steps:

[0029] After introducing the historical design database using Latin hypercube sampling, output several initial variable sets;

[0030] Calculate the fitness value of each initial variable set through the fitness function, select some initial variable sets for randomization operation based on the fitness value, and output the variable sets after the randomization operation as the alternative set;

[0031] Repeat the fitness value calculation, selection, and randomization operations for all initial variable sets in the alternative set;

[0032] When the convergence condition is met, output all alternative sets, and select the variable with the largest fitness value in all alternative sets as the optimal variable set for output.

[0033] In a preferred embodiment, the fitness value of each initial variable set is calculated through a fitness function, and based on the fitness value, the roulette wheel method is used to select some initial variable sets for randomization operations, including the following steps:

[0034] Calculate the selection probability of the initial variable sets according to the fitness values of all initial variable sets, and the expression is: In the formula, P(X i ) is the selection probability of the i-th initial variable set, f(X i ) is the fitness value of the i-th initial variable set. Map the selection probability of the initial variable sets to the sector areas of the virtual roulette wheel. The larger the selection probability, the larger the corresponding sector area. Drive the virtual roulette wheel to rotate. When it stops, select the initial variable set corresponding to the sector area pointed by the pointer. When the number of selected initial variable sets is equal to the quantity threshold, perform crossover operations and mutation operations on all the selected initial variable sets.

[0035] In a preferred embodiment, perform finite element mesh division on the geometric model and optimize the material distribution of the geometric model based on the topology optimization algorithm, including the following steps:

[0036] Use tetrahedral or hexahedral elements to divide the main structure of the geometric model, and balance the calculation accuracy and efficiency through adaptive mesh technology;

[0037] Implement mesh refinement processing on the stress concentration areas and set up boundary layer meshes to capture the dynamic load effects;

[0038] Check the mesh quality through the Jacobian ratio and element distortion degree, and take minimizing the strain energy and maximizing the lightweight ratio as the optimization objectives;

[0039] Set the non-critical areas as optimizable areas and the critical areas as non-optimizable areas. Input multi-condition loads and boundary conditions, describe the material distribution through the material density field, and combine the Heaviside projection filter to eliminate the checkerboard phenomenon.

[0040] In a preferred embodiment, after normalizing the obtained strain energy and lightweight ratio, map the value ranges of the strain energy and lightweight ratio to between [0, 1]. Subtract the strain energy from the normalized lightweight ratio to obtain the optimization coefficient. Compare the optimization coefficient of the non-critical area with the optimization threshold. If the optimization coefficient of the non-critical area is less than the optimization threshold, analyze that the non-critical area still needs to be optimized. If the variation coefficient of the non-critical area is greater than or equal to the optimization threshold, analyze that the non-critical area does not need to be optimized.

[0041] In a preferred embodiment, based on the transmission ratio, torque, and rotational speed parameters, the processing end automatically establishes a three-dimensional parametric geometric model through parametric design software and defines the number of teeth and module of the gear and the wall thickness of the box body;

[0042] Integrate the dynamic load spectrum in the database. The dynamic load spectrum includes gear meshing impact force and bearing alternating load;

[0043] Integrate the static load spectrum in the database. The static load spectrum includes installation reaction force, and call the data of alloy steel density, elastic modulus, and yield strength to support subsequent mechanical simulation;

[0044] Use the HyperMesh tool to repair the geometric defects of the geometric model. The geometric defects include gaps and overlapping defects.

[0045] In the above technical solution, the technical effects and advantages provided by the present invention are:

[0046] In the present invention, the processing end establishes a three-dimensional parametric geometric model according to the functional requirements of the reducer gearbox, performs finite element mesh division on the geometric model, optimizes the material distribution of the geometric model based on the topology optimization algorithm, parameterizes the topology optimization result into geometric features, uses a random generation tool to generate several initial variable sets, uses the genetic algorithm to output the optimal variable set, reconstructs the geometric model according to the topology optimization result and the genetic algorithm result, performs dynamic-static mechanical simulation on the reconstructed geometric model, evaluates whether the performance of the reconstructed geometric model meets the standard. If not, optimize the genetic algorithm parameters according to the evaluation result and loop to reconstruct the geometric model until the performance of the reconstructed geometric model meets the standard. After designing the system topology optimization, perform intelligent optimization on the local high-stress area through finite element analysis to ensure the balance of strength and stiffness of the structure while meeting the lightweight requirements. Brief Description of the Drawings

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings.

[0048] Figure 1 It is the method flow chart of the present invention.

