A v-belt life optimization design method based on particle swarm algorithm

Abstract

The application relates to a V-belt life optimization design method based on a particle swarm algorithm, which comprises the following steps: constructing a life calculation model of a rubber V-belt; adopting a uniform test design method to take the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt as sample inputs, and dividing a training set, a verification set and a test set; obtaining a life prediction value by using a pre-established life calculation model; taking the maximum value of the life of the V-belt as an objective function, the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt as to-be-optimized parameters, and the slip rate and tension force failure threshold of the dynamic operation of the V-belt as constraint conditions. Compared with traditional optimization of the volume and size of the whole belt transmission system and simple physical calculation optimization of the life, the application has better global search capability and faster convergence speed for multi-parameter optimization, and has obvious practical value and broad application prospect.

Description

Technical Field

[0001] The present invention relates to the field of product life optimization design, and more particularly to a V-belt life optimization design method based on particle swarm algorithm. Background Art

[0002] As the most widely used type of belt drive, rubber V-belts are widely used in mechanical power transmission due to their simple structure, smooth transmission, low cost, lack of lubrication requirements, vibration damping, and ease of maintenance. They are primarily used in automotive transmissions, agricultural machinery power transmission, wind turbine power generation, and large-scale engineering equipment, occupying a crucial position in various industries. However, in actual use, rubber V-belts inevitably wear out and eventually break. Therefore, optimizing the lifespan of V-belts is not only of great engineering value, but can also significantly improve their performance and reliability.

[0003] Traditional V-belt optimization design primarily focuses on overall transmission system objectives, such as reducing pulley size, optimizing center distance, and minimizing the number of belts. However, optimizing V-belt performance and lifespan often relies solely on single-factor analysis, lacking comprehensive consideration of optimization parameters. This limitation can easily lead to biased and unstable lifespan optimization results, making it difficult to meet the demands for more efficient and reliable designs. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the present invention aims to provide a V-belt life optimization design method based on particle swarm optimization.

[0005] To achieve the above object, the present invention provides the following technical solution: a V-belt life optimization design method based on particle swarm optimization, characterized in that it includes the following steps:

[0006] Step 1: Establish a V-belt life prediction calculation model, collect physical property data and corresponding life to verify the model, and determine the parameters to be optimized as tensile strength, reference force elongation, hardness and elastic modulus and their upper and lower limits;

[0007] Step 2: For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits. The uniform experimental design method is used to obtain multiple sets of physical parameter combination schemes as input data. These schemes are substituted into the V-belt life prediction calculation model established in step 1, and the V-belt life value is recorded as output data.

[0008] Step 3: Determine the number of input layers, hidden layers, output layers, and the number of hidden layer nodes of the BP neural network and establish a BP neural network model; randomly select 70% of the input data as training data, 15% as verification data, and 15% as test data from several groups of input data, and train and verify the BP neural network until the error meets the requirement of within 5%;

[0009] Step 4: Use the particle swarm algorithm to perform optimization, taking the maximum life of the V-belt as the optimization target, the tensile strength, reference force elongation, hardness, and elastic modulus of the V-belt as the parameters to be optimized, and the upper and lower limits of the parameters to be optimized and the slip rate and tension failure threshold of the V-belt during dynamic operation as constraints;

[0010] Step 5: Set the particle swarm algorithm parameters, write a program, and iterate step by step until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

[0011] As a further improvement of the present invention, the step 1 of establishing a life prediction calculation model for a V-belt and collecting physical property data and corresponding life to verify the model specifically includes:

[0012] Step 1: Determine the type of V-belt, then collect the four physical properties of tensile strength, reference force elongation, hardness and elastic modulus, as well as the two dynamic time series parameters of slip rate and tension;

[0013] In steps 1 and 2, the four physical parameters and two dynamic time series parameters are fused into comprehensive features F1 and F2 using the SVR regression algorithm. The correlation between F1 and F2 is analyzed using a binary Copula function, and then a V-belt life prediction model is constructed based on a binary Wiener process.

[0014] Step 13: Design a V-drive static test under standard working conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

[0015] As a further improvement of the present invention, the specific method of establishing the BP neural network model in step 3 is as follows: the V-belt tensile strength, reference force elongation, hardness and elastic modulus are used as the input layer of the BP neural network, the number of which is determined to be 4; the output layer is the V-belt life, the number of which is determined to be 1; the hidden layer adopts a single hidden layer, and the calculation expression of the hidden layer node number is:

[0016]

[0017] Among them, l is the number of nodes, m is the number of input layer nodes, and n is the number of output layer nodes. After calculation, the number of hidden layer nodes is finally determined to be 10. Based on the determined basic model parameters, the BP neural network model of the V-belt is established with the help of MATLAB.

