A three-phase optimization method and system for a forklift drive axle half shaft

Abstract

The application relates to the technical field of structure optimization, and discloses a three-phase optimization method and system for a forklift driving axle half shaft. The method comprises the following steps: encoding a spline tooth number population and performing conditional interval mapping to obtain a satellite sub-population; processing the satellite sub-population through a three-phase search algorithm to obtain a fitness value; performing three-phase search processing on an anchor point population according to the fitness value, inheriting the satellite sub-population in a neighborhood, and performing boundary correction to obtain an updated population; and screening to obtain an optimal structure parameter group. According to the application, a parameter population is generated according to a constraint chain, and a three-phase search and a neighborhood inheritance mechanism are combined, so that the parameter search efficiency and the feasibility and rationality of the final structure parameter combination are improved.

Description

Technical Field

[0001] This application relates to the field of structural optimization technology, and in particular to a three-phase optimization method and system for forklift drive axle half-shafts. Background Technology

[0002] The floating half-shaft of a forklift drive axle is a rotary transmission component that bears alternating torsional loads. Its three structural parameters—the number of spline teeth, shaft diameter, and transition fillet radius—jointly determine the fatigue life and manufacturing cost of the half-shaft. Existing half-shaft structural parameter design methods mostly rely on swarm intelligence optimization techniques such as genetic algorithms and particle swarm optimization to randomly sample or iteratively search the above structural parameters within a pre-defined value range. The performance of candidate parameter combinations is evaluated by combining fatigue strength verification formulas or finite element simulations, and then the parameter combination that meets the strength requirements is selected.

[0003] However, the number of spline teeth, as an integer variable, determines the pitch circle diameter of the spline connection. The shaft diameter must maintain a strength continuity relationship with the spline pitch circle diameter, and the acceptable range of the transition fillet radius is further constrained by the shaft diameter. There is a sequentially passed geometric constraint chain among these three factors. Existing methods typically sample the three variables independently and randomly within their respective fixed intervals, without deriving the sampling range step by step according to this constraint chain. This results in a significant proportion of the generated parameter combinations falling into practically infeasible areas, requiring additional verification and elimination steps. At the same time, existing search processes often employ single-stage random optimization without progressively narrowing the search range from coarse to fine. The large-scale exploration in the early stage and the small-scale convergence in the later stage are mixed in the same optimization stage, making it difficult to balance convergence speed and search accuracy. Furthermore, fatigue life and manufacturing cost, two mutually constraining performance indicators, are often assessed separately or simply one of them by existing methods, without a weighted comprehensive evaluation based on their inverse relationship.

[0004] Based on the aforementioned geometric constraint chain and hierarchical optimization requirements, to generate a parameter population according to the dependency order of spline tooth count, shaft diameter, and transition fillet radius, the first problem to solve is how to derive the feasible ranges of shaft diameter and transition fillet radius step by step from the integer values ​​of the spline tooth count variable. On this basis, when optimizing the derived combinations of shaft diameter and transition fillet radius values, how to achieve hierarchical convergence of the search range from coarse to fine while considering the mutually constraining indicators of fatigue life and manufacturing cost becomes a further problem to be solved. Since the spline tooth count itself also needs to participate in the optimization iteration, and each change in the tooth count will cause the downstream feasible ranges of shaft diameter and transition fillet radius to shift as a whole, if the shaft diameter and transition fillet radius are searched again from scratch after the tooth count changes, the already converged search results will be discarded. How to reuse existing converged results instead of searching again when the tooth count changes slightly, and how to correct the inherited values ​​for the shifted feasible range after reuse, thus becomes a problem that needs to be further solved. Summary of the Invention

[0005] This application provides a three-phase optimization method and system for forklift drive axle half-shafts. The technical problem to be solved by this application is that existing half-shaft structural parameter optimization methods do not generate feasible parameters step by step according to the geometric constraint chain between the three structural parameters, and the optimization process does not achieve hierarchical convergence and inheritance reuse, resulting in low search efficiency and a high proportion of infeasible parameter combinations. By generating a parameter population according to the constraint chain and combining three-phase search and neighborhood inheritance mechanisms, the parameter search efficiency and the feasibility and rationality of the final structural parameter combination are improved.

[0006] In a first aspect, this application provides a three-phase optimization method for forklift drive axle half-shafts, the three-phase optimization method for forklift drive axle half-shafts comprising: Step S1: Perform population encoding on the spline tooth count variable to obtain the anchor point population. Based on the anchor point population, perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable to obtain the satellite subpopulation. Step S2: The satellite subpopulation is subjected to solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing using a three-phase search algorithm to obtain the fitness value of the anchor point individuals; Step S3: Based on the fitness value of the anchor individuals, the three-phase search algorithm is applied to the anchor population. During the gas phase exploration process, new anchor individuals are generated. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood range, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that exceed the feasible domain are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. Step S4: Select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

[0007] Secondly, this application provides a three-phase optimization system for a forklift drive axle half-shaft, the forklift drive axle half-shaft three-phase optimization system comprising: The encoding module is used to perform population encoding on the spline tooth count variable to obtain the anchor point population, and to perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable based on the anchor point population to obtain the satellite subpopulation; The exploration module is used to perform solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing on the satellite subpopulation using a three-phase search algorithm to obtain the fitness value of anchor point individuals. The correction module is used to process the anchor population using the three-phase search algorithm based on the fitness value of the anchor individuals. During the gas phase exploration process, a new anchor individual is generated. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood range, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that exceed the feasible domain are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. The filtering module is used to select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

[0008] Thirdly, a forklift drive axle half-shaft three-phase optimization device is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the forklift drive axle half-shaft three-phase optimization device to execute the above-described forklift drive axle half-shaft three-phase optimization method.

[0009] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to perform the above-described three-phase optimization method for forklift drive axle half-shafts.