[0049] Figure 2 It is the mind map of the present invention. Detailed Embodiments

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] Please refer to Figure 1 and Figure 2 As shown, the lightweight design method of the reducer gearbox based on topology optimization in this embodiment includes the following steps:

[0052] S1: The processing end establishes a three-dimensional parametric geometric model according to the functional requirements of the reducer gearbox;

[0053] S2: Perform finite element mesh division on the geometric model, and optimize the material distribution of the geometric model based on the topology optimization algorithm;

[0054] S3: Parameterize the topology optimization results into geometric features, generate several initial variable sets using a random generation tool, and output the optimal variable set using a genetic algorithm;

[0055] S4: Reconstruct the geometric model according to the topology optimization results and the genetic algorithm results. After performing dynamic-static simulation on the reconstructed geometric model, evaluate whether the performance of the reconstructed geometric model meets the standards;

[0056] S5: If not, optimize the genetic algorithm parameters according to the evaluation results and loop to reconstruct the geometric model until the performance of the reconstructed geometric model meets the standards.

[0057] The processing end establishes a three-dimensional parametric geometric model according to the functional requirements of the reducer gearbox (such as transmission ratio, torque, speed, etc.), and obtains the load conditions (static / dynamic load, gear meshing force, bearing support reaction force, etc.), constraint conditions (installation fixing surface, symmetry constraint), and material properties (such as alloy steel density, elastic modulus, yield strength, etc.) through manual input or database. The steps include:

[0058] The processing end establishes a three-dimensional parametric geometric model based on core parameters such as transmission ratio, torque, and speed. The design system automatically defines key variables such as the number of teeth and module of the gear, and the wall thickness of the box body through parametric design software (such as SolidWorks or CATIA).

[0059] The process of establishing a three-dimensional parametric geometric model based on core parameters such as transmission ratio, torque, and speed can be divided into the following steps, and automated design is realized in combination with parametric design software (such as SolidWorks, CATIA):

[0060] Define input variables: core parameters such as transmission ratio (F), input torque (T), rotational speed (n), power (P), etc., and set their value ranges and constraint conditions. Connect with the software parameter interface through Excel or design table to achieve dynamic parameter transfer (such as Design-Table of CATIA or Equation-driven of SolidWorks).

[0061] Calculate the number of teeth (z), module (m), and pressure angle (α) according to the torque and transmission ratio. The expressions are as follows: In the formula, where K is the load factor, ψd is the tooth width coefficient, [σ H is the allowable contact stress. Calculate the wall thickness based on the torque and material strength. The expression is: Where D is the diameter of the box body, τallow is the allowable shear stress, and A is the section modulus.

[0062] Create reference geometries (such as gear pitch circles, box body contours) in the software, define tooth profile curves (driven by involute equations), bearing seat positioning and other features through parametric sketches, and use macro commands or API scripts (such as CATIA-VBA, SolidWorks macro) to batch generate repetitive structures (such as stiffeners, heat dissipation holes).

[0063] Establish logical relationships between parameters (such as the inverse proportional constraint between the number of teeth and the module) to ensure that the model is automatically updated when the core parameters are modified. Example: After adjusting the input transmission ratio, the tooth number combination of the gear pair is automatically matched and updated. Set process limit conditions: minimum tooth root fillet radius of the gear (≥0.5mm), minimum wall thickness of the box body for casting (≥3mm), draft angle (≥3°), etc.

[0064] Integrate the dynamic load spectra (such as gear meshing impact force, bearing alternating load) and static loads (such as installation reaction force) in the database, and call data such as the density of alloy steel (7.85g / cm 3 ), elastic modulus (210GPa), yield strength (≥785MPa), etc. to support subsequent mechanical simulations. Use the HyperMesh tool to repair geometric defects such as model gaps and overlaps.

[0065] Repair geometric defects such as model gaps and overlaps in HyperMesh mainly through geometric cleaning tools. The following is an example of the step-by-step operation process and the corresponding Tcl script code:

[0066] I. Model Import and Defect Detection

[0067] # Import geometric model (example in STEP format) hm_importmodel "D: / model.stp" 1 # Activate topological color display mode and check free edges (red) and duplicate faces (yellow) *createmark - surfaces 1 all *visualization autotopologycolor 1 1.

[0068] II. Repair gaps (GapRepair)

[0069] # Set tolerance (adjust according to model size, usually 0.1 - 1mm) settol 0.5 # Merge free edges (automatically repair small gaps) hm_createmark edges 1 "byconfig" free *edgeedit checkedgeconnectivity 1 $tol 1 1 *edgeedit edgeequivalence 1 $tol 1 # Manually repair large gaps (select edges to be stitched) hm_createmark edges 1 "byray" hm_createmark edges 2 "byray" *edgeedit edgereplace 1 2 $tol.

[0070] III. Delete duplicate faces (DuplicateSurfaces)

[0071] # Automatically find and delete duplicate faces hm_createmark surfaces 1 all *defeature cleansurfaces 1 $tol 1 1 # Manually delete remaining duplicate faces hm_createmark surfaces 1 "bycolor" yellow *deletemarksurfaces 1.

[0072] IV. Geometric simplification (FeatureRemoval)

[0073] # Delete small holes (diameter ≤ _createmarksurfs 1 all *defeature pinholes 1 3 1 1 # Delete chamfers (radius ≤ 2mm) hm_createmark edges 1 all *defeature edgefillets 1 2 1 1 # Suppress short edges (length ≤ 1mm) hm_createmark edges 1 "bylength" 0 1 *edgeedit edgesuppress 1 $tol.

