CN115495923A - Milling parameter multi-objective optimization and decision method based on chaotic genetic algorithm - Google Patents
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Abstract
The invention discloses a milling parameter optimization and decision method based on a chaotic genetic algorithm, which comprises the following steps: s1: establishing a milling parameter multi-objective optimization model; s2: obtaining an initial population Q by the milling parameters through Tent chaotic mapping t (ii) a S3: initial population Q t Substituting a chaotic genetic algorithm to solve the milling parameter multi-objective optimization model to obtain a Pareto solution set; and the Pareto solution set is a milling parameter optimization result. According to the invention, milling parameters are subjected to multi-objective optimization to obtain an initial population through Tent chaotic mapping, the Tent chaotic mapping is subjected to population initialization to obtain a better effect than a pseudo random number, the uniformity of the initial population can be improved to a certain extent, and the diversity of the population and the distribution of solutions are further improved; further optimizing the model for multiple targets in the chaotic genetic algorithmWhen the solution is carried out, the obtained Pareto solution is concentrated on any individual, namely the milling parameter, and the processing efficiency and the processing quality can be optimized after the milling is actually carried out.
Description
Technical Field
The invention relates to the field of numerical control milling, in particular to a milling parameter multi-objective optimization and decision method based on a chaotic genetic algorithm.
Background
During numerical control milling, milling parameters need to be set, and a reasonable milling parameter combination can reduce the abrasion of the milling cutter and prolong the service life of the milling cutter when the milling cutter keeps the working efficiency or improves the working efficiency.
In the prior art, the selection of milling parameters is often determined by referring to the past machining experience data of a factory and matching with manual simple calculation, so that the mode is limited by manual experience, and the machining efficiency of the selected milling parameters cannot be guaranteed to be optimal. In addition, in the actual production process, there are often a plurality of optimization targets of the milling parameters, and different optimization targets may cause the milling parameters to conflict during selection, which affects the actual processing efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the milling parameter multi-objective optimization method based on the chaotic genetic algorithm, which can optimize and select a plurality of optimization targets by milling parameters and ensure the working efficiency of actual processing.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows:
the milling parameter multi-objective optimization method based on the chaotic genetic algorithm comprises the following steps:
s1: establishing a milling parameter multi-objective optimization model;
s2: obtaining initial species by the chaos mapping of Tent for milling parametersGroup Q t ；
S3: initial population Q t Substituting a chaos genetic algorithm to solve the milling parameter multi-target optimization model to obtain a Pareto solution set; and the Pareto solution set is a milling parameter optimization result.
Further, the optimization targets of the milling parameters comprise a milling force F and a material removal rate MRR, and the optimization variables of the milling parameter multi-objective optimization model comprise: milling speed v c Milling depth a p Milling width a e And feed per tooth f z (ii) a The milling parameter multi-objective optimization model comprises the following steps:
wherein C is an influence constant; a is 1 The index coefficient of the milling speed empirical model is used; b 1 Is an exponential coefficient of the milling depth empirical model; c. C 1 The index coefficient of the milling width empirical model is obtained; d 1 An exponential coefficient of an empirical model of the feed per tooth; z is the cutter tooth number; d is the diameter of the cutter; ra is the surface roughness of the workpiece; ra (Ra) max The maximum roughness of the surface of the workpiece; st is a constraint range.
Further, the initial population Q t The generation method comprises the following steps:
a1: randomly generating a random number matrix by using Tent chaotic mapping;
a2: converting random numbers in the random number matrix to obtain a chaotic value g (x);
the random number matrix comprises N rows and V columns of random numbers x, wherein x belongs to [0,1];
x ij ＝rand(0,1)；
wherein x is ij The random number is the ith row and the jth column in the matrix; n is the set population size, and V is the number of optimization variables of the milling parameter multi-objective optimization model;
a3: mapping a plurality of chaotic values g (x) to a value interval [ minv ] of a milling parameter ij ，maxv ij ]In (2), obtaining an initial population Q t [z 11 ，z 12 ，z 13 ，...z ij ...z NV ]；
The model of the mapping process is:
z ij ＝minv ij +g(x ij )(maxv ij -minv ij )；
wherein z is ij Namely the milling parameters after chaos optimization.
