Bearing roller heat treatment process robustness design method based on simulation test and model calibration

Abstract

The invention discloses a bearing roller heat treatment process robustness design method based on simulation test and model calibration. The method comprises the following steps: step 1, establishing a heat treatment simulation model of a bearing roller; 2, calibrating the heat treatment simulation model based on a Gaussian process model and a particle swarm optimization algorithm; 3, establishing a response curved surface model between process parameters and response parameters of heat treatment; and 4, carrying out heat treatment process parameter robustness design. According to the method, the process simulation test is calibrated through model calibration, the accuracy of the heat treatment simulation model is improved, process parameter robustness design is carried out on the basis of the process simulation test, and the quality and robustness of the heat treatment process are effectively improved. The method is also suitable for other process types capable of being simulated, and has very high universality and operability.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of heat treatment process optimization design, and in particular to a bearing roller heat treatment process robustness design method based on simulation test and model calibration. BACKGROUND

[0002] As an important material performance control method, the heat treatment process is widely used in the fields of metallurgy, automobiles, aerospace, precision machinery and the like. By controlling the heating, holding and cooling processes of a workpiece, the internal organization of the workpiece can be changed, so that the hardness, strength, toughness and dimensional stability of the workpiece can be significantly improved. Especially in the parts with high requirements for fatigue life and wear resistance, the heat treatment process plays a key role in ensuring the quality of the final product. The core performance of the bearing roller, as a representative of the rotating load-bearing parts, depends on the reasonable control of the uniformity of the organization, the consistency of the hardness and the distribution of the residual stress, and therefore higher requirements are put forward for the robustness of the heat treatment process.

[0003] In order to improve the robustness of the heat treatment process, a computer simulation method is widely used to model and simulate the heat treatment process. This method can predict the temperature field distribution, the organization evolution process and the residual stress change through numerical simulation, and assist in the selection and optimization of the heat treatment process parameters. In actual engineering, simulation has become an important auxiliary tool for heat treatment process design, and gradually replaces the previous process test method which relies on experience and trial and error.

[0004] However, the existing heat treatment process simulation still faces many technical bottlenecks in the actual process design application. On the one hand, the simulation model relies on expert experience to set parameters when it is constructed, and lacks a systematic model calibration method based on test data, which leads to a significant deviation between the simulation results and the actual heat treatment effect, and reduces the credibility and usability of the model; on the other hand, the existing optimization design usually focuses on the optimization of deterministic indicators, and fails to fully consider the input disturbance caused by the equipment precision fluctuation in the manufacturing process, thereby ignoring the robustness analysis of the process parameters. These problems make it difficult for the simulation-assisted heat treatment process optimization to meet the quality consistency requirements of high-reliability parts. Therefore, it is urgent to propose a heat treatment process parameter optimization design method which combines the simulation model calibration mechanism and the robustness optimization strategy, so as to realize the dual improvement of the quality and stability of the heat treatment process. SUMMARY

[0005] The application relates to a bearing roller heat treatment process robustness design method based on simulation test and model calibration, in particular to a bearing roller heat treatment method which calibrates a process simulation model by combining a Gaussian process regression with a particle swarm optimization algorithm, and further realizes parameter robust optimization through a Taguchi method and a Monte Carlo simulation.

[0006] The pre-preparation work required by the present application is as follows: 1. three-dimensional model of bearing roller; 2. heat treatment process scheme of bearing roller; 3. heat treatment simulation software; 4. heat treatment process test data of bearing roller.

[0007] The present application is realized by the following steps: Step one: establish the heat treatment simulation model of bearing roller.

[0008] According to the three-dimensional model of bearing roller and the heat treatment process scheme, the heat treatment simulation model of bearing roller is established by using heat treatment simulation software, including dividing grid, setting process parameters, material data, calculation conditions and other parameters, and outputting heat treatment process quality response results.

[0009] Step two: calibrate the heat treatment simulation model based on Gaussian process model and particle swarm optimization algorithm.