[0074] Instructions for script execution:

[0075] Parameter adjustment: The tolerance value (tol variable) and the feature size threshold need to be modified according to the actual size of the model;

[0076] Interactive operation: For some manual selection operations (such as hm_createmark - edges1 "byray"), the target edges need to be box - selected in the GUI;

[0077] Batch processing mode: It can be automated by executing hmbatch - tcl - script.tcl through the command line.

[0078] Perform finite - element mesh generation on the geometric model to ensure mesh refinement in key areas (gear meshing area, bearing housing), and optimize the material distribution of the geometric model based on the topology optimization algorithm, including the following steps:

[0079] Use tetrahedral or hexahedral elements to divide the main structure, balance the calculation accuracy and efficiency through adaptive mesh technology, implement mesh refinement in stress - concentrated areas such as the gear meshing area and the root of the bearing housing, ensure that the element size is 1 / 3 - 1 / 5 of other areas, and set up boundary - layer meshes to capture dynamic load effects.

[0080] The following is the implementation plan for mesh generation and adaptive technology based on finite - element analysis. Combining the characteristics of tetrahedral / hexahedral elements and dynamic load requirements, the key operations are described step by step:

[0081] Complex geometric regions (such as gear tooth root fillets): Preferentially use second - order tetrahedral elements, which can automatically adapt to irregular surfaces and can improve the accuracy by 56 through adaptive refinement.

[0082] Regular geometric regions (such as shaft - like components): Select first - order hexahedral elements and utilize their high calculation efficiency advantage to reduce the overall node scale by 17.

[0083] Hybrid - element strategy: In geometric transition regions (such as the connection between the bearing housing and the shaft), use pyramid elements or prism elements as transitions to avoid stress distortion caused by mesh discontinuity.

[0084] In stress - concentrated areas such as the gear meshing area and the root of the bearing housing, set the initial element size to 1 / 3 - 1 / 5 of the global size, and dynamically refine it through iterative calculations until the difference in stress results between two adjacent times is < 3%. Example code (ANSYS APDL):

[0085] ESEL,S,TYPE,,SOLID187! Select second - order tetrahedral elements ADAPT,5,0.03! Maximum refinement 5 times, convergence tolerance 3%.

[0086] Perform a second-order elevation of the hexahedron elements to improve the accuracy of the shape functions, reduce the number of refinements, arrange 3-5 layers of boundary layer meshes along the normal direction of the tooth surface, with the element aspect ratio ≤ 5, capture the contact stress gradient, use the swept mesh technique to generate the hexahedron boundary layer, and avoid low-quality elements (such as using the SolidMap function of HyperMesh). Divide the fillet region into ≥ 4 layers of elements to avoid stress underestimation caused by low-order tetrahedrons (comparison: the accuracy of 4 layers of second-order tetrahedrons ≈ 12 layers of first-order hexahedrons).

[0087] In the dynamic contact areas such as the meshing surface of the gear pair and the bearing raceway, set 3 layers of inflation layer meshes with a thickness of 10%-20% of the characteristic length to capture the transient contact pressure wave. Example parameters (Fluent-Meshing): InflationLayer: 3 layers, GrowthRate = 1.2, TotalThickness = 0.2 mm.

[0088] For the surfaces affected by fluid loads (such as the gearbox housing), use prism layer meshes to reduce the vortex dissipation error. The height of the first layer of the boundary layer satisfies y+ ≈ 1. Displacement error: the relative change in the global displacement < 1%. Stress convergence: the difference in the maximum Mises stress between two adjacent times < 5%. Use coarse meshes + low-order elements for non-critical areas (such as gear spokes) to reduce the computational amount, and use parallel computing technology to accelerate the adaptive iteration process (such as Domain-Parallelization in Abaqus). The summary table of key parameters is shown in Table 1:

[0089] Table 1 Summary Table of Key Parameters

[0090] Region type Recommended cell type Cell size ratio Adaptive method Boundary layer requirement Gear meshing area Second-order tetrahedron 1 / 5 H+P adaptivity 3-layer inflation layer Root of bearing seat First-order hexahedron 1 / 4 H adaptivity No special requirement Dynamic contact surface Second-order hexahedron 1 / 3 Fixed encryption Prismatic layer mesh Non-critical area First-order tetrahedron / hexahedron 1 None None

[0091] Implementation tools include:

[0092] Preprocessing: HyperMesh (complex geometry cutting), ANSA (boundary layer generation).

[0093] Solver: Abaqus (contact non-linearity), ANSYS Mechanical (H-adaptivity).

[0094] Verification tools: nCode (fatigue hot spot identification), ParaView (stress contour comparison).

