Deep groove ball bearing optimization design method based on constrained flower pollination algorithm

Abstract

The invention relates to the technical field of optimization design, in particular to a constrained flower pollination algorithm-based deep groove ball bearing optimization design method, which comprises the following steps of S1, establishing a bearing optimization design model; s2, algorithm parameters are set, and an initial population is generated and evaluated; according to the method, automatic and intelligent search in a design space is realized by using a global search operator and a local search operator of a flower pollination algorithm, and the tedious processes of manual graph and table lookup and repeated calculation in a traditional design method are replaced; the method has the advantages of being simple in implementation process, high in operation speed, high in optimization capacity and good in convergence performance, and can be conveniently integrated into a bearing CAD system.

Description

Technical Field

[0001] The invention relates to the technical field of optimization design, and in particular to an optimization design method for a deep groove ball bearing based on a constrained flower pollination algorithm. Background Art

[0002] Bearings are widely used in rotating equipment in various fields such as machinery, electricity, petrochemicals, energy, transportation, aerospace, etc., and are known as the "joints of industry". Deep groove ball bearings have the characteristics of simple structure and easy use. They are the type of bearings with the largest production batch and the widest application range. With the continuous development of science and technology, the performance requirements of mechanical products are getting higher and higher, and the performance requirements for key bearing components are also constantly improving. The smooth operation and high fatigue life of bearings are important indicators for evaluating the service performance of bearings, and both are closely related to the structural parameters of bearings. Related research on improving the service performance of bearings by optimizing the design of bearing structural parameters has always attracted people's attention. Traditional bearing optimization design methods require manual reference to mechanical design manuals and other materials. Due to the complexity of bearing types and size parameters, a large number of formulas and charts are often required, which is inefficient. Some studies on bearing CAD systems can realize functions such as query selection, size calculation and drawing generation, but in the optimization design part, deterministic search methods are generally used, and it is difficult to obtain the optimal design results. Summary of the invention

[0003] The purpose of the present invention is to solve the shortcomings existing in the background technology and propose a deep groove ball bearing optimization design method based on a constrained flower pollination algorithm.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is: a deep groove ball bearing optimization design method based on a constrained flower pollination algorithm, comprising the following steps:

[0005] S1. Establish a bearing optimization design model;

[0006] S2, set algorithm parameters, generate initial population and evaluate;

[0007] S3, performing iterative solution;

[0008] Wherein, step S2 includes: B1, setting parameter values ​​of constrained flower pollination algorithm, including population size N P , transition probability p, maximum number of iterations T max The maximum number of objective function evaluations FE max ;

[0009] B2. Initialize the number of iterations t=0 and randomly generate N in the design space. P Initial solutions to complete population initialization:

[0010]

[0011] Among them, X i represents the i-th candidate solution, N P is the population size, and are the upper and lower bounds of the j-th design variable, rand is a random number between [0,1], and M represents the number of design variables contained in each design scheme;

[0012] B3. Round off the number of rolling elements in each candidate solution in the initial population, and calculate the objective function value and constraint violation degree of each candidate solution according to the mathematical model of deep groove ball bearing optimization design;

[0013] B4. Use the following heuristic rules to compare the advantages and disadvantages of each candidate solution in the initial solution population and determine the best individual solution. The heuristic rules include:

[0014] A feasible solution is always better than an infeasible solution;

[0015] Among two feasible solutions, the one with a smaller objective function value is better;

[0016] Of the two infeasible solutions, the one with the smaller constraint violation is better.

[0017] Preferably, step S1 comprises the following steps:

[0018] A1. Determine design variables and optimization goals:

[0019] Rolling element diameter D w , bearing pitch diameter D j , the number of rolling elements Z, the outer ring raceway groove curvature radius coefficient f o and the inner ring raceway curvature radius coefficient f i Parameters are used as optimization design variables, with the rated dynamic load of the bearing (C r ) and rated static load (C or ) is the joint optimization target, and the optimization design model of deep groove ball bearing is constructed, in which the rated dynamic load C r Calculate as follows:

[0020]

[0021] Where b m is the rating factor related to common bearing steel and good processing methods. For deep groove ball bearings, it is 1.3. c is the basic coefficient of bearing parts;

[0022] A2. Determine the constraints, which include: rolling element diameter constraint, pitch circle diameter constraint, rolling element number constraint, wall thickness constraint and raceway groove curvature radius coefficient constraint.

[0023] Preferably, the constraint condition in step A2 is:

[0024] Rolling element diameter constraint: ;

[0025] Pitch circle diameter constraint: ;

[0026] Rolling element number constraints: ;

[0027] Wall thickness constraint: ;

[0028] Raceway groove curvature radius coefficient constraint: .