[0018] As a further improvement of the present invention, the life prediction calculation model of the V-belt is constructed as follows:

[0019]

[0020] Where k = 1, 2; w1 is the failure threshold of the physical property fusion feature F1, w2 is the failure threshold of the dynamic time series feature F2, feature F1 corresponds to the parameters (μ1, σ1), feature F2 corresponds to the parameters (μ2, σ2); f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F1(t), F2(t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (t|w k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum function value is the predicted calculated value of the V-belt life.

[0021] As a further improvement of the present invention, the constraints in step 4 are specifically as follows:

[0022]

[0023] Wherein, tensile strength is σ, elongation at reference force is ξ, hardness is H, and elastic modulus is E.

[0024] As a further improvement of the present invention, in step five, the particle swarm algorithm parameters are set, a program is written, and it is gradually iterated until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value. The specific method is as follows: first, the particle swarm is initialized, and then, combined with the established BP neural network model, the particle fitness is calculated, which is the optimized life value of the V-belt, and the particle speed and position are continuously updated to obtain the fitness extreme value; finally, the PSO optimization solution is performed to obtain the result, which includes tensile strength, reference force elongation, elastic modulus, and hardness. Finally, after multiple iterations, convergence is achieved to reach the optimal value of the V-belt life.

[0025] Beneficial effects of the present invention:

[0026] A comprehensive analysis of the impact of multiple factors on V-belt life, including static performance and dynamic fatigue indicators, was conducted to construct a more accurate V-belt life prediction model. The optimization parameters were then comprehensively considered to determine the dynamic failure indicators and thresholds for the V-belts. With maximizing V-belt life as the optimization goal, a BP neural network combined with a particle swarm algorithm was used to determine the optimal combination of parameters to optimize V-belt life.

[0027] The theoretical basis model of the present invention has high accuracy and strong robustness, and adopts a combination of a neural network agent model and a particle swarm optimization algorithm, which has better global search capabilities, greatly improving the optimization efficiency and accuracy. It can provide a basic reference for the life improvement research in the V-belt transmission industry, and has important theoretical significance and engineering application value for improving the efficiency and service life of V-belt transmission and achieving high reliability of mechanical transmission systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of the present invention;

[0029] Figure 2 It is the probability density distribution diagram of the V-belt life prediction model, and the maximum value corresponds to the V-belt life value;

[0030] Figure 3 This is a comparison chart of the prediction accuracy verification results of the V-belt life prediction model;

[0031] Figure 4 This is the training and verification result diagram of the BP neural network model;

[0032] Figure 5 This figure shows the optimization iterative results of the BP neural network combined with the PSO particle swarm algorithm. DETAILED DESCRIPTION

[0033] The present invention will be further described below with reference to the embodiments shown in the accompanying drawings.

[0034] Reference Figures 1 to 5 As shown, a V-belt life optimization design method based on particle swarm optimization in this embodiment includes the following steps:

[0035] S1. Establish a V-belt life prediction model, collect physical property data and corresponding lifespan to verify the model, and ensure that the accuracy of the calculation model is above 95%. Determine the parameters to be optimized as tensile strength, reference force elongation, hardness, and elastic modulus, as well as their upper and lower limits.

[0036] The specific implementation of the above steps includes the following sub-steps:

[0037] S11. Determine the B-type V-belt with a length of 1499mm as the research object. Under the conditions of Zhejiang Manufacturing Standard "T / ZZB 0060-2016 Ordinary V-belts for Transmission", design dynamic and static tests and collect pre-processed test data.

[0038] The nonlinear mapping relationship between the physical parameters of V-belts, such as tensile strength, reference force elongation, hardness, and elastic modulus, and their lifespan was further explored. The relationship between slip rate and tension of V-belts in dynamic timing conditions and their lifespan was analyzed and summarized.

[0039] S12. The four physical properties and two dynamic time series parameters are fused into comprehensive features F1 and F2 using the SVR regression algorithm. The correlation between F1 and F2 is analyzed using a binary Copula function. A V-belt life prediction model is then constructed based on a binary Wiener process.