[0095] Check the mesh quality through the Jacobian Ratio and element distortion degree to avoid calculation errors caused by low-quality meshes. With the optimization goals of minimizing strain energy (maximizing stiffness) and maximizing the lightweight ratio (volume constraint), set non-critical areas (such as non-load-bearing panels) as optimizable areas, and retain non-optimizable areas such as mounting surfaces and bearing holes. Input multi-condition loads (static torque, dynamic meshing impact force, bearing alternating load) and boundary conditions (fixed surface constraint, symmetry constraint). Describe the material distribution through the material density field, and combine the Heaviside projection filter to eliminate the checkerboard phenomenon.

[0096] To check the mesh quality through the Jacobian Ratio and element distortion degree and achieve the goals of structural lightweight and stiffness optimization, which is used to measure the deformation degree of mesh elements. The calculation formula is: In the formula, Jacobian Ratio is the Jacobian ratio, J is the Jacobian determinant, and the ideal value is 1, indicating no deformation; if it is close to 0 or negative, the mesh quality is poor.

[0097] Evaluate the distortion by the degree of deviation of the element angle from the ideal value. The calculation formula is:

[0098] In the formula, Skewness is the degree of angle deviation, θmax is the maximum angle of the element, θmin is the minimum angle of the element, and θideal is the ideal angle of the element. The greater the degree of angle deviation, the more serious the distortion of the element angle.

[0099] After normalizing the obtained strain energy and lightweight ratio, map the value ranges of the strain energy and lightweight ratio to between [0,1]. Subtract the strain energy from the normalized lightweight ratio to obtain the optimization coefficient. The smaller the optimization coefficient, the less qualified the optimization of the non-critical area. Compare the optimization coefficient of the non-critical area with the optimization threshold. If the optimization coefficient of the non-critical area is less than the optimization threshold, analyze that the non-critical area still needs to be optimized. If the variation coefficient of the non-critical area is greater than or equal to the optimization threshold, analyze that the non-critical area does not need to be optimized.

[0100] The calculation expression of the strain energy U is: In the formula, E is the elastic modulus, V is the volume, and □ is the strain. Obtain the weight difference by subtracting the optimized weight from the initial weight, and divide the weight difference by the initial weight to obtain the lightweight ratio.

[0101] Parameterize the topology optimization results into geometric features, including the following steps:

[0102] Convert the material density field of the topology optimization into geometric parameters:

[0103] According to the high-density area distribution, define the axis coordinates, width, and height gradient of the rib (such as using B-spline curves to control the path), describe the weight reduction area with the hole center coordinates, radius, and distribution density matrix, fit the thickness variation law through radial basis functions (RBF) or polynomials, and embed manufacturing constraints (such as minimum wall thickness ≥ 3mm, hole spacing ≥ 2 times the hole diameter), which is achieved through variable boundaries or penalty functions. The specific code example is as follows:

[0104] # Example: Optimization process based on scipy

[0105] from scipy.optimize import minimize

[0106] def objective(x):

[0107] # x contains parameters such as hole positions, radii, and RBF weights

[0108] T = RBF_eval(x) # Calculate the thickness field

[0109] mass = integrate_density(D, T) # Calculate the mass

[0110] penalty = collision_penalty(x) # Hole spacing penalty term

[0111] return -mass + penalty

[0112] cons = ({'type': 'ineq', 'fun': lambda x:

[0113] T_min_constraint(x)})

[0114] result = minimize(objective, x0, method='SLSQP', constraints=cons)。

[0115] Use a random generation tool to generate several initial variable sets, and use a genetic algorithm to output the optimal variable set, including the following steps:

[0116] Use Latin hypercube sampling (LHS) to ensure uniform coverage of the design space, avoid local optima, introduce several initial variable sets from the historical design database (such as gearbox parameters), and improve the convergence efficiency.

[0117] Generate the initial variable set through Latin hypercube sampling (LHS), and introduce the historical design database to improve the convergence efficiency. The specific scheme is as follows:

[0118] Set variable range constraints, including the upper and lower limits of parameters such as the wall thickness of the gearbox, hole size, and rib position. Use the LHS method to uniformly sample in the high-dimensional design space to avoid falling into local optima, generate N groups of initial variables, where each group of variables represents a set of design solutions. Obtain the historical design parameters of similar gearboxes and add them as an additional variable set to the initial population to improve the optimization efficiency. Combine the LHS sampling and the historical variable set to construct the final initial variable set, and the content of each initial variable set includes the wall thickness of the gearbox, hole size, and rib position.

[0119] Calculate the fitness value of each initial variable set through the fitness function. Based on the fitness value, use the roulette wheel method to select some initial variable sets for randomization operations (including crossover operations and mutation operations), and output the variable sets after the randomization operations as the alternative set. Repeat the calculation of the fitness value, selection, and randomization operations for all initial variable sets in the alternative set. When the convergence condition is met, output all alternative sets and select the variable set with the largest fitness value among all alternative sets as the optimal variable set for output.