[0010] In the technical solution provided in this application, an anchor population is obtained by population encoding the spline tooth count variable, and a satellite subpopulation is obtained by conditional interval mapping of the shaft diameter variable and the transition fillet radius variable based on the anchor population. The three originally interrelated structural parameters are generated step by step according to the geometric dependence that the spline tooth count determines the feasible range of the shaft diameter, and the shaft diameter further determines the feasible range of the transition fillet radius. This ensures that each parameter combination in the population is within the feasible range that satisfies the structural constraints from the beginning of generation. This avoids the situation in the independent random sampling method where a large number of parameter combinations need to be eliminated afterward because they do not meet the geometric constraints. It also reduces the computational resources occupied by invalid searches and allows the search process to be more focused on the truly engineering-meaning feasible domain. Based on this, the satellite subpopulation is sequentially processed through gas phase exploration, liquid phase transition, and solid phase development using a three-phase search algorithm. This allows the search range to gradually narrow from a large-scale traversal to a small-scale fine adjustment as the processing stages progress. This hierarchical convergence search rhythm aligns with the general principle in structural parameter optimization problems of first ensuring coverage and then gradually approaching the local optimum. This ensures that the evaluation of the fitness value of individual anchor points is based on a weighted average of two mutually constraining indicators: fatigue life and manufacturing cost. As a result, the final parameter combination obtained can achieve a relatively balanced result between strength performance and economy.

[0011] To address the issue of small variations in the integer variable of spline tooth count during optimization iterations, this application employs neighborhood inheritance. When the difference in spline tooth count between the new anchor point individual and existing anchor point individuals is small, the new anchor point individual directly reuses the convergence results of the corresponding satellite subpopulation of the existing anchor point individual. Furthermore, it corrects the boundaries of the inherited individuals to address the feasible interval shift caused by tooth count variations. This eliminates the need to re-execute the complete three-phase search process after each tooth count change, reducing redundant computation. In the specific application scenario of forklift drive axle half-shafts subjected to alternating torsional loads and with chain-like geometric constraints among structural parameters, the aforementioned encoding method, hierarchical search mechanism, and inheritance correction mechanism are not simply applications of general optimization algorithms. Rather, they are targeted designs specific to the engineering context of the dependency relationship between spline tooth count, shaft diameter, and transition fillet radius, as well as the interplay between fatigue life and manufacturing cost. The algorithm's features align perfectly with the structural characteristics of the application domain, enabling the improvement in search efficiency and parameter feasibility to be effectively realized in this application scenario. Attached Figure Description

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

[0013] Figure 1This is a schematic diagram of an embodiment of the three-phase optimization method for the forklift drive axle half-shaft in this application. Figure 2 This is a graph showing the optimal fatigue life and maximum stress at the critical section as a function of iteration number during a three-phase search performed by the satellite subpopulation for a fixed spline tooth number variable in this embodiment of the application. Figure 3 This is a comparative bar chart showing the number of iterations required to converge to the optimal structural parameter set as a function of the anchor layer iterations when satellite subpopulations are generated using random initialization and neighborhood inheritance merging methods, respectively, in the embodiments of this application. Detailed Implementation

[0014] This application provides a three-phase optimization method and system for forklift drive axle half-shafts. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0015] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the three-phase optimization method for forklift drive axle half-shafts in this application includes: Step S1: Perform population encoding on the spline tooth count variable to obtain the anchor point population. Based on the anchor point population, perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable to obtain the satellite subpopulation. Specifically, the spline tooth count variable refers to the number of teeth at the meshing part of the floating half-shaft and the differential half-shaft gear. Population coding processing involves randomly sampling this variable within a preset integer value range and removing duplicate values ​​to form an anchor population. Each individual in the anchor population carries only the spline tooth count variable. Conditional interval mapping refers to the process where the shaft diameter variable and the transition fillet radius variable are not independently and randomly selected within their respective fixed intervals. Instead, based on the geometric correspondence between the number of spline teeth and the shaft diameter determined by the spline pitch circle diameter formula, the feasible range of the shaft diameter is first calculated. After sampling the shaft diameter value within this range, the feasible range of the transition fillet radius is calculated based on the proportional relationship between the shaft diameter and the transition fillet radius. Finally, the transition fillet radius value is sampled within this range. This processing order of first determining the number of spline teeth and then sequentially deriving the feasible ranges of the two downstream continuous variables is because once the number of spline teeth is determined, the strength continuity design criterion of the shaft and spline connection section has already locked the feasible range of the shaft diameter. After the shaft diameter is determined, the stress concentration factor calculation locks the feasible range of the transition fillet radius. This sequential dependency is determined by the geometric constraints of the spline structure itself and cannot be reversed or processed separately. The satellite subpopulation is a collection of individuals formed by such paired shaft diameter values ​​and transition fillet radius values.

[0016] Step S2: The satellite subpopulation is subjected to solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing using a three-phase search algorithm to obtain the fitness value of the anchor point individuals. Specifically, the three-phase search algorithm sequentially reduces the variation range of individual values ​​in the satellite subpopulation through three stages: solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing. In the gas-phase exploration processing stage, the worst-performing individuals are resampled within the entire feasible range of the shaft diameter and transition fillet radius to ensure that the search range initially covers the entire feasible range. In the liquid-phase transition processing stage, the variation range is narrowed to a medium-range perturbation around the current best individual, forming a transition between the gas and solid phases. In the solid-phase development processing stage, the variation range is further narrowed, with fine adjustments made only within a very small neighborhood of the current best individual. This gradual reduction in variation range corresponds to the physical requirement of the search process gradually transitioning from a large-scale traversal to a small-scale convergence. The fitness value of the anchor point individual is calculated by substituting the converged values ​​of the shaft diameter and transition fillet radius obtained after solid-phase development treatment of the satellite subpopulation into the stress concentration factor and nominal torsional stress to obtain the maximum stress of the critical section, and then calculating the fatigue life value and manufacturing cost value based on this. The fatigue life value and manufacturing cost value are then added together according to their weights to obtain a comprehensive value. The weighted addition is used instead of taking only one indicator because improving the fatigue life in the design of the half-shaft structure often requires increasing the shaft diameter or reducing the stress concentration, which will lead to a simultaneous increase in material cost and processing cost. The two indicators are mutually restrictive, and using only a single indicator to measure the quality of an individual cannot reflect this restrictive relationship.

