Helical gear reducer design method based on multi-target marine predator algorithm

Abstract

The invention discloses a helical gear reducer design method based on a multi-objective marine predator algorithm, which comprises the following steps of: carrying out multi-objective optimization on gear light weight, overlap ratio and vibration stability, setting three objective functions, determining constraint conditions, and carrying out multi-objective optimization on the gear light weight, the overlap ratio and the vibration stability; and obtaining a mathematical model of the gear transmission system according to the bending strength and contact strength design parameters of the designed gear material. The global search capability of a multi-target marine predator algorithm is utilized, a reference point strategy is adopted as a selection method of an elite matrix to obtain a solution set, and an optimal solution is selected according to the importance degree of each target function and a target speed reducer emphasized optimization target. According to the method, the fast convergence speed and the high stability of the marine predator algorithm can be effectively utilized, the conflict problem of multiple objective functions can be balanced, multiple design optimization objectives needing to be optimized are considered, a good balance point is found, and therefore the comprehensive performance of the gear structure is improved, the cost is reduced, and the design efficiency is improved.

Description

Technical Field

[0001] The invention relates to a reducer design technology of a multi-objective ocean predator algorithm, and in particular to a helical gear reducer design method based on the multi-objective ocean predator algorithm. Background Art

[0002] Helical cylindrical gear reducers have been widely used in various mechanical equipment due to their high-precision transmission characteristics. The working principle of the helical cylindrical gear reducer is mainly to achieve the purpose of deceleration by driving the large gear on the output shaft through the small gear on the input shaft. The helical cylindrical gear reducer adopts a helical gear design. Compared with spur gears, the helical gears have a larger overlap and a smoother meshing process. In the future, the trend of helical cylindrical gear reducers will develop in the direction of lightweighting, improving transmission efficiency, reducing vibration and noise, and enhancing load-bearing capacity.

[0003] With the continuous improvement of the requirements for the working of mechanical equipment due to industrial upgrading, the quality of the reduction system not only requires more material input in the initial stage of system manufacturing, but also consumes more energy during operation, which cannot meet the requirements of building an environmentally friendly low-carbon society. On the other hand, the helical cylindrical gear reducer can provide a larger gear meshing overlap during the transmission process. If the overlap is insufficient, it will be difficult to ensure the operating stability of the system when the high-speed gear rotates, thereby affecting the transmission accuracy of the reducer. In addition, the gear manufacturing accuracy and assembly errors will cause high-speed gear meshing vibration, and the noise generated will affect the health of the staff and even cause fatigue failure of the transmission system.

[0004] Currently, most research in the field of gear structure design often focuses on the optimization design of a single objective, which makes it difficult to improve the comprehensive performance of the entire gear structure at the same time. Summary of the invention

[0005] In view of the above problems, the present invention provides a design method for a helical cylindrical gear reducer, which uses a multi-objective marine predator algorithm (MOMPA) to simultaneously optimize the weight, overlap and vibration stability of the gear pair, and analyzes and verifies the optimized gear model to improve the performance of the gear and improve the overall performance of the gear.

[0006] To achieve the above object, the present invention adopts the following technical solution: A helical gear reducer design method based on MOMPA algorithm, the steps of which are as follows:

[0007] 1) Multi-objective optimization of gear lightweight, overlap and vibration stability; select the main independent parameters that can effectively affect the transmission performance as design variables, including the number of gear teeth z and normal module m in the gear transmission system n , helix angle β, gear tooth width b are independent parameters, and the optimal design variable X is obtained;

[0008] 2) Establish the first objective function: reduce the volume of the gear to make the gear lighter, and use the center distance of the gear transmission system as an indicator to measure the weight, which is the first objective function f1(x);

[0009] 3) Establish the second objective function: Select the appropriate gear overlap to ensure that more gear pairs are engaged at any given time to reduce load fluctuations, and use the overlap as the second objective function f2(x);

