Lightweight design method for screw rotor

Abstract

According to the lightweight design method for the screw rotor, a lightweight model of the screw rotor is constructed, the thicknesses of the end faces of the two ends, the thickness of a working tooth surface, the width of an inner supporting rod and the diameter of an inner supporting column are selected as design variables, and a multi-objective optimization mathematical model containing three objectives including mass, maximum total deformation and first-order inherent frequency is established; the method comprises the steps that firstly, an XGBoost prediction model is established, then a Latin hypercube sampling method is adopted to generate sample data to train the XGBoost prediction model, meanwhile, hyper-parameters of the XGBoost prediction model are optimized through an SNBRO algorithm to obtain an SNRBO-XGBoost multi-target prediction model, then the SNRBO-XGBoost multi-target prediction model serves as a fitness function of an NSGA-III algorithm, a multi-target optimization mathematical model is combined, and finally an NSGA-III multi-target optimization model is established. The method is used for optimizing the structural parameters of the screw rotor, so that the lightweight design of the screw rotor is achieved. By adopting the design method to carry out lightweight design on the screw rotor, the mass of the screw rotor can be reduced, the material utilization rate can be improved, and the dynamic and static performance of the screw rotor can be enhanced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of mechanical engineering optimization design, and specifically relates to a lightweight design method for screw rotors, which is suitable for structural optimization of core components of rotary machines such as compressors and vacuum pumps. BACKGROUND

[0002] In the field of mechanical manufacturing, screw rotors, as key components of rotary machines such as compressors and vacuum pumps, directly affect the operating efficiency and quality of the equipment. However, traditional design and processing methods face many challenges, such as material waste, insufficient processing precision, and high manufacturing costs, making it difficult to meet the needs of modern manufacturing for high-performance, high-precision, and lightweight screw rotors.

[0003] Lightweight technology provides a new path for the performance improvement of screw rotors. This technology can reduce material usage through optimized design, improving operating efficiency while reducing weight, energy consumption, and raw material waste, in line with green manufacturing and sustainable development requirements. However, achieving effective lightweight design is not easy, as it requires precise determination of structural parameters to ensure strength and stiffness while minimizing weight, which poses high requirements for the accuracy and efficiency of optimization algorithms. However, existing lightweight design methods mainly rely on parameter adjustment based on experience combined with finite element simulation. Designers need to manually change structural dimensions and perform multiple simulation verifications to obtain acceptable structural performance. Such methods generally have long design cycles, low efficiency, rely on human experience, and are difficult to fully explore the design space. Moreover, traditional methods are difficult to simultaneously consider multiple target performances such as mass, deformation, and first-order natural frequency. In addition, in modern manufacturing scenarios with complex working conditions and high performance requirements, traditional design methods are prone to trial-and-error cycles, lack the ability to deeply explore the nature of structural performance, and are difficult to meet the actual needs of efficient and high-quality design. Therefore, it is urgent to introduce advanced intelligent optimization algorithms and surrogate models to efficiently solve complex design problems. SUMMARY

[0004] The application provides a screw rotor lightweight design method based on SNRBO-XGBoost-NSGA III, aiming to improve the material utilization rate and dynamic and static performance of the screw rotor, and is suitable for structural optimization design of core components of rotary machines such as compressors. The screw rotor lightweight design method of the application firstly constructs a multi-objective optimization mathematical model according to initial screw rotor model data, then generates sample data by a Latin hypercube sampling method to train an XGBoost prediction model, simultaneously, the SNBRO algorithm is used to optimize the hyperparameters of the XGBoost prediction model to obtain an SNRBO-XGBoost multi-objective prediction model, which is used as a fitness function of the NSGA-III algorithm, and a NSGA-III multi-objective optimization model is established by combining the multi-objective optimization mathematical model, which is used for optimizing the structural parameters of the screw rotor to achieve lightweight design of the screw rotor; the mass and moment of inertia of the screw rotor after optimization design are reduced, and the lightweight performance and dynamic and static performance are improved. Experimental verification shows that the method is superior to the traditional design method in terms of prediction model accuracy and lightweight optimization effect, and the design cycle is greatly shortened.

[0005] The technical scheme of the application is:

[0006] The screw rotor lightweight design method comprises the following steps:

[0007] Step 1, a screw rotor lightweight model is constructed, the screw rotor comprises a spiral shell and an inner support column, the inner support column is located in the spiral shell and connected with the spiral shell through an inner support rod; then, multi-physical field coupling simulation is performed by means of ANSYS software to obtain the initial mass, maximum total deformation and first-order natural frequency of the screw rotor;

[0008] Step 2, the thickness of the end face of the screw rotor lightweight model, the thickness of the working tooth surface, the width of the inner support rod and the diameter of the inner support column are taken as design variables, the upper and lower limits of the design variables and the objective functions are taken as constraint conditions, the minimum mass, the minimum maximum total deformation and the maximum first-order natural frequency of the screw rotor lightweight model are taken as objective functions, and a multi-objective optimization mathematical model is constructed;

[0009] Step 3, a sample data set is constructed by a Latin hypercube sampling, and the sample data set is used to train an XGBoost prediction model; simultaneously, the SNBRO algorithm is used to optimize the hyperparameters of the XGBoost prediction model to construct a high-precision SNRBO-XGBoost multi-objective prediction model;

[0010] Step 4, taking the SNBRO-XGBoost multi-objective prediction model as the fitness function of the NSGA-III algorithm, and combining the multi-objective optimization mathematical model, finally establishing the NSGA-III multi-objective optimization model, optimizing and outputting the optimized structure parameter value, which is used as the design parameter of the screw rotor.

