Lightweight optimization method and electronic device for fixed-axle-planetary combination speed reducer under multiple constraints

Abstract

This invention relates to the field of mechanical transmission design, and in particular to a lightweight optimization method and electronic device for a fixed-axis-planetary combined reducer under multiple constraints. This method targets a three-stage hybrid transmission configuration of fixed-axis-planetary-planetary, proposing a three-stage optimization process of "input-level candidate set construction – multi-objective algorithm optimization – parameter verification and adjustment" under constraints such as geometric compatibility, assembly conditions, transmission ratio accuracy, strength performance, and manufacturing process. First, an input-level fixed-axis gear parameter candidate set is constructed through exhaustive search and clustering. Then, with the objectives of minimizing the total system mass and maximizing the minimum contact and bending strength safety factors, a multi-objective optimization model is established, and multiple metaheuristic optimization algorithms are used in parallel to obtain the Pareto optimal solution set. Finally, after comprehensive performance evaluation and engineering correction, the optimal lightweight design scheme that meets the constraints is output, achieving a reduction in the mass of transmission components of approximately 11%.

Description

Technical Field

[0001] This invention relates to the field of lightweight design of mechanical transmission systems, and in particular to a lightweight optimization method for fixed-axis planetary combined reducers and its electronic equipment applicable to multiple constraints and multiple objectives. Background Technology

[0002] Planetary gearboxes, as core components, are widely used in heavy machinery, wind power, aerospace, and other critical equipment sectors. Their gears, planetary carriers, and housings account for the majority of the total weight of the equipment; therefore, lightweight design is crucial for reducing energy consumption and increasing power density. This is especially true for gearboxes like the JGR and GRP, which are assembled by separating the internal gear ring and housing. Even minor changes in the planetary gear train dimensions can directly cause interlocking adjustments to the supporting structures such as the planetary carrier and housing. Therefore, achieving lightweighting of the transmission system itself is a prerequisite and key to overall lightweighting.

[0003] Currently, research on the optimization design of single-type (pure fixed-axis or pure planetary) transmission systems is relatively mature. However, for hybrid configuration reducers that combine the advantages of fixed-axis and planetary transmissions, the design optimization problem becomes exceptionally complex, and existing research faces the following significant technical bottlenecks: (1) System-level modeling and coupled optimization challenges: The fixed-axis-planetary hybrid transmission system includes fixed-axis gear trains and planetary gear trains with vastly different kinematic descriptions. The transmission ratio distribution, parameter transfer, and motion coordination between the two at the system level result in complex and highly coupled constraint conditions. Any change in a single-stage design parameter will trigger a systemic cascading effect through the transmission chain, affecting the load, geometry, and strength characteristics of other stages. This strong coupling makes the traditional strategy of decomposing multi-stage transmissions into several single stages for independent optimization difficult to implement, and it is easy to fall into local optima, making it impossible to achieve global performance optimization at the system level.

[0004] (2) The inherent conflict between lightweight design and structural strength: Lightweight design pursues the minimum structural mass and tends to use gear parameters with small module and narrow tooth width; while satisfying the safety factor of tooth surface contact and tooth root bending strength requires the use of larger module and tooth width to ensure load-bearing capacity. This essential contradiction is further amplified in hybrid configurations because the fixed-axis and planetary-axis stages have different weights in their influence on system performance, and the parameter adjustment exhibits nonlinear characteristics, making it difficult for the safety factor to simultaneously approach the constraint threshold, which greatly inhibits the potential for lightweight design while ensuring reliability.

[0005] (3) The feasible region under multiple constraints is extremely sparse: The design of planetary gear trains must simultaneously satisfy a series of strict geometric compatibility constraints such as adjacency conditions, assembly conditions, concentricity conditions, and overlap requirements. These constraints are interconnected and mutually restrictive, forming an extremely complex nonlinear constraint system. In addition, the center distance limit and the discreteness of the standard module series together result in an extremely limited combination of parameters that can satisfy all conditions. The feasible region of the design exhibits a highly sparse and discontinuous "island" distribution characteristic, which makes the search efficiency of conventional optimization algorithms extremely low.

[0006] (4) Challenges in Adaptability of Mixed Variable Models and Algorithms: The optimization model of a gear transmission system is essentially a high-dimensional mixed variable problem, which includes discrete variables (module), integer variables (number of teeth, number of planetary gears), and continuous variables (displacement coefficient, tooth width coefficient). The heterogeneity of variable types renders traditional mathematical programming methods, which heavily rely on gradient information, ineffective. Many modern heuristic algorithms also generally suffer from problems such as mismatched search mechanisms, premature convergence, and low computational efficiency when dealing with such high-dimensional, mixed variable problems.