[0040] The specific implementation method is as follows: Using the SVR regression algorithm, the weight factors of the physical property and dynamic time series characteristic models are calculated. Then, the four physical property parameters and two dynamic time series parameters are integrated into comprehensive features F1 and F2, and the corresponding V-belt fatigue failure thresholds are determined. Based on the AIC information criterion, the binary Frank Copula function is selected to analyze the correlation between F1 and F2. Then, a V-belt life prediction calculation model is constructed based on the binary Wiener process. That is, the expression of the V-belt life probability density distribution function is as follows:

[0041]

[0042] Where k = 1, 2; w1 is the failure threshold of the physical property fusion feature F1, w2 is the failure threshold of the dynamic time series feature F2, feature F1 corresponds to the parameters (μ1, σ1), feature F2 corresponds to the parameters (μ2, σ2); f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F1(t), F2(t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (t|w k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum value of the function is the predicted value of the V-belt life (see the attached Figure 2 shown).

[0043] S13. Design a V-drive static test under standard operating conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

[0044] The specific implementation method is: design a V-belt static test under the working conditions of Zhejiang Manufacturing Standard "T / ZZB 0060-2016 Ordinary V-belts for Transmission", obtain the required test index data, use the maximum likelihood function method to estimate the unknown parameters at 15h as the unit time point, obtain the life prediction calculation value, compare it with the V-belt life value recorded in the test, and finally verify that the accuracy of the established life prediction calculation model is above 95% (see attached Figure 3 This lays the theoretical foundation for subsequent calculations.

[0045] Taking the B-type V-belt as the research object, the physical parameters to be optimized and their upper and lower limits are determined as follows: tensile strength is [5.0, 10.0] KN, reference force elongation is (0, 0.07), hardness is [78, 83] and elastic modulus is (69, 100) MPA.

[0046] S2. For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits. Using the uniform experimental design method, multiple sets of physical parameter combinations are obtained as input data. These are substituted into the V-belt life prediction calculation model to obtain the V-belt life value as output data.

[0047] The specific implementation method is: the tensile strength, reference force elongation, hardness and elastic modulus of the V-belt are divided into 10 levels within the upper and lower limit ranges (as shown in Table 1). Using the uniform experimental design method, 40 groups of physical property parameter combinations can be obtained. The life value is calculated based on the established V-belt life prediction model.

[0048] Table 1

[0049]

[0050]

[0051] S3. Determine the number of input layers, hidden layers, and output layers, as well as the number of hidden layer nodes, of the BP neural network and establish a BP neural network model. Randomly select 70% of the input data as training data, 15% as validation data, and 15% as test data from several sets of input data, and train and validate the BP neural network until the error is within 5%.

[0052] The specific implementation method is as follows: the input layer of the BP neural network is the four parameters to be optimized, and the number is determined to be 4; the output layer is the V-belt life, and the number is determined to be 1; in order to avoid wasting resources and improve optimization efficiency, the hidden layer adopts a single-layer structure, and the number of hidden layer nodes is determined to be 10. The BP neural network model is constructed with the help of MATLAB's neural network toolbox. The 40 groups of solutions obtained by the uniform experimental design are randomly divided into 70%, 15%, and 15% distributions as training, verification, and test sets. Finally, the BP neural network model of the V-belt is established and verified to achieve excellent prediction accuracy (as shown in the attached figure). Figure 4 shown).

[0053] S4. Optimize the V-belt using a particle swarm optimization algorithm, taking the optimal lifespan of the V-belt as the optimization objective. The V-belt's tensile strength, reference force elongation, hardness, and elastic modulus are the parameters to be optimized. The upper and lower limits of the parameters to be optimized, as well as the slip rate η and tension force F failure thresholds during dynamic operation of the V-belt, are used as constraints.

[0054] The specific implementation method is to combine the BP neural network model with the particle swarm optimization algorithm (PSO) to determine the V-belt parameters to be optimized as tensile strength σ, reference force elongation ξ, hardness H and elastic modulus E. The optimization constraints are as follows:

[0055]

[0056] S5. Set the parameters of the particle swarm algorithm, write a program, and iterate step by step until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

[0057] The specific implementation method is as follows: complete the subroutine writing of fitness function and constraint conditions in MATLAB, and set the population size to 100, the maximum evolutionary generation to 50 generations, first initialize the particle swarm, and then combine the established BP neural network model to calculate the particle fitness, which is the life value of the V-belt after optimization, and continuously update the particle speed and position to obtain the fitness extreme value; finally, perform PSO optimization solution and calculate the results: tensile strength is 10KN, reference force elongation is 4.256%, elastic modulus is 70.0593MPA, hardness is 78, and finally iterates 26 times and converges to reach the optimal value of V-belt life of 272.056h (see attached) Figure 5 Compared with the life of the V-belt before optimization, the life of the V-belt is increased by 13.4%, which verifies that the optimization method is effective and practical.