[0011] Compared with the prior art, the screw rotor lightweight design method of the application firstly constructs a screw rotor lightweight model, selects the thickness of the two end faces, the thickness of the working tooth surface, the width of the inner support rod and the diameter of the inner support column as the design variables, establishes a multi-objective optimization mathematical model containing three objectives of mass, maximum total deformation and first-order natural frequency, then uses the Latin hypercube sampling method to generate sample data to train the XGBoost prediction model, at the same time, uses the SNBRO algorithm to optimize the hyperparameters of the XGBoost prediction model to obtain the SNBRO-XGBoost multi-objective prediction model, then takes this as the fitness function of the NSGA-III algorithm, and combines the multi-objective optimization mathematical model, finally establishes the NSGA-III multi-objective optimization model (i.e. establishes a three-objective optimization system: minimizes the rotor mass, minimizes the maximum deformation, and maximizes the first-order natural frequency; the model can ensure the uniform distribution of Pareto solution in high-dimensional space through the reference point mechanism), which is used for optimizing the structure parameters (the thickness of the two end faces, the thickness of the working tooth surface, the width of the inner support rod and the diameter of the inner support column) of the screw rotor, and then achieving the lightweight design of the screw rotor. The design method of the application is used for the lightweight design of the screw rotor, which not only can reduce the mass of the screw rotor and improve the material utilization rate, but also can enhance the dynamic and static performance of the screw rotor.

[0012] Further, the aforementioned screw rotor lightweight design method further comprises step 5: modifying the design variable value of the screw rotor lightweight model according to the optimized structure parameter value, and performing multi-physical field coupling simulation by means of ANSYS software to obtain the numerical values of the optimized mass, maximum deformation and first-order natural frequency, and comparing them with the initial numerical values for verification.

[0013] Further, in step 3, the sample data set is divided into a training set and a test set; wherein the data in the training set is used to train the XGBoost prediction model, and the data in the test set is used to evaluate the performance of the SNBRO-XGBoost multi-objective prediction model.

[0014] Further, in step 2, the formula of the multi-objective optimization mathematical model is as follows: , ; wherein, is the output function of each optimization objective, For the set of variables to be optimized, M is the mass, U is the maximum total deformation, F1 is the first order natural frequency; the constraint condition is: , is the design variable, and are the lower and upper bounds of the constraint, respectively.

[0015] Further, in step 3, the hyperparameter optimization process of the XGBoost prediction model is as follows: step I, set the optimization population size N, and determine the search range of the three key hyperparameters of the XGBoost prediction model, the number of decision trees T, the maximum depth of the tree d, and the learning rate η, thereby constructing the hyperparameter search space, the dimension is set as dim=3, and the maximum number of iterations Max_iter of the optimization algorithm is set; step II, taking the mean square error between the predicted value of the XGBoost prediction model and the true value of the simulation in the test set as the fitness function of the optimization algorithm, the MSE of mass, deformation and first order natural frequency is calculated for each population individual, and the population is sorted in ascending order, and the best individual position Best_pos and the worst individual position Worst_pos are recorded; step III, in each iteration, apply Newton-Raphson search rule (NRSR) to each individual i in the population for position update; step IV, in order to further enhance the population diversity and avoid premature convergence of the algorithm, a genetic algorithm optimization mechanism is introduced into the SNBRO algorithm, including selection, crossover and mutation genetic operations, which are complementary to the main optimization loop and can improve the global exploration ability of the algorithm for complex search space; the three genetic operations are executed after each main optimization iteration, as a supplementary means for population update; step V, repeat steps II-IV until the current iteration number = maximum iteration number, output the optimal hyperparameter combination , train the XGBoost prediction model with the optimal hyperparameter combination: (the formula is the core of the XGBoost prediction model, which forms the final prediction value by accumulating the outputs of multiple decision trees , and builds a mass-maximum total deformation-first order natural frequency three-objective predictor), and finally builds a high-precision SNRBO-XGBoost multi-objective prediction model. Through the strategy fusion of chaotic initialization, genetic algorithm and dynamic decision factor, the hyperparameters of the XGBoost prediction model are optimized, which can significantly improve the prediction model accuracy and the quality of multi-objective solution.

[0016] Further, in step I, the initial solution vector is generated by perturbation using Logistic chaotic mapping, and the Logistic mapping equation is: ; wherein is the control parameter, x kis the kth iteration value; a dim-dimensional vector [x1, x2, x3] is randomly generated, each dimension taking a value in the range (0, 1), and an initial population is generated by iteration. In this way, the uniformity of population initialization and the global search capability can be enhanced.

[0017] Further, in step III, the position updating process is as follows: a, two individuals k1 and k2 are randomly selected from the population, and the disturbance factor of individual i is calculated in combination with the current optimal individual Best_pos: ; wherein, is the position of individual k1 and k2 in space, is the position of individual i in space; b, the position information of the current worst individual Worst_pos is introduced, the distance between it and the current individual is normalized, and a Newtonian direction vector is formed in combination with the disturbance factor: ; c, taking the current individual and the optimal individual as reference points respectively, combining the search vector NRSR with the disturbance factor to construct two candidate solutions: ; ; d, an adaptive factor is introduced to make the search step length decrease with the iteration number, and the position updating expression is as follows: ; in the formula, is the current iteration number, is the maximum iteration number; ; a1, a2 [0, 1], are two independent random numbers, which are used to further increase the uncertainty and flexibility of the update direction. Using the above specific rules for position updating is conducive to enhancing the local search capability of individuals, and the above process constructs a hybrid updating mechanism combining global guidance and local development, which can ensure a balance between convergence efficiency and accuracy.

[0018] Further, in order to further improve the ability of the algorithm to jump out of the local optimum, a trap avoidance mechanism (TAO) is introduced in step III, which enhances the jumping ability of the population through a nonlinear disturbance mechanism. The specific operation is as follows:

[0019] 1) DF defined by Sigmoid function is used to control whether the disturbance operation is performed: ; in the formula, in the formula, iter represents the current iteration number, and Max_iter represents the preset maximum iteration number.

