A milling parameter multi-objective optimization and decision-making method based on chaotic genetic algorithm

Abstract

The application discloses a kind of milling parameter optimization and decision-making method based on chaotic genetic algorithm, it includes the following steps: S1: establishing milling parameter multi-objective optimization model;S2: milling parameter is obtained initial population Q by Tent chaotic mapping t ;S3: initial population Q t It is brought into chaotic genetic algorithm to solve milling parameter multi-objective optimization model and obtain Pareto solution set;Pareto solution set is milling parameter optimization result.The present application carries out multi-objective optimization to milling parameter, and initial population is obtained by Tent chaotic mapping, and population initialization can be better than pseudo-random number by Tent chaotic mapping, can improve the uniformity of initial population to some extent, and then improve the diversity of population and the distribution of solution;Then when chaotic genetic algorithm is solved to multi-objective optimization model, any individual in the obtained Pareto solution set, i.e.milling parameter is used in actual milling processing, and the processing efficiency and processing quality can be optimized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical control milling, in particular to a milling parameter multi-objective optimization and decision-making method based on chaotic genetic algorithm. BACKGROUND

[0002] In numerical control milling, milling parameters need to be set, and a reasonable milling parameter combination can reduce the wear of the milling cutter while maintaining or improving the working efficiency and increasing the service life of the milling cutter. For numerical control milling, a reasonable and excellent milling parameter combination can reduce production costs and improve production efficiency. The selection of milling parameters is very important.

[0003] In the prior art, the selection of milling parameters is often based on the past processing experience data of the factory and the simple calculation of manual work. Such a method is limited by human experience, and the processing efficiency of the selected milling parameters cannot be guaranteed to be optimal. Moreover, in actual production and processing, there are often multiple optimization objectives for milling parameters, and different optimization objectives will cause conflicts in the selection of milling parameters, affecting the actual processing efficiency. SUMMARY

[0004] In view of the above shortcomings of the prior art, the present application provides a milling parameter multi-objective optimization method based on chaotic genetic algorithm, which can optimize the selection of milling parameters for multiple optimization objectives and ensure the working efficiency of actual processing.

[0005] To achieve the above-mentioned application purposes, the technical solutions adopted by the present application are as follows:

[0006] A milling parameter multi-objective optimization method based on chaotic genetic algorithm is provided, which includes the following steps:

[0007] S1: Establish a milling parameter multi-objective optimization model;

[0008] S2: Obtain an initial population Q t by Tent chaotic mapping of the milling parameters;

[0009] S3: Bring the initial population Q t into the chaotic genetic algorithm to solve the milling parameter multi-objective optimization model to obtain a Pareto solution set; the Pareto solution set is the optimization result of the milling parameters.

[0010] Further, the optimization objectives of the milling parameters include milling force F and material removal rate MRR, and the optimization variables of the milling parameter multi-objective optimization model include milling speed v c , milling depth a p , milling width a e , and feed per tooth fz ; the milling parameter multi-objective optimization model is as follows:

[0011]

[0012] wherein C is an influence constant; a1 is an index coefficient of the milling speed empirical model; b1 is an index coefficient of the milling depth empirical model; c1 is an index coefficient of the milling width empirical model; d1 is an index coefficient of the per-tooth feed amount empirical model; z is the number of tool teeth; d is the tool diameter; Ra is the workpiece surface roughness; Ra max is the maximum workpiece surface roughness; and st is a constraint condition range.

[0013] Further, the generation method of the initial population Q t includes the following steps:

[0014] A1: a random number matrix is randomly generated using Tent chaotic mapping;

[0015] A2: chaotic values g(x) are converted from the random numbers in the random number matrix;

[0016] The random number matrix includes N rows and V columns of random numbers x, x∈[0,1];

[0017]

[0018] x ij =rand(0,1);

[0019] wherein x ij is the random number in the i-th row and the j-th column of the matrix; N is the set population size, and V is the number of optimization variables of the milling parameter multi-objective optimization model;

[0020] A3: a plurality of chaotic values g(x) are mapped to the value interval [minv ij , maxv ij ] of the milling parameters, to obtain the initial population Q t [z 11 , z 12 , z 13 ,...z ij ...z NV ];

[0021] The model of the mapping process is as follows:

[0022] z ij =minv ij +g(x ij )(maxv ij -minv ij );

[0023] wherein zij That is, the milling parameters after chaos optimization.

[0024] Further, the solving process of the milling parameter multi-objective optimization model by the chaos genetic algorithm includes the following steps:

[0025] S31: the initial population Q t is brought into the binary tournament to obtain the mutant offspring population R t , and the initial population Q t and the mutant offspring population R t are merged to obtain the merged population Z t .

[0026] S32: the same population size of the iteration population P t as the initial population Q t is selected from the merged population Z t by the elite selection strategy.