Further, the solving process of the milling parameter multi-objective optimization model by the chaotic genetic algorithm comprises the following steps:
s31: initial population Q t Obtaining variant offspring population R by bringing into binary competitive bidding t And the initial population Q t And variant progeny population R t Merging to obtain a merged population Z t ；
S32: for combined population Z t Selecting and initial population Q through elite selection strategy t Iterative population P of the same population size t ；
S33: let P t ＝Q t+1 Returning to S31 to execute iteration until the iteration time t reaches the maximum, outputting an iteration population to obtain P tmax ，P tmax Namely, the Pareto solution set of the milling parameter multi-objective optimization model is obtained.
Further, step S32 includes:
b1: for combined population Z t Carrying out non-dominated sorting to obtain the hierarchy of each individual;
b2: carrying out congestion degree calculation on each individual level to obtain a congestion degree distance between adjacent individuals in the same level;
b3: selecting an iterative population P according to the obtained hierarchy and crowding degree distance of each individual t ：
In merging the population Z t In the method, two individuals are randomly extracted,
when two individuals are in the same hierarchy, the individual with smaller hierarchy sequence value is brought into the iterative population P t ；
When two individuals are in different levels, the individual with larger crowding distance is included in the iterative population P t Until iteration of the population P t Number of individuals in (1) and initial population Q t Are equal in number.
Further, the population size of the chaotic genetic algorithm is 70; the number of iterations is 150; the variation probability is 0.05; the cross-over difference rate was 0.8.
A milling parameter decision method based on a chaotic genetic algorithm comprises the following steps:
c1: calculating the Pareto solution set by an analytic hierarchy process to obtain the subjective weight of the milling force
Subjective weighting of material removal rate
And surface roughness subjective weighting
C2: entropy weight method calculation is carried out on the Pareto solution set to obtain objective milling force weight
Objective weight of material removal Rate
And objective weight of surface roughness
C3: according to subjective weight
And
and objective weight
And
calculating to obtain comprehensive weight W of milling force 1 Material removal rate comprehensive weight W 2 And surface roughness integrated weight W 3 ；
C4: and substituting the comprehensive weight into a TOPSIS method to calculate the score of each individual in the Pareto solution set, and selecting the individual with the highest score as the optimal parameter of the milling parameter.
The beneficial effects of the invention are as follows:
1. according to the invention, milling parameters are subjected to multi-objective optimization to obtain an initial population through Tent chaotic mapping, the Tent chaotic mapping is subjected to population initialization to obtain a better effect than a pseudo random number, the uniformity of the initial population can be improved to a certain extent, and the diversity of the population and the distribution of solutions are further improved; and further, when the chaos genetic algorithm is used for solving the multi-objective optimization model, the obtained Pareto solution is concentrated on any individual, namely the milling parameter, and the processing efficiency and the processing quality can be optimized after the milling parameter is applied to actual milling.
2. The optimized milling parameters obtained by multi-objective optimization are subjected to hierarchical analysis and entropy weight method to distribute weights, the optimized result is scored by using a TOPSIS method, and the milling parameters are selected according to the scoring result, so that decision making by means of artificial subjective experience is avoided, decision making reasonability is improved, and milling processing is scientific and reasonable.