[0017] Step S3: Based on the fitness values ​​of individual anchors, the anchor population is processed by a three-phase search algorithm. New anchor individuals are generated during the gas phase exploration process. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that are outside the feasible region are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. Specifically, the new anchor point individual is the spline tooth count individual generated by resampling the anchor point population during the gas phase exploration processing stage. The neighborhood range is a pre-set threshold for the difference in spline tooth count. The absolute value of subtracting the spline tooth count of the new anchor point individual from the spline tooth count of each existing anchor point individual in the anchor point population is taken. As long as any difference falls within this threshold, the new anchor point individual is determined to be within the neighborhood range of the existing anchor point individual. This threshold can be set because the spline pitch circle diameters calculated from two adjacent or similar spline tooth counts are very close, and the corresponding feasible ranges of shaft diameters highly overlap. At this time, the existing individual distribution in the satellite subpopulation corresponding to the existing anchor point individual can be directly used for the new anchor point individual. This is equivalent to inheriting the search experience that has already converged from the existing anchor point individual, without having to randomly initialize and search again from the beginning for the satellite subpopulation corresponding to the new anchor point individual. The boundary correction process is necessary because the inherited satellite subpopulation individuals were originally generated based on the feasible range calculated from the number of spline teeth of existing anchor point individuals. After changing to the number of spline teeth of new anchor point individuals, the feasible range boundary of the shaft diameter and transition fillet radius will change. The inherited individuals may contain values ​​that exceed the new feasible range. These values ​​need to be reset to the boundary values ​​corresponding to the new feasible range. After resetting the shaft diameter, the feasible range of the transition fillet radius needs to be recalculated based on the new shaft diameter, and the transition fillet radius also needs to be verified. The updated anchor point population and the updated satellite subpopulation are obtained by merging the new anchor point individuals into the original anchor point population and merging the corrected individuals with the individuals that did not exceed the feasible range into the satellite subpopulation.

[0018] Step S4: Select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

[0019] Specifically, the updated anchor point population and the updated satellite subpopulation obtained after repeated iterations and convergence are used for final extraction. The anchor point with the highest fitness value is selected from the updated anchor point population, and the individual with the highest fitness value is selected from its corresponding satellite subpopulation. The shaft diameter and transition fillet radius values ​​of this individual are extracted, and these two values ​​are compared with the material stress constraints. If the constraints are exceeded, the individual with the second highest fitness value in the same satellite subpopulation is used for re-verification until the constraints are met. The optimal structural parameter set is the final design result composed of the three values ​​of the number of spline teeth, shaft diameter, and transition fillet radius that have passed the verification.

[0020] In one specific embodiment, step S1 includes: The spline tooth count variable is subjected to interval random sampling to obtain the set of spline tooth count values; The set of spline tooth count values ​​is deduplicated and merged to obtain the anchor point population; The pitch circle diameter of the spline is calculated by processing the spline tooth number variable in the anchor population based on the spline module. Based on the spline pitch circle diameter, interval boundary calculations are performed on the shaft diameter variable to obtain a feasible interval for the shaft diameter. Based on the feasible interval for the shaft diameter, random sampling is performed on the shaft diameter variable to obtain the shaft diameter value. Based on the shaft diameter value, interval boundary calculations are performed on the transition fillet radius variable to obtain a feasible interval for the transition fillet radius. Based on the feasible interval for the transition fillet radius, random sampling is performed on the transition fillet radius variable to obtain the transition fillet radius value. The shaft diameter value and the transition fillet radius value constitute the satellite subpopulation.

[0021] Specifically, the spline tooth count variable takes integer values ​​in the spline connection structure of the floating half-shaft and differential half-shaft gear. The random sampling process generates several spline tooth count values ​​evenly distributed within a pre-defined integer range of 16 to 28. The upper and lower limits of this range are determined based on the dual constraints of tooth root strength and assembly space when the spline connection structure adapted to the floating half-shaft transmits rated torque. Too few teeth will lead to excessive load on a single tooth, causing tooth root fracture; too many teeth will compress the usable diameter of the shaft, resulting in structural redundancy. The range of 16 to 28 covers the range of tooth count values ​​for commonly used spline connection structures of forklift drive axle floating half-shafts. The deduplication and merging process retains only one spline tooth with the exact same value from the sampled spline tooth count set. Each spline tooth in the retained set is treated as an individual, and the set of these individuals constitutes the anchor point population. The anchor point population does not contain duplicate individuals with the same spline tooth count value. The spline module is the basic parameter for determining the tooth profile size in the national standard for splines. It is set to 1.5 mm. This value is selected based on the standard module series of spline connectors that are matched with the floating half shaft. The pitch circle diameter is calculated by multiplying the number of spline teeth in each anchor point population by the spline module to obtain the corresponding spline pitch circle diameter. This pitch circle diameter reflects the reference geometric dimensions of the spline connection.

[0022] The boundary calculation for the feasible range of shaft diameter is based on the spline pitch circle diameter. The lower boundary is the spline pitch circle diameter plus 1.0 mm, and the upper boundary is the spline pitch circle diameter plus 3.5 mm. This technical allowance is determined according to the design principle of strength continuity at the transition between the shaft and spline connection. If the allowance is too small, it will cause a step-like abrupt change at the connection between the shaft and spline, leading to stress concentration. If the allowance is too large, it will increase the amount of shaft material used and raise manufacturing costs. The shaft diameter variable is obtained by random sampling within this feasible range using a uniform distribution. The unit of this value is millimeters. The boundary calculation for the feasible range of transition fillet radius is based on the shaft diameter. The lower boundary is the shaft diameter multiplied by 0.06, and the upper boundary is the shaft diameter multiplied by 0.12. This proportional coefficient is determined based on the conventional proportional relationship between the transition fillet radius and the shaft diameter for shaft-type parts. If the ratio is too small, it will cause the transition fillet radius to be too small, resulting in a high stress concentration factor. If the ratio is too large, it will weaken the effective load-bearing section of the shaft. The transition fillet radius variable is randomly sampled in a uniform distribution within the feasible interval to obtain the transition fillet radius value. The shaft diameter value and the transition fillet radius value are paired to form a satellite individual. The collection of all satellite individuals constitutes the satellite subpopulation corresponding to the number of spline teeth. Each spline tooth number in the anchor point population corresponds to an independently generated satellite subpopulation.