[0027] S33: P t = Q t+1 , and the iteration is performed by returning to S31 until the iteration number t reaches the maximum, and the iteration population is output to obtain P tmax , P tmax is the Pareto solution set of the milling parameter multi-objective optimization model.

[0028] Further, step S32 includes:

[0029] B1: the non-dominated sorting of the merged population Z t is performed to obtain the level of each individual;

[0030] B2: the crowding degree of each individual level is calculated to obtain the crowding distance between adjacent individuals in the same level;

[0031] B3: the iteration population P t is selected according to the obtained level of each individual and the crowding distance:

[0032] two individuals are randomly extracted from the merged population Z t ,

[0033] when the two individuals are in the same level, the individual with the smaller level sequence value is included in the iteration population P t ;

[0034] when the two individuals are in different levels, the individual with the larger crowding distance is included in the iteration population P t , until the number of individuals in the iteration population P t is equal to the number of individuals in the initial population Q t .

[0035] Further, the population size of the chaotic genetic algorithm is 70; the iteration number is 150; the mutation probability is 0.05; and the crossover difference rate is 0.8.

[0036] A milling parameter decision-making method based on a chaotic genetic algorithm, comprising the following steps:

[0037] C1: milling force subjective weight obtained by calculating the Pareto solution set by an analytic hierarchy process Material removal rate subjective weight And surface roughness subjective weight

[0038] C2: milling force objective weight obtained by calculating the Pareto solution set by an entropy weight method Material removal rate objective weight And surface roughness objective weight

[0039] C3: milling force comprehensive weight W1, material removal rate comprehensive weight W2 and surface roughness comprehensive weight W3 are calculated according to subjective weight And And objective weight And

[0040]

[0041]

[0042]

[0043] C4: the score of each individual in the Pareto solution set is calculated by bringing the comprehensive weight into a TOPSIS method, and the individual with the highest score is selected as the best milling parameter.

[0044] The beneficial effects of the present application are:

[0045] 1. The present application optimizes the milling parameters through Tent chaotic mapping to obtain an initial population, and the Tent chaotic mapping for population initialization can achieve better results than pseudo-random numbers, can improve the uniformity of the initial population to a certain extent, and further improve the diversity of the population and the distribution of the solution; and further make the milling parameters in the Pareto solution set obtained by the chaotic genetic algorithm for solving the multi-objective optimization model can optimize the processing efficiency and processing quality after being applied to actual milling processing.

[0046] ​2. The milling parameters obtained by multi-objective optimization are subjected to weight distribution by analytic hierarchy process and entropy weight method, and the TOPSIS method is used to score the optimization results, and the milling parameters are selected according to the scoring results, so as to avoid relying on human subjective experience for decision-making, improve the rationality of decision-making, and make the milling process scientific and reasonable. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 Fig. 1 is a schematic diagram of the milling parameter multi-objective optimization and decision-making process based on the chaotic genetic algorithm;

[0048] Figure 2 Fig. 4 is a Pareto solution set distribution diagram of the milling parameter multi-objective optimization model in the embodiment. DETAILED DESCRIPTION

[0049] The specific embodiments of the present application are described below to facilitate understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, as long as various changes are within the spirit and scope of the present application defined and determined by the appended claims, all applications utilizing the concept of the present application are included in the protection.

[0050] As shown in Figure 1 Fig. 1, a milling parameter multi-objective optimization and decision-making method based on a chaotic genetic algorithm includes the following steps: in this embodiment, the implementation process of the present application is described in detail taking the milling of Ti6Al4V titanium alloy using a hard alloy ball nose milling cutter as an example.

[0051] S1: Establish a milling parameter multi-objective optimization model.

[0052] The optimization objectives of the milling parameters include milling force F and material removal rate MRR, and the optimization variables of the milling parameter multi-objective optimization model include milling speed v c , milling depth a p , milling width a e , and feed per tooth f z ; the milling parameter multi-objective optimization model is as follows:

[0053]

[0054] wherein C is an influence constant; a1 is an index coefficient of the milling speed empirical model; b1 is an index coefficient of the milling depth empirical model; c1 is an index coefficient of the milling width empirical model; d1 is an index coefficient of the feed per tooth empirical model; z is the number of tool teeth; d is the tool diameter; Ra is the workpiece surface roughness; Ra max is the maximum workpiece surface roughness; and st is the constraint condition range.