[0029] Preferably, the basic coefficients of the bearing parts in step A1 include bearing geometry, manufacturing accuracy and manufacturing material. c The expression is:

[0030] Where λ is the reduction coefficient. For deep groove ball bearings, λ is 0.95, γ=D w / D j .

[0031] Preferably, the rated static load C in step A1 or Calculate as follows:

[0032]

[0033] Where a i 、b i They are the major and minor semi-axes of the contact ellipse between the ball and the inner raceway of the bearing with dimension 1;

[0034] Preferably, the rated static load C or Perform optimal processing and take C during optimization r and C or The weighted sum of is used as the optimization objective: , where α1 and α2 represent C r and C or , and satisfies α1+α2=1.

[0035] Preferably, the constraint violation degree in step B3 is defined as:

[0036]

[0037] Where m is the number of constraints.

[0038] Preferably, step S3 comprises the following steps:

[0039] C1. Try to update each candidate solution in the current solution population. For each individual solution, first generate a random number between [0, 1]. If the random number is greater than the preset transition probability p, try to update the candidate solution using the global search operator. Otherwise, try to update the candidate solution using the local search operator.

[0040] The global search operator is as follows:

[0041]

[0042] In the formula, is the i-th candidate solution in the current population, Is The generated new solution, is the optimal solution in the current population, is the scaling factor of the step length, which is 0.01;

[0043] Where L is the step size determined by the Lévy distribution and is calculated as follows:

[0044]

[0045] In the formula, β is 1.5, U is consistent with the mean of 0 and the variance of σ 2 V is a random number with a normal distribution and a mean of 0 and a variance of 1. 2 Calculate as follows:

[0046]

[0047] The local search operator is as follows:

[0048]

[0049] in, and is a randomly selected solution from the current solution population, different from There are two candidate solutions for , r1 is a random number that conforms to the uniform distribution between [0, 1];

[0050] Get a new solution After that, check Is it within the design space? If not, use the following formula to correct it;

[0051] C2, according to the heuristic rule in step B4, compare the obtained and The pros and cons of Better, use replace , otherwise Directly discard;

[0052] C3. After completing a round of trial updates for each solution in the current solution population, determine the optimal solution individual in the current new population;

[0053] C4. Update the number of iterations t and check whether the current number of iterations reaches the preset maximum number of iterations T max If it is reached, the solution is completed and the optimal solution individual in the current population is output as the solution result; otherwise, go to step B2 and start the next iteration.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] The present invention utilizes the global search operator and the local search operator of the flower pollination algorithm to realize automatic and intelligent search in the design space, replacing the tedious manual map and table lookup and repeated calculation process in the traditional design method. It has the characteristics of simple implementation process, fast calculation speed, strong optimization ability and good convergence performance, and can be easily integrated into the bearing CAD system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of a deep groove ball bearing optimization design method based on a constrained flower pollination algorithm of the present invention;

[0057] Figure 2 The invention provides a method for optimizing the design of deep groove ball bearings based on a constrained flower pollination algorithm with a rated dynamic load C r The process of solving the optimization goal;

[0058] Figure 3 The invention discloses a method for optimizing the design of deep groove ball bearings based on a constrained flower pollination algorithm. or The process of solving the optimization goal;

[0059] Figure 4 The invention provides a solution process of a deep groove ball bearing optimization design method based on a constrained flower pollination algorithm with a combined load as the optimization target; DETAILED DESCRIPTION

[0060] The following description is used to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are only examples, and those skilled in the art may think of other obvious variations.

[0061] like Figure 1-Figure 4 A deep groove ball bearing optimization design method based on a constrained flower pollination algorithm is shown, and the method mainly includes the following steps:

[0062] S1. Establish the bearing optimization design model as follows:

[0063] A1. Determine design variables and optimization goals:

[0064] Rolling element diameter D w , bearing pitch diameter D j , the number of rolling elements Z, the outer ring raceway groove curvature radius coefficient f o and the inner ring raceway curvature radius coefficient f i The five parameters such as the bearing dynamic load rating (C r ) and rated static load (C or ) is the joint optimization target, and the optimization design model of deep groove ball bearing is constructed, in which the rated dynamic load C r Calculate as follows:

[0065]

[0066] Where b m is the rated factor related to common bearing steel and good processing methods, and is taken as 1.3 for deep groove ball bearings; f c It is a coefficient related to the geometric shape, manufacturing accuracy and material of bearing parts. Its general expression is:

[0067] Where λ is the reduction coefficient. For deep groove ball bearings, λ is 0.95; γ=D w / D j .

[0068] Rated static load C or Calculate as follows:

[0069]

[0070] Where a i 、b i They are the major and minor semi-axes of the contact ellipse with dimension 1 between the ball and the inner ring raceway of the bearing.