[0020] 2) When the number satisfies , the following disturbance operation is performed for the updated individual : a, the disturbance coefficient is defined: , ; With is the coefficient determined by introducing a random number; The value range is between -1 and 1, The value range is between -0.5 and 0.5.b, the proportion factor is set: , ; In the formula, With According to the random number The value; when , The value is , The value is ; when , With Both take the value 1, and the position adjustment range is relatively narrow.c, calculate the disturbance vector: , ; In the formula, Best_pos represents the optimal individual position obtained at present, Position i is the position of the individual i to be implemented with the disturbance operation, represents the mean of the positions of all individuals in the population. Based on the optimal individual position, the tendency to approach the optimal solution is embodied, and the adjustment is implemented with the proportion factors u1 and u2; then Based on the population average position calculation, the overall distribution situation of the population is comprehensively considered, and the effect of the individual position is also adjusted through u1 and u2.d, get the disturbance position expression: ; In the formula, The value changes with the number of iterations, in the initial stage of iteration, The value is relatively large, and the disturbance range is relatively large; along with the iteration, The value gradually decreases, and the disturbance range is correspondingly narrowed. When , the individual position After disturbance is updated as the reference, the adjusted value of the disturbance coefficient , and the disturbance vector , is superimposed to realize the disturbance exploration based on the current updated individual; when , The current optimal individual position is taken as the starting point for adjustment. This design ensures that the algorithm can carry out exploration based on the current individual update state, and can also implement search guided by the optimal individual under different conditions, effectively helping the population to get out of the local optimal dilemma, maintaining population diversity, and improving the global efficiency of optimization search.

[0021] Furthermore, in step IV, a tournament selection operation is employed, the purpose of which is to select individuals with superior fitness from the current population as parents. The specific steps are as follows: K=3 candidate individuals are randomly selected from the population; the fitness values ​​of the candidate individuals are compared, and the individual with the best fitness is selected as the parent. The selection rule is as follows: Among them, Fitness corresponds to the fitness value. This is a set of indices for K randomly selected candidate individuals.

[0022] Furthermore, in step IV, the crossover operation employs arithmetic crossover, and the execution rule is: if the random number If cr is the crossover probability, then offspring are generated according to the following formula: ;in, and Two parent individuals were selected for the tournament; The crossover coefficients are randomly generated. Arithmetic crossover preserves the characteristics of parent individuals through linear combination, avoiding the problem of excessive jumps in the search space that may be caused by traditional single-point crossover, and is beneficial to maintaining the local search capability of the population.

[0023] Furthermore, in step IV, the mutation operation employs non-uniform mutation, specifically following the rule: for each dimension... If random number If mr is the mutation probability, then mutation is performed: ;in, For variable asynchronous length, the calculation formula is: In the formula, and The first The upper and lower bounds of a dimension, This represents the current iteration number. Maximum number of iterations. Step size for non-uniform variation. In the early stages of iteration, the space is relatively large, allowing offspring individuals to explore extensively within the search space; as iterations progress... The mutation process gradually decreases, shifting towards local fine-tuning to balance global exploration with local development capabilities. The mutated offspring individuals then undergo boundary constraint processing, as detailed in the following formula: By assessing their fitness, the population is updated using a worst-case replacement strategy. By replacing the worst individuals, the overall quality of the population is gradually improved, while preserving potential better solutions generated by genetic operations and avoiding population degradation caused by random mutations. Attached Figure Description

[0024] Figure 1 This is a flowchart of the lightweight screw rotor design method of this application;

[0025] Figure 2 is a structural diagram of the XGBoost prediction model in the present application;

[0026] Figure 3 is a flow chart of the SNBRO algorithm in the present application;

[0027] Figure 4 is a three-dimensional model diagram of the screw rotor of the screw air compressor in the embodiment;

[0028] Figure 5 is the surface pressure distribution result of the screw rotor in Figure 4

[0029] Figure 6 is the temperature distribution result of the screw rotor in Figure 4

[0030] Figure 7 is the three-field coupling boundary condition setting of the screw rotor in Figure 4

[0031] Figure 8 is the calculation result of the maximum total deformation and the first-order natural frequency of the screw rotor in Figure 4

[0032] Figure 9 is a cross-sectional diagram of the lightweight model of the male screw rotor in the embodiment;

[0033] Figure 10 is the calculation result of the maximum total deformation and the first-order natural frequency of the lightweight model of the male screw rotor in the embodiment;

[0034] Figure 11 is the simulation verification result of the maximum total deformation and the first-order natural frequency of the optimized lightweight model of the male screw rotor in the embodiment.

[0035] The marks in the drawings are: x1 - thickness of both end faces; x2 - thickness of working tooth surface; x3 - width of inner support rod; x4 - diameter of inner support column. DETAILED DESCRIPTION

[0036] The present application will be further described below in conjunction with the drawings and embodiments, but it is not limited to the basis of the application.

[0037] ​​​​In view of the limitations of the existing screw rotor lightweight design method, the present application proposes a screw rotor lightweight design method based on SNRBO-XGBoost-NSGA III; the method trains the XGBoost (extreme gradient boosting) prediction model by generating sample data sets through the Latin hypercube sampling method, simultaneously initializes the population by using the Logistic chaotic mapping technology, generates highly diverse initial solutions through the iterative equation, integrates the dynamic decision factor (DF) control mechanism and the genetic algorithm optimization module, and on this basis, constructs the multi-strategy fusion Newton-Raphson optimization algorithm-SNRBO, optimizes the tree number, maximum depth and learning rate of the XGBoost prediction model three key hyperparameters through the SNRBO, so as to effectively balance the global exploration and local development capability; the optimized SNRBO-XGBoost multi-objective prediction model is used as the fitness function of the NSGA-III algorithm (non-dominated sorting genetic algorithm based on reference point), and combined with the multi-objective optimization mathematical model, a three-objective optimization system is established: minimizing the rotor mass, minimizing the maximum deformation, and maximizing the first-order natural frequency, and the reference point mechanism is used to ensure the uniform distribution of Pareto solutions in high-dimensional space. The technical scheme breaks through the local optimal limit in the traditional design, realizes the comprehensive improvement of the rotor lightweight performance and the static and dynamic performance, and provides an innovative solution for the lightweight design of high-speed rotating machinery. Experimental verification shows that the method is superior to the traditional design method in terms of prediction model accuracy and lightweight optimization effect, and greatly shortens the design cycle. Figures 1 to 3 The screw rotor lightweight design method of the present application specifically includes the following steps.