[0010] The process of simulation model calibration is as follows: 2.1 Select the model parameters of bearing roller heat treatment simulation model which have significant influence on the simulation results of bearing roller heat treatment, such as material attribute parameters, define them as calibration parameters and specify the value range; 2.2 According to the heat treatment process test data of bearing roller, define the response parameters of heat treatment process quality, such as hardness, size deformation, etc., as the basis for simulation model calibration; 2.3 According to the selected model parameters and their value range, use test design method to design simulation test scheme, such as Latin hypercube design method, output a group of bearing roller heat treatment simulation test scheme; 2.4 According to the simulation test scheme, use the heat treatment simulation model of bearing roller to carry out simulation calculation, and obtain the response results of bearing roller heat treatment process quality corresponding to each test scheme; 2.5 Based on the simulation test results, use Gaussian process model to establish the function relationship model between calibration parameters and process quality response parameters, which is used to replace the time-consuming heat treatment process simulation model, and the form of Gaussian process model is as follows:

[0011] Among them, is the response variable, is the column vector composed of normalized input variables, is the dimension of input variables, is the column vector composed of known functions, is the column vector composed of regression coefficients, is the dimension of regression coefficient is the dimension of regression coefficient is the dimension of regression coefficient is the dimension of regression coefficient is a stationary Gaussian process with zero mean and covariance function Given two points and , the covariance function between and is expressed as follows:

[0012] where denotes the i th input variable vector, denotes the j th input variable vector, denotes the corresponding response value, denotes the corresponding response value, denotes the variance of the Gaussian process, denotes the correlation function between and , , , n is the maximum integer value of i and j .

[0013] The two most widely used types of correlation functions are the power exponential correlation function and the Matérn correlation function when and . The expressions of these two types of correlation functions are as follows: (a) Power exponential correlation function:

[0014] (b) Matérn correlation function:

[0015] and

[0016] where is a vector of scale parameters and satisfies , is a vector of power parameters and satisfies , denotes the smoothness parameter, is the absolute value of the difference between the th element in and the th element in .

[0017] Suppose that n sample points are designed in the sample space by experimental design, denoted as the matrix And the observation data corresponding to all sample points were obtained through simulation experiments, denoted as .make It is an uninformed prior distribution, i.e. For a certain new point You can get its response. The expectation is:

[0018] in, Indicates that in a given , , and Under the conditions Expected value; express Row vectors consisting of known function values; express and middle n column vectors The row vector formed by the relevant function values; , and express and , , The relevant function values; for The Middle i The column vector and the first j The inverse of the matrix composed of the correlation functions between the column vectors; express middle n column vectors The matrix composed of corresponding function values; express The transpose of .

[0019] The unknown parameters in equation (6) , and The solution can be obtained using the maximum likelihood estimation method. Once the maximum likelihood estimate is obtained... , and Afterwards, , and Substituting into equation (6) will complete the prediction of the simulation model response.

[0020] 2.6 Based on the established Gaussian process model, a calibration model is established with the optimization objective of minimizing the root mean square error between the model predicted response value and the corresponding test observation value, as shown below:

[0021] wherein, represents the s th model predicted value, represents the s th test observation value, represents the l th calibration parameter, represents the l th lower limit of the calibration parameter, represents the l th upper limit of the calibration parameter, , , m represents the number of test observation values, q represents the number of calibration parameters.

[0022] The equation (7) is solved by the particle swarm optimization algorithm. The basic process of the particle swarm optimization algorithm is as follows: 1) Initialize particles: set the number of particles, the maximum number of iterations, the speed range, the inertia factor and the learning factor, and randomly generate the initial particles and the initial speed of the particles in the solution space; 2) Calculate the fitness value: according to the optimization objective in equation (7), the root mean square error between the response value predicted by the model and the test observation value is defined as the fitness function. Calculate the fitness value of all current particles, find the group optimal value, and take the fitness of the current particle as the individual historical optimal value; 3) Update the particle position and speed: update the speed of the particle according to the group optimal value and the individual optimal value, and the particle moves to the next position with this speed. The update calculation formula of the position and the speed is as follows:

[0023]

[0024] wherein, is the speed of the id th particle, is the position of the id th particle, is the inertia weight, is the learning factor, is a random number between 0 and 1, is the individual historical optimal position of the particle, is the optimal position of the group particle. Generally is set to about 0.9, Take 0-4, usually take 2.

[0025] After obtaining the global optimal solution that minimizes the root mean square error of the model predicted response value and the observed test value, the optimal solution is input into the heat treatment process simulation model, and the calibration of the process simulation model is completed.

[0026] Step three: establish the response surface model between the process parameters and the response parameters of heat treatment.