[0010] 4) Establish the third objective function: In the process of gear transmission, by improving the parameters of the gear pair, reducing the vibration and noise of the gear system, taking vibration stability as the optimization goal, performing vibration analysis on the gears in the transmission process, and using the double-spring vibration model to derive the driving gear speed n1 and the actual maximum gear speed n under normal working conditions. cr ; Taking the minimum vibration noise as the optimization goal, it is transformed into the third objective function: f3(x) = -|n1-n cr |;

[0011] 5) Determine the constraints. In order to make the optimized parameters better meet the actual needs of the project, the constraints of the gear include geometric parameter constraints and strength constraints; the constraints include the helix angle, normal module, tooth width, number of teeth of the master and driven wheels, tooth root bending fatigue strength and tooth surface contact fatigue strength. (1) ~g (i) The mathematical formula expression of the constraint conditions, where i is the number of mathematical expressions obtained;

[0012] 6) The pressure angle of the cylindrical gear is 20°, and the tooth height coefficient is selected as The head clearance coefficient is c * =0.25;

[0013] 7) According to the bending strength and contact strength design parameters of the designed gear material, the mathematical model of the relevant gear transmission system is obtained, thereby obtaining the parameter expressions f1(x), f2(x) and f3(x) of the corresponding objective function;

[0014] 8) The MOMPA algorithm uses the marine predator algorithm (MPA) as the basic algorithm, takes advantage of the global search capability of the MPA algorithm, and adopts the reference point strategy as the selection method of the elite matrix. At the same time, in order to ensure the diversity of the population and the global search capability, a Gaussian perturbation mechanism is introduced; there are two key parts for the solution. The first part is the archive, which is used to store the optimal solution of the Pareto frontier; the second part is the top predator selection strategy, which selects the appropriate top predator in the archive for the subsequent iteration process;

[0015] 9) The objective function mathematical model established by the objective functions f1(x), f2(x) and f3(x) is calculated using the MOMPA algorithm using MATLAB software; in the MOMPA algorithm, the center distance, overlap and driving wheel speed difference objective functions are solved using the MOMPA algorithm, and the population size, number of iterations and fish aggregation effect parameters (FADs) are set; for the multi-objective optimization design of the reducer, the final non-dominated solution is distributed in the solution space and distributed on the Pareto front of the reducer objective function; each point represents the Pareto optimal solution, and the Pareto front reflects the characteristics of the mutual constraints between the center distance, overlap and driving wheel speed difference. The optimal solution is selected according to the importance of each objective function and the optimization target of the target reducer.

[0016] After comparison, the MPA algorithm of the present invention has good solving performance and solving speed for single-peak and multi-peak problems, and has good stability; because the reducer problem is a multi-objective problem and has a large range of constraints, by selecting the MOMPA algorithm with a wide solution range as the basic algorithm, the liberation obtained by the non-dominated sorting method is sorted into the Pareto frontier, and it is necessary to balance the conflict of multiple objective functions, and the MPA algorithm can effectively utilize the fast convergence speed and strong stability. It can balance the conflict of multiple objective functions, consider the multiple design optimization goals that need to be optimized, and find the best trade-off point, thereby improving the comprehensive performance of the gear structure, reducing costs, and improving design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 3D model structural diagram of a single-stage helical cylindrical gear reducer according to an embodiment of the present invention;

[0018] Figure 2 It is a schematic diagram of a double spring model of the present invention;

[0019] Figure 3 It is a block diagram of the steps of the multi-target marine predator algorithm of the present invention;

[0020] Figure 4 It is the Pareto front state distribution diagram of the objective function of the single-stage reducer in the present invention. DETAILED DESCRIPTION

[0021] The present invention is further described below with reference to the accompanying drawings and embodiments. Figures 1 to 4 The present invention uses an optimization method to improve the MPA algorithm into a MOMPA algorithm suitable for multiple objectives, multiple constraints and a wide solution range, and is applied to multiple objective optimizations related to helical cylindrical gears.