[0023] In one specific embodiment, step S2 includes: Gas phase exploration processing was performed on the satellite subpopulation. Within the feasible range of shaft diameter and transition fillet radius, the individuals with the worst fitness values ​​were resampled to obtain the gas phase processed satellite subpopulation. The satellite subpopulation after gas phase processing is subjected to liquid phase transition processing. Based on the current best individual, a random offset is superimposed and the boundary is reset to obtain the satellite subpopulation after liquid phase processing. After liquid phase processing, solid phase development processing is performed on the satellite subpopulation. The current best individual is superimposed with an offset smaller than that of liquid phase transition processing and then a local fine search is performed to obtain solid phase convergent satellite individuals. The stress concentration factor and nominal torsional stress of the solid-phase convergent satellite individual are calculated to obtain the maximum stress of the critical section. The maximum stress of the critical section is then input into the fatigue life calculation formula to obtain the fatigue life value. The manufacturing cost of the solid-phase convergent satellite individual is calculated to obtain the manufacturing cost value. The fatigue life value and the manufacturing cost value are then weighted and summed to obtain the fitness value of the anchor point individual.

[0024] Specifically, each satellite subpopulation consists of 15 individuals, each of which is a pair of shaft diameter values ​​and transition fillet radius values. The gas phase exploration process sorts the 15 individuals in the satellite subpopulation according to their current fitness values ​​from high to low, and identifies the six individuals with the worst fitness values ​​as the bottom six individuals. For these six individuals, new shaft diameter values ​​and transition fillet radius values ​​are generated by uniformly sampling within the entire feasible range of shaft diameter and transition fillet radius, replacing the original values. The nine individuals that are not replaced remain unchanged. All 15 individuals together constitute the satellite subpopulation after gas phase processing. The liquid-phase transition process involves selecting the individual with the highest fitness value from the gas-phase processed satellite subpopulation as the current optimal individual. A random offset within ±1.2 mm is added to the individual's shaft diameter value, and a random offset within ±0.3 mm is added to the transition fillet radius value. This generates a new individual after perturbation. If a perturbed value exceeds the feasible range of either the shaft diameter or the transition fillet radius, the boundary reset process directly replaces that value with the boundary value corresponding to the direction it exceeds. The processed individual, along with the unperturbed individuals from the original satellite subpopulation, constitutes the liquid-phase processed satellite subpopulation. The solid-phase development process involves selecting the current optimal individual from the liquid-phase processed satellite subpopulation, adding an offset within ±0.3 mm to its shaft diameter value, and an offset within ±0.08 mm to its transition fillet radius value. This offset amplitude is smaller than that used in the liquid-phase transition process. Through repeated iterations and convergence, a solid-phase converged satellite individual is obtained.

[0025] The solid-phase convergence satellite individual includes two values: the shaft diameter and the transition fillet radius. The stress concentration factor is calculated by substituting the ratio of the transition fillet radius to the shaft diameter into the power function relationship between the stress concentration factor and this ratio. The nominal torsional stress is calculated by substituting the rated input torque of the floating half-shaft (850 Nm) into the relationship between torsional stress and the cube of the shaft diameter. The maximum stress at the critical section is obtained by multiplying the stress concentration factor by the nominal torsional stress. The maximum stress at the critical section is then substituted into the fatigue life calculation formula. This formula uses the material fatigue limit of 320 MPa, the material constant of 6.5, and the reference cycle base of one million cycles as fixed parameters. The fatigue life value is obtained by multiplying the ratio of the fatigue limit to the maximum stress at the critical section by the material constant raised to the power of the reference cycle base. The material constant and the reference cycle base are determined based on the fatigue characteristic curve of the alloy structural steel material used in the floating half-shaft. The manufacturing cost calculation process involves substituting the shaft diameter value into the half-shaft blank volume formula to obtain the volume. The volume is then multiplied by the material density of 7850 kg / m³ and the material unit price of 6.2 yuan / kg to obtain the material cost. For every four additional spline teeth, the processing cost increases by 8.5 yuan. For every grade increase in the transition fillet radius precision tolerance level, the processing cost increases by 3.2 yuan. The material cost and processing cost are added together to obtain the manufacturing cost value. The weighted summation process involves multiplying the fatigue life value by 0.7, adding the reciprocal of the manufacturing cost value by 1000, and then multiplying by 0.3 to obtain the individual fitness value of the anchor point. The weighting coefficients of 0.7 and 0.3 are determined based on the design priority that the tolerance for fatigue failure risk of the floating half-shaft, as a rotating transmission component bearing alternating loads, is higher than the tolerance for manufacturing economics.

[0026] Figure 2 This is a graph showing the changes in the optimal fatigue life and the maximum stress at the critical section with the number of iterations during a three-phase search for a fixed spline tooth number by the satellite subpopulation in this embodiment of the application. The horizontal axis represents the number of iterations, the left side of the vertical axis represents the fatigue life value in hours, and the right side of the vertical axis represents the maximum stress at the critical section in megapascals. The solid line in the graph corresponds to the trajectory of the optimal fatigue life value changing with the number of iterations, and the dashed line corresponds to the trajectory of the maximum stress at the critical section changing with the number of iterations. The two vertical dashed lines in the graph divide the horizontal axis into three segments, corresponding to the gas phase exploration processing stage, the liquid phase transition processing stage, and the solid phase development processing stage, respectively. The current optimal individual obtained by convergence in the previous stage serves as the starting individual for the local fine search processing in the next stage. The three stages proceed sequentially. The optimal fatigue life value gradually increases and tends to converge with the increase of the number of iterations, while the maximum stress at the critical section gradually decreases and tends to converge with the increase of the number of iterations. The trends of the two are mutually corresponding.