Drawings
FIG. 1 is a schematic diagram of milling parameter multi-objective optimization and decision flow based on a chaotic genetic algorithm;
FIG. 2 is a Pareto solution set distribution diagram of the milling parameter multi-objective optimization model in the embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, a milling parameter multi-objective optimization and decision method based on a chaotic genetic algorithm includes the following steps: in the embodiment, the implementation process of the invention is described in detail by taking an example of milling in a Ti6Al4V titanium alloy by using a cemented carbide ball end mill;
s1: establishing a milling parameter multi-objective optimization model;
the optimization targets of the milling parameters comprise milling force F and material removal rate MRR, and the optimization variables of the milling parameter multi-target optimization model comprise: milling speed v c Milling depth a p Milling width a e And feed per tooth f z (ii) a The milling parameter multi-objective optimization model comprises the following steps:
wherein C is an influence constant; a is 1 The index coefficient of the milling speed empirical model is used; b is a mixture of 1 Is an exponential coefficient of the milling depth empirical model; c. C 1 The index coefficient of the milling width empirical model is obtained; d 1 An exponential coefficient of an empirical model of the feed per tooth; z is the cutter tooth number; d is the diameter of the cutter; ra is the surface roughness of the workpiece; ra max The maximum roughness of the surface of the workpiece;st is a constraint range.
S2: obtaining an initial population Q by carrying out Tent chaotic mapping on the milling parameters t ；
Initial population Q t The generation method comprises the following steps:
a1: randomly generating a random number matrix by using Tent chaotic mapping; the random number matrix comprises N rows and V columns of random numbers x, wherein x belongs to [0,1]; n is the set population size, and V is the optimized variable number of the milling parameter multi-objective optimization model;
a2: converting random numbers in the random number matrix to obtain a chaotic value g (x);
x ij ＝rand(0,1)；
wherein x is ij The random number is the ith row and the jth column in the matrix;
a3: mapping a plurality of chaotic values g (x) to a value interval [ minv ] of a milling parameter ij ，maxv ij ]In (2), obtaining an initial population Q t [z 11 ，z 12 ，z 13 ，...z ij ...z NV ]；
The model of the mapping process is:
z ij ＝minv ij +g(x ij )(maxv ij -minv ij )；
wherein z is ij Namely the milling parameters after chaos optimization.
S3: initial population Q t Substituting a chaos genetic algorithm to solve the milling parameter multi-target optimization model to obtain a Pareto solution set; and the Pareto solution set is a milling parameter optimization result.
The solving process of the milling parameter multi-target optimization model by the chaotic genetic algorithm comprises the following steps: setting the population size of the chaotic genetic algorithm to be 70; the number of iterations is 150;
s31: initial population Q t Obtaining variant offspring population R by bringing into binary competitive bidding t The variation probability is 0.05; crossingThe difference rate is 0.8; and the initial population Q t And variant progeny population R t Merging to obtain a merged population Z t ；
S32: merging populations Z t Selecting initial population Q by elite selection strategy t Iterative population P of the same population size t ；
The method comprises the following steps:
b1: for combined population Z t Carrying out non-dominated sorting to obtain the hierarchy of each individual;
b2: calculating the crowding degree of each individual level to obtain the crowding degree distance between adjacent individuals in the same level;
b3: selecting an iterative population P according to the obtained hierarchy and crowding degree distance of each individual t ：
In merging populations Z t Two individuals are randomly drawn in the process of drawing,
when two individuals are in the same hierarchy, the individual with smaller hierarchy sequence value is brought into the iterative population P t ；
When the two individuals are in different levels, the individual with larger crowding distance is brought into the iterative population P t Until iteration of the population P t Number of individuals in (1) and initial population Q t Are equal in number.
S33: let P t ＝Q t+1 Returning to S31 to execute iteration until the iteration time t reaches the maximum, outputting an iteration population to obtain P tmax ，P tmax Namely, the Pareto solution set of the milling parameter multi-objective optimization model is obtained.
The Pareto solution set is shown in fig. 2, the abscissa is the magnitude of the milling force, the ordinate is the magnitude of the material removal rate, and each point represents an element in the Pareto solution set.
Setting a reference group, wherein the reference group data is as follows: the material removal rate is 130.1mm 3 Min, cutting force 83.47N and surface roughness 0.37 micron; the gains of the three target variables of milling force, material removal rate and surface roughness were calculated for each individual in the Pareto solution set as compared to the reference set, and the gains are limited by the space, and ten sets of optimized solutions as shown in Table 1 are listed along with the three target variables of milling force, material removal rate and surface roughnessA gain rate;
TABLE 1
As can be seen from table 1, the gain ratios of the individuals in any Pareto solution set on the three target variables are all greater than 0, which significantly optimizes the milling parameters.