[0022] by Figure 1Taking the single-stage helical gear reducer as an example, a driving gear pinion 3 is installed in the reducer housing 1, and the driving gear pinion 3 is meshed with the driven gear large gear 2 as an integrated structure, and the large gear 2 adopts a web type. The specific implementation method is as follows:

[0023] Step 1: Establish an optimization design model: adopt multi-objective optimization in three aspects: gear lightweight, overlap, and vibration stability. The main independent parameters that can effectively affect the transmission performance in the gear transmission system are the design variables: the number of teeth z1 of the small gear 3, the number of teeth z2 of the large gear 2, and the normal module m. n , helix angle β, tooth width b1 of small gear 3 and tooth width b2 of large gear 2. Therefore, the optimal design variables are:

[0024] X=[x1,x2,x3,x4,x5,x6] T =[m n ,z1,z2,β,b1,b2] T ;

[0025] Step 2: derive the objective function:

[0026] (1) Lightweight:

[0027] In the process of lightweight design of gears, the gear volume is reduced to achieve lightweight processing, and the center distance of the gear transmission system is used as an indicator to measure the weight. The calculation formula is:

[0028]

[0029] Where: m n represents the normal module, β represents the helix angle of the helical gear, z1,z2 represents the number of teeth on the large and small gears. The above formula is the first objective function.

[0030] (2) Degree of coincidence:

[0031] In order to make the helical gear run smoothly and improve the transmission efficiency, the overlap is used as the second objective function:

[0032] ε=ε α +ε β ;

[0033] ε α = z1(tanα a1 -tanα′)+z2(tanα a2 -tanα′);

[0034]

[0035] The second objective function is derived from the overlap target. However, since the problem to be solved is a minimization problem, a negative sign is added to the second objective function to solve the minimum value:

[0036]

[0037] Where: α is the end face overlap of the helical gear transmission, ε β is the axial overlap of the helical gear transmission, α' is the meshing angle, α a1 , α a2 is the tooth tip circle pressure angle.

[0038] (3) Vibration stability:

[0039] During the gear transmission process, the dynamic excitation force between the gear pairs is caused by multiple factors in the gear transmission system. By improving the parameters of the gear pairs, the vibration and noise of the gear system can be reduced. Therefore, vibration stability is taken as the third optimization goal.

[0040] To analyze the vibration of the gears during the transmission process, the moment of inertia of the meshing gears can be equivalent to the meshing line of the gears for analysis. J1 and J2 represent the moment of inertia of the small gear and the large gear respectively, and the equivalent masses M1 and M2 of the large and small gears can be calculated:

[0041] J=0.125mD 2 ;

[0042]

[0043] Among them: r1, r2 represent the base circle radius of the small gear and the large gear respectively; D represents the pitch circle diameter; m n represents the normal modulus; β represents the helix angle; α t represents the end face pressure angle; z1 and z2 represent the number of teeth on the pinion and gear respectively;

[0044] The moment of inertia can be calculated equivalently by:

[0045]

[0046] Among them: ρ represents density, d represents the pitch circle diameter, and b represents the tooth width.

[0047] like Figure 2 As shown, the large gear M1 and the small gear M2 are assumed to be objects with uniform stiffness, and their average stiffness is K1 and K2. Therefore, the gear model is assumed to be a double spring model, in which each gear is regarded as an object connected to a spring block. Figure 2 M1 and M2 in the figure, where the average stiffness of the small gear M2 and the large gear M1 is:

[0048]

[0049] Where: E represents the elastic modulus, B1 and B2 represent the tooth width of the small gear and the large gear respectively.

