A quenching and tempering evaluation method for 42CrMo quenched and tempered steel crankshaft

Abstract

A kind of quenching and tempering evaluation method for 42CrMo quenching and tempering steel crankshaft, there is no accurate evaluation method for the hardness of 42CrMo quenching and tempering steel crankshaft at present;The quenching and tempering evaluation method in the application is based on the risk quantitative evaluation normal distribution theory to carry out early warning evaluation on crankshafts produced in different heats, form crankshaft data produced in different heats, respectively establish crankshaft hardness field finite element analysis model and tempering mechanical property prediction model, carry out crankshaft different quenching and tempering process center compound experiment through crankshaft hardness field finite element analysis model and tempering mechanical property prediction model, according to the linear regression equation of response surface characteristics fitting tempering hardness, tensile strength, yield strength and quenching temperature, tempering temperature, after optimization treatment of linear regression equation by Matlab genetic algorithm, standard equation is obtained, according to standard equation and actual acquisition of crankshaft data produced in different heats, comparison is completed to complete the evaluation process.

Description

Technical Field

[0001] This invention specifically relates to a method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts, belonging to the field of internal combustion engine technology. Background Technology

[0002] As a core component of internal combustion engines, the crankshaft's performance requirements directly affect the engine's reliability, durability, and efficiency. In particular, hybrid crankshafts used in automobiles require extremely high tensile strength under extreme operating conditions, while keeping the hardness within a certain range. This poses a significant challenge in selecting the tempering process, and often, a single experiment is costly. Some studies have explored combining machine learning with experiments to effectively control costs and maximize profits.

[0003] The crankshaft quenching and tempering process mainly includes two stages: pre-heat treatment and quenching and tempering. Pre-heat treatment, typically performed before quenching and tempering, eliminates internal stresses and microstructure inhomogeneities generated during forging or casting, laying a good foundation for subsequent quenching and tempering. This step mainly involves normalizing or annealing. Normalizing involves heating the crankshaft to a suitable temperature, holding it for a period of time, and then air-cooling or wind-cooling. The purpose of normalizing is to eliminate forging stress, obtain appropriate hardness, and improve the microstructure, preparing for quenching and tempering. Annealing may be necessary to reduce hardness and improve plasticity and toughness, creating favorable conditions for subsequent machining and quenching and tempering. Quenching and tempering is a crucial step in crankshaft heat treatment, including two main processes: quenching and tempering. Quenching involves heating the crankshaft above its austenitizing temperature and holding it for a period to ensure austenite homogenization. Cooling involves rapidly cooling the crankshaft to room temperature or slightly above to obtain a martensitic microstructure. The quenching medium can be water, oil, or a salt bath, the specific choice depending on the crankshaft's material and dimensions. Tempering involves heating the quenched crankshaft to a suitable temperature of 500–650°C and holding it for a period of time. Then, it is air-cooled or furnace-cooled to room temperature. The purpose of tempering is to eliminate quenching stress and decompose the martensite into tempered martensite or tempered sorbite to obtain the required strength and toughness.

[0004] Currently, there is a lack of stable and systematic guidance for optimizing quenching and tempering processes. This hinders precise control of temperature and time, particularly during quenching and tempering. Accurate control of heating temperature, holding time, and cooling rate is crucial to minimize inhomogeneity in microstructure transformation and the generation of internal stresses. Only through standardized quenching and tempering can crankshafts achieve good comprehensive mechanical properties and fatigue strength, meeting the performance requirements of internal combustion engines. Current research on optimizing quenching and tempering processes using machine learning is limited, especially for crankshafts. There is currently no precise method for evaluating the hardness of 42CrMo quenched and tempered steel crankshafts. Summary of the Invention:

[0005] The present invention addresses the lack of a precise evaluation method for the hardness of 42CrMo quenched and tempered steel crankshafts, and proposes a quenching and tempering evaluation method for 42CrMo quenched and tempered steel crankshafts.