[0055] S2: Obtain initial population Q by Tent chaotic mapping of milling parameters t ;

[0056] Initial population Q t The generation method comprises the following steps:

[0057] A1: Randomly generate a random number matrix using Tent chaotic mapping; the random number matrix comprises N rows and V columns of random numbers x, x∈[0, 1]; N is a set population size, and V is the number of optimization variables of the milling parameter multi-objective optimization model;

[0058] A2: Convert the random numbers in the random number matrix to obtain chaotic values g(x);

[0059]

[0060] x ij =rand(0,1);

[0061] wherein x ij is the random number in the i-th row and the j-th column of the matrix;

[0062] A3: Map a plurality of chaotic values g(x) to the value interval [minv ij , maxv ij ] of the milling parameters to obtain the initial population Q t [z 11 , z 12 , z 13 ,...z ij ...z NV ];

[0063] The model of the mapping process is:

[0064] z ij =minv ij +g(x ij )(maxv ij -minv ij );

[0065] wherein z ij is the milling parameter after chaotic optimization.

[0066] S3: Bring the initial population Q t into the chaotic genetic algorithm to solve the milling parameter multi-objective optimization model to obtain a Pareto solution set; the Pareto solution set is the milling parameter optimization result.

[0067] The solving process of the chaotic genetic algorithm for the milling parameter multi-objective optimization model comprises the following: the population size of the chaotic genetic algorithm is set to 70; and the iteration number is 150;

[0068] S31: Set the initial population Q t The mutant offspring population R was obtained by introducing it into a binary bidding competition. t The mutation probability is 0.05; the crossover difference rate is 0.8; and the initial population Q is... t and the variant offspring population R t The merged population Z is obtained by merging. t ;

[0069] S32: Merge population Z t Select individuals from the initial population Q using an elite selection strategy. t Iterative population P of the same population size t ;

[0070] include:

[0071] B1: For the merged population Z t Perform a non-dominated sort to obtain the hierarchy of each individual;

[0072] B2: Calculate the crowding degree of each individual's level to obtain the crowding degree distance between adjacent individuals at the same level;

[0073] B3: Select the iterative population P based on the obtained hierarchy and crowding distance of each individual. t :

[0074] In merging population Z t Two individuals are randomly selected from the group.

[0075] When two individuals are at the same level, the individual with the smaller level sequence value is included in the iterative population P. t ;

[0076] When two individuals belong to different levels, the individual with the larger crowding distance is included in the iterative population P. t Until the iterative population P t The number of individuals in the population and the initial population Q t The number of individuals is equal.

[0077] S33: Let P t =Q t+1 Return to S31 to perform iterations until the number of iterations t reaches its maximum, then output the iterative population and obtain P. tmax P tmax This is the Pareto solution set of the multi-objective optimization model for milling parameters.

[0078] Pareto solution set such as Figure 2 As shown, the horizontal axis represents the milling force, and the vertical axis represents the material removal rate. Each point represents an element in the Pareto solution set.

[0079] A reference group was set up, with the following data: material removal rate of 130.1 mm. 3 / min, cutting force 83.47N, surface roughness 0.37μm; calculate the gain of the three target variables of milling force, material removal rate and surface roughness for each individual in the Pareto solution set compared with the reference group. Due to space limitations, the ten optimized solutions and the gain rates of the three target variables of milling force, material removal rate and surface roughness are listed in Table 1.

[0080] Table 1

[0081]

[0082] As shown in Table 1, the gain ratio of any individual in the Pareto solution set compared to the reference group is greater than 0 on all three target variables, which clearly optimizes the milling parameters.

[0083] C3: Based on subjective weighting and and objective weight and The comprehensive weights of milling force W1, material removal rate W2, and surface roughness W3 are calculated.

[0084]

[0085]

[0086]

[0087] Subjective weight, objective weight, and comprehensive weight are shown in Table 2;

[0088] Table 2

[0089] Item Material removal rate Milling force Surface roughness Subjective weight 0.300 0.110 0.590 Objective weight 0.4187 0.3622 0.2191 Comprehensive weight 0.4262 0.1352 0.4386

[0090] As shown in Table 2, the weight of milling force < the weight of material removal rate < the weight of surface roughness, which is consistent with the requirements of high quality and high processing efficiency pursued in actual processing.

[0091] C4: Using the comprehensive weights, the score of each individual in the Pareto solution set is calculated by substituting them into the TOPSIS method, and the individual with the highest score is selected as the optimal milling parameters.

[0092] The top five solutions in the Pareto solution set obtained by the TOPSIS method are shown in Table 3.

[0093] Table 3

[0094]

[0095] According to the score of Table 3, the No. 1 parameter combination has the highest score, the material removal rate of the No. 1 parameter combination is higher than the fifth group compared with the No. 5 parameter combination; and the No. 1 is compared with the initial reference group, the milling force, the material removal rate and the surface roughness are respectively optimized by 16.53%, 7.49% and 10.34%. After the decision analysis, the parameter combination with higher score can meet the actual processing requirements, and the optimized parameter combination is still within the constraint range. Therefore, the parameter combination after optimization decision can not only improve the processing efficiency and ensure the stability of processing, but also ensure the final processing quality, and can provide high-quality processing scheme for actual processing.