[0027] In one specific embodiment, step S3 involves processing the anchor population using a three-phase search algorithm based on the fitness values ​​of individual anchors, including: The anchor population was subjected to gas phase exploration. Within the range of spline tooth number variable, the anchor individuals with the worst fitness values ​​were resampled to obtain new anchor individuals. The anchor population is subjected to liquid phase transition processing. The perturbation processing is performed based on the spline tooth number variable of the current best anchor individual and the random offset, resulting in the anchor individual after liquid phase processing. The anchor population is subjected to solid-phase development treatment. The spline tooth number variable of the current best anchor individual is superimposed with an offset that is less than that of the liquid-phase transition treatment, and a local fine search is performed to obtain the anchor individual after solid-phase treatment.

[0028] Specifically, the anchor population consists of 20 anchor individuals, each carrying a spline tooth count value. The spline tooth count variable takes values ​​from 16 to 28, the basis for which this range was determined as explained in the spline tooth count variable population encoding process. The gas phase exploration process involves sorting the 20 anchor individuals in the population according to their fitness values ​​from highest to lowest. The last six anchor individuals are identified as having the worst fitness values. For these six individuals, the spline tooth count variable is randomly sampled again from the entire range of 16 to 28 using a uniform distribution to generate new integer values, replacing the original spline tooth count values. The remaining 14 anchor individuals remain unchanged. The newly generated spline tooth count values ​​are then used as the new anchor individuals.

[0029] The liquid phase transition treatment involves taking the anchor individual with the highest fitness value in the current anchor population as the current optimal anchor individual, and superimposing a random integer offset within the range of positive and negative two onto its spline tooth count variable. This offset is randomly selected from four integers: negative two, negative one, positive one, and positive two, excluding zero values ​​to ensure that actual perturbation is generated. If the spline tooth count value after superposition exceeds the range of sixteen to twenty-eight, the value is reset to the integer value of the range boundary corresponding to the direction of the excess. The anchor individual after the treatment is recorded as the anchor individual after liquid phase treatment. The solid-phase development process involves selecting the anchor point with the highest fitness value among the anchor points after liquid-phase treatment as the current optimal anchor point. A random integer offset within a range of ±1 is superimposed on its spline tooth number variable, i.e., one is randomly selected from negative one and positive one. This offset amplitude is smaller than the ±2 range used in the liquid-phase transition treatment stage. The setting of these two offset amplitudes, ±1 and ±2, is determined based on the structural characteristic that the smallest unit of change for the spline tooth number variable as an integer variable is one tooth. The narrowing of the offset amplitude reflects the gradual transition of the search range from the larger jumps in the liquid-phase stage to the fine adjustment of the smallest unit in the solid-phase stage. Through repeated iterations and convergence, the anchor point after solid-phase treatment is obtained.

[0030] In one specific embodiment, step S3, which involves obtaining the satellite subpopulation corresponding to the new anchor individual through inheritance processing of the existing anchor individual's corresponding satellite subpopulation, includes: The difference in the number of spline teeth between the new anchor point individual and the existing anchor point individuals in the anchor point population is calculated to obtain the neighborhood difference. The neighborhood difference is compared with a preset neighborhood threshold to filter out target individuals with existing anchor points within the neighborhood range; The satellite subpopulation corresponding to the existing anchor point individual of the target is copied to obtain the inherited satellite subpopulation corresponding to the new anchor point individual.

[0031] Specifically, existing anchor individuals refer to the fourteen anchor individuals in the anchor population that were not replaced in this round of gas phase exploration processing. Each of these fourteen anchor individuals has a ready-made satellite subpopulation that has been converged after solid phase development processing. New anchor individuals, on the other hand, are spline tooth count values ​​generated by resampling during gas phase exploration processing and do not yet have any associated satellite subpopulations. The spline tooth count difference calculation process involves subtracting the spline tooth count of the new anchor individual from the spline tooth counts of the fourteen existing anchor individuals one by one and taking the absolute value, thereby obtaining fourteen neighborhood differences. The preset neighborhood threshold is an integer of 2, which is two teeth. This value is calculated based on a spline module of 1.5 mm: for every difference of 1 tooth in the number of spline teeth, the corresponding change in the spline pitch circle diameter is 1.5 mm. The upper and lower boundaries of the feasible range of shaft diameter derived from this are shifted by a small amount. When the difference in the number of teeth does not exceed 2, the feasible range of shaft diameter and the feasible range of transition fillet radius still largely overlap. The inherited individuals can still fall into the new range after boundary correction. If the threshold is set to be larger, the range offset caused by the difference in the number of teeth will cause a large number of inherited individuals to exceed the new feasible range. The workload of boundary correction is no different from regeneration, and inheritance becomes meaningless. When multiple differences among the fourteen neighborhoods do not exceed the threshold of 2, the existing anchor individual with the smallest difference is selected as the target existing anchor individual to avoid the situation where the result is not unique when two or more individuals meet the conditions. When all fourteen neighborhood differences exceed the threshold of 2 and there is no existing anchor individual that meets the conditions, the satellite subpopulation corresponding to the new anchor individual is regenerated independently according to the condition interval mapping process, and the inheritance process of this embodiment is not executed.