[0006] A method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts is proposed. After acquiring crankshaft data from different heat batches, a risk quantification assessment based on the normal distribution theory is used to conduct early warning assessments of crankshafts from different heat batches. Finite element analysis models of crankshaft hardness and tempering mechanical properties are established for the crankshaft data from different heat batches. Composite experiments are conducted at the center of different quenching and tempering processes using these models. Linear regression equations for tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature are fitted based on the response surface characteristics. The linear regression equations are then optimized using a Matlab genetic algorithm to obtain a standard equation. The evaluation process is completed by comparing the standard equation with the actual crankshaft data from different heat batches.

[0007] As a preferred option: After obtaining crankshaft data from different batches of production, the process of conducting early warning assessments of crankshafts from different batches of production based on the normal distribution theory of risk quantification assessment is as follows: The crankshaft data is processed by normal distribution assessment to screen out hardness values ​​that conform to the normal distribution as target samples. The mathematical expectation μ value of the target samples is calculated. The probability P of the data points in a specific interval (μ-kσ, μ+kσ) is evaluated according to Chebyshev's inequality, where k is a constant and σ is the standard deviation of the crankshaft data. For the hardness test of the crankshaft production process, the interval (μ-kσ, μ+kσ) corresponding to the probability P is determined as the reliable fluctuation interval of the crankshaft hardness. μ-kσ and μ+kσ are used as the lower limit and upper limit of hardness early warning, respectively.

[0008] The calculation process for the warning value is as follows:

[0009] According to the normal distribution theory, the boundary value is calculated when the data X follows a general normal distribution, i.e., X ~ N(μ, σ). 2 The probability that the data in the sample falls within the interval is calculated using the following formula:

[0010]

[0011] Standardize this type of general normal distribution, let Conclusion:

[0012]

[0013] Further simplification yields:

[0014]

[0015] When the data is in the middle of (μ-kσ, μ+kσ), substituting the two endpoints into the above formula yields:

[0016] P={μ-kσ <X<μ+kσ}=Φ(k)-Φ(-k)=2Φ(k)-1 (5-4)

[0017] Where σ is the standard deviation of the data, μ is the expected value, Φ(x) is the standard normal distribution function, and the probability P of the hardness data is 70%;

[0018] After calculating the standard deviation σ and expected value μ using the Spass software, the value of k is found to be 1.04 when Φ(k) = 0.85. The theoretical lower limit of hardness warning μ-kσ and the theoretical upper limit of hardness warning μ+kσ can then be calculated. When the P value is 70%, the 15% of the hardness data sorted by size is the actual lower limit of warning, and the 85% is the actual upper limit of warning.

[0019] As a preferred solution: After calculating the lower and upper limits of the hardness warning based on the normal distribution theory, the crankshaft hardness data is evaluated. When the crankshaft hardness data is in the non-corner area, the surface crankshaft hardness is in a safe state. When the crankshaft hardness data is in the corner area, it indicates that the crankshaft hardness is outside the warning value, and the furnace process where the crankshaft is located is in a warning failure state.

[0020] As a preferred approach: A finite element analysis model of crankshaft hardness field and a prediction model of tempering mechanical properties are established respectively. A composite experiment is then conducted at the crankshaft tempering center using both the finite element analysis model and the prediction model of tempering mechanical properties. The process of fitting linear regression equations for tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature based on the response surface characteristics is as follows:

[0021] Based on the principle of central composite design combined with single-factor variable experiments of quenching and tempering, a quantitative assessment model for crankshaft hardness failure risk was established using a two-factor, five-level design method. The results were verified based on this model. Quenching temperature and tempering temperature were represented by T1 and T2, respectively, and variable levels were represented by -2, -1, 0, 1, and 2, forming a two-factor, five-level experimental design code. The average value of the two-factor, five-level experimental design code was calculated using hardness simulation and tempering performance prediction formulas. A two-dimensional multivariate fitting was designed using Design Expert software, and a significance test was performed. The fitted equation and the actual temperature formula are as follows:

[0022] HRC=-7125.0142959912+10.816882183927T1+8.5991954023188T2+0.00024999999997561T1T2-0.006517241379313T12 -0.0072672413793098T2 2

[0023] Rm=-110415.65775901+164.88793103504T1+138.16172413843T2+0.005999999999396T1T2-0.10003448275874T1 2 -0.11803448275862T2 2

[0024] Re=-81624.416379443+209.7697988507T1-18.019137930769T2+0.0014999999997T1T2-0.12501724137927T1 2 +0.01248275862068T2 2 ;

[0025] The above calculations show that, based on the response surface optimization of the tempering mechanical property prediction model, the various mechanical properties are clearly layered on the response surface projection plane. Combining the 3D surface model and the projection plane, the process range that meets the performance requirements of tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature is obtained.