[0027] In order to effectively reduce the simulation calculation time cost of robust design, a proxy model between process parameters and response parameters needs to be established based on the calibrated heat treatment process simulation model to replace the high time-consuming process simulation model. The response surface model is used to replace the process simulation model, and the specific process is as follows: 3.1 Select the process parameters that have a significant impact on the heat treatment process quality, such as quenching preheating temperature, tempering temperature, etc., and determine the value range of the process parameters; 3.2 Select the process quality response parameters to be concerned, such as residual stress, deformation and residual austenite content, etc.; 3.3 According to the selected process parameters and their value range, use experimental design method to design simulation test scheme, such as factor design, central composite design method, etc., output a set of bearing roller heat treatment simulation test scheme; 3.4 According to the simulation test scheme, use the calibrated heat treatment simulation model to perform simulation calculation, and obtain the response results of bearing roller heat treatment process quality corresponding to each test scheme; 3.5 Based on the simulation test results, use the response surface model to establish the functional relationship model between the process parameters and the process quality response parameters, which is used to replace the time-consuming heat treatment process simulation model. The form of the second-order response surface model is as follows:

[0028] Among them, represents the model output variable, and respectively represent the first a and b independent variables, , , , represent the regression coefficients, represents the error term, , , M represent the number of variables. The regression coefficients can be obtained by using stepwise regression analysis method. In order to ensure the modeling accuracy, the minimum number of sample points required by the second-order model is .

[0029] Step four: Robustness design of heat treatment process parameters.

[0030] Based on the response surface model in step three, considering the dispersion characteristics of process parameters, a process parameter robustness design model is established. The objective function is modeled using a linear combination strategy of the mean and standard deviation of the process quality response parameters, and the constraint condition is the value range of the process parameters.

[0031] 4.1 For the response parameters of the small characteristic The objective function can be expressed as:

[0032] 4.2 For the response parameters of the large characteristic The objective function can be expressed as:

[0033] 4.3 For the response parameters of the target characteristic The objective function can be expressed as:

[0034] Wherein, represents the objective function, represents the mean of the response parameter, represents the standard deviation of the response parameter, represents the initial mean of the response parameter, represents the initial standard deviation of the response parameter, represents the target mean, and represent the weight coefficient and . It should be noted that when the response parameters include more than one type of characteristic parameters, the linear accumulation can be performed on different types of characteristic parameters, and the sum of all weight coefficients is ensured to be 1.

[0035] From the above, the process parameter robustness design model can be established as follows:

[0036] Wherein, represents the c th process parameter, and represent the upper limit and lower limit of , respectively, represents the number of process parameters.

[0037] Under the condition of given process parameter distribution characteristics, the mean and standard deviation of the response parameter are estimated by combining the response surface model and the Monte Carlo sampling method. The response surface model is modeled according to step three. The Monte Carlo sampling adopts a simple random sampling strategy for sampling. First, random sampling is performed on the uniform distribution of (0, 1), and a set of random numbers on (0, 1) is generated according to the specified sample size. Then, for each random number, the corresponding process parameter value is calculated according to the distribution characteristics of each process parameter, and all the process parameter values constitute a sampling sample data. Finally, the process parameter sample data of the specified sample size is generated. Based on the response surface model, the response value corresponding to each process parameter sample data is calculated to constitute the sample data of the response parameter, and the mean and standard deviation of the response parameter can be calculated based on this.

[0038] The particle swarm optimization algorithm is used to solve formula (14) to obtain the optimal process parameter combination, which improves the process quality while reducing the process dispersion.

[0039] The advantages and beneficial effects of the present application are: 1. The present application proposes to use process simulation test for bearing roller heat treatment process robustness design, which can effectively reduce the dependence on actual process test, realize rapid iteration design of process scheme, improve the robustness of process, reduce the research and development risk, and control the research and development cost.

[0040] 2. The present application proposes a heat treatment process simulation model calibration method based on Gaussian process model and particle swarm optimization algorithm, which can quickly and effectively improve the accuracy of heat treatment process simulation prediction and enhance the credibility of simulation results.

[0041] 3. The process simulation model calibration method and process robustness design method proposed in the present application have good universality and strong operability, and can be popularized to other process types. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a three-dimensional model of a certain type of bearing roller provided by the present application.

[0043] Figure 2 is a bearing roller grid model provided by the present application.