[0038] Step 1, construct a screw rotor lightweight model (modeling can be done in SolidWorks), the screw rotor includes a spiral shell and an inner support column, the inner support column is located in the spiral shell and connected with the spiral shell through an inner support rod; then, perform multi-physical field coupling simulation by means of ANSYS software to obtain the initial mass, maximum total deformation and first-order natural frequency of the screw rotor.

[0039] Step 2, take the thickness of the end face of the screw rotor lightweight model, the working tooth surface thickness, the inner support rod width and the inner support column diameter as design variables, take the upper and lower limits of the design variables and the objective functions as constraint conditions, take the minimum mass, the minimum maximum total deformation and the maximum first-order natural frequency of the screw rotor lightweight model as objective functions, and construct a multi-objective optimization mathematical model;

[0040] Step 3, construct the test sample points by Latin Hypercube Sampling method (LHS), and input the sample point information into the ANSYS simulation model, calculate the mass, maximum total deformation and first order natural frequency, build the sample data set, and divide it into training set and test set according to 7:3; then use the training set sample data to train the XGBoost prediction model, and introduce the improved SNRBO algorithm to optimize the hyperparameters of the XGBoost prediction model, improve the prediction accuracy of the model by introducing the Logistic chaotic mapping population initialization design method, dynamic adjustment of decision factors and genetic algorithm cooperative optimization part, and determine the coefficient of determination R 2 and root mean square error RMSE evaluation, build the SNRBO-XGBoost multi-objective prediction model, and realize high-precision mapping between design parameters and rotor structure performance.

[0041] Step 4, use the SNBRO-XGBoost multi-objective prediction model as the fitness function of the NSGA-III algorithm, and combine the multi-objective optimization mathematical model to finally establish the NSGA-III multi-objective optimization model, perform optimization and output the optimized structure parameter value, which is used as the design parameter of the screw rotor for modeling, and the multi-physical field coupling simulation verification is performed to complete the collaborative optimization of rotor lightweight and stiffness and dynamic performance improvement; at this time, the complete process of "modeling-prediction-optimization-verification" is formed, which provides a system solution for rotor lightweight design.

[0042] Embodiment:

[0043] In this embodiment, the screw rotor lightweight design method described above is used to design the screw rotor of the screw air compressor; the specific process is as follows.

[0044] (1) Referring to Figure 4 , a three-dimensional model of the screw rotor of the screw air compressor is constructed, and the material of the rotor is 316L stainless steel. Then, according to the actual inlet and outlet air pressure of the screw air compressor, the inlet is set to 0.1 mpa and the outlet is set to 0.8 mpa in the Fluent module, and the wall surface rotating speeds of the male and female rotors are 2000 rpm and 3000 rpm respectively, and finally the air pressure distribution on the surface of the male and female screw rotors is calculated, as shown in Figure 5 . Then, according to the actual inlet and outlet temperature of the screw air compressor, the inlet is set to 25° and the outlet is set to 50° in the ANSYS steady-state thermal module, and the convective heat transfer coefficient is set to 1.63e -5 W / mm2·℃, the temperature field distribution of the screw rotor is calculated, as shown in Figure 6 ; finally, the air pressure distribution and temperature field distribution data calculated in the fluid field are imported into the static field, and the relevant constraints and loads are set according to the actual assembly mode of the screw rotor, and the specific boundary condition design method is as follows Figure 7The maximum total deformation of the original screw rotor under multi-physical field coupling is calculated, as shown in Figure 8 The first-order natural frequency of the original screw rotor can be calculated in the modal analysis of ANSYS, and the boundary conditions are set according to the actual rotor assembly mode, and the result is shown in Figure 8 b.

[0045] (2) In order to achieve the lightweight of the screw rotor, the hollow inner support screw rotor structure is adopted in the embodiment, and the structure lightweight of the screw rotor is realized by selecting and designing the structure of the internal support framework and determining the appropriate thickness of the rotor shell. In the design of the shell, since the screw rotor is a surface rotating engagement work, the internal structure does not directly participate, so in the lightweight design of the screw rotor, only the internal region is subtracted and filled with the corresponding internal support framework under the condition of not changing the original surface shape and meeting certain strength and stiffness conditions, which is the design variable and design space of the selected lightweight model of the screw rotor. In the male and female rotors, the female rotor tooth surface is thin and the inner diameter is small, and the male rotor has a larger inner diameter space and a certain thickness of the tooth surface, so the lightweight design is only for the male rotor in the embodiment. In the selection of structural parameters, the thickness X1 of the two end faces, the thickness X2 of the working tooth surface, the width X3 of the internal support rod and the diameter X4 of the internal support column are selected as the objects, and the lightweight model structure of the male screw rotor is shown in Figure 9 The calculation method of the maximum total deformation and the first-order natural frequency of the lightweight model of the male screw rotor is consistent with that of the original screw rotor, and the specific calculation results are shown in Figure 10 a, 10b. In the design of the constraint condition, attention should be paid to the interference problem between the sizes to avoid the failure of the later model reconstruction, and the specific design variable information is shown in Table 1.