[0071] As shown in the following formula, when optimizing, take C r and C or The weighted sum of the combined rated load is taken as the optimization target: ,

[0072] Where α1 and α2 represent C r and C or The weight coefficients of α1 and α2 satisfy α1+α2=1. The values ​​of the two can be determined according to the optimization process for C r and C or The level of attention should be adjusted.

[0073] A2. Determine the constraints, mainly considering the following constraints:

[0074] ①Rolling element diameter constraint:

[0075]

[0076] ②Pitch circle diameter constraint:

[0077]

[0078] ③Constraints on the number of rolling elements:

[0079]

[0080] ④Wall thickness constraint:

[0081] ⑤Constraints on the curvature radius coefficient of the raceway groove: ,

[0082] S2. Set algorithm parameters, generate the initial population and evaluate it, as follows:

[0083] B1. Set the parameter values ​​of the constrained pollination algorithm, including the population size N P , transition probability p, maximum number of iterations T max Or the maximum number of objective function evaluations FE max wait.

[0084] B2. Initialize the number of iterations t=0 and randomly generate N in the design space. P Initial solutions to complete population initialization:

[0085]

[0086] Among them, X i represents the i-th candidate solution (design), N P is the population size, and are the upper and lower bounds of the j-th design variable, rand is a random number between [0,1], and M represents the number of design variables contained in each design scheme.

[0087] B3. Round off the number of rolling elements in each candidate solution in the initial population, and calculate the objective function value and constraint violation degree of each candidate solution according to the mathematical model of deep groove ball bearing optimization design. The constraint violation degree is defined as:

[0088] ,

[0089] Where m is the number of constraints.

[0090] B4. Use the following heuristic rules to compare the advantages and disadvantages of each candidate solution in the initial solution population and determine the best individual solution.

[0091] ① A feasible solution is always better than an infeasible solution;

[0092] ② Among the two feasible solutions, the one with a smaller objective function value is better;

[0093] ③ Among two infeasible solutions, the one with smaller constraint violation is better.

[0094] S3, perform iterative solution as follows:

[0095] C1. Try to update each candidate solution in the current solution population. For each individual solution, first generate a random number between [0, 1]. If the random number is greater than the preset transition probability p, try to update the candidate solution using the global search operator; otherwise, try to update the candidate solution using the local search operator.

[0096] The global search operator is as follows:

[0097] ,

[0098] in, is the i-th candidate solution in the current population, Is The generated new solution, is the optimal solution in the current population, is the scaling factor of the step length, generally 0.01. L is the step length determined by the Lévy distribution and is calculated by the following formula:

[0099]

[0100] Among them, β is generally taken as 1.5, and U is consistent with the mean of 0 and the variance of σ 2 V is a random number with a normal distribution and a mean of 0 and a variance of 1. 2 Calculate as follows:

[0101]

[0102] The local search operator is as follows:

[0103]

[0104] in, and is a randomly selected solution from the current solution population, different from There are two candidate solutions for , r1 is a random number that follows a uniform distribution between [0, 1].

[0105] Get a new solution After that, check Is it within the design space? If not, use the following formula to correct it.

[0106] C2. Compare the obtained and The pros and cons of Better, use replace , otherwise Discard directly.

[0107] C3. After completing a round of trial updates for each solution in the current solution population, determine the optimal solution individual in the current new population.

[0108] C4. Update the number of iterations t and check whether the current number of iterations reaches the preset maximum number of iterations T max If it is reached, the solution is completed and the optimal solution individual in the current population is output as the solution result; otherwise, go to step B2 and start the next iteration.

[0109] In implementation: Taking the widely used 6206 deep groove ball bearing as an example, the effectiveness of this design method is demonstrated. Before optimization, the outer diameter D of the bearing is 62 mm, the inner diameter d is 30 mm, the curvature sum is 0.5916, and the constraint coefficient a i =3.738, b i =0.4166. Set algorithm parameters: population size N p =40, transition probability p=0.8, maximum number of iterations T max =500; respectively, the rated dynamic load of the bearing is C r For the optimization target (α1=1, α2=0), the rated static load C of the bearing or The algorithm solution process is as follows: Figure 2 , Figure 3 , Figure 4 As shown, the final design scheme and the corresponding objective function value are shown in the following table.

[0110]

[0111] The present invention proposes a deep groove ball bearing optimization design method based on a constrained flower pollination algorithm, which utilizes the global search operator and local search operator of the flower pollination algorithm to realize automatic and intelligent search in the design space, replacing the tedious manual map and table lookup and repeated calculation processes in traditional design methods. The method has the characteristics of simple implementation process, fast calculation speed, strong optimization capability and good convergence performance, and can be easily integrated into the bearing CAD system.