[0026] As a preferred approach: the linear regression equation is optimized using a Matlab genetic algorithm to obtain a standard equation. The evaluation process is then completed by comparing the standard equation with crankshaft data from different production batches.

[0027] After determining the optimal ranges for various mechanical properties, quenching temperature, and tempering temperature of the crankshaft, and considering the inhibitory relationship between multiple objectives, the multi-objective optimization of the crankshaft's mechanical properties and heat treatment process were completed using the GA toolbox in MATLAB's genetic algorithm. That is, the minimum value of the function is the optimal value, so the tensile strength and yield strength settings need to be set with opposite values. Therefore, the multi-objective optimization function is obtained as follows:

[0028] minf(x)=[f1(x),-f2(x),-f3(x)] (5-5)

[0029] In the above formula, f1(x) is the hardness, f2(x) is the tensile strength, and f3(x) is the yield strength;

[0030] The above function can be solved using the GA solver in the Matlab Genetic Algorithm Toolbox.

[0031] As the preferred option, the Matlab genetic algorithm optimizes the objective function using the Pareto method to ensure that all mechanical properties meet the target requirements. At the same time, it ensures that the heat treatment process range is within the range of the results obtained from the response surface. The optimization results are experimentally verified. When the hardness is reduced and the tensile strength is slightly reduced, the reduction of area and elongation after fracture are slightly increased, indicating that the crankshaft has good impact toughness and fatigue strength, a relatively higher metallographic grade, and better microstructure clarity and uniformity than the initial process.

[0032] The beneficial effects of this invention are:

[0033] Based on the normal distribution theory of risk quantification assessment, early warning assessments are conducted on crankshafts produced in different batches. Data on crankshafts from different batches is generated, and finite element analysis models of crankshaft hardness field and prediction models of tempering mechanical properties are established. Composite experiments of crankshaft data centers are conducted using these models. Linear regression equations of tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature are fitted based on the response surface characteristics. The linear regression equations are then optimized using a Matlab genetic algorithm to obtain standard equations. Subsequent evaluation conclusions are derived based on these standard equations, forming a standardized and reasonable optimization strategy. This facilitates accurate assessment and guidance of crankshaft performance and service life, making it suitable for widespread application. Attached Figure Description

[0034] Figure 1 A bar chart showing the comparison between theoretical and actual values ​​for the 85% probability interval of furnace batch two;

[0035] Figure 2 A bar chart showing the comparison between theoretical and actual values ​​in the 85% probability interval of the third furnace run;

[0036] Figure 3 A bar chart showing the comparison between the theoretical and actual values ​​for the 85% probability interval of furnace batch four;

[0037] Figure 4 A bar chart showing the comparison between theoretical and actual values ​​for the 85% probability interval of a single furnace batch;

[0038] Figure 5 This is a schematic diagram of the structure in a 3D curved surface state for the hardness response model.

[0039] Figure 6 This is a schematic diagram of the structure with the hardness response model in the bottom projection state;

[0040] Figure 7 This is a schematic diagram of the structure in a 3D curved surface state, representing the tensile strength response model.

[0041] Figure 8This is a schematic diagram of the structure in the bottom projection state of the tensile strength response model;

[0042] Figure 9 This is a schematic diagram of the structure in a 3D curved surface state, showing the yield strength response model.

[0043] Figure 10 This is a schematic diagram of the structure under the bottom projection state of the yield strength response model;

[0044] Figure 11 A schematic diagram for multi-objective optimization of Pareto solutions;

[0045] Figure 12a To optimize the physical diagram of pre-tempered sorbite;

[0046] Figure 12b The image shows the optimized tempered sorbite specimen. Detailed implementation method:

[0047] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will be further described below with reference to specific embodiments and accompanying drawings. However, the invention is not limited to these embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0048] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0049] Specific implementation method one: Combining Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12a and Figure 12bThis embodiment describes a method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts. After obtaining crankshaft data from different heat batches, a risk quantification assessment based on the normal distribution theory is used to conduct early warning assessments, generating crankshaft data for different heat batches. This data includes crankshaft hardness warning values. A finite element analysis model of the crankshaft hardness field and a tempering mechanical property prediction model are established. A composite experiment of the crankshaft data center is conducted using these models. Linear regression equations for tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature are fitted based on the response surface characteristics. The linear regression equations are then optimized using a Matlab genetic algorithm to obtain a standard equation. The evaluation process is completed by comparing the standard equation with the actual crankshaft data from different heat batches.