[0044] Figure 3a , Figure 3b is a heat treatment simulation model schematic diagram provided by the present application.

[0045] Figure 4 is the hardness simulation result corresponding to the initial process scheme provided by the present application. DETAILED DESCRIPTION

[0046] With reference to the accompanying drawings: clear and complete description of the technical solutions in the embodiments of the present application will be described below. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the scope of the present application.

[0047] A three-dimensional model of a certain type of bearing roller is shown in Figure 1 , with a diameter of 9.525 mm and a material of 8Cr4Mo4V. The initial heat treatment process scheme and the hardness measurement results of the roller obtained by process test are shown in Table 1. In this example, the heat treatment simulation of the bearing roller is modeled using the SYSWELD software of the Visual-Environment platform.

[0048] Table 1 Heat treatment process scheme and roller hardness measurement results

[0049] Step 1: Establish a heat treatment simulation model of the bearing roller.

[0050] 1) Mesh division The Visual-Mesh module of the Visual-Environment platform is used to divide the mesh of the roller, and the surface mesh is locally refined to ensure the mesh quality of the position with sharp temperature change. The final number of meshes is 63500, as shown in Figure 2 .

[0051] 2) Establish a heat treatment simulation model The Visual-Weld module (i.e. SYSWELD software) of the Visual-Environment platform is used to model the heat treatment simulation. According to the software operation wizard, the corresponding process parameters, material data, calculation conditions and other parameters are set according to the process scheme, and the heat treatment process simulation modeling of the bearing roller is completed, Figure 3a , Figure 3b Some simulation model setting diagrams are given.

[0052] 3) Simulation results of the initial process scheme The roller hardness simulation results obtained based on the initial process scheme are shown in Figure 4 , and the simulation hardness values are shown in Table 2. It can be seen that the hardness value predicted by the simulation model is 14.98HV lower than the test hardness value.

[0053] Table 2 Comparison of process test results and simulation results

[0054] Step two: calibration of the heat treatment simulation model based on the Gaussian process model and particle swarm optimization algorithm.

[0055] 1) Define calibration parameters and specify value ranges According to expert experience, the MS point (martensite transformation start temperature) and KM value (hardness calculation related constant) were selected as calibration parameters, and the value ranges are shown in Table 3.

[0056] Table 3 Heat treatment parameter range

[0057] 2) Define the response parameter of heat treatment process quality Considering that the hardness of the roller was mainly measured in the process test, the hardness was selected as the response parameter of the heat treatment process quality in this example.

[0058] 3) Develop a heat treatment process simulation test scheme Latin hypercube design was used to generate 25 sample points, each containing an MS and KM value, as shown in Table 4.

[0059] 4) Heat treatment process simulation calculation According to the simulation test scheme, the MS point and KM value were modified in the heat treatment process simulation model, and simulation calculation was performed to extract the simulation hardness results under each sample. The obtained parameter combinations and simulation hardness data are shown in Table 4.

[0060] Table 4 Latin hypercube design scheme and corresponding hardness simulation results

[0061] 5) Establish the Gaussian process model between the calibration parameters and the process quality response parameters Based on the sample data in Table 4, a Gaussian process model was constructed with MS and KM as input and hardness as output. After the model training was completed, 6-fold cross-validation was performed for prediction accuracy evaluation, and the evaluation results are shown in Table 5.

[0062] Table 5 Gaussian process model accuracy evaluation results

[0063] As shown in Table 5, the root mean square error of the Gaussian process model is 2.43, and the average absolute error is 1.7044, and the model accuracy meets the requirements.

[0064] 6) Process simulation model calibration On the basis of the Gaussian process model, a calibration model is established according to formula (7). Since there is only one set of process test data in this example, the objective function in the calibration model can be simplified as the absolute difference between the simulation predicted hardness and the test observed hardness. The particle swarm optimization algorithm is used to solve the optimal calibration parameters, 30 particles are initialized, the maximum iteration number is set to 100, the initial value of the inertia factor is 0.9 and decreases linearly with iteration, the individual learning factor and the group learning factor are both set to 2, and the parameter range is consistent with the sample space. After optimization, the optimal solution MS=325, KM=0.0105 is obtained, corresponding to the predicted hardness of the Gaussian process model is 846.89 HV, and the deviation from the target value is only 0.21 HV. In the subsequent heat treatment simulation, the MS point in the model is set to 325 and the KM value is set to 0.0105.