[0046] Table 1 Lightweight design parameter table of screw rotor

[0047] Parameter Variable Name Unit Value Range Both end face thickness X1 Mm [5,35] Working tooth surface thickness X2 Mm [4,40] Internal support rod width X3 Mm [4,16] Internal support column diameter X4 Mm [20,78]

[0048] (3) After determining the parameter value range and the number of test points, the system will randomly form 180 test point combinations in the range, and then input the sample point information into the ANSYS simulation model to calculate the mass, the maximum total deformation and the first-order natural frequency. The local combination data table is shown in the table below.

[0049] Table Local data table

[0050] Parameter 1 2 3 4 5 X1 31.7 16.62 21.9 18.1 19.6 X2 28.4 38.89 31.4 38 4.3 X3 5.1 8.87 4.5 13.8 15.4 X4 41.3 49.55 57.2 65.3 43.3 Mass 94.67 104.15 99.67 107.82 52 Maximum total deformation 0.08498 0.081 0.08449 0.08575 0.08936 First order natural frequency 371.88 366.48 368.88 365.43 489.83

[0051] (4) The 180 groups of data calculated by simulation are divided into training set and test set; the training set is used to train the XGBoost prediction model, and the SNRBO algorithm of multi-strategy fusion is used to optimize the hyperparameters of the XGBoost prediction model, and the SNRBO-XGBoost multi-objective prediction model is further constructed, and the coefficient of determination R 2 and the root mean square error RMSE are used as the evaluation parameters of the prediction performance of the model. The specific operation is as follows.

[0052] I, set the optimization population size N, and determine the search range of the three key hyperparameters of the XGBoost prediction model, the number of decision trees T, the maximum depth of the tree d, and the learning rate η, thereby constructing the hyperparameter search space, the dimension is set as dim=3, and the maximum number of iterations Max_iter of the optimization algorithm is set.

[0053] In order to enhance the uniformity of population initialization distribution and global search ability, the initial solution vector is disturbed by using Logistic chaotic mapping to generate; the Logistic mapping equation is: ; Wherein is the control parameter, x k is the kth iteration value; a dim-dimensional vector [x1, x2, x3] is randomly generated, each dimension takes value in the range of (0, 1), and the initial population is generated by iteration. Finally, it is mapped to the hyperparameter space: , , ; In the formula, and represent the lower and upper boundaries of the number of trees, and represent the lower and upper boundaries of the maximum depth, and represent the lower and upper boundaries of the learning rate; , , represent the actual value of the corresponding dimension of individual i in three-dimensional parameters. Through the above formula, the mapping of the normalized chaotic sequence to the actual parameter space is completed.

[0054] II, the mean square error between the prediction value of the XGBoost prediction model and the true value in the test set is used as the fitness function of the optimization algorithm, the MSE of the quality, the deformation and the first-order natural frequency of each population individual is calculated, the whole population is sorted in order from small to large, and the best individual position Best_pos and the worst individual position Worst_pos are recorded;

[0055] III, in each iteration, each individual i in the population is updated in position by applying the Newton-Raphson search rule (NRSR): a, the disturbance vector Two individuals k1 and k2 are randomly selected from the population, combined with the current best individual Best_pos, to calculate the disturbance factor of individual i: ; wherein, is the position of individual k1 and k2 in space, is the position of individual i in space; b, the position information of the current worst individual Worst_pos is introduced, and the distance between them is normalized, and combined with the disturbance factor to form a Newtonian direction vector: ; this update method simulates the iterative direction based on gradient and Hessian information in Newton method, but does not require derivative, which is suitable for black box optimization problem; c, respectively, with the current individual and the optimal individual as the reference point, combined with the search vector NRSR and the disturbance factor Two candidate solutions X1 and X2 are constructed: ; ; d, the adaptive factor is introduced, so that the search step decreases with the number of iterations, so as to transition from rough search to fine development, and the final position update expression is as follows: ; in the formula, is the current iteration number, is the maximum iteration number; ; a1, a2 [0,1], are two independent random numbers, which are used to further increase the uncertainty and flexibility of the update direction. This process constructs a hybrid update mechanism that combines global guidance and local development, which can ensure the balance between convergence efficiency and accuracy.

[0056] In order to balance the global exploration and local development ability of the algorithm, and further improve the ability of the algorithm to jump out of the local optimum, a trap avoidance mechanism (TAO) is also introduced in step III. The principle is to enhance the jumping ability of the population through a nonlinear disturbance mechanism. The specific operation is as follows:

[0057] 1) The Sigmoid function is used to dynamically adjust the parameters of the dynamic decision factor (DF): ; wherein, wherein, iter represents the current iteration number, and Max iter represents the preset maximum iteration number. Since the DF of the original NRBO algorithm is a fixed value of 0.6, the algorithm has limited help for searching the overall space in the early iteration period, and has a higher probability of disturbance in the fine search of the algorithm in the later iteration period, which affects the efficiency of the search. The SNRBO algorithm of the present application uses the characteristics of the Sigmoid function to give DF a specific variation law. In the early iteration period of the algorithm, the iter value is relatively small, DF tends to 0.9, at this time the disturbance operation execution probability is higher, which helps the algorithm to actively explore the search space, and then jump out of the local optimal region. With the progress of the iteration process, iter gradually increases, DF tends to 0.1, and the disturbance execution probability decreases, and the algorithm focuses on fine search in the current optimal region, improving the search stability.