[0050] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One, combined with... Figures 1 to 4 As shown, this embodiment mainly performs a normality test on crankshafts produced in four batches to obtain statistical analysis data on the hardness of each batch, and then uses this data as a reference for the overall hardness warning value. Before applying this theory for statistical analysis, the first step is to perform a normality test on the dataset. This test belongs to the category of non-parametric methods, which mainly infer the distribution characteristics of the population from sample data. Researchers usually use two widely accepted methods: one is the Kolmogorov-Smirnov test, which is suitable for large-scale samples and is often simply referred to as the KS test; the other is the Shapiro-Wilk test, which is more suitable for small-scale samples and is often referred to as the SW test.

[0051] In this embodiment, the sample size is 40, which is less than 50 samples, making the SW test suitable. The data from each group were imported into SPASS software, and the results are shown in Table 1. When the P-value is ≥ 0.05, the data is considered to be normally distributed. The results show that among the crankshaft hardness data from the four batches, only one group has a P-value of 0.004 < 0.05, which does not strictly conform to a normal distribution. The remaining P-values ​​≥ 0.05 conform to a normal distribution. Therefore, we first use the data that conforms to a normal distribution to perform theoretical calculations of normality.

[0052] Table 1. Normal distribution test of crankshaft hardness data from different furnace batches.

[0053]

[0054] Based on the above analysis, the experimental data from furnaces two, three, and four all conform to a normal distribution. For hardness values ​​that conform to a normal distribution, the expected value μ of the sample data must first be calculated. Then, the probability P of a data point falling within a specific interval (μ-kσ, μ+kσ) is evaluated using Chebyshev's inequality, where k is a constant and σ is the standard deviation of the sample data. For hardness testing in the crankshaft production process, industry standards and historical test data can be combined, and based on reliability requirements, the interval (μ-kσ, μ+kσ) corresponding to a certain probability P can be determined as the "reliable" fluctuation range for crankshaft hardness. This interval can be defined as the normal fluctuation range, with its upper and lower limits serving as normal thresholds for quality control. According to reliability screening theory, the k value represents tolerance, and the hardness threshold can be calculated using empirical rules. In practical engineering applications, an 85% probability range is typically used as the normal interval, and the upper and lower limits, μ-kσ and μ+kσ, are used as hardness warning values.

[0055] In this embodiment, after obtaining crankshaft data from different batches of production, the process of conducting early warning assessments of crankshafts from different batches of production based on the normal distribution theory of risk quantification assessment is as follows: The crankshaft data is processed by normal distribution assessment to screen out hardness values ​​that conform to the normal distribution as target samples. The mathematical expectation μ value of the target samples is calculated. The probability P of the data points in a specific interval (μ-kσ, μ+kσ) is evaluated according to Chebyshev's inequality, where k is a constant and σ is the standard deviation of the crankshaft data. For the hardness test of the crankshaft production process, the interval (μ-kσ, μ+kσ) corresponding to the probability P is determined as the reliable fluctuation interval of the crankshaft hardness. μ-kσ and μ+kσ are used as the lower limit value and the upper limit value of hardness early warning, respectively.