[0032] The replication process involves copying the axis diameter and transition fillet radius values ​​of each of the fifteen satellite individuals in the satellite subpopulation corresponding to the existing anchor individuals, forming an inherited satellite subpopulation of the same fifteen individuals. The replication process does not change the values ​​or recalculate fitness. This inherited satellite subpopulation directly applies the value distribution obtained from multiple rounds of solid-phase convergence of the existing anchor individuals to the new anchor individuals, eliminating the computational burden of re-performing conditional interval mapping and three-phase search on the new anchor individuals. This is especially important in the gas phase exploration stage, where a large-scale resampling across the entire feasible interval is required; the inheritance process skips this step, which is the computational efficiency advantage of this embodiment compared to regenerating the satellite subpopulation one by one. Since the inherited satellite subpopulation is generated based on the feasible interval calculated from the spline tooth count of the existing anchor individuals, the interval boundary will shift after changing to the spline tooth count of the new anchor individuals. Therefore, there may still be individuals in the inherited satellite subpopulation that exceed the new feasible interval; the correction of these individuals is handled by boundary correction processing.

[0033] Figure 3 This is a bar chart comparing the number of iterations required to converge to the optimal structure parameter set when satellite subpopulations are generated using random initialization and neighborhood inheritance merging methods, respectively, as a function of the anchor layer iterations. The horizontal axis represents the anchor layer iterations, and the vertical axis represents the number of iterations required for the corresponding satellite subpopulation to converge. The bars filled with diagonal lines on the left correspond to the number of iterations required when the satellite subpopulation is generated using the random initialization method, while the bars filled with grids on the right correspond to the number of iterations required when the satellite subpopulation is generated using the neighborhood inheritance merging method. Each set of bars is labeled with its corresponding numerical value. In the first generation, there are no existing anchor individuals in the anchor layer population that can be inherited. In both methods, the satellite subpopulation is generated by random initialization. Therefore, the two pillar values ​​corresponding to the first generation are the same. From the third generation onwards, there are anchor individuals generated in the previous iteration in the anchor layer population. If the difference in the number of spline teeth between the newly generated anchor individual and the existing anchor individual is within the neighborhood, the corresponding satellite subpopulation is generated by neighborhood inheritance and merging. The trend of the difference in the number of iterations required for convergence under the two methods as the number of iterations of the anchor layer increases is reflected by the height difference of the corresponding pillars in the figure.

[0034] In one specific embodiment, step S3 involves boundary correction processing for individuals in the inherited satellite subpopulation that exceed the feasible domain, including: Based on the individual new anchor points, the interval boundary calculation of the shaft diameter variable is performed to obtain the feasible interval of the target shaft diameter; The axis diameter values ​​of individuals in the inherited satellite subpopulation are compared with the feasible range of the target axis diameter. Individuals that exceed the feasible range of the target axis diameter are selected and their axis diameter values ​​are reset to the corresponding range boundary values ​​to obtain the corrected axis diameter values. Based on the corrected shaft diameter value, the transition fillet radius variable is processed by interval boundary calculation to obtain the feasible interval of the target transition fillet radius. Based on the feasible interval of the target transition fillet radius, the transition fillet radius value of the boundary overflow individual is reset to obtain the boundary corrected individual. The updated satellite subpopulation is formed by the individuals after boundary correction and the individuals in the inherited satellite subpopulation that have not exceeded the feasible domain. The new anchor point individuals are then incorporated into the anchor point population to obtain the updated anchor point population.

[0035] Specifically, the calculation of the feasible range of the target shaft diameter follows the same rule as multiplying the number of spline teeth by the spline module to obtain the spline pitch circle diameter, and then using the spline pitch circle diameter plus 1.0 mm as the lower boundary and plus 3.5 mm as the upper boundary. However, the number of spline teeth substituted here is the number of spline teeth of the new anchor point individual rather than the number of spline teeth of the target existing anchor point individual. Therefore, the boundary value of the feasible range of the target shaft diameter obtained in this way will be shifted due to the difference in the number of spline teeth compared with the feasible range originally based on the inherited satellite subpopulation. The comparison process involves comparing the axis diameter values ​​of each of the fifteen individuals in the inherited satellite subpopulation with the upper and lower boundaries of the feasible range of the target axis diameter. Individuals with values ​​lower than the lower boundary are identified as having a lower overflow, and individuals with values ​​higher than the upper boundary are identified as having an upper overflow. These two types of individuals are collectively referred to as boundary overflow individuals. The reset process replaces the axis diameter values ​​of individuals with lower overflow with the lower boundary value of the feasible range of the target axis diameter, and replaces the values ​​of individuals with upper overflow with the upper boundary value. The axis diameter values ​​of individuals that have not overflowed remain unchanged. After the replacement is completed, the corrected axis diameter values ​​are obtained.

[0036] The calculation of the feasible range of the target transition fillet radius follows the proportional relationship of multiplying the shaft diameter value by 0.06 as the lower boundary and multiplying by 0.12 as the upper boundary. The shaft diameter value substituted is the corrected shaft diameter value of each boundary overflow individual. Since the corrected shaft diameter values ​​of different boundary overflow individuals may be different, the feasible range of the target transition fillet radius for each individual will also be different. The reset process compares the original transition fillet radius value of the boundary overflow individual with its corresponding feasible range of the target transition fillet radius. Values ​​lower than the lower boundary are replaced with the lower boundary value, values ​​higher than the upper boundary are replaced with the upper boundary value, and values ​​within the range are retained without replacement. This yields the boundary-corrected individuals. For individuals in the inherited satellite subpopulation whose original shaft diameter did not exceed the feasible range of the target shaft diameter, their transition fillet radius value is also compared and verified with the feasible range recalculated based on their own shaft diameter value. If it exceeds the range, it is reset according to the above rules to avoid omitting individuals with a qualified shaft diameter but an unqualified transition fillet radius. The updated satellite subpopulation consists of individuals whose boundaries have been corrected after resetting and individuals that have been verified to be within the feasible region, with a total of fifteen individuals. The updated anchor population consists of new anchor individuals and fourteen existing anchor individuals from the original anchor population that have not been replaced. The new anchor individuals and their corresponding updated satellite subpopulations correspond one-to-one according to the number of spline teeth, which is used for the calculation of fitness values ​​and the selection of optimal parameter sets in subsequent steps.