[0065] Step three: Establish the response surface model between the process parameters and the response parameters of heat treatment.

[0066] 1) Select the process parameters that significantly affect the quality of heat treatment process and determine the value range of process parameters According to the experience of experts, four heat treatment process parameters, including heating rate, quenching preheating temperature, quenching final heating temperature and tempering temperature, are selected, and the value range of the parameters is given, as shown in Table 6.

[0067] Table 6 Heat treatment process parameters and value range

[0068] 2) Select the process quality response parameters to be concerned.

[0069] In this example, the residual stress, deformation and austenite content output by the process simulation model are selected as the process quality response parameters.

[0070] 3) Formulate the bearing roller heat treatment simulation test scheme.

[0071] According to the boundary value of the value range of the process parameters, the heating rate, quenching preheating temperature, quenching final heating temperature and tempering temperature are respectively set to two levels, a two-level full-factor design is adopted, and a heat treatment simulation test scheme containing 16 groups of parameter combinations is constructed, as shown in Table 7.

[0072] 4) Heat treatment process simulation calculation Based on the simulation test scheme, each set of process parameters is input into the calibrated simulation model, and the simulation results corresponding to each scheme are calculated, and the corresponding residual stress, deformation and residual austenite volume fraction are extracted as responses, as shown in Table 7.

[0073] Table 7 Process simulation test scheme and simulation results

[0074] 5) Establish the response surface model between the process parameters and the response parameters of process quality.

[0075] Based on the sample data in Table 7, the second-order response surface models between the residual stress, deformation and residual austenite volume fraction and the process parameters were established by using stepwise regression analysis method, and the evaluation results of modeling accuracy are shown in Table 8. As can be seen from the table, the three response surface models have very high accuracy, which meet the requirements.

[0076] Table 8 Evaluation results of response surface model accuracy

[0077] Note: R-sq represents the determination coefficient; R-sq (adjusted) represents the adjusted determination coefficient.

[0078] Step four: carry out the robustness design of heat treatment process parameters.

[0079] In this example, the residual stress, deformation and residual austenite volume fraction are all small characteristic parameters, therefore, the objective function construction method of small characteristic parameters is adopted, and the weights of objective functions are considered to be equal. In this case, the process parameter robustness design model is established as follows:

[0080] wherein, represents the mean of response parameter under the condition of represents the standard deviation of response parameter under the condition of represents the mean of response parameter under the initial process scheme (fixed value); represents the standard deviation of response parameter under the initial process scheme (fixed value).

[0081] For and ​​​​​​​​​​​​​​The calculation considers the equipment accuracy deviation existing in the actual process, four process parameters are regarded as random variables, and it is assumed that each parameter is subject to normal distribution, the standard deviation is determined according to the equipment control accuracy (as shown in Table 9), and the mean value is determined according to the value of the process parameter Under the given process parameter distribution characteristics, based on the response surface model established in step three, the mean value and the standard deviation of each response parameter can be calculated by using the Monte Carlo sampling method.

[0082] Table 9 Standard deviation of process parameters

[0083] Further, the formula (13) is solved by using the particle swarm optimization algorithm to obtain the optimal process parameter combination, and the optimal process parameters are simulated and verified by process simulation, and the results are shown in Table 10, and it can be seen from the results that the error of the robustness optimization result is within 1.5%, and the optimization result is reliable. Table 11 shows the comparison between the robustness design scheme and the original design scheme, and it can be seen that the residual stress, deformation and austenite content of the robustness design scheme are significantly reduced.

[0084] Table 10 Robustness optimization results and comparison with simulation results

[0085] Table 11 Comparison before and after optimization

[0086] The results show that the bearing roller heat treatment process robustness design can be realized by using the method, and the purpose of improving the quality and robustness of the bearing roller heat treatment process is achieved.

[0087] In summary, the bearing roller heat treatment process robustness design method based on simulation test and model calibration is given. The method relies on the bearing roller heat treatment process simulation test, and comprehensively utilizes the test design, Gaussian process model, particle swarm optimization algorithm, response surface model, Monte Carlo sampling, robustness design and other methods, realizes the calibration of the heat treatment simulation model, and takes this as the basis, considers the influence of the random deviation of the process parameters, completes the robustness design of the heat treatment process, and achieves the purpose of improving the quality and robustness of the heat treatment process. The specific steps of the method are as follows: firstly, the heat treatment simulation model of the bearing roller is established, secondly, the heat treatment simulation model is calibrated by using the Gaussian process model and the particle swarm optimization algorithm based on the process test data, then the response surface model of the heat treatment process parameters and the response parameters is established based on the calibrated simulation model, and finally, the heat treatment process parameter robustness design is carried out. The present application is also applicable to other types of processes that can be simulated, and has strong universality and operability.