[0112] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A deep groove ball bearing optimization design method based on constrained flower pollination algorithm, characterized in that: The following steps are involved: S1. Establish a bearing optimization design model; S2, set algorithm parameters, generate initial population and evaluate; S3, performing iterative solution; Wherein, step S2 includes: B1, setting parameter values ​​of constrained flower pollination algorithm, including population size N P , transition probability p, maximum number of iterations T max The maximum number of objective function evaluations FE max ; B2. Initialize the number of iterations t=0 and randomly generate N in the design space. P Initial solutions to complete population initialization: Among them, X i represents the i-th candidate solution, N P is the population size, and are the upper and lower bounds of the j-th design variable, rand is a random number between [0,1], and M represents the number of design variables contained in each design scheme; B3. Round off the number of rolling elements in each candidate solution in the initial population, and calculate the objective function value and constraint violation degree of each candidate solution according to the mathematical model of deep groove ball bearing optimization design; B4. Use the following heuristic rules to compare the advantages and disadvantages of each candidate solution in the initial solution population and determine the best individual solution. The heuristic rules include: A feasible solution is always better than an infeasible solution; Among two feasible solutions, the one with a smaller objective function value is better; Of the two infeasible solutions, the one with the smaller constraint violation is better.

2. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 1 is characterized in that: The step S1 comprises the following steps: A1. Determine design variables and optimization goals: Rolling element diameter D w , bearing pitch diameter D j , the number of rolling elements Z, the outer ring raceway groove curvature radius coefficient f o and the inner ring raceway curvature radius coefficient f i Parameters are used as optimization design variables, with the rated dynamic load of the bearing (C r ) and rated static load (C or ) is the joint optimization target, and the optimization design model of deep groove ball bearing is constructed, in which the rated dynamic load C r Calculate as follows: Where b m is the rating factor related to common bearing steel and good processing methods. For deep groove ball bearings, it is 1.

3. c is the basic coefficient of bearing parts; A2. Determine the constraints, which include: rolling element diameter constraint, pitch circle diameter constraint, rolling element number constraint, wall thickness constraint and raceway groove curvature radius coefficient constraint.

3. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 2 is characterized in that: The constraints in step A2 are: Rolling element diameter constraint: ; Pitch circle diameter constraint: ; Rolling element number constraints: ; Wall thickness constraint: ; Raceway groove curvature radius coefficient constraint: .

4. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 2 is characterized in that: The basic coefficients of the bearing parts in step A1 include bearing geometry, manufacturing accuracy and manufacturing materials. c The expression is: Where λ is the reduction coefficient. For deep groove ball bearings, λ is 0.95, γ=D w / D j .

5. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 2 is characterized in that: The rated static load C in step A1 or Calculate as follows: Where a i 、b i They are the major and minor semi-axes of the contact ellipse with dimension 1 between the ball and the inner ring raceway of the bearing.

6. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 5 is characterized in that: For the static load rating C or Perform optimal processing and take C during optimization r and C or The weighted sum of is used as the optimization objective: , where α1 and α2 represent C r and C or , and satisfies α1+α2=1.

7. The deep groove ball bearing optimization design method based on the constrained flower pollination algorithm according to claim 1 is characterized in that: The constraint violation degree in step B3 is defined as: Where m is the number of constraints.

8. The deep groove ball bearing optimization design method based on constrained flower pollination algorithm according to claim 1 is characterized in that: The step S3 comprises the following steps: C1. Try to update each candidate solution in the current solution population. For each individual solution, first generate a random number between [0, 1]. If the random number is greater than the preset transition probability p, try to update the candidate solution using the global search operator. Otherwise, try to update the candidate solution using the local search operator. The global search operator is as follows: In the formula, is the i-th candidate solution in the current population, Is The generated new solution, is the optimal solution in the current population, is the scaling factor of the step length, which is 0.01; Where L is the step size determined by the Lévy distribution and is calculated as follows: In the formula, β is 1.5, U is consistent with the mean of 0 and the variance of σ 2 V is a random number with a normal distribution and a mean of 0 and a variance of 1. 2 Calculate as follows: The local search operator is as follows: in, and is a randomly selected solution from the current solution population, different from There are two candidate solutions for , r1 is a random number that conforms to the uniform distribution between [0, 1]; Get a new solution After that, check Is it within the design space? If not, use the following formula to correct it; C2, according to the heuristic rule in step B4, compare the obtained and The pros and cons of Better, use replace , otherwise Directly discard; C3. After completing a round of trial updates for each solution in the current solution population, determine the optimal solution individual in the current new population; C4. Update the number of iterations t and check whether the current number of iterations reaches the preset maximum number of iterations T max If it is reached, the solution is completed and the optimal solution individual in the current population is output as the solution result; otherwise, go to step B2 and start the next iteration.

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