[0056] The calculation process for the warning value is as follows:

[0057] According to the normal distribution theory, the boundary value is calculated when the data X follows a general normal distribution, i.e., X ~ N(μ, σ). 2 The probability that the data in the sample falls within the interval is calculated using the following formula:

[0058]

[0059] Standardize this type of general normal distribution, let Conclusion:

[0060]

[0061] Further simplification yields:

[0062]

[0063] When the data is in the middle of (μ-kσ, μ+kσ), substituting the two endpoints into the above formula yields:

[0064] P = {μ - kσ < X < μ + kσ} = Φ(k) - Φ(-k) = 2Φ(k) - 1 (5 - 4)

[0065] where σ is the data standard deviation, μ is the mathematical expectation, Φ(x) is the standard normal distribution function, and the probability P of the hardness data is 70%;

[0066] After calculating the data standard deviation σ and the mathematical expectation μ using spass software, the lower limit value μ - kσ and the upper limit value μ + kσ of the hardness warning can be calculated; after calculating the data standard deviation σ and the mathematical expectation μ using spass software, the value of k can be found by looking up the table according to Φ(k), and then the lower limit value μ - kσ and the upper limit value μ + kσ of the theoretical hardness warning can be calculated; when the P value is 70%, 15% of the hardness data sorted by size is the actual lower limit value of the warning, and 85% is the actual upper limit value of the warning.

[0067] The process of finding the value of k by looking up the table according to Φ(k) in the above calculation process is an existing technology, and its derivation principle is the same as the existing process of finding the value of k by looking up the table according to Φ(k), where looking up the table refers to the existing standard normal distribution table corresponding to Φ(k).

[0068] Taking a set of hardness data measured in the third furnace as an example, taking the probability P of the hardness data as 70%, the calculation is carried out according to the following steps:

[0069] Let P = {μ - kσ < X < μ + kσ} = 2Φ(k) - 1 = 0.70, Φ(k) = 0.85. Looking up the normal distribution table, k = 1.04 can be obtained. Using spass software, the data standard deviation σ is calculated to be 0.89, the mathematical expectation μ is 30.61, μ - kσ = 29.68, and μ + kσ = 31.54. According to the above method, when the P value is 70%, the theoretical and actual warning values when the upper and lower limits of the data interval are 85% and 15% respectively can be calculated. In order to test the universality of this calculation and statistical method, that is, for the crankshafts produced in different furnace batches, whether the hardness warning values obtained by this method have a certain accuracy. Now, the test data of the second furnace and the fourth furnace are statistically analyzed and a normal distribution test is carried out. The results are shown in Table 2 and Figure 2 as shown. The data errors between several groups of theoretical warning values and actual probability values obtained according to the calculation standard distribution method are all less than 3%, meeting the error requirements for the risk assessment of crankshaft hardness failure.

[0070] Table 2 Calculation results of hardness failure warning values

[0071]

[0072]

[0073] Based on the normal distribution theory warning value calculation method analyzed above, the non-normally distributed data in the test results were verified. The hardness data with P-values ​​< 0.05 within one furnace cycle were subjected to a normal distribution test. The test results are shown in Table 3 and... Figure 3 As shown.

[0074] Table 3 Calculation results of hardness failure early warning value for furnace batch 1

[0075]

[0076] Similarly, taking 70% as a reasonable range for hardness failure, Table 3 shows that the error between the theoretical and actual warning values ​​is less than 2%. This indicates that although the hardness data of furnace batch one does not strictly follow a normal distribution, its statistical characteristics are highly consistent with a normal distribution. The warning value calculation method based on normal distribution theory has high reliability and can provide an effective calculation method for the heat treatment failure risk assessment of crankshafts of this material type. This method can well meet the needs of risk assessment in practical applications while maintaining theoretical rigor and practicality. The theoretical value is derived based on the normal distribution formula, and its range is defined by the upper and lower limits of the warning value, and described by the area enclosed by the normal distribution curve and the X-axis. The actual value is reflected by the area covered by the normal distribution curve, the upper and lower warning values, and the X-axis, which accounts for 85% of the area. The deviation between the theoretical and actual values ​​mainly stems from the assumption of continuous distribution characteristics in normal distribution theory, while actual test data may not completely conform to this characteristic, and there may be cases of data duplication and accumulation. This difference needs to be considered through further analysis and correction in practical applications. In actual production, the warning value is defined as the average of four batches. That is, after calculating the lower and upper limits of the hardness warning based on the normal distribution theory, the crankshaft hardness data is evaluated. It is concluded that when the crankshaft hardness data is in the non-corner area, the surface crankshaft hardness is in a safe state. When the crankshaft hardness data is in the corner area, it indicates that the crankshaft hardness is outside the warning value and the process of the furnace where the crankshaft is located is in a warning failure state.