Claims

1. A bearing roller heat treatment process robustness design method based on simulation test and model calibration, characterized in that: Comprising the following steps: Step one: Establishing a bearing roller heat treatment simulation model; According to the three-dimensional model of the bearing roller and the heat treatment process, the heat treatment simulation software is used to establish the heat treatment simulation model of the bearing roller, including dividing the grid, setting the process parameters, material data, calculation conditions, and outputting the heat treatment process quality response results; Step two: Calibration of the heat treatment simulation model based on the Gaussian process model and particle swarm optimization algorithm; Step three: Establishing the response surface model between the process parameters and the response parameters of heat treatment; Step four: Robustness design of heat treatment process parameters; Considering the dispersion characteristics of process parameters, a process parameter robustness design model is established, the objective function is modeled using the linear combination strategy of the mean and standard deviation of the process quality response parameters, and the constraint condition is the value range of the process parameters.

2. The bearing roller heat treatment process robustness design method based on simulation test and model calibration according to claim 1, characterized in that: In step two, the process of simulation model calibration is as follows: Step 2.1 Select the model parameters of the bearing roller heat treatment simulation model that have a significant impact on the simulation results of the bearing roller heat treatment, define them as calibration parameters and specify the value range; Step 2.2 According to the bearing roller heat treatment process test data, define the response parameters of the heat treatment process quality as the basis for simulation model calibration; Step 2.3 According to the selected model parameters and value range, use the experimental design method to design the simulation test scheme, output a set of bearing roller heat treatment simulation test schemes; Step 2.4 According to the simulation test scheme, use the heat treatment simulation model of the bearing roller to perform simulation calculation, and obtain the response results of the bearing roller heat treatment process quality corresponding to each test scheme; Step 2.5 Based on the simulation test results, a Gaussian process model is established to establish the functional relationship model between the calibration parameters and the process quality response parameters, which is used to replace the time-consuming heat treatment process simulation model; Step 2.6 Based on the Gaussian process model established above, the optimization objective is to minimize the root mean square error between the model predicted response parameters and the corresponding observed test parameters, and the calibration model is established.

3. The bearing roller heat treatment process robustness design method based on simulation test and model calibration according to claim 1 or 2, characterized in that: The form of the Gaussian process model is as follows: ； where, is the response variable, is a column vector of normalized input variables, is the dimension of the input variables, is a column vector of known functions, is a column vector of known functions, is a column vector of regression coefficients, is a column vector of regression coefficients, is the dimension of the regression coefficients, is a stationary Gaussian process with zero mean and covariance function is a stationary Gaussian process with zero mean and covariance function Given two points and , the covariance function between and is given by ； wherein, denotes the i input variable vector, denotes the j input variable vector, denotes the corresponding response value, denotes the corresponding response value, denotes the variance of the Gaussian process, denotes the correlation function between and , , n is the maximum integer value of i and j .

4. The bearing roller heat treatment process robustness design method based on simulation test and model calibration according to claim 3, characterized in that: the power exponential correlation function and the Matérn correlation function when and ; the expressions for these two classes of correlation functions are as follows: Power exponential correlation function: ； Matern correlation function: ； And ； wherein, is a vector of scale parameters and satisfies , is a vector of power parameters and satisfies , denotes a smoothing parameter, is and the absolute value of the difference of the th element in and .

5. The bearing roller heat treatment process robustness design method based on simulation test and model calibration according to claim 4, characterized in that: A series of sample points are designed in the sample space by design of experiment, denoted as , and observation data corresponding to all sample points are obtained by simulation experiment, denoted as ; let be the non-informative prior distribution, i.e. ; for a new point , the expectation of the response is obtained. ； Where, denotes the expected value under the condition that , , and the expected value;​ denotes a row vector consisting of known function values; representing with in n a column vector a row vector of correlation function values , and denote and , , the correlation function values of for The Middle i The column vector and the first j The inverse of the matrix composed of the correlation functions between the column vectors; representing in n a column vector a matrix of corresponding function values; denotes the transpose of The unknown parameters in equation (6) , and are solved by the maximum likelihood estimation method. When the maximum likelihood estimate values , and are obtained, , and are substituted into equation (6), the prediction of the response of the simulation model is completed.