[0120] Repeat the calculation of the fitness value, selection, and randomization operations for all initial variable sets in the alternative set. When there is an initial variable set with a fitness value greater than or equal to the fitness threshold in the alternative set output in any iteration, it is judged that the convergence condition is met.

[0121] The calculation expression of the fitness function is:

[0122] In the formula, f(X i ) is the fitness value of the i-th initial variable set, Mi is the weight of the gearbox produced by the i-th initial variable set, Si is the stiffness of the gearbox produced by the i-th initial variable set, Mmax is the maximum weight, Mmin is the minimum weight, Smax is the maximum stiffness, Smin is the minimum stiffness, and w1, w2 are weight coefficients;

[0123] Calculate the selection probability of the initial variable set based on the fitness values of all initial variable sets. The expression is: In the formula, P(X i ) is the selection probability of the i-th initial variable set. Map the selection probability of the initial variable set to the sector area of the virtual roulette wheel. The larger the selection probability, the larger the corresponding sector area. Drive the virtual roulette wheel to rotate. When it stops, select the initial variable set corresponding to the sector area pointed by the pointer. When the number of selected initial variable sets is equal to the number threshold, perform crossover operations and mutation operations on all the selected initial variable sets.

[0124] Randomly select two variable sets from the selected variable set, exchange part of the variable values according to a certain crossover probability to generate a new variable set (crossover operation), and randomly change part of the variable values with a certain probability to prevent convergence to a local optimum (mutation operation).

[0125] Reconstruct the geometric model based on the topology optimization results and the genetic algorithm results, including the following steps:

[0126] Generate a preliminary geometric contour from the density field generated by topology optimization (such as the 0-1 distribution generated by the SIMP method) through isosurface extraction technology (such as the Marching-Cubes algorithm). Key regions (such as the gear meshing area) need to be retained with a high-density material distribution through threshold screening (such as cells with a density ≥ 0.5).

[0127] Generate a preliminary geometric contour using the density field generated by topology optimization (such as the 0-1 distribution generated by the SIMP method), through isosurface extraction technology (such as the Marching-Cubes algorithm), and perform threshold screening on key regions (such as the gear meshing area) (such as only retaining cells with a density ≥ 0.5), and finally generate an optimized geometric model. The specific scheme is as follows:

[0128] Generate the unit density distribution of the design area based on the topology optimization algorithm (such as the SIMP method):

[0129] The density variable ρ of the SIMP method takes values in the range of 0-1:

[0130] ρ = 0 indicates no material (removed area), ρ = 1 indicates solid material (retained area), and ρ between 0 and 1 indicates a transition area (requiring further processing). The result is a three-dimensional density field matrix, such as: In the formula, ρijk represents the density value of the grid cell (i, j, k).

[0131] Set a threshold ρthresh, for example, ρthresh = 0.5, and only retain the cells with a density ρ greater than or equal to 0.5 as part of the optimized structure. A higher threshold can be set for key regions (such as the gear meshing area). For example, ρ greater than or equal to 0.7 to ensure the structural strength.

[0132] Store all density field data as a three-dimensional grid. Each grid cell has spatial coordinates and corresponding density values. Input: topology optimization density field and isosurface threshold. Output: a smooth three-dimensional geometric contour of the isosurface.

[0133] Use Laplacian smoothing to reduce surface roughness and improve manufacturing feasibility:

[0134] v' i = v i + λ∑ j∈N(i) (vj -v i ) where v' i is the position of vertex i after smoothing, v i is the position of vertex i before smoothing, vj is the position of vertex j, N(i) is the set of neighboring vertices, and λ is the smoothing coefficient (usually taken as 0.1 - 0.3). The processed STL, OBJ, or STEP file is used for subsequent parametric modeling.

[0135] Convert the density field into manufacturable geometric features using a parametric geometry engine (such as NURBS curves / surfaces), including:

[0136] Reinforcing ribs: Generate a parametric rib layout according to the stress field direction and define a thickness gradient 3;

[0137] Hole distribution: Describe the position and size of the weight-reducing holes through a honeycomb parameter matrix 1;

[0138] Wall thickness gradient: Use a gradient function to control the thickness change from critical areas to non-critical areas.

[0139] Map the optimal variable set output by the genetic algorithm (such as rib spacing, hole diameter, etc.) to the parametric geometric model. For example:

[0140] Use a parameter matrix to encode the distribution pattern of the holes, ensure the minimum hole diameter constraint for the casting process through a variable screening mechanism, import the optimized wall thickness gradient function into 3D software to generate a parametric shell structure, and based on the Voronoi diagram or mesh merging algorithm, convert the discrete optimization results into a continuous geometric body, eliminate irregular structures (such as overhanging surfaces), and apply a curvature continuity algorithm (such as B-spline fitting) to optimize the manufacturability of the geometric boundary.