[0077] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method One or Two. Response surface methodology is a statistical method used to optimize process parameters and product design, widely applied in engineering, chemistry, biology, and other fields. It can find the optimal parameter combination with a small number of experiments, significantly reducing the number of experiments and time. It is suitable for optimizing complex systems with multiple factors and levels, and can simultaneously analyze the influence of multiple factors and their interactions on the response, providing more comprehensive information. The model it establishes is more intuitive; by fitting a mathematical model between the target value and the independent variables, it more intuitively shows the relationship between the dependent and independent variables, making it easier for users to understand and predict. Furthermore, it has high prediction accuracy, a small error range, and reliable system optimization results. Based on the experiments and mechanical performance predictions in the previous chapter, in order to determine the quenching-tempering process for obtaining excellent mechanical properties in crankshaft heat treatment, and to study the interaction between the quenching-tempering process and tensile strength-hardness, this section selects representative conditions and uses the response surface methodology and CCD center composite design method to formulate experiments and optimize the heat treatment process.

[0078] Specific Implementation Method Four: This implementation method is a further limitation of Specific Implementation Method Three. In this implementation method, based on the crankshaft hardness warning values ​​of different batches of production, a crankshaft hardness field finite element analysis model and a tempering mechanical property prediction model are established respectively. A crankshaft data center composite experiment is conducted through the crankshaft hardness field finite element analysis model and the tempering mechanical property prediction model. The process of fitting the linear regression equations of tempering hardness, tensile strength, yield strength and quenching temperature and tempering temperature based on the response surface characteristics is as follows:

[0079] Based on the principle of central composite design combined with single-factor variable experiments of quenching and tempering, a quantitative assessment model for crankshaft hardness failure risk was established using a two-factor, five-level design method. Results were calculated based on this model, with quenching and tempering temperatures denoted as T1 and T2, respectively, and variable levels represented by -2, -1, 0, 1, and 2, forming a two-factor, five-level experimental design code. The average value of this code was calculated using hardness simulation and tempering performance prediction formulas. Specific code levels are shown in Tables 4, 5, 6, and 7. Experimental results were calculated using hardness simulation and the tempering performance prediction formulas from the previous chapter, and multiple averages were taken.

[0080] Table 4. Coding values ​​for two-factor, five-level experimental design

[0081]

[0082] Table 5 CCD Design Test Results

[0083]

[0084]

[0085] Table 6

[0086]

[0087] A quadratic multivariate fitting was designed using Design Expert software, and a significance test was performed. The fitted equation is as follows. The actual temperature formula applied in this paper is:

[0088] HRC=-7125.0142959912+10.816882183927T1+8.5991954023188T2+0.00024999999997561T1T2-0.006517241379313T1 2 -0.0072672413793098T2 2

[0089] Rm=-110415.65775901+164.88793103504T1+138.16172413843T2+0.005999999999396T1T2-0.10003448275874T1 2 -0.11803448275862T2 2

[0090] Re=-81624.416379443+209.7697988507T1-18.019137930769T2+0.0014999999997T1T2-0.12501724137927T1 2 +0.01248275862068T2 2

[0091] Table 7 Performance Evaluation Indicators for Response Target Values

[0092]

[0093]

[0094] As can be seen from the response indicators in Table 7, R 2 The values ​​are all greater than 0.9, R 2 The larger the surface response surface, the better the fit to the experiment, and the higher the Adj-R value. 2All values ​​are close to 1, indicating that the predicted values ​​are close to the experimental values, and the fit to the polynomial is high. The P-values ​​for all three targets are less than 0.05. The P-value represents the significance of the target value to the model. A value less than 0.05 indicates that the response result is relatively significant. At the same time, the F-values ​​of 16.60, 31.98, and 29.40 are relatively large, further confirming the significance of the model, indicating a high correlation between the mechanical properties and the heat treatment process. In addition, the AP value determines the accuracy of the response surface, requiring a value greater than 4. The AP values ​​of the three target properties in the table above are much greater than 4, indicating that the response surface model is relatively accurate.

[0095] In this embodiment, the tempering mechanical property prediction model optimized by the response surface shows that the various mechanical properties are clearly layered on the response surface projection plane. Combining the 3D surface model and the projection plane, the process range that meets the performance requirements of tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature is obtained.