[0058] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiment. All technical solutions based on the concept of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A V-belt life optimization design method based on particle swarm optimization, characterized by: The steps include: Step 1: Establish a V-belt life prediction calculation model, collect physical property data and corresponding life to verify the model, and determine the parameters to be optimized as tensile strength, reference force elongation, hardness and elastic modulus and their upper and lower limits; Step 2: For the physical parameters that need to be optimized, several levels are divided within the specified upper and lower limits. The uniform experimental design method is used to obtain multiple sets of physical parameter combination schemes as input data. These schemes are substituted into the V-belt life prediction calculation model established in step 1, and the V-belt life value is recorded as output data. Step 3: Determine the number of input layers, hidden layers, output layers, and the number of hidden layer nodes of the BP neural network and establish a BP neural network model; randomly select 70% of the input data as training data, 15% as verification data, and 15% as test data from several groups of input data, and train and verify the BP neural network until the error meets the requirement of within 5%; Step 4: Use the particle swarm algorithm to perform optimization, taking the maximum life of the V-belt as the optimization target, the tensile strength, reference force elongation, hardness, and elastic modulus of the V-belt as the parameters to be optimized, and the upper and lower limits of the parameters to be optimized and the slip rate and tension failure threshold of the V-belt during dynamic operation as constraints; Step 5: Set the particle swarm algorithm parameters, write a program, and iterate step by step until convergence to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value.

2. The V-belt life optimization design method based on particle swarm optimization according to claim 1 is characterized in that: The step 1 of establishing a life prediction calculation model for a V-belt and collecting physical property data and corresponding life to verify the model specifically includes: Step 1: Determine the type of V-belt, then collect the four physical properties of tensile strength, reference force elongation, hardness and elastic modulus, as well as the two dynamic time series parameters of slip rate and tension; In steps 1 and 2, the four physical parameters and two dynamic time series parameters are fused into comprehensive features F1 and F2 using the SVR regression algorithm. The correlation between F1 and F2 is analyzed using a binary Copula function, and then a V-belt life prediction model is constructed based on a binary Wiener process. Step 13: Design a V-drive static test under standard working conditions to obtain the required test index data and verify the accuracy and effectiveness of the established life prediction calculation model.

3. The V-belt life optimization design method based on particle swarm optimization according to claim 1 or 2, characterized in that: The specific method of establishing the BP neural network model in step 3 is as follows: The tensile strength, reference force elongation, hardness and elastic modulus of the V-belt are used as the input layer of the BP neural network, and the number is determined to be 4. The output layer is the V-belt life, and the number is determined to be 1. The hidden layer uses a single hidden layer, and the calculation expression of the hidden layer node number is: Among them, l is the number of nodes, m is the number of input layer nodes, and n is the number of output layer nodes. After calculation, the number of hidden layer nodes is finally determined to be 10. Based on the determined basic model parameters, the BP neural network model of the V-belt is established with the help of MATLAB.

4. The V-belt life optimization design method based on particle swarm optimization according to claim 2, characterized in that: The life prediction calculation model of the V-belt is constructed as follows: Where k = 1, 2; w1 is the failure threshold of the physical property fusion feature F1, w2 is the failure threshold of the dynamic time series feature F2, feature F1 corresponds to the parameters (μ1, σ1), feature F2 corresponds to the parameters (μ2, σ2); f 1RUL (t), f 2RUL (t) are their respective marginal distribution functions, c(F1(t), F2(t); θ) is the probability density function corresponding to the selected binary Copula function; f RUL (tw k ,μ k ,σ k ,θ) is the probability density distribution function of the V-belt life, and the time corresponding to the maximum function value is the predicted calculated value of the V-belt life.

5. The V-belt life optimization design method based on particle swarm optimization according to claim 1 or 2, characterized in that: The constraints in step 4 are as follows: Wherein, tensile strength is σ, elongation at reference force is ξ, hardness is H, and elastic modulus is E.

6. The V-belt life optimization design method based on particle swarm optimization according to claim 1 or 2, characterized in that: In step five, the particle swarm algorithm parameters are set, a program is written, and the algorithm is iterated step by step until convergence is achieved to obtain the optimal V-belt physical parameter combination scheme and the optimized V-belt life value. The specific method is as follows: first, the particle swarm is initialized, and then, combined with the established BP neural network model, the particle fitness is calculated, which is the optimized life value of the V-belt. The particle speed and position are continuously updated to obtain the fitness extreme value; finally, the PSO optimization solution is performed to obtain the results, which include tensile strength, reference force elongation, elastic modulus, and hardness. Finally, after multiple iterations, the algorithm converges to reach the optimal value of the V-belt life.

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