Claims

1. A multi-objective optimization method for milling parameters based on chaotic genetic algorithm, characterized in that, Includes the following steps: S1: Establish a multi-objective optimization model for milling parameters; S2: Obtain the initial population by applying the milling parameters through the Tent chaotic mapping. Q t ; S3: Initial population Q t The Pareto solution set is obtained by substituting the chaotic genetic algorithm into the multi-objective optimization model of milling parameters; the Pareto solution set is the optimization result of milling parameters. The optimization objectives of the milling parameters include milling force. F and material removal rate MRR The optimization variables of the multi-objective optimization model for milling parameters include: milling speed. v c Milling depth a p Milling width a e and feed per tooth f z The multi-objective optimization model for milling parameters is as follows: ； in, C For influence constants; a 1 represents the exponential coefficient of the empirical model for milling speed; b 1 represents the exponential coefficient of the empirical model for milling depth; c 1 represents the exponential coefficient of the empirical model for milling width; d 1 represents the exponential coefficient of the empirical model for feed per tooth; z This refers to the number of teeth on the cutting tool. d The diameter of the cutting tool; Ra For workpiece surface roughness; Ra max This represents the maximum surface roughness of the workpiece. st The range of constraints; The initial population Q t The generation method includes the following steps: A1: Use the Tent chaotic mapping to randomly generate a random number matrix; the random number matrix consists of N rows and V columns of random numbers. x , x ∈[0,1]; N is the set population size, and V is the number of optimization variables in the multi-objective optimization model of milling parameters; A2: Convert the random numbers in the random number matrix to obtain chaotic values. g ( x ); ； ； in, x ij The first in the matrix i Okay, number j Random numbers in the column; A3: Given several chaotic values g ( x Mapped to the range of milling parameters [min] v ij max v ij In the process, the initial population was obtained. Q t [ z 11 , z 12 , z 13 ,... z ij ... z NV ]; The model for the mapping process is as follows: ； in, z ij These are the milling parameters optimized by chaos.

2. The multi-objective optimization method for milling parameters based on chaotic genetic algorithm according to claim 1, characterized in that, The process of solving the multi-objective optimization model for milling parameters using the chaotic genetic algorithm includes the following: S31: Initial population Q t Introducing the mutant offspring population into a binary bidding competition R t and the initial population Q t and variant offspring population R t Merging yields a merged population Z t ; S32: Merging populations Z t Selecting from the initial population using an elite selection strategy Q t Iterative populations of the same size P t ; S33: Order P t = Q t+1 Return to S31 to perform the iteration, until the specified number of iterations is reached. t When the maximum is reached, the output yields the iterative population. P tmax , P tmax This is the Pareto solution set of the multi-objective optimization model for milling parameters.

3. The multi-objective optimization method for milling parameters based on chaotic genetic algorithm according to claim 2, characterized in that, Step S32 includes: B1: For merged populations Z t Perform a non-dominated sort to obtain the hierarchy of each individual; B2: Calculate the crowding degree of each individual's level to obtain the crowding degree distance between adjacent individuals at the same level; B3: Select an iterative population based on the hierarchy and crowding distance of each individual. P t : In merging populations Z t Two individuals are randomly selected from the group. When two individuals are at the same level, the individual with the smaller level sequence value is included in the iterative population. P t ; When two individuals belong to different hierarchical levels, the individual with the larger crowding distance is included in the iterative population. P t Until the iterative population P t The number of individuals in the initial population Q t The number of individuals is equal.

4. The multi-objective optimization method for milling parameters based on chaotic genetic algorithm according to claim 2, characterized in that, The chaotic genetic algorithm has a population size of 70, an iteration count of 150, a mutation probability of 0.05, and a crossover rate of 0.

8.

5. A method for making milling parameter decisions based on the multi-objective optimization method for milling parameters based on chaotic genetic algorithm as described in any one of claims 1-4, characterized in that, Includes the following steps: C1: The subjective weight of the milling force is obtained by performing analytic hierarchy process on the Pareto solution set. Subjective weighting of material removal rate Subjective weighting of surface roughness ; C2: The objective weight of the milling force is obtained by calculating the entropy weight method using the Pareto solution set. Objective weighting of material removal rate and the objective weight of surface roughness ; C3: Based on subjective weighting , and and objective weight , and Calculate the overall weight of milling force W 1. Overall weight of material removal rate W 2 and surface roughness combined weight W 3; ； ； ； C4: Substitute the comprehensive weights into the TOPSIS method to calculate the score of each individual in the Pareto solution set, and select the individual with the highest score as the optimal milling parameters.

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