[0050] I represents the moment of inertia as follows:

[0051]

[0052] Since the vibration model corresponding to the double-spring model can be assumed to be a single-side spring vibration, it can be simplified to a single-spring model. At the gear meshing line, the equivalent mass is:

[0053]

[0054] Spring model equivalent stiffness K e for:

[0055]

[0056] The natural vibration frequency f of the gear system n for:

[0057]

[0058] When f = f n When f<<f n , the vibration of the gear is small, so the vibration of the gear is closely related to the difference between the meshing excitation frequency and the natural frequency of the active gear. Let f = f n , the formula is as follows:

[0059]

[0060] n1 represents the speed of the driving gear under normal working conditions, n cr Indicates the actual maximum speed of the gear, where α t Represents the end pressure angle.

[0061] Corresponding formula:

[0062]

[0063] The optimization goal of minimizing vibration noise can be transformed into the following objective function:

[0064] f3(x)=-|n1-n cr |;

[0065] n1 represents the driving gear speed, n cr Represents the actual maximum speed of the gear;

[0066] Step 3: Determine the constraints: In order to make the optimized solution parameters better meet the actual engineering needs, the gear constraints include geometric parameter constraints and strength constraints. The constraints include the helix angle (g (1) ~g (2) ), normal modulus (g (3) ~g (4) )、tooth width(g (5) ~g (10) ), the number of teeth of the driving and driven wheels (g (11) ~g (14) ), tooth root bending fatigue strength and tooth surface contact fatigue strength constraints (g (15) ~g (17) ) and select the parameter constraint range as required.

[0067] The above constraints are converted into mathematical formulas as follows:

[0068]

[0069]

[0070] in:

[0071]

[0072] Y Fa -Tooth shape coefficient; Y Sa -Stress correction factor; Y ε - coincidence coefficient; Y β - Helix angle coefficient;

[0073] [σ F ]-allowable bending strength; [σ H ]-allowable fatigue strength;

[0074]

[0075] K=K A K V K Hβ K Hα ,

[0076] Z H -Zone coefficient; Z E -Elastic modulus; Z g - coincidence coefficient; Z β - Helix angle coefficient;

[0077] ε α -End face overlap; ε β - longitudinal overlap;

[0078] K-load factor; KA -Utilization factor; K F -Dynamic load factor; K β - tooth load distribution coefficient;

[0079] K α - load distribution coefficient between teeth; u represents the gear ratio;

[0080] Under the condition that the two gears are made of the same material, since the number of teeth of the pinion 3 is less than that of the large gear 2, the contact of the pinion 3 is more than that of the large gear 1 in one working cycle. Therefore, the pinion 3 is more susceptible to acoustic fatigue failure, and the tooth surface contact fatigue strength needs to be checked according to the pinion.

[0081] Step 4: The pressure angle of the helical gear is 20°, and the tooth top height coefficient is selected as The headspace coefficient is c*=0.25.

[0082] Step 5: In order to verify the correctness and effectiveness of this method, specific materials are selected to illustrate:

[0083] according to Figure 1 The three-dimensional model of the single-stage helical cylindrical gear reducer shown in the figure, as well as the working conditions and working requirements of the designed reducer, the corresponding initial parameters calculated are shown in Table 1:

[0084] Table 1

[0085]

[0086] The material of the pinion gear is 40Cr, with a density of 7870kg / m 3 , the elastic modulus is 2.11×10 11 Pa, Poisson's ratio 0.277.

[0087] The large gear is made of 45# steel with a density of 7890kg / m 3 , elastic modulus 2.09×10 11 Pa, Poisson's ratio is 0.269. The relevant parameters for calculating bending strength and contact strength in the gear transmission system are obtained.

[0088] Substitute the relevant parameters into g (15) , g (16) , Y Fa The relevant calculation formula gives the mathematical model of the gear transmission system:

[0089]

[0090] Thus, the parameter expression of the corresponding objective function is obtained:

[0091]

[0092] Step 6: Use the MOMPA algorithm for multi-objective optimization design: The mathematical model established by the objective functions of formula f1(x), f2(x), and f3(x) is calculated using the MOMPA algorithm. In the MOMPA algorithm, the center distance, overlap, and driving wheel speed difference objective functions are solved using the MOMPA algorithm, with the population size set to 100, the number of iterations set to 10,000, and the FADs set to 0.2.