[0096] Specific Implementation Method Five: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, or Four, combined with... Figures 5 to 10 As shown, in this embodiment, the standard equation is obtained by optimizing the linear regression equation using a Matlab genetic algorithm. The evaluation process is completed by comparing the standard equation with crankshaft data from different batches of production. This involves determining the optimal ranges for various mechanical properties of the crankshaft, the optimal range for quenching temperature, and the optimal range for tempering temperature. Considering the inhibitory relationship between multiple objectives, the multi-objective optimization of the crankshaft's mechanical properties and the optimization of the heat treatment process are performed using the GA toolbox in the Matlab genetic algorithm. That is, the minimum value of the function is the optimal value. Therefore, when setting the tensile strength and yield strength, the opposite values ​​need to be set. Thus, the multi-objective optimization function is obtained as follows:

[0097] minf(x)=[f1(x),-f2(x),-f3(x)] (5-5)

[0098] In the above formula, f1(x) is the hardness, f2(x) is the tensile strength, and f3(x) is the yield strength;

[0099] The above function was solved using the GA solver in the Matlab Genetic Algorithm Toolbox. The specific process was as follows: the initial population was set to 100, the number of generations was 200, the crossover probability was 0.85, the mutation probability was 0.04, and the optimal individualization coefficient was 0.3. The multi-objective optimization results are shown in Table 8.

[0100] Table 8 Results of the multi-objective optimization model

[0101]

[0102]

[0103] The tensile strength and yield strength are negative in the results, but we take the absolute values ​​of the optimized results. Since the essence of multi-objective optimization is that optimizing one objective function value sacrifices the others, it's impossible for all three objective values ​​to be optimal. However, we can obtain the desired multi-objective values ​​based on our own set conditions. Here, we require hardness less than 34.4 HRC, tensile strength greater than 900 MPa, and yield strength greater than 800 MPa.

[0104] Combination Figure 11 As shown, the points that meet the requirements in the multi-objective optimization solution set are 1, 3, 8, 9, and 16. Point 1 has a heat treatment process of quenching at 845.6℃ + tempering at 616.9℃, a hardness of 32.0 HRC, a tensile strength of 988.1 MPa, and a yield strength of 826.2 MPa. Point 3 has a heat treatment process of quenching at 842.3℃ + tempering at 595.0℃, a hardness of 30.0 HRC, a tensile strength of 921.1 MPa, and a yield strength of 856.7 MPa. Point 8 has a heat treatment process of quenching at 843.7℃. The first heat treatment process involves quenching at 842.2℃ and tempering at 598.8℃, resulting in a hardness of 32.4 HRC, a tensile strength of 975.9 MPa, and a yield strength of 821.5 MPa. The second heat treatment process involves quenching at 842.2℃ and tempering at 598.8℃, resulting in a hardness of 30.9 HRC, a tensile strength of 939 MPa, and a yield strength of 848.8 MPa. The third heat treatment process involves quenching at 841.9℃ and tempering at 591.0℃, resulting in a hardness of 31.3 HRC, a tensile strength of 947.5 MPa, and a yield strength of 844.5 MPa.

[0105] Since the multi-objective genetic algorithm uses the Pareto method to optimize the objective function, the values ​​of these five points belong to parallel ranges and are not superior or inferior. Furthermore, based on the optimal range derived from the response surface methodology in the previous section, the processes of these five solutions fall precisely within the range obtained from the response surface model, further proving its accuracy. During the genetic algorithm's solution process, the randomness of crossover and mutation operations leads to variations in the results of each run. However, these differences are usually small because adjustments to the results are often achieved through compromises with other objective functions. This indicates that, under certain conditions, the results of the five experimental groups are not significantly superior or inferior and are considered parallel; therefore, they can be selected based on actual requirements and specific needs.