[0058] 2) When a randomly generated number in the interval [0, 1] satisfies , the following disturbance operation will be performed for the updated individual : a, the disturbance coefficient is defined as: , ; and are coefficients determined by introducing random numbers; , the value range is between -1 and 1, , the value range is between -0.5 and 0.5; both play a scaling and direction adjustment role in the subsequent disturbance vector calculation process, introducing randomness and diversity to the population individual position update to explore a wider search space. b, the proportion factor is set as: , ; wherein, and are valued according to random numbers ; when , takes the value of , takes the value of , which can increase the individual position adjustment amplitude in certain situations and strengthen the search randomness; when , and both take the value of 1, the position adjustment amplitude is relatively narrow; this design aims to flexibly control the disturbance intensity and direction according to different random conditions, and optimize the search strategy. c, calculate the disturbance vector: , ; wherein, Best pos represents the current optimal individual position, Position i is the position of the individual i to be disturbed, represents the mean of the positions of all individuals in the population. Based on the optimal individual position construction, the tendency to approach the optimal solution is embodied, and adjustment is implemented with the help of proportional factors u1 and u2; then Based on the population average position calculation, the overall distribution situation of the population is comprehensively considered, and the effect of individual position is adjusted by u1 and u2. d, the perturbed position expression is obtained: ; In the formula, The numerical value changes with the number of iterations, in the initial stage of iteration, The value is relatively large, and the perturbation amplitude is relatively large; with the advancement of iteration, The value gradually decreases, and the perturbation amplitude is correspondingly narrowed. When , the individual position after perturbation Take the updated individual As the benchmark, superimpose the adjusted value of the perturbation coefficient , And the perturbation vector , The adjusted value realizes the perturbation exploration based on the current updated individual; when , The current optimal individual position As the starting point for adjustment. This design ensures that the algorithm can carry out exploration based on the current individual update state, and can also search with the optimal individual as the guide, effectively helping the population to get out of the local optimal dilemma, maintaining the population diversity, and improving the global efficiency of optimization search.

[0059] IV, in order to further enhance the population diversity and avoid premature convergence of the algorithm, genetic algorithm optimization mechanism is introduced into SNBRO algorithm, including selection, crossover and mutation three genetic operations; The three genetic operations are executed after the end of each main optimization iteration, as a supplement to population update (its core parameters include: crossover probability cr=0.8: control the execution probability of crossover operation; Mutation probability mr=0.2: control the execution probability of mutation operation; Tournament selection size K=3: the number of candidates for selecting parent individuals).

[0060] Among them, the selection operation adopts tournament selection operation, the purpose of which is to select individuals with better fitness as parents from the current population; The specific steps are as follows: randomly select K=3 candidate individuals from the population; Compare the fitness values of the candidate individuals, select the individual with the best fitness as the parent individual parent, and the selection rule is: ; In the formula, Fitness corresponds to the fitness value, Is the index set of K randomly selected candidate individuals. The crossover operation adopts arithmetic crossover, which generates offspring individuals through linear combination of parent individuals to enhance the diversity of the population, and the execution rule is: if the random number , the offspring is generated according to the following formula: ; wherein, and are two parent individuals selected from the tournament; is a randomly generated crossover coefficient. Arithmetic crossover preserves the characteristics of parent individuals through linear combination, avoiding the problem of excessive search space jumps caused by traditional single-point crossover, and is conducive to maintaining the local search ability of the population. Mutation operation adopts non-uniform mutation, and the mutation range is dynamically adjusted with the number of iterations. The specific rules are as follows: for each dimension , if the random number , then mutation is performed: ; wherein, is the mutation step size, and the calculation formula is: ; wherein, and are the upper and lower bounds of the th dimension, respectively, is the current iteration number, is the maximum iteration number. The step size of non-uniform mutation is larger at the beginning of iteration, allowing the offspring to explore the search space extensively; as the iteration progresses, the step size gradually decreases, and the mutation operation shifts to local fine-tuning, balancing global exploration and local development capabilities. The mutated offspring needs to be processed by boundary constraint, and the specific formula is as follows: . Through the evaluation of its fitness, the worst replacement strategy is used to update the population, by replacing the worst individual, to ensure that the overall quality of the population gradually improves, while retaining potential better solutions generated by genetic operations, avoiding population degradation caused by random mutation.

[0061] V, repeat steps II-IV until the current iteration number = maximum iteration number, output the optimal hyperparameter combination , train the XGBoost prediction model with the optimal hyperparameter combination: (the formula is the core of the XGBoost prediction model, which accumulates the output of multiple decision trees to form the final prediction value , and constructs a quality-maximum total deformation-first order natural frequency three-objective predictor), and finally constructs a high-precision SNRBO-XGBoost multi-objective prediction model.

[0062] VI, the SNRBO-XGBoost multi-objective prediction model is compared with the Kriging, XGBoost and NRBO-XGBoost prediction models based on the same experimental data; Table 3 is the SNBRO-XGBoost multi-objective prediction model hyperparameters, and Table 4 is the evaluation parameters of each prediction model. Among them, the population size and maximum iteration number of the NRBO and SNRBO algorithms are 50 and 500, respectively; the root mean square errors of the SNRBO-XGBoost multi-objective prediction model with respect to the maximum total deformation, mass and first-order natural frequency are 0.0008, 1.8084 and 5.0453, respectively, and the determination coefficients R 2 are 0.978, 0.990 and 0.982, respectively, all of which are the best among the four models. It can be seen that the prediction model constructed in this embodiment has higher prediction accuracy.

[0063] Table

[0064] Parameter Value Decision tree number 252 Maximum depth of tree 3 Learning rate 0.0687

[0065] Table

[0066] Prediction model [R 2 ]] RMSE Kriging 0.943，0.990，0.955 0.0013，2.3522，8.0353 XGBoost 0.936，0.979，0.965 0.0011，4.0975，7.8032 NRBO-XGBoost 0.966，0.977，0.980 0.0009，3.0694，5.2939 SNRBO-XGBoost 0.978，0.990，0.982 0.0008，1.8084，5.0453

[0067] (5) Design objective function: In the selection of the objective function, the lightweight design criterion, the static performance optimization criterion and the dynamic performance optimization criterion are selected as the selection criteria of the objective function.