[0007] In summary, existing technologies lack systematic optimization methods that can effectively address the challenges posed by the strong coupling, inherent conflict of objectives, sparse feasible domain, and mixed design variables in fixed-axis-planetary hybrid gearbox configurations. Therefore, developing a lightweight multi-objective optimization method for fixed-axis-planetary combined gearboxes under multiple constraints has become a critical technical problem urgently needing to be solved in this field. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-objective optimization method and electronic device for lightweighting fixed-axis-planetary combined reducers under multiple constraints. This method systematically solves the technical problems faced by the lightweight design of fixed-axis and planetary hybrid transmission configurations, such as complex system-level coupling modeling, inherent conflict between lightweighting objectives and strength constraints, sparse feasible domains under multiple geometric and assembly constraints, and difficulty in convergence of optimization algorithms due to mixed variables. This enables deep lightweighting of the reducer transmission system while satisfying all engineering constraints.

[0009] The technical solution of this invention is: a multi-objective optimization method for lightweighting a fixed-axis-planetary combined reducer under multiple constraints, comprising the following steps: S1: Parameter definition and constraint modeling: Establish a comprehensive mathematical model of the input stage fixed-axis gear system and the first and second stage planetary gear systems, and determine design variables such as module, number of teeth, displacement coefficient, and face width coefficient; the constraints include transmission ratio constraints, geometric compatibility constraints, contact strength safety factor constraints, bending strength safety factor constraints, and manufacturing and assembly constraints. S2: Input stage candidate set construction: Based on the overall transmission ratio requirement of the reducer, the fixed center distance constraint of the input stage, the integer tooth number constraint, and the displacement coefficient constraint, the parameters of the fixed-axis gear pair of the input stage are exhaustively enumerated and screened to construct a candidate solution set of the input stage gear parameters, and an index is assigned to each candidate solution; S3: Multi-objective optimization modeling: Using the input-level candidate index, the geometric parameters of the first and second-level planetary gear trains and the layout parameters as mixed design variables, a lightweight multi-objective optimization mathematical model is established with minimizing the total mass of the gear system as the first objective and approaching the lower limit of the threshold for the contact and bending safety factor of the weakest gear as the second objective. S4: Multi-constraint integration and algorithm solution: Define and integrate multiple engineering constraints, including transmission ratio constraints, geometric parameter constraints, assembly feasibility constraints, and gear strength safety factor constraints; use a variety of metaheuristic multi-objective optimization algorithms to solve the model in parallel, including algorithms based on dominance relations, decomposition, and swarm intelligence, and search for combinations of design variables that satisfy the multiple constraints through Pareto optimality theory; S5: Performance evaluation and optimal solution selection: Based on the preset performance index system (including HV, IGD, GD, Spread, Coverage and computation time), the algorithm solution results are comprehensively evaluated, and the reducer design scheme with the best overall performance is selected from the Pareto optimal solution set. S6: Engineering Correction and Verification: The center distance of the planetary gear train in the optimal scheme is rounded and the displacement coefficient is recalculated to ensure that the manufacturing and assembly conditions are met; and the final scheme is subjected to dynamic simulation and finite element verification to output the final lightweight reducer parameters that meet the constraints.

[0010] Preferably, the process of constructing the candidate solution set of the input-level gear parameters includes: First-level screening: Obtain all design schemes that meet the calculation relationship of transmission ratio, fixed center distance and displacement coefficient; Second-level screening: Select design schemes that simultaneously meet the safety factor requirements for contact strength and bending strength from the first-level screening. Third-level clustering: Based on the second level, without considering the difference in displacement coefficient, if the module, number of teeth of the driving helical gear, number of teeth of the driven helical gear, helix angle and pressure angle of the design scheme are the same, and only the tooth width coefficient is different, then these design schemes are clustered and only the design scheme with the smallest tooth width coefficient, that is, the design scheme with the smallest mass, is retained.

[0011] Preferably, the design variables are mixed variables, including: Discrete variables: modulus of input level, first-level planetary level, and second-level planetary level; index of candidate solution at input level; number of planetary gears. Integer variables: the number of teeth in the input stage, sun gear, planet gears, and internal gear ring; Continuous variables: tooth width factor, displacement factor, helix angle.