[0141] Encode the hole distribution pattern through a parameter matrix, combine the variable screening mechanism to ensure the minimum hole diameter constraint for the casting process, and import the optimized wall thickness gradient function into 3D software to generate a parametric shell structure. Subsequently, based on the Voronoi diagram or mesh merging algorithm, convert the discrete optimization results into a continuous geometric body, eliminate irregular structures (such as overhanging surfaces). Finally, apply a curvature continuity algorithm (such as B-spline fitting) to optimize the geometric boundary and improve the manufacturability.

[0142] Set the grid distribution of the holes and represent it using a binary encoding matrix:

[0143] 1 represents the perforated area (retaining material).

[0144] 0 represents the non-perforated area (removing material).

[0145] Example: Among them, M(i,j) represents the hole state at the (i,j) position. Set the minimum aperture constraint (for example, the aperture in the casting process is required to be ≥3mm), traverse the parameter matrix M, and screen and remove the openings that do not meet the constraint.

[0146] Set the wall thickness gradient function T(x,y,z) to change with the force:

[0147] T(x,y,z) = T min +(T max -T min )·f(σ), where T min , T max are the minimum and maximum wall thicknesses, f(σ) represents the stress field distribution, ensure that the wall thickness is thickened in the high stress area, assign T(x,y,z) to the model, and make the hole wall thickness meet the optimization requirements.

[0148] Use the Voronoi diagram to divide the optimization area: Take the center point of the hole as the seed point, and form a smooth hole boundary through Voronoi subdivision. Detect the overhanging surface (i.e., the unsupported isolated surface) in the optimized structure, make it continuous through local mesh reconstruction, calculate the consistency of the normal vectors of adjacent triangular meshes, and adjust the meshes with inconsistent normals to smooth the boundary.

[0149] Adopt N-order B-spline to fit the hole boundary: where P(u) is the fitting curve, Ni,p(u) is the B-spline basis function, W is the number of hole center points, Pi is the control point, and use G2 curvature continuity to ensure the smoothness of the boundary and avoid sharp corners affecting manufacturing.

[0150] After performing dynamic-static simulation on the reconstructed geometric model, evaluate whether the performance of the reconstructed geometric model meets the standards, including the following steps:

[0151] Obtain key parameters such as stress distribution, modal frequency, and fatigue life through dynamic-static simulation, extract the key parameters in the simulation results (such as maximum stress, deformation, natural frequency, mass, etc.), and compare them with the preset thresholds (such as yield strength, stiffness requirements, weight limit, etc.). If the stress exceeding standard area is concentrated in the gear meshing area, it is necessary to identify the insufficient material distribution in the topology optimization or the key constraints not captured by the genetic algorithm.

[0152] After quantifying and normalizing the simulation parameters, perform weighted calculation on the processed simulation parameters to obtain the performance score of the reconstructed geometric model. The larger the performance score, the less the reconstructed geometric model meets the standards. Compare the obtained performance score with the preset performance threshold. If the performance score is less than or equal to the performance threshold, analyze that the performance of the reconstructed geometric model meets the standards. If the performance score is greater than the performance threshold, analyze that the performance of the reconstructed geometric model does not meet the standards.

[0153] Through dynamic-static simulation, key parameters such as stress distribution, modal frequency, fatigue life, etc. are obtained, and the maximum stress, deformation, natural frequency, mass and other data in the simulation results are extracted and compared with the preset thresholds (such as yield strength, stiffness requirements, and weight limit). If it is found that the stress-exceeding area is concentrated in the gear meshing area, it is necessary to analyze the possibility that the topology optimization material distribution is insufficient or the genetic algorithm has not captured the key constraints.

[0154] Load conditions: static load (gear meshing force, bearing reaction force), dynamic load (impact, vibration).

[0155] Boundary conditions: fixed constraints (mounting surface), symmetry constraints (symmetric geometry).

[0156] Material parameters: density, elastic modulus, yield strength, etc.

[0157] Get simulation data: maximum equivalent stress (measure of strength), maximum deformation (measure of stiffness), natural frequency (measure of vibration performance), fatigue life (measure of service life)).

[0158] If the stress-exceeding area is concentrated in the gear meshing area: analyze whether the topology optimization material distribution is reasonable (local material shortage), analyze whether the genetic algorithm captures the key constraints (constraints are lost during crossover and mutation), set the performance parameter vector G: G = [σmax, δmax, fn, Nf], where σmax is the maximum equivalent stress, δmax is the maximum deformation, fn is the natural frequency, and Nf is the fatigue life. The performance parameter vector is weighted and calculated to obtain the performance score, and the expression is:

[0159] SD = β1·σmax+β2·δmax-β3·fn-β4·Nf, where SD is the performance score, and β1, β2, β3, and β4 are weight coefficients.

[0160] If the standard is not met, the genetic algorithm parameters are optimized according to the evaluation results and the geometric model is reconstructed cyclically until the performance of the reconstructed geometric model meets the standard, including the following steps:

[0161] If the performance of the reconstructed geometric model does not meet the standard, it indicates that the preset fitness threshold is small (that is, the fitness requirement for the variable set is small). Therefore, the fitness threshold in the genetic algorithm is dynamically corrected according to the obtained performance score. The expression is: Zsnew = Zsold (1 + P), where Zsnew is the corrected fitness threshold, Zsold is the preset fitness threshold, and P is the performance score.