C3: according to subjective weight
And
and objective weight
And
calculating to obtain comprehensive weight W of milling force 1 Material removal rate integrated weight W 2 And surface roughness integrated weight W 3 ；
The subjective weight, objective weight and comprehensive weight are shown in table 2;
TABLE 2
| Item(s) | Material removal rate | Force of milling | Surface roughness |
| Subjective weighting | 0.300 | 0.110 | 0.590 |
| Objective weight | 0.4187 | 0.3622 | 0.2191 |
| Composite weight | 0.4262 | 0.1352 | 0.4386 |
As shown by the comprehensive weights in table 2, the milling force weight < the material removal rate weight < the surface roughness weight match the requirements of high quality and high processing efficiency pursued by actual processing;
c4: and calculating the score of each individual in the Pareto solution set by substituting the comprehensive weight into a TOPSIS method, and selecting the individual with the highest score as the optimal parameter of the milling parameter.
Individuals with five top scores calculated by the TOPSIS method are prepared as shown in the table 3;
TABLE 3
A score according to table 3 wherein the No.1 parametric combination scores the highest and the No.1 parametric combination has a higher material removal rate than the fifth group compared to the No.5 parametric combination; and No.1 was optimized for milling force, material removal rate, and surface roughness by 16.53%, 7.49%, and 10.34%, respectively, as compared to the initial reference group. The parameter combination with higher score after decision analysis can meet the requirement of actual processing, and the parameter combination after optimization is still in the constraint range. Therefore, through the parameter combination of the optimization decision, the processing efficiency can be improved, the processing stability can be ensured, the final processing quality can be ensured, and a high-quality processing scheme can be provided for the actual processing.
Claims (7)
1. A milling parameter multi-objective optimization method based on a chaotic genetic algorithm is characterized by comprising the following steps:
s1: establishing a milling parameter multi-objective optimization model;
s2: obtaining an initial population Q by the milling parameters through Tent chaotic mapping t ；
S3: initial population Q t Substituting a chaotic genetic algorithm to solve the milling parameter multi-objective optimization model to obtain a Pareto solution set; and the Pareto solution set is a milling parameter optimization result.
2. The chaotic genetic algorithm based milling parameter multi-objective optimization method according to claim 1, wherein the optimization objectives of the milling parameters comprise milling force F and material removal rate MRR, and the optimization variables of the milling parameter multi-objective optimization model comprise: milling speed v c Milling depth a p Milling width a e And feed per tooth f z (ii) a The milling parameter multi-objective optimization model is as follows:
wherein C is an influence constant; a is a 1 An exponential coefficient of the milling speed empirical model; b is a mixture of 1 The index coefficient of the milling depth empirical model is obtained; c. C 1 The index coefficient of the milling width empirical model is obtained; d 1 The index coefficient of the empirical model of the feed amount of each tooth is taken as the index coefficient; z is the number of teeth of the tool; d is the diameter of the cutter; ra is the surface roughness of the workpiece; ra max The maximum roughness of the surface of the workpiece; st is a constraint range.
3. The chaotic genetic algorithm based milling parameter multi-objective optimization method according to claim 1, wherein the initial population Q t The generation method comprises the following steps:
a1: randomly generating a random number matrix by using Tent chaotic mapping; the random number matrix comprises N rows and V columns of random numbers x, wherein x belongs to [0,1]; n is the set population size, and V is the optimized variable number of the milling parameter multi-objective optimization model;
a2: converting random numbers in the random number matrix to obtain a chaotic value g (x);
x ij ＝rand(0,1)；
wherein x is ij Random numbers of ith row and jth column in the matrix;
a3: mapping a plurality of chaotic values g (x) to a value interval [ minv ] of a milling parameter ij ，maxv ij ]In the method, an initial population Q is obtained t [z 11 ，z 12 ，z 13 ，...z ij ...z NV ]；
The model of the mapping process is:
z ij ＝min v ij +g(x ij )(max v ij -min v ij )；
wherein z is ij Namely the milling parameters after chaos optimization.