[0037] In one specific embodiment, step S4 includes: The target anchor individual with the best fitness value is selected from the updated anchor population, and the target satellite subpopulation corresponding to the target anchor individual is obtained. The target satellite individual with the best fitness value is obtained by screening the target satellite subpopulation in the updated satellite subpopulation, and the target shaft diameter value and the target transition fillet radius value are obtained; Based on the target shaft diameter and target transition fillet radius, material stress constraint verification is performed. Individual target satellites that exceed the material stress constraint are reset to individuals with the second-best fitness value in the target satellite subpopulation, thus obtaining the verified satellite individuals. The optimal structural parameter set is composed of the spline tooth count of the target anchor point individual, the shaft diameter of the verified satellite individual, and the transition fillet radius.

[0038] Specifically, the fitness value of each anchor individual in the updated anchor population is obtained by weighting and summing the fatigue life value and manufacturing cost value of its corresponding satellite subpopulation after solid-phase development processing and convergence. The target anchor individual is the one with the highest fitness value in the entire updated anchor population, and the target satellite subpopulation is the updated satellite subpopulation corresponding to the target anchor individual. The fitness values ​​of the fifteen satellite individuals in the target satellite subpopulation are also calculated by multiplying the fatigue life value by 0.7, adding the reciprocal of the manufacturing cost value by 1000, and then multiplying by 0.3. The individual with the highest fitness value is determined as the target satellite individual, and the target shaft diameter value and target transition fillet radius value are read from this individual.

[0039] The material stress constraint verification process involves substituting the target shaft diameter and target transition fillet radius values ​​back into the formulas for calculating the stress concentration factor and nominal torsional stress to determine the maximum stress at the critical section. This stress is then compared with the allowable stress of 380 MPa. The allowable stress is determined by dividing the yield strength of the alloy structural steel material used in the floating half-shaft, which is 610 MPa, by a safety factor of 1.6. The safety factor of 1.6 is a value selected to account for the alternating torsional load on the floating half-shaft and to allow for fatigue crack propagation. When the maximum stress at the critical section exceeds 380 MPa, it is determined to exceed the material stress constraint. In this case, the target satellite individual is reset to the individual with the second-highest fitness value in the target satellite subpopulation. The shaft diameter and transition fillet radius values ​​of this second-highest individual are then substituted back into the stress concentration factor and nominal torsional stress calculation formula. If it still exceeds 380 MPa, the next individual is selected in order of fitness value, and the above verification is repeated until an individual with a maximum stress at the critical section not exceeding 380 MPa is found. This individual is then selected as the verified satellite individual. If the target satellite individual itself does not exceed the material stress constraint, it is not reset and is directly used as the verified satellite individual. The optimal structural parameter set is composed of the spline tooth number variable of the target anchor point individual, the shaft diameter value of the verified satellite individual, and the transition fillet radius value, which serve as the final floating half-shaft structure design parameters output by this application.

[0040] The forklift drive axle half-shaft three-phase optimization method in this application embodiment has been described above. The forklift drive axle half-shaft three-phase optimization system in this application embodiment is described below. One embodiment of the forklift drive axle half-shaft three-phase optimization system in this application embodiment includes: The encoding module is used to perform population encoding on the spline tooth count variable to obtain the anchor point population, and to perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable based on the anchor point population to obtain the satellite subpopulation; The exploration module is used to perform solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing on the satellite subpopulation using a three-phase search algorithm to obtain the fitness value of anchor point individuals. The correction module is used to process the anchor population using the three-phase search algorithm based on the fitness value of the anchor individuals. During the gas phase exploration process, a new anchor individual is generated. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood range, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that exceed the feasible domain are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. The filtering module is used to select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

[0041] This invention also provides a three-phase optimization device for forklift drive axle half-shafts, which can be a server. The device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor, designed as a computer, provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores the data corresponding to this embodiment. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it implements the above-described method.

[0042] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the three-phase optimization method for the forklift drive axle half-shaft.

[0043] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0044] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a forklift drive axle half-shaft three-phase optimization device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0045] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A three-phase optimization method for forklift drive axle half-shafts, characterized in that, The method includes: Step S1: Perform population encoding on the spline tooth count variable to obtain the anchor point population. Based on the anchor point population, perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable to obtain the satellite subpopulation. Step S2: The satellite subpopulation is subjected to solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing using a three-phase search algorithm to obtain the fitness value of the anchor point individuals; Step S3: Based on the fitness value of the anchor individuals, the three-phase search algorithm is applied to the anchor population. During the gas phase exploration process, new anchor individuals are generated. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood range, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that exceed the feasible domain are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. Step S4: Select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

2. The three-phase optimization method for forklift drive axle half-shafts according to claim 1, characterized in that, Step S1 includes: The spline tooth count variable is subjected to interval random sampling to obtain the set of spline tooth count values; The set of spline tooth count values ​​is deduplicated and merged to obtain the anchor point population; The pitch circle diameter of the spline is calculated by performing a process on the spline tooth number variable in the anchor population based on the spline module. Based on the spline pitch circle diameter, the shaft diameter variable is processed by interval boundary calculation to obtain a feasible interval for the shaft diameter. Based on the feasible interval for the shaft diameter, the shaft diameter variable is randomly sampled to obtain a shaft diameter value. Based on the shaft diameter value, the transition fillet radius variable is processed by interval boundary calculation to obtain a feasible interval for the transition fillet radius. Based on the feasible interval for the transition fillet radius, the transition fillet radius variable is randomly sampled to obtain a transition fillet radius value. The shaft diameter value and the transition fillet radius value constitute the satellite subpopulation.