[0068] I. In order to improve the material utilization rate during the manufacture of the screw male rotor, the following lightweight design criteria are formulated: ; M is the mass;

[0069] II. During the operation of the screw air compressor, the male and female rotors are driven through the synchronous gear, and there is no direct contact between them. However, the rotors will be subjected to the combined action of the torque output by the motor, the gas pressure in the compression chamber and the thermal stress induced by the temperature field, resulting in a small static deformation. Static deformation will change the fit clearance between the rotor and the inner wall of the cylinder, as well as the fit clearance between the male and female rotors, resulting in an increase in the leakage of compressed gas, reducing the volumetric efficiency of the air compressor; it may also cause the spatial posture of the rotor to deviate, interfering with the meshing accuracy of the synchronous gear, causing running vibration and noise, and accelerating the wear of the gear and bearing. In addition, the internal stress concentration caused by static deformation is prone to crack under cyclic loading, and even leads to rotor fracture, which seriously shortens its service life. Therefore, the following static performance optimization criteria are formulated: ; U is the maximum total deformation; in order to ensure the working efficiency, running reliability and structural durability of the air compressor.

[0070] The dynamic performance of the screw air compressor rotor of the III mainly reflects the anti-vibration performance and the running stability during the operation process. As the core component of the air compressor, the dynamic performance of the rotor directly affects the compression efficiency, the noise level and the reliability of the whole machine. The rotor has multiple modes in theory, and the low-order mode, especially the first-order natural frequency, is the most easily excited frequency band in actual operation. When the first-order natural frequency of the rotor is close to the working frequency of the screw air compressor, resonance is easily caused, which leads to a significant increase in the vibration amplitude, aggravates the clearance fluctuation between the rotor and the cylinder wall, the impact load of the synchronous gear, and even causes bearing failure or rotor structure fatigue damage, seriously affecting the stable operation and service life of the air compressor. Therefore, the first-order natural frequency of the rotor needs to be as high as possible to avoid the working frequency band of the air compressor to suppress the risk of resonance. Accordingly, the following dynamic performance optimization criteria are formulated: ; F1 is the first-order natural frequency.

[0071] Then, the constraint conditions are set: , i = 1, 2, …, n; is the i-th design variable of the bed, and n is the number of design variables.

[0072] A multi-objective optimization mathematical model is constructed: , ; is the output function of each optimization objective, is the set of variables to be optimized.

[0073] (6) The multi-objective optimization mathematical model is applied, the SNBRO-XGBoost multi-objective prediction model is used as the fitness function of the NSGA-III algorithm, and finally the NSGA-III multi-objective optimization model is established to perform multi-objective optimization of the lightweight model of the screw male rotor. In this embodiment, the initial population size is set to 50, the maximum real evaluation number is set to 200, and the optimized parameters are shown in Table 5 below.

[0074] Table

[0075] Design variable Optimized value Both end face thickness (Mm) 27.34 Working tooth surface thickness (Mm) 4.11 Internal support rod width (Mm) 4.72 Internal support column diameter (Mm) 24.16

[0076] The material properties of the optimized lightweight screw male rotor model are assigned to obtain the mass information after optimization, and multi-field coupling analysis and modal analysis are performed to obtain the numerical values of the maximum deformation, mass and first-order natural frequency after optimization, and comparison is made with before optimization, as shown in Table 6, to investigate the feasibility of the optimization scheme of the screw male rotor designed by the design method of the present application.

[0077] Table

[0078] Optimization variable Initial value Optimized value Change amount Maximum total deformation (Mm) 0.08923 0.08896 -0.3% Mass (Kg) 113.14 44.46 -60.7% First order natural frequency (Hz) 301.9 517.11 +71.29%

[0079] From the table, it can be seen that the multi-objective optimization not only ensures the constraint condition, but also reduces the maximum total deformation of the screw male rotor by 0.3%, reduces the mass by 60.7%, and increases the first-order natural frequency by 71.29% after the size parameter optimization.

[0080] Finally, the rotor model is constructed using the optimized design parameters, and simulation calculation verification is performed, and the calculation results of the maximum total deformation, mass and first-order natural frequency are 0.085295, 40.38 and 529.87 respectively (the calculation results of the maximum total deformation and the first-order natural frequency are shown in Figs. Figure 11 a and 11b), and the errors of the calculation results and the prediction results of the SNRBO-XGBoost multi-objective prediction model are 4.1%, 3.6% and 4.1% respectively, which further illustrates the high accuracy of the prediction model.

[0081] The results show that the optimization design method can effectively reduce the weight of the screw rotor structure and optimize the dynamic and static performance, improve the material utilization rate, save energy and protect the environment, reduce the vibration and noise of the screw rotor during operation, and improve the reliability of the screw rotor structure. In addition, through this design method, multiple objectives of the screw male rotor can be optimized at the same time, and the size optimization of the lightweight model of the screw rotor of the same category can also refer to this optimization scheme.

[0082] By the above-mentioned optimization design method, the rotor mass and moment of inertia can be reduced, the kinetic energy loss and starting torque of the air compressor can be reduced, the energy consumption can be reduced, the response speed can be improved, and the operation stability can be enhanced. At the same time, although the cost of single piece manufacturing may increase, by optimizing the processing technology and production process, and improving the production efficiency and product quality, the overall production cost can be reduced in the long run. The optimized rotor has more uniform stress distribution under complex working conditions, reduces the risk of fatigue failure, prolongs the service life of the equipment, improves the market competitiveness, promotes the intelligentization and low-carbonization of the mechanical manufacturing industry, and injects new kinetic energy into the high-quality development of the industry.

[0083] The content described in the embodiments of the present specification is only a list of implementation forms of the inventive concept, and the protection scope of the present application should not be regarded as limited to the specific forms described in the embodiments, and the protection scope of the present application also extends to equivalent technical means that can be thought of by those skilled in the art according to the inventive concept.