[0012] Preferably, the geometric parameter constraints include discrete value constraints for the module, integer and range constraints for the number of teeth, value constraints for the pressure angle and helix angle, range constraints for the tooth width coefficient, displacement coefficient allocation constraints based on the balanced slip ratio, tooth tip thickness constraints, internal gear ring wall thickness constraints, and planetary gear rim thickness constraints.

[0013] Preferably, the assembly feasibility constraints include the adjacency condition, concentricity condition, assembly condition, and overlap condition of the planetary gear train.

[0014] Preferably, the multiple metaheuristic multi-objective optimization algorithms include: (1) Dominance-based algorithm ①NSGA-Ⅱ (Second Generation Non-Dominated Sorting Genetic Algorithm) ②NSGA-Ⅲ (Third Generation Non-Dominated Sorting Genetic Algorithm) ③SPEA2 (Improved Strength Pareto Evolutionary Algorithm) (2) Decomposition-based algorithms ①MOEA / D (Multi-objective Evolutionary Algorithm Based on Decomposition) ②MOEA / D-DE (Multi-objective evolutionary algorithm based on decomposition and differential evolution) ③MOEA / D-M2M (a multi-objective evolutionary algorithm based on decomposition and multiple mappings) (3) Swarm Intelligence-based algorithms ①MOPSO (Multi-Objective Particle Swarm Optimization Algorithm) ②MOGWO (Multi-Objective Grey Wolf Optimization Algorithm) ③MOWOA (Multi-Objective Whale Optimization Algorithm).

[0015] Preferably, the optimization results are output in the form of Pareto front. The balance characteristics between lightweight and safety indicators of different algorithms are analyzed by radar charts and three-dimensional target spatial distribution maps. Among the candidate design schemes that meet the contact safety factor constraints, the MOPSO algorithm shows a relative advantage in lightweight design and obtains a Pareto solution set with better overall quality indicators than other algorithms.

[0016] Preferably, the swarm intelligence-based algorithm is a multi-objective particle swarm optimization algorithm, and its core control parameters are set as follows: inertia weight 0.4, individual learning factor 1.0, social learning factor 2.0, inertia decay rate 0.99, number of grids 10, grid expansion rate 0.1, and velocity limit coefficient 0.2.

[0017] Preferably, the performance index system includes generation distance for evaluating convergence, reverse generation distance for evaluating overall quality, hypervolume for evaluating convergence and distribution, Spread index for evaluating distribution uniformity, Coverage index for comparing algorithms, and computation time.

[0018] Preferably, the objective function of the multi-objective optimization mathematical model includes: Minimize the total mass of the gear system: ; Maximize the minimum contact safety factor: ; Maximize the minimum bending safety factor: ; Standard question format: min ; Design variable vector: ; Through the aforementioned multi-objective optimization, the guiding algorithm searches for a combination of design variables that minimizes the total mass and makes the safety factor approach the lower limit of a set threshold, while satisfying all constraints.

[0019] An electronic device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described in any of the preceding claims.

[0020] Compared with the prior art, the present invention has the following significant advantages: 1. Systematically solve the problem of complex coupled optimization: By using the "input-level candidate set construction" strategy, the coupled optimization problem of fixed axis and planetary transmission is effectively decomposed and reintegrated, which significantly reduces the problem dimensionality and complexity, and improves optimization efficiency and success rate.

[0021] 2. Achieve deep lightweight design: By establishing a multi-objective optimization model for quality and safety factors, the safety factor is guided to approach the threshold. Under the premise of strictly ensuring strength and reliability, the lightweight potential is fully explored, and the weight of transmission components is reduced by 10%-15%.

[0022] 3. Enhance the robustness of the optimization process: By running multiple optimization algorithms with different mechanisms in parallel and conducting comprehensive performance evaluation, the limitations of a single algorithm are effectively avoided, ensuring that the globally optimal or near-global optimal solution is obtained.

[0023] 4. Enhance engineering applicability: Through engineering correction and professional simulation verification, the optimization results are ensured to be directly applicable to engineering design and production, significantly improving the practical value and conversion efficiency of the method.

[0024] 5. Provide complete solutions: From parameter definition and optimization modeling to engineering verification, a complete lightweight design closed loop is formed, providing systematic methodological support for the optimization design of complex transmission systems.