3. The three-phase optimization method for forklift drive axle half-shafts according to claim 2, characterized in that, Step S2 includes: The satellite subpopulation was subjected to gas phase exploration processing. Within the feasible range of shaft diameter and transition fillet radius, the individuals with the worst fitness values ​​were resampled to obtain the gas phase processed satellite subpopulation. The gas-phase processed satellite subpopulation is subjected to liquid-phase transition processing. Based on the current best individual, a random offset is superimposed and boundary reset processing is performed to obtain the liquid-phase processed satellite subpopulation. After liquid phase processing, the satellite subpopulation is subjected to solid phase development processing. The current best individual is superimposed with an offset smaller than that of the liquid phase transition processing and then subjected to local fine search processing to obtain solid phase convergent satellite individuals. The stress concentration factor and nominal torsional stress of the solid-phase convergent satellite individual are calculated to obtain the maximum stress of the critical section. The maximum stress of the critical section is then input into the fatigue life calculation formula to obtain the fatigue life value. The manufacturing cost of the solid-phase convergent satellite individual is calculated to obtain the manufacturing cost value. The fatigue life value and the manufacturing cost value are then weighted and summed to obtain the fitness value of the anchor point individual.

4. The three-phase optimization method for forklift drive axle half-shafts according to claim 3, characterized in that, Step S3, which involves processing the anchor population using the triphasic search algorithm based on the fitness values ​​of the individual anchors, includes: The anchor population is subjected to gas phase exploration processing. Within the range of the spline tooth number variable, the anchor individuals with the worst fitness values ​​are resampled to obtain the new anchor individuals. The anchor population is subjected to liquid phase transition processing. The perturbation processing is performed based on the spline tooth number variable of the current best anchor individual superimposed with random offset, so as to obtain the anchor individual after liquid phase processing. The anchor population is subjected to solid-phase development processing. The spline tooth number variable of the current best anchor individual is superimposed with an offset that is less than that of the liquid-phase transition processing, and a local fine search is performed to obtain the anchor individual after solid-phase processing.

5. The three-phase optimization method for forklift drive axle half-shafts according to claim 4, characterized in that, Step S3, which involves obtaining the satellite subpopulation corresponding to the new anchor individual through inheritance processing of the satellite subpopulation corresponding to the existing anchor individual, includes: The difference in the number of spline teeth between the new anchor point individual and the existing anchor point individuals in the anchor point population is calculated to obtain the neighborhood difference. The neighborhood difference is compared with a preset neighborhood threshold to filter out target individuals with existing anchor points within the neighborhood range; The satellite subpopulation corresponding to the existing anchor point individual of the target is copied to obtain the inherited satellite subpopulation corresponding to the new anchor point individual.

6. The three-phase optimization method for forklift drive axle half-shafts according to claim 5, characterized in that, Step S3 involves boundary correction processing for individuals in the inherited satellite subpopulation that exceed the feasible domain, including: Based on the new anchor point individual, the interval boundary calculation process is performed on the shaft diameter variable to obtain the feasible interval of the target shaft diameter; The axis diameter value of individuals in the inherited satellite subpopulation is compared with the feasible range of the target axis diameter. Individuals that exceed the feasible range of the target axis diameter are selected and their axis diameter values ​​are reset to the corresponding range boundary values ​​to obtain the corrected axis diameter values. Based on the corrected shaft diameter value, the transition fillet radius variable is processed by the interval boundary calculation to obtain the feasible interval of the target transition fillet radius. Based on the feasible interval of the target transition fillet radius, the transition fillet radius value of the boundary overflow individual is reset to obtain the boundary corrected individual. The updated satellite subpopulation is formed by the individuals after boundary correction and the individuals in the inherited satellite subpopulation that have not exceeded the feasible domain. The new anchor point individuals are then incorporated into the anchor point population to obtain the updated anchor point population.

7. The three-phase optimization method for forklift drive axle half-shafts according to claim 1, characterized in that, Step S4 includes: The target anchor individual with the optimal fitness value is selected from the updated anchor population to obtain the target satellite subpopulation corresponding to the target anchor individual; The target satellite individual with the optimal fitness value is obtained by screening the target satellite subpopulation in the updated satellite subpopulation, and the target shaft diameter value and the target transition fillet radius value are obtained; Based on the target shaft diameter and the target transition fillet radius, material stress constraint verification is performed. Individual target satellites that exceed the material stress constraints are reset to individuals with the second-best fitness values ​​in the target satellite subpopulation, thus obtaining verified satellite individuals. The optimal structural parameter set is composed of the spline tooth count of the target anchor point individual, the shaft diameter of the verified satellite individual, and the transition fillet radius.

8. A three-phase optimization system for a forklift drive axle half-shaft, characterized in that, For implementing the three-phase optimization method for forklift drive axle half-shafts as described in any one of claims 1-7, the three-phase optimization system for forklift drive axle half-shafts comprises: The encoding module is used to perform population encoding on the spline tooth count variable to obtain the anchor point population, and to perform conditional interval mapping on the shaft diameter variable and the transition fillet radius variable based on the anchor point population to obtain the satellite subpopulation; The exploration module is used to perform solid-phase development processing, liquid-phase transition processing, and gas-phase exploration processing on the satellite subpopulation using a three-phase search algorithm to obtain the fitness value of anchor point individuals. The correction module is used to process the anchor population using the three-phase search algorithm based on the fitness value of the anchor individuals. During the gas phase exploration process, a new anchor individual is generated. If the difference between the new anchor individual and the existing anchor individuals in the anchor population is within the neighborhood range, the satellite subpopulation corresponding to the existing anchor individual is inherited to obtain the satellite subpopulation corresponding to the new anchor individual. Individuals in the inherited satellite subpopulation that exceed the feasible domain are subject to boundary correction processing to obtain the updated anchor population and the updated satellite subpopulation. The filtering module is used to select the optimal set of structural parameters that satisfy the constraints from the updated anchor population and the updated satellite subpopulation.

9. A three-phase optimization device for forklift drive axle half-shafts, characterized in that, The method includes a memory and a processor, wherein the memory stores a computer program that can run on the processor, and the processor executes the computer program to implement the three-phase optimization method for the forklift drive axle half-shaft as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to execute the three-phase optimization method for the forklift drive axle half-shaft as described in any one of claims 1 to 7.

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