4. The chaotic genetic algorithm based milling parameter multi-objective optimization method according to claim 1, wherein the chaotic genetic algorithm comprises the following steps of solving a milling parameter multi-objective optimization model:
s31: initial population Q t Obtaining variant offspring population R by bringing into binary competitive bidding t And the initial population Q t And variant progeny population R t Merging to obtain a merged population Z t ；
S32: for combined population Z t Selecting initial population Q by elite selection strategy t Iterative population P of the same population size t ；
S33: let P t ＝Q t+1 Returning to S31 to execute iteration until the iteration time t reaches the maximum, and outputting to obtain an iteration population P tmax ，P tmax Namely a Pareto solution set of the milling parameter multi-objective optimization model.
5. The milling parameter multi-objective optimization method based on the chaotic genetic algorithm as claimed in claim 4, wherein the step S32 comprises:
b1: for combined population Z t Carrying out non-dominated sorting to obtain the hierarchy of each individual;
b2: calculating the crowding degree of each individual level to obtain the crowding degree distance between adjacent individuals in the same level;
b3: selecting an iterative population P according to the obtained hierarchy and crowding degree distance of each individual t ：
In merging the population Z t In the method, two individuals are randomly extracted,
when two individuals are in the same hierarchy, the individual with smaller hierarchy sequence value is included in the iterative population P t ；
When two individuals are in different levels, the individual with larger crowding distance is included in the iterative population P t Until iteration of the population P t Number of individuals in (1) and initial population Q t Are equal in number.
6. The chaotic genetic algorithm based milling parameter multi-objective optimization method according to claim 4, wherein the population size of the chaotic genetic algorithm is 70; the number of iterations is 150; the variation probability is 0.05; the cross-over difference rate was 0.8.
7. A method for milling parameter decision based on the chaotic genetic algorithm based milling parameter multi-objective optimization method disclosed by any one of claims 1 to 6 is characterized by comprising the following steps:
c1: calculating the Pareto solution set by an analytic hierarchy process to obtain the subjective weight of the milling force
Subjective weight of material removal rate
And surface roughness subjective weighting
C2: entropy weight method calculation is carried out on the Pareto solution set to obtain objective milling force weight
Objective weight of material removal Rate
And objective weight of surface roughness
C3: according to subjective weight
And
and objective powerHeavy load
And
calculating to obtain comprehensive weight W of milling force 1 Material removal rate comprehensive weight W 2 And surface roughness integrated weight W 3 ；
C4: and substituting the comprehensive weight into a TOPSIS method to calculate the score of each individual in the Pareto solution set, and selecting the individual with the highest score as the optimal parameter of the milling parameter.
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| CN116108753A (en) * | 2023-02-28 | 2023-05-12 | 哈尔滨理工大学 | Parameter optimization method for milling titanium alloy by micro-texture ball end mill |
| CN116646568A (en) * | 2023-06-02 | 2023-08-25 | 陕西旭氢时代科技有限公司 | Fuel cell stack parameter optimizing method based on meta heuristic |
| CN117669982A (en) * | 2023-12-18 | 2024-03-08 | 山东建筑大学 | Park comprehensive energy system capacity configuration method considering user multi-comfort |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116108753A (en) * | 2023-02-28 | 2023-05-12 | 哈尔滨理工大学 | Parameter optimization method for milling titanium alloy by micro-texture ball end mill |
| CN116646568A (en) * | 2023-06-02 | 2023-08-25 | 陕西旭氢时代科技有限公司 | Fuel cell stack parameter optimizing method based on meta heuristic |
| CN116646568B (en) * | 2023-06-02 | 2024-02-02 | 陕西旭氢时代科技有限公司 | Fuel cell stack parameter optimizing method based on meta heuristic |
| CN117669982A (en) * | 2023-12-18 | 2024-03-08 | 山东建筑大学 | Park comprehensive energy system capacity configuration method considering user multi-comfort |
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