[0093] Depend on Figure 3 The multi-objective marine predator algorithm flow chart is shown as follows: after the parameters are set and the population is initialized, the iteration begins. If the number of iterations t is less than the maximum number of iterations T, the individual target value is calculated, and the non-dominated optimal solution is found and the archive is updated. After the archive is updated, there are two situations: archive overflow and archive non-overflow.

[0094] An archive is a collection of non-dominated optimal solutions. The capacity of the collection is set to half the size of the population. The update process of the archive is to collect solutions from the population and compare and update the original solutions with the new solutions generated after iteration. The update process of the archive follows the following guidelines:

[0095] (1) Screening new solutions: If any objective function in the newly generated solution cannot be better than the corresponding objective function in the original solution, the new solution is said to be non-dominated by the old solution, and the newly generated solution will not be archived;

[0096] (2) Solution replacement: If any objective function in the newly generated solution is better than the original solution, the new solution is said to dominate the old solution, and the original solution will be removed from the archive, and the new solution will replace the original solution set;

[0097] (3) Adding solutions: If the new solution and the original solution are both better than each other, the new solution will be archived and placed on the same Pareto front as the old solution.

[0098] When the archive is full, if the new solution meets the archive update criteria, it will not be able to enter the archive, resulting in the loss of the optimal solution. The solution is to randomly remove a solution from the archive, but the distribution of the solution set in the archive must be considered during the removal process. The removed solution is the one that has the least impact on the distribution of the solution set. Therefore, it is necessary to evaluate the crowdedness index of the solution set in the Pareto front, where the distance is calculated as follows:

[0099]

[0100] Among them, max represents the maximum value of the target, min represents the minimum value, and Archive size represents the size of the archive. When there are two targets, the optimal solution of the Pareto frontier is usually a line, and when there are multiple targets, it is a hypersurface.

[0101] Each solution in the archive is kept at a preset distance, and the number of nearby solutions is calculated within this distance range. The number is used as an indicator of crowding, which is called crowding metric. A solution with a lower crowding metric means that the space explored by the solution is new, so it needs to be retained; on the contrary, a solution with a higher crowding metric means that it is more concentrated in the solution space, so it is more likely to be removed.

[0102] In a population, the top predator is the individual with the best optimization effect. It guides the foraging of other individuals. Whether the marine predator algorithm can converge mainly depends on the elite predator matrix. Since different optimization objectives have different objective functions in the multi-objective search space, it is impossible to directly select the top predator. Therefore, the non-dominated sorting method will be used to find the top predator, so the individual is selected from the archive as the top predator. The principle is as follows:

[0103] Each individual has an independent fitness metric that is only used to compare predators:

[0104] f i =N i ;

[0105] By calculating the new fitness value of each individual, the individual with the highest fitness value is selected as the top predator. Multi-target marine predators may select multiple top predators. Finding the sparse distribution area of ​​the solution through the elite matrix is ​​conducive to the algorithm to obtain the solution set distribution. The elite matrix of multi-target marine predators is as follows:

[0106]

[0107] in: Represents the selected top predator, where the parameter m ranges from 1<m<k, and the parameter k ranges from k≤Archive size. The elite matrix provides the current best prey position for each predator. In the algorithm, N represents the population size, and D represents the dimension in the optimization problem.

[0108] If archive overflow does not occur: select the top predator and reconstruct the elite matrix.

[0109] In the MOMPA algorithm, the matrix formed by recording the positions of predators with high capabilities is the elite matrix, and the data in the elite matrix will be shared with all predators.

[0110] There are two main processes of non-dominated sorting: domination and sorting. Domination is used to compare the advantages and disadvantages of multiple solutions.