Claims

1. A screw rotor lightweight design method characterized by, The method comprises the following steps: Step 1, a screw rotor lightweight model is constructed, the screw rotor comprising a spiral shell and an inner support column, the inner support column being located in the spiral shell and being connected with the spiral shell through an inner support rod; then, initial mass, maximum total deformation and first-order natural frequency of the screw rotor are obtained through multi-physical field coupling simulation by means of ANSYS software; Step 2, thicknesses of two end faces of the screw rotor lightweight model, working tooth surface thickness, inner support rod width and inner support column diameter are taken as design variables, upper and lower limits of the design variables and objective functions are taken as constraint conditions, mass minimization, maximum total deformation minimization and first-order natural frequency maximization of the screw rotor lightweight model are taken as objective functions, and a multi-objective optimization mathematical model is constructed; Step 3, a sample data set is constructed through a Latin hypercube sampling method, and the sample data set is used for training an XGBoost prediction model; meanwhile, hyperparameters of the XGBoost prediction model are optimized by using an SNBRO algorithm, and then a high-precision SNBRO-XGBoost multi-objective prediction model is constructed; Step 4, the SNBRO-XGBoost multi-objective prediction model is taken as a fitness function of an NSGA-III algorithm, and a multi-objective optimization mathematical model is finally established by combining the multi-objective optimization mathematical model, optimization solving is carried out and optimized structure parameter values are output, which are taken as design parameters of the screw rotor.

2. The screw rotor lightweight design method according to claim 1, characterized by: Step 5, the design variable values of the screw rotor lightweight model are modified according to the optimized structure parameter values, and multi-physical field coupling simulation is carried out by means of ANSYS software, so that numerical values of optimized mass, maximum deformation and first-order natural frequency are obtained, and the numerical values are compared with initial numerical values for verification.

3. The screw rotor lightweight design method according to claim 1, characterized by: In step 3, the sample data set is divided into a training set and a test set; wherein, data in the training set is used for training the XGBoost prediction model, and data in the test set is used for evaluating performance of the SNBRO-XGBoost multi-objective prediction model.

4. The screw rotor lightweight design method according to claim 3, characterized by, The formula of the multi-objective optimization mathematical model in step 2 is as follows: , ; wherein, is an output function of each optimization objective, is a set of variables to be optimized, M is mass, U is maximum total deformation, and F1 is first-order natural frequency; the constraint condition is: , is a design variable, and are lower and upper limits of the constraint, respectively.

5. The screw rotor lightweight design method according to claim 4, characterized by, In step 3, the hyperparameter optimization process of the XGBoost prediction model is as follows: Step I, the optimization population size N is set, and the search ranges of three key hyperparameters of the XGBoost prediction model, i.e., the number of decision trees T, the maximum depth of the tree d and the learning rate η, are determined, so as to construct a hyperparameter search space, the dimension is set as dim=3, and the maximum iteration number Max_iter of the optimization algorithm is set; Step II, the mean square error between the prediction value of the XGBoost prediction model and the real value in the test set is taken as the fitness function of the optimization algorithm, the MSE of mass, deformation and first-order natural frequency is calculated for each population individual, the whole population is sorted in ascending order, and the optimal individual position Best_pos and the worst individual position Worst_pos are recorded; Step III, in each iteration, the Newton-Raphson search rule is applied to each individual i in the population for position updating; Step IV, the genetic algorithm is introduced into the SNBRO algorithm to optimize the mechanism, including selection, crossover, mutation of three genetic operations, and is executed at the end of each main optimization iteration as a supplementary means of population update; Step V, repeat steps II-IV until the current iteration number = maximum iteration number, output the optimal hyperparameter combination With the optimal hyperparameter combination, the XGBoost prediction model is trained, and finally a high-precision SNRBO-XGBoost multi-objective prediction model is constructed.

6. The screw rotor lightweight design method according to claim 5, characterized by: In the step I, the initial solution vector is disturbed by using the Logistic chaotic mapping, and the Logistic mapping equation is: ; wherein is a control parameter, x k is the kth iteration value; a dim-dimensional vector [x1, x2, x3] is randomly generated, each dimension takes a value in the range of (0, 1), and the initial population is generated by iteration.

7. The screw rotor lightweight design method according to claim 6, characterized in that: In step III, the specific process of position updating is as follows: a, two individuals k1 and k2 are randomly selected from the population, and the disturbance factor of individual i is calculated in combination with the current optimal individual Best_pos; b, the position information of the current worst individual Worst_pos is introduced, the distance between the current individual and the worst individual is normalized, and a Newtonian direction vector is formed in combination with the disturbance factor; c, the current individual and the optimal individual are respectively taken as reference points, the search vector NRSR is combined with the disturbance factor Two candidate solutions X1 and X2 are constructed; d, an adaptive factor is introduced The search step length decreases with the number of iterations, and the final position updating expression is as follows: ; in the formula, is the current iteration number, is the maximum iteration number; ; a1, a2 [0,1], which are two independent random numbers.

8. The screw rotor lightweight design method according to claim 7, characterized in that: In the step IV, the selection operation adopts a tournament selection operation; the specific steps are as follows: K=3 candidate individuals are randomly extracted from the population; the fitness values of the candidate individuals are compared, and the individual with the optimal fitness value is selected as the parent individual parent, and the selection rule is: ; wherein Fitness corresponds to the fitness value, is a randomly extracted K candidate individual index set.

9. The screw rotor lightweight design method according to claim 8, characterized by, In step IV, the crossover operation adopts arithmetic crossover, and the execution rule is: if the random number is less than the crossover probability cr, the offspring is generated according to the following formula: ; wherein, and are two parent individuals obtained through tournament selection; is a randomly generated crossover coefficient.

10. The screw rotor lightweight design method according to claim 9, characterized by, In step IV, the mutation operation adopts non-uniform mutation, and the specific rules are as follows: for each dimension , if the random number , mr is the mutation probability, then the mutation is performed: ; wherein, is the mutation step length, and the calculation formula is: ; in the formula, and are the upper limit and the lower limit of the first dimension respectively, is the current iteration number, is the maximum iteration number; the mutated offspring individual needs to be subjected to boundary constraint processing, and the specific formula is as follows: .

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