[0025] 6. This invention is particularly applicable to the design of fixed-axis-planetary combined reducers under heavy-load conditions. It is not only suitable for parameter optimization and lightweight design of fixed-axis-planetary hybrid transmission configurations, but also has broad application prospects in lightweight design of transmission systems in wind power, mining machinery, heavy transportation and other fields. Attached Figure Description

[0026] Figure 1 This is a flowchart of the optimization method; Figure 2a A three-dimensional distribution diagram of the target space of the total gear mass minus the minimum safety factor, comparing the Pareto solution distributions of nine algorithms; Figure 2b A two-dimensional distribution diagram of the target space for the total gear mass minus the minimum contact safety factor, comparing the Pareto solution distributions of nine algorithms; Figure 2c A two-dimensional distribution diagram of the target space of the total gear mass minus the minimum bending safety factor, comparing the Pareto solution distributions of nine algorithms; Figure 3 Radar chart showing the performance comparison of 9 optimization algorithms; Detailed Implementation

[0027] The combined reducer in this embodiment adopts a combined configuration of "input stage fixed-axis gear pair + first-stage planetary gear train + second-stage planetary gear train". Figure 1 The flowchart shown illustrates the lightweight design optimization of a three-stage reducer with an input torque of 7500 N·m, an input speed of 1490 r / min, and a total transmission ratio of 80 ± 2%. The specific steps are as follows: S1: Parameter Definition and Constraint Modeling 1.1 Definition of Design Variables For a three-stage gear system, the following parameter set is established: (1) Input stage fixed-axis gear pair

[0028] in: For modulus, For the number of teeth of the driving helical gear, For the number of teeth of the driven helical gear, For pressure angle, Tooth width coefficient, For the helix angle, For driving helical gear displacement coefficient, The displacement coefficient of the driven helical gear; (2) First-order planetary gear train (sun gear + planet gears + internal gear ring) Defined as:

[0029] in: For modulus, For the number of teeth of the sun gear, For the number of planetary gear teeth, For the number of teeth of the internal gear ring, For pressure angle, For tooth width coefficient, For the sun gear displacement coefficient, For planetary gear displacement coefficient, For the internal gear ring displacement coefficient, This refers to the number of planetary gears; (3) Second-level planetary gear system

[0030] in: For modulus, For the number of teeth of the sun gear, For the number of planetary gear teeth, For the number of teeth of the internal gear ring, For pressure angle, For tooth width coefficient, For the sun gear displacement coefficient, For planetary gear displacement coefficient, For the internal gear ring displacement coefficient, This refers to the number of planetary gears; Ultimately, a unified design variable vector was created. ,

[0031] In the formula: —Index to combinations of input-level design variables (discrete variables); — The number of feasible solutions after clustering.

[0032] The total dimension of the design variables is approximately 19 to 23, which belongs to a high-dimensional mixed variable space. 1.2 Transmission ratio constraint modeling The maximum transmission ratio of a planetary gear train decreases as the number of planetary gears increases. Considering the overall transmission ratio requirement of equipment 80 and the 3-stage reduction structure, a layout with 3 or 4 planetary gears should be preferred for the planetary gear train; the transmission ratio constraint is: the allowable deviation of the overall transmission ratio should not exceed 2%. 1.3 Geometric Compatibility Constraints include: ① Modulus ③ Pressure angle ④ Helix angle ⑤ Tooth width coefficient ⑥ Displacement coefficient ⑦ Center distance: The center distance is fixed at 400mm. ⑧ Tooth tip thickness ⑨ Internal gear ring wall thickness ⑩ Planetary gear rim thickness 1.4 Strength Constraints Adopting ISO 6336 standard: (1) Contact safety factor Requirements: S H ≥1.2; Bending safety factor Requirements: S F ≥1.8; 1.5 Assembly Constraints include: ① Adjacency condition: requires that the planetary gears do not interfere with each other. ②Concentric conditions ③ Assembly conditions:

[0033] ④ Overlap ratio requirement: Overlap ratio of each gear pair All values ​​must not be less than 1.2 to meet the minimum requirements for gear operation; S2: Input-level candidate set construction Based on a fixed center distance constraint of 400mm, a three-layer screening method is used to construct the input-level candidate set: 1. By exhaustively listing all possible combinations of teeth, 1508 preliminary schemes were obtained that satisfy the transmission ratio and center distance. 2. After screening by strength safety factor, 253 schemes remain that meet the contact and bending strength requirements; 3. After clustering by module, number of teeth, helix angle, and pressure angle, retain the 53 optimal schemes with the smallest tooth width coefficient; 4. Form the final candidate set and assign a unique index to each solution. ; S3: Multi-objective optimization modeling Minimize the total mass of the gear system: ; Maximize the minimum contact safety factor: ; Maximize the minimum bending safety factor: ; Standard question format: min ; Design variable vector: ; Through the multi-objective optimization, the guided algorithm searches for a combination of design variables that minimizes the total mass and makes the safety factor approach the lower limit of a set threshold, while satisfying all constraints. S4: Multi-constraint integration and algorithm solution Nine metaheuristic multi-objective optimization algorithms were used in parallel to solve the problem, and the core control parameters of each algorithm were set. All algorithms were set with the same random seed, population size, and maximum number of iterations, and were run in parallel on the processor. The output results are shown in Figure 2. 4.1 The MOPSO algorithm process is as follows: 1. Initialize the particle swarm 2. Randomly select input-level candidate indices for each particle. 3. Encoding planetary gear train design variables 4. Speed ​​Update 5. Mesh generation for crowding handling 6. Pareto's control judgment updates external files. 7. Handling constraint-violation particles (penalty function: increase f1) 8. Output Pareto frontier after 50 iterations 4.2 NSGA-II and NSGA-III Procedures: 1. Quick Non-Dominated Sort 2. Crowded Distance Calculation 3. Crossover variation 5. Population merging 6. Retention of Elites 4.3 MOEA / D / DE / M2M Process: 1. Weight Vector Generation 2. Neighborhood Update 3. Multi-mapping mechanism (M2M) improves solution distribution 4.4 MOGWO, MOWOA: 1. Based on natural swarm intelligence models (wolf packs / whale pods) 2. Random perturbations enhance the probability of escaping local optima. S5: Performance Evaluation and Optimal Solution Selection The following comprehensive performance metrics were used to compare nine Pareto fronts: Hypervolume (HV), Inverted Generational Distance (IGD), Generational Distance (GD), Spread (uniformity), Coverage (uniformity of distribution), and Time (computation time). The performance of each algorithm was analyzed using radar charts and 3D target space visualization. Figure 3 As shown; The results show that, under the condition of satisfying the strength constraints, MOPSO performs best in terms of transmission system mass and obtains a lighter Pareto solution set; finally, the design point with the best overall performance is selected from the MOPSO solution set. S6: Engineering Correction and Verification The optimal solution is then engineered: 1. Round the center distance of the second-stage planetary gear train from 317.50mm to 320mm, and the third-stage from 392.20mm to 390mm; 2. Recalculate the displacement coefficient based on the equilibrium slip ratio; 3. Detailed models were established in the system simulation software for dynamic simulation and finite element analysis. The verification results showed that the mass of all levels was reduced by 10% to 15% compared with the traditional scheme, with SH≥1.25 and SF≥1.85.

[0034] The above embodiments fully demonstrate the effectiveness and engineering applicability of the method of the present invention in solving the problem of lightweight design of fixed-axis-planetary combined reducers.

Claims

1. A lightweight optimization method for fixed-axis-planetary combined reducers under multiple constraints, characterized in that, Includes the following steps: S1: Parameter definition and constraint modeling: Establish a comprehensive mathematical model of the input stage fixed-axis gear system and the first and second stage planetary gear systems, and determine design variables such as module, number of teeth, displacement coefficient, and face width coefficient; the constraints include transmission ratio constraints, geometric compatibility constraints, contact strength safety factor constraints, bending strength safety factor constraints, and manufacturing and assembly constraints. S2: Input stage candidate set construction: Based on the overall transmission ratio requirement of the reducer, the fixed center distance constraint of the input stage, the integer tooth number constraint, and the displacement coefficient constraint, the parameters of the fixed-axis gear pair of the input stage are exhaustively enumerated and screened to construct a candidate solution set of the input stage gear parameters, and an index is assigned to each candidate solution; S3: Multi-objective optimization modeling: Using the input-level candidate index, the geometric parameters of the first and second-level planetary gear trains and the layout parameters as mixed design variables, a lightweight multi-objective optimization mathematical model is established with minimizing the total mass of the gear system as the first objective and approaching the lower limit of the threshold for the contact and bending safety factor of the weakest gear as the second objective. S4: Multi-constraint integration and algorithm solution: Define and integrate multiple engineering constraints, including transmission ratio constraints, geometric parameter constraints, assembly feasibility constraints and gear strength safety factor constraints; The model is solved in parallel using a variety of metaheuristic multi-objective optimization algorithms, including algorithms based on dominance relations, decomposition, and swarm intelligence. Pareto optimality theory is used to search for combinations of design variables that satisfy multiple constraints. S5: Performance evaluation and optimal solution selection: Based on the preset performance index system, including HV, IGD, GD, Spread, Coverage and calculation time, the algorithm solution results are comprehensively evaluated, and the reducer design scheme with the best overall performance is selected from the Pareto optimal solution set. S6: Engineering Correction and Verification: The center distance of the planetary gear train in the optimal scheme is rounded and the displacement coefficient is recalculated to ensure that the manufacturing and assembly conditions are met; and the final scheme is subjected to dynamic simulation and finite element verification to output the final lightweight reducer parameters that meet the constraints.

2. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The process of constructing the candidate solution set of the input-level gear parameters includes: First-level screening: Obtain all design schemes that meet the calculation relationship of transmission ratio, fixed center distance and displacement coefficient; Second-level screening: Select design schemes that simultaneously meet the safety factor requirements for contact strength and bending strength from the first-level screening. Third-level clustering: Based on the second level, without considering the difference in displacement coefficient, if the module, number of teeth of the driving helical gear, number of teeth of the driven helical gear, helix angle and pressure angle of the design scheme are the same, and only the tooth width coefficient is different, then these design schemes are clustered and only the scheme with the smallest tooth width coefficient is retained, that is, the design scheme with the smallest mass.

3. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The design variables are mixed variables, including: Discrete variables: modulus of input level, first-level planetary level, and second-level planetary level; index of candidate solution at input level; number of planetary gears. Integer variables: the number of teeth in the input stage, sun gear, planet gears, and internal gear ring; Continuous variables: tooth width factor, displacement factor, helix angle.

4. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The geometric parameter constraints include discrete value constraints for the module, integer and range constraints for the number of teeth, value constraints for the pressure angle and helix angle, range constraints for the tooth width coefficient, displacement coefficient allocation constraints based on the balanced slip ratio, tooth tip thickness constraints, internal gear ring wall thickness constraints, and planetary gear rim thickness constraints.

5. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The assembly feasibility constraints include the adjacency condition, concentricity condition, assembly condition, and overlap condition of the planetary gear train.

6. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The various metaheuristic multi-objective optimization algorithms include: (1) Dominance-based algorithm ① The second-generation non-dominated sorting genetic algorithm NSGA-II ② The third-generation non-dominated sorting genetic algorithm NSGA-III ③ Improved Strength Pareto Evolutionary Algorithm SPEA2 (2) Decomposition-based algorithms ① MOEA / D, a multi-objective evolutionary algorithm based on decomposition ② MOEA / D-DE, a multi-objective evolutionary algorithm based on decomposition and differential evolution. ③ MOEA / D-M2M, a multi-objective evolutionary algorithm based on decomposition and multiple mappings (3) Swarm Intelligence-based Algorithms ① Multi-objective particle swarm optimization algorithm (MOPSO) ② Multi-objective gray wolf optimization algorithm MOGWO ③ Multi-objective whale optimization algorithm (MOWOA).

7. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 6, characterized in that, The optimization results are output in the form of Pareto fronts. The balance characteristics between lightweight and safety indicators of different algorithms are analyzed by radar charts and three-dimensional target spatial distribution maps. Among the candidate design schemes that meet the contact safety factor constraints, the MOPSO algorithm shows a relative advantage in lightweight design and obtains a Pareto solution set with a better overall quality index than other algorithms. The algorithm based on swarm intelligence is a multi-objective particle swarm optimization algorithm. Its core control parameters are set as follows: inertia weight 0.4, individual learning factor 1.0, social learning factor 2.0, inertia decay rate 0.99, number of grids 10, grid expansion rate 0.1, and velocity limit coefficient 0.

2.

8. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The performance index system includes generation distance for evaluating convergence, reverse generation distance for evaluating overall quality, hypervolume for evaluating convergence and distribution, spread index for evaluating distribution uniformity, Coverage index for comparing algorithms, and computation time.

9. The lightweight optimization method for a fixed-axis-planetary combined reducer under multiple constraints according to claim 1, characterized in that, The objective function of the multi-objective optimization mathematical model includes: Minimize the total mass of the gear system: ； Maximize the minimum contact safety factor: ； Maximize the minimum bending safety factor: ； Standard question format: min ; Design variable vector: ； Through the aforementioned multi-objective optimization, the guiding algorithm searches for a combination of design variables that minimizes the total mass and makes the safety factor approach the lower limit of a set threshold, while satisfying all constraints.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-9.

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