6. The bearing roller heat treatment process robustness design method based on simulation test and model calibration of claim 2, wherein: The calibration model is as follows: ； wherein, represents the prediction value of the i-th model, s represents the i-th observed value of the test, s represents the i-th calibration parameter, l represents the lower limit of the i-th calibration parameter, l represents the upper limit of the i-th calibration parameter, l , , m represents the number of observed values of the test, q represents the number of calibration parameters;​​​​​ Solve formula (7) by particle swarm optimization algorithm, specifically: Initialize particles: Set the number of particles, maximum iteration times, velocity range, inertia factor and learning factor parameters, randomly generate initial particles and initial particle velocities in the solution space; Calculate fitness value: According to the optimization objective in formula (7), define the root mean square error between the response value predicted by the model and the observed value in the test as the fitness function, calculate the fitness value of all particles, and find the global optimal value, taking the fitness of each particle as the individual historical optimal value; Update particle position and velocity: Update the velocity of the particle according to the global optimal value and individual optimal value, and the particle moves to the next position with this velocity, where the update calculation formula of position and velocity is as follows: ； ； in, For the first id The speed of each particle For the first id The position of each particle. For inertial weights, As a learning factor, A random number between 0 and 1. This represents the optimal position in the history of an individual particle. The optimal position for the group of particles; After obtaining the global optimal solution that minimizes the root mean square error between the model predicted response value and the observed test value, input this optimal solution into the heat treatment process simulation model to complete the calibration of the process simulation model.

7. The bearing roller heat treatment process robustness design method based on simulation test and model calibration of claim 1, wherein: In step three, the response surface model is used to replace the process simulation model, and the specific process is as follows: Step 3.1 Select the process parameters that have a significant impact on the quality of heat treatment, and determine the value range of the process parameters; Step 3.2 Select the process quality response parameters to be concerned; Step 3.3 According to the selected process parameters and value range, use the experimental design method to design the simulation test scheme, and output a set of bearing roller heat treatment simulation test scheme; Step 3.4 According to the simulation test scheme, use the calibrated heat treatment simulation model to perform simulation calculation, and obtain the response result of bearing roller heat treatment process quality corresponding to each test scheme; Step 3.5 Based on the simulation test results, a response surface model is used to establish a functional relationship model between the process parameters and the process quality response parameters, which is used to replace the time-consuming heat treatment process simulation model.

8. The bearing roller heat treatment process robustness design method based on simulation test and model calibration according to claim 7, characterized in that: The form of the second-order response surface model is as follows: ； wherein, represents a model output variable, and represent the first a and b independent variables, respectively, , , , represent regression coefficients, represents an error term, , , M represents the number of variables; the regression coefficients are obtained using a stepwise regression analysis method; and to ensure modeling accuracy, the minimum number of sample points required for a second-order model is .

9. The bearing roller heat treatment process robustness design method based on simulation test and model calibration of claim 1, wherein: In step four, specifically: Step 4.1 Response parameter for the desired property The objective function is represented as: ；； Step 4.2 Response parameters for the desired characteristics The objective function is represented as: ； Step 4.3 Response parameter for the eye-sight characteristic The objective function is expressed as: ； wherein represents the mean of the response parameter, represents the standard deviation of the response parameter, represents the initial mean of the response parameter, represents the initial standard deviation of the response parameter, represents the target mean, and represents the weight coefficient and ; it is noted that when the response parameter comprises more than one parameter of different characteristic types, the parameters of different characteristic types are linearly accumulated and the sum of all weight coefficients is ensured to be 1.

10. The bearing roller heat treatment process robustness design method based on simulation test and model calibration of claim 9, wherein: The process parameter robustness design model is established as follows: ； wherein, represents the upper limit and the lower limit, respectively, c of the process parameter, and represents the upper limit and the lower limit, respectively, of the process parameter, represents the number of process parameters; Under the condition of given process parameter distribution characteristics, the mean and standard deviation of the response parameter are estimated by combining the response surface model and the Monte Carlo sampling method.

Images