[0111] Sorting is to stratify the dominance relationships between the identified solution sets. Subsequently, the Hypervolume evaluation index will be used to determine the superiority of each level based on the index values. Non-dominated sorting first identifies all non-dominated solutions and forms the first front with these non-dominated solutions. From the remaining dominated solutions, non-dominated solutions are identified again to form the second front, and the above process is repeated until all solution sets are sorted into the fronts.

[0112] When the iteration number t < T / 3, it is the exploration stage in the MOMPA algorithm, and at this time, the population performs Brownian motion. When T / 3 < t < 2T / 3, it is the transition from the exploration stage to the exploitation stage in the MOMPA algorithm. At this time, 1 / 2 of the population performs Brownian motion, and the other 1 / 2 performs Lévy motion. When the iteration number satisfies 2T / 3 < t < T, the population performs Lévy motion, and finally, the ocean memory and FADs effects are considered. If the iteration number is less than 10,000, the above steps are repeated; otherwise, the optimal solution is obtained.

[0113] If the archive overflows: Calculate the crowding degree, manage the new archive, and then return to the step of selecting the top predator and reconstructing the elite matrix and proceed downward until the optimal solution is obtained.

[0114] Step 7, obtain the results: For the multi-objective optimization design of the reducer, the distribution of the non-dominated solutions in the final generation in the solution space is as Figure 4 The Pareto front of the objective function of the single-stage reducer. Each point represents a Pareto optimal solution, and there is no superiority or inferiority among each Pareto optimal solution, reflecting the mutual restraint characteristics among the center distance, contact ratio, and active wheel speed difference. The optimal solution is selected according to the importance of each objective function and the experience of the designer.

[0115] In this example, the lightest weight is given priority. Therefore, the solution sets with smaller center distances and smaller tooth width parameters are selected, and a set of compromise solution sets is selected for comparison with the initial design scheme.

[0116] Round the optimized parameters. The results of the multi-objective optimization after solution are shown in Table 2:

[0117] Table 2

[0118]

[0119] For the objective function values after optimizing the multi-objective indicators, the optimized values of each objective function are balanced. Among them, the center distance is reduced by 16.59%, the contact ratio is increased by 8.05%, and at the same time, the active wheel speed difference is increased by 14.8%.

[0120] Step 8: Compare the results of single-objective optimization and multi-objective optimization of MPA algorithm with those of MOMPA algorithm: As shown in Table 3 below, Scheme 1 is a single-objective optimization design based on center distance, Scheme 2 is a single-objective optimization design based on overlap, Scheme 3 is a single-objective optimization design based on driving wheel speed difference, and Scheme 4 is a multi-objective optimization design. The comparison of optimization results is shown in Table 3:

[0121] Table 3

[0122]

[0123] From the comparison of the optimization results before and after in Table 3, it can be seen that: the center distance obtained by Scheme 4 is worse than that of Scheme 1, and the driving wheel speed difference index is better than that of Scheme 1, and the driving wheel speed difference index of Scheme 1 is much lower than that of Scheme 2, so it cannot be selected in practice. The overlap index obtained by Scheme 4 is worse than that of Scheme 2, and the driving wheel speed difference and center distance index are better than those of Scheme 2. The driving wheel speed difference obtained by Scheme 4 is worse than that of Scheme 3, and the center distance index is better than that of Scheme 3. In addition, due to the large tooth width, it will cause an increase in weight and cannot achieve the lightweight goal well. The single-objective optimization design of Schemes 1, 2 and 3 can optimize in the single-objective direction that needs to be optimized, but ignores the performance of other aspects of the reducer. Scheme 4 can comprehensively consider the performance of the reducer in the three target directions of center distance, overlap and driving wheel speed difference, and solve the optimal solution that balances multiple objectives.

[0124] Reducers are widely used in the engineering field and have specific requirements in terms of usage space, load-bearing capacity, vibration and noise. Multiple different parameter combinations are needed to meet engineering needs. Multi-objective optimization can be adopted to select the optimal solution set in the Pareto front.