[0162] After the modified fitness threshold is input into the genetic algorithm, the global optimization process of the variable set is performed again until the performance of the geometric model reconstructed after any analysis reaches the standard, the conditions are judged to be met, and the final geometric model is output.

[0163] In practical applications, it is possible that the performance of the geometric model after several analysis and reconstructions does not meet the standards, resulting in the algorithm being unable to converge and the design system entering an infinite loop. Therefore, when the number of iterations is equal to the threshold number of times, and the fitness value is still less than the corrected fitness threshold or the performance of the geometric model after analysis and reconstruction still does not meet the standards, the design system jumps out of the loop and sends a warning signal to the administrator for prompting.

[0164] In this application, the processing end establishes a three-dimensional parametric geometric model according to the functional requirements of the reducer gearbox, performs finite element mesh division on the geometric model, optimizes the material distribution of the geometric model based on the topology optimization algorithm, parameterizes the topology optimization results into geometric features, uses a random generation tool to generate several initial variable sets, uses the genetic algorithm to output the optimal variable set, reconstructs the geometric model according to the topology optimization results and the genetic algorithm results, and after performing dynamic-static simulation on the reconstructed geometric model, evaluates whether the performance of the reconstructed geometric model meets the standards. If not, the genetic algorithm parameters are optimized according to the evaluation results and the geometric model is cyclically reconstructed until the performance of the reconstructed geometric model meets the standards. After the topology optimization of the design system, intelligent optimization is performed on the local high-stress area through finite element analysis to ensure the balance of the strength and stiffness of the structure while meeting the lightweight requirements.

[0165] The above formulas are all dimensionless and take their numerical calculations. The formula is a formula obtained by collecting a large amount of data for software simulation to approximate the real situation. The preset parameters in the formula are set by those skilled in the art according to the actual situation.

[0166] In the description of this specification, the descriptions referring to terms such as "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0167] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not elaborate on all the details, nor do they limit the present invention to only the specific implementation manners. Obviously, many modifications and variations can be made according to the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the present invention, so that those skilled in the art in the relevant technical field can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A lightweight design method for the reducer gearbox based on topology optimization, characterized in that: The design method comprises the following steps: S1: The processing end establishes a three-dimensional parameterized geometric model according to the functional requirements of the reducer gearbox; S2: Perform finite element meshing on the geometric model and optimize the material distribution of the geometric model based on the topology optimization algorithm; S3: Parameterize the topology optimization results into geometric features, use the random generation tool to generate several initial variable sets, and use the genetic algorithm to output the optimal variable set; S4: Reconstruct the geometric model based on the topology optimization results and the genetic algorithm results, perform static-dynamic simulation on the reconstructed geometric model, and evaluate whether the performance of the reconstructed geometric model meets the requirements; S5: If the standard is not met, the genetic algorithm parameters are optimized according to the evaluation results and the geometric model is reconstructed cyclically until the performance of the reconstructed geometric model meets the standard.

2. The lightweight design method of the reducer gearbox based on topology optimization according to claim 1, characterized in that: Reconstructing the geometric model based on the topology optimization results and the genetic algorithm results includes the following steps: The density field generated by topology optimization is used to generate a preliminary geometric outline through isosurface extraction technology, and the high-density material distribution is retained in the key area through the threshold screening method; Use a parametric geometry engine to convert density fields into manufacturable geometry features, including ribs, hole distribution, and wall thickness gradients; The optimal variable set output by the genetic algorithm is mapped into a parametric geometric model, and the distribution pattern of the holes is encoded using a parameter matrix. The minimum hole diameter constraint of the casting process is met through a variable screening mechanism. The optimized wall thickness gradient function is imported into the 3D software to generate a parametric shell structure. The discrete optimization results are converted into continuous geometric bodies based on the Voronoi diagram or mesh merging algorithm, the irregular structure is eliminated, and the curvature continuity algorithm is applied to optimize the geometric boundaries of the geometric model.

3. The lightweight design method of the reducer gearbox based on topology optimization according to claim 2, wherein: After the dynamic-static simulation of the reconstructed geometric model, the performance of the reconstructed geometric model is evaluated to see whether it meets the requirements, including the following steps: Obtain stress distribution, modal frequency and fatigue life through dynamic-static simulation, and extract parameters from simulation results; The simulation parameters are quantified and normalized, and the processed simulation parameters are weighted to obtain the performance score of the reconstructed geometric model; The obtained performance score is compared with the preset performance threshold. If the performance score is less than or equal to the performance threshold, the performance of the reconstructed geometric model after analysis is up to standard. If the performance score is greater than the performance threshold, the performance of the reconstructed geometric model after analysis is not up to standard.

4. The lightweight design method of the reducer gearbox based on topology optimization according to claim 3, characterized in that: If the standard is not met, the genetic algorithm parameters are optimized according to the evaluation results and the geometric model is reconstructed cyclically until the performance of the reconstructed geometric model meets the standard, including the following steps: If the performance of the reconstructed geometric model does not meet the standard, the fitness threshold in the genetic algorithm is dynamically corrected according to the obtained performance score. The expression is: Zsnew = Zsold (1 + P), where Zsnew is the corrected fitness threshold, Zsold is the preset fitness threshold, and P is the performance score; After the modified fitness threshold is input into the genetic algorithm, the global optimization process of the variable set is performed again until the performance of the geometric model reconstructed after any analysis reaches the standard, the conditions are judged to be met, and the final geometric model is output.

5. The lightweight design method of the reducer gearbox based on topology optimization according to claim 4, characterized in that: Parameterizing the topology optimization results into geometric features includes the following steps: According to the high-density area distribution, define the axis coordinates, width, and height gradient of the rib, describe the weight reduction area with the hole center coordinates, radius, and distribution density matrix, fit the thickness change law through radial basis functions or polynomials, and embed manufacturing constraints through variable boundaries or penalty functions.

6. The lightweight design method of the reducer gearbox based on topology optimization according to claim 5, characterized in that: Use a random generation tool to generate several initial variable sets, and use a genetic algorithm to output the optimal variable set, including the following steps: After introducing the historical design database using Latin hypercube sampling, output several initial variable sets; Calculate the fitness value of each initial variable set through the fitness function, select some initial variable sets for randomization operations based on the fitness value using the roulette wheel method, and output the variable sets after the randomization operation as the alternative set; Repeat the calculation, selection, and randomization operations of the fitness value for all initial variable sets in the alternative set; When the convergence condition is met, output all alternative sets, and select the variable with the largest fitness value in all alternative sets as the optimal variable set for output.

7. The lightweight design method of the reducer gearbox based on topological optimization according to claim 4, characterized in that: Calculate the fitness value of each initial variable set through the fitness function, and select some initial variable sets for randomization operations based on the fitness value using the roulette wheel method, including the following steps: Calculate the selection probability of the initial variable set based on the fitness values of all initial variable sets, and the expression is: In the formula, P(X i ) is the selection probability of the i-th initial variable set, f(X i ) is the fitness value of the i-th initial variable set. Map the selection probability of the initial variable set to the sector area of the virtual roulette. The larger the selection probability, the larger the corresponding sector area. Drive the virtual roulette to rotate. When it stops, select the initial variable set corresponding to the sector area pointed by the pointer. When the number of selected initial variable sets is equal to the quantity threshold, perform crossover operation and mutation operation on all the selected initial variable sets.

8. The lightweight design method of the reducer gearbox based on topology optimization according to claim 7, characterized in that: Perform finite element mesh division on the geometric model, and optimize the material distribution of the geometric model based on the topology optimization algorithm, including the following steps: Use tetrahedral or hexahedral elements to divide the main structure of the geometric model, and balance the calculation accuracy and efficiency through adaptive mesh technology; Implement mesh refinement for the stress concentration area and set up boundary layer meshes to capture the dynamic load effect; Check the mesh quality through the Jacobian ratio and element distortion degree, with the goal of minimizing the strain energy and maximizing the lightweight ratio; Set the non-critical area as the optimizable area and the critical area as the non-optimizable area, input multi-condition loads and boundary conditions, describe the material distribution through the material density field, and combine the Heaviside projection filter to eliminate the checkerboard phenomenon.

9. The lightweight design method of the reducer gearbox based on topological optimization according to claim 8, characterized in that: After normalizing the obtained strain energy and lightweight ratio, map the value ranges of the strain energy and lightweight ratio to between [0,1], subtract the strain energy from the normalized lightweight ratio to obtain the optimization coefficient, compare the optimization coefficient of the non-critical area with the optimization threshold. If the optimization coefficient of the non-critical area is less than the optimization threshold, analyze that the non-critical area still needs to be optimized. If the variation coefficient of the non-critical area is greater than or equal to the optimization threshold, analyze that the non-critical area does not need to be optimized.

10. The lightweight design method of the reducer gearbox based on topology optimization according to claim 9, characterized in that: The processing end automatically establishes a three-dimensional parametric geometric model through parametric design software based on the transmission ratio, torque, and rotational speed parameters, and defines the number of teeth and module of the gear and the wall thickness of the box body; Integrate the dynamic load spectrum in the database, and the dynamic load spectrum includes gear meshing impact force and bearing alternating load; Integrate the static load spectrum in the database, and the static load spectrum includes installation reaction force, and call the data of alloy steel density, elastic modulus, and yield strength to support subsequent mechanical simulations; Use the HyperMesh tool to repair the geometric defects of the geometric model, and the geometric defects include gaps and overlapping defects.

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