[0125] pass Figure 4 It can be clearly seen from the Pareto front solution set of the single-stage reducer objective function that there is a mutual constraint relationship between the minimum center distance of the reducer, the maximum overlap, and the maximum difference in the speed of the driving wheel. Therefore, the ideal design goal can be selected through the Pareto front to complete the optimization of the gear transmission system. However, since the objective function, constraints, and parameter variables of multi-objectives are more complex than those of single-objective optimization, it is suitable for optimizing reducers with complex conflict problems.

Claims

1. A helical gear reducer design method based on a multi-objective marine predator algorithm, characterized in that: The steps are as follows: 1) Multi-objective optimization of gear lightweight, overlap and vibration stability; select the main independent parameters that can effectively affect the transmission performance as design variables, including the number of gear teeth z and normal module m in the gear transmission system n , helix angle β, gear tooth width b are independent parameters, and the optimal design variable X is obtained; 2) Establish the first objective function: reduce the volume of the gear to make the gear lighter, and use the center distance of the gear transmission system as an indicator to measure the weight, which is the first objective function f1(x); 3) Establish the second objective function: Select the appropriate gear overlap to ensure that more gear pairs are engaged at any given time to reduce load fluctuations, and use the overlap as the second objective function f2(x); 4) Establish the third objective function: In the process of gear transmission, by improving the parameters of the gear pair, reducing the vibration and noise of the gear system, taking vibration stability as the optimization goal, performing vibration analysis on the gears in the transmission process, and finally deriving the active gear speed n1 and the actual maximum gear speed n under normal working conditions using the double-spring vibration model. cr ; Taking the minimum vibration noise as the optimization goal, it is transformed into the third objective function: f3(x) = -|n1-n cr |; 5) Determine the constraints. In order to make the optimized parameters better meet the actual needs of the project, the constraints of the gear include geometric parameter constraints and strength constraints; the constraints include the helix angle, normal module, tooth width, number of teeth of the master and driven wheels, tooth root bending fatigue strength and tooth surface contact fatigue strength. (1) ~g (i) The mathematical formula expression of the constraint conditions, where i is the number of mathematical expressions obtained; 6) The pressure angle of the cylindrical gear is 20°, and the tooth height coefficient is selected as The head clearance coefficient is c * =0.25; 7) According to the bending strength and contact strength design parameters of the designed gear material, the mathematical model of the relevant gear transmission system is obtained, thereby obtaining the parameter expressions f1(x), f2(x) and f3(x) of the corresponding objective function; 8) The multi-objective marine predator algorithm uses the marine predator algorithm as the basic algorithm, takes advantage of the global search capability of the marine predator algorithm, and adopts the reference point strategy as the selection method of the elite matrix. At the same time, in order to ensure the diversity of the population and the global search capability, the Gaussian perturbation mechanism is introduced; there are two key parts for the solution. The first part is the archive, which is used to store the optimal solution of the Pareto frontier; the second part is the top predator selection strategy, which selects the appropriate top predator in the archive for the subsequent iterative process; 9) The objective function mathematical model established by the objective functions f1(x), f2(x) and f3(x) is calculated using MATLAB software and a multi-objective marine predator algorithm; in the multi-objective marine predator algorithm, the center distance, overlap and driving wheel speed difference are used as objective functions, and the multi-objective marine predator algorithm is used to solve the problem, and the population size, number of iterations and fish aggregation effect parameters are set; for the multi-objective optimization design of the reducer, the final non-dominated solution is distributed in the solution space and on the Pareto front of the reducer objective function; each point represents the Pareto optimal solution; the Pareto front reflects the characteristics of the mutual constraints between the center distance, overlap and driving wheel speed difference, and the optimal solution is selected according to the importance of each objective function and the optimization target of the target reducer.

Images