[0106] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, or Five. The specific process of result analysis of the response surface model in this implementation method is as follows:

[0107] Combination Figures 5 to 10As shown, the effects of quenching and tempering temperatures on crankshaft hardness, tensile strength, and yield strength are investigated. Response surface models for various mechanical properties at different quenching and tempering temperatures are obtained based on the fitted regression equations. Figure 5 It can be seen that in the T1 direction, which is the quenching temperature axis, the shape is bowl-shaped and curves downwards, indicating that the hardness first increases and then decreases with increasing quenching temperature. However, in the T2 direction, which is the tempering temperature axis, the hardness decreases with increasing temperature. The trend range shows that the quenching temperature has a greater impact on hardness than the tempering temperature. The red area appears at the middle of the quenching temperature and the minimum at the tempering temperature. Figure 6 As shown in the diagram, the red area represents the location of the maximum hardness, while the blue area represents the location of the minimum hardness. At this point, the quenching temperature is the minimum and the tempering temperature is the maximum. According to the crankshaft performance requirements in this paper, the hardness requirement is relatively low rather than the minimum, so the green area represents the temperature range required by this paper.

[0108] Combination Figure 7 and Figure 8 As shown, in this embodiment, on the tensile strength response surface, in the T1 direction (i.e., the quenching temperature direction), the tensile strength first increases significantly with increasing temperature and then decreases slowly, reaching a maximum of 940 MPa at around 845°C. In the T2 direction, the tensile strength decreases with increasing temperature, reaching its minimum at the highest temperature, generally exhibiting an arched shape. According to the 3D diagram, the yellow area appears at the quenching temperature of 845°C and the tempering temperature of 595°C. Figure 8 The bottom projection is more intuitive. The minimum value is at the lowest quenching temperature and the highest tempering temperature. Finally, according to the method of the present invention, the region with high tensile strength and yield strength with the same trend is selected as the selected range, that is, the yellow area. This region can ensure that relevant data with high tensile strength and yield strength with the same trend are obtained.

[0109] Combination Figure 9 and Figure 10 As shown, based on the analysis of the 3D response diagram and the performance requirements of the crankshaft in this paper, the hardness requirement is reduced but not the minimum, i.e., the green area of ​​the projection diagram. The tensile strength and yield strength are better the higher they are, i.e., the yellow area of ​​the projection diagram. Combining the three projection diagrams, it can be seen that the range that meets the three performance requirements is a quenching temperature of 835~850℃ and a tempering temperature of 590~620℃.

[0110] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Methods One, Two, Three, Four, Five, or Six. The Matlab genetic algorithm optimizes the objective function using the Pareto method to ensure that all mechanical properties meet the target requirements. At the same time, it ensures that the heat treatment process range is within the range of the results obtained from the response surface. The optimization results are experimentally verified. When the hardness is reduced while the tensile strength is slightly reduced, the reduction of area and elongation after fracture are slightly increased, indicating that the crankshaft has good impact toughness and fatigue strength, a relatively higher metallographic grade, and better microstructure clarity and uniformity than the initial process.

[0111] The Pareto solution set of the optimization results of this invention was used for verification, and the optimized value closest to the target process was selected. The optimal data for quenching and tempering determined by this invention are: quenching 845.6℃ + tempering 616.9℃, with a quenching holding time of 60 min. Mechanical property tests and microstructure analysis were performed on the optimized crankshaft product, and the results compared with those before optimization are shown in Table 9. Figure 12a and Figure 12b As shown, the hardness index decreased from 34.5 HRC to 32.0 HRC, a reduction of 7.25%, which meets the target range for crankshaft hardness. The tensile strength decreased from 1022 MPa to 988 MPa, a reduction of 3.33%, which also meets the target requirements of this study. The achievement of reducing hardness while slightly decreasing tensile strength, and slightly increasing reduction of area and elongation at fracture, indicates that the product exhibits good impact toughness and fatigue strength under this target process. Combined with… Figure 12a and Figure 12b As shown, the optimized tempered sorbite exhibits a clearer morphology, finer and more uniformly distributed carbide particles, and more complete precipitation of carbides from the supersaturated solid solution without aggregation. Microscopic standard spectra comparison shows the optimized sample is close to grade 4, compared to grade 3 before optimization. The clarity and uniformity of the microstructure are superior to the initial process. In conclusion, the crankshaft sample after this optimized process demonstrates excellent overall performance, meets production requirements, and significantly improves production yield.

[0112] Table 9 Comparison of mechanical properties before and after optimization

[0113]

[0114] This invention enables the quantification of crankshaft hardness value failure risk early warning assessment using normal distribution theory. Based on quenching simulation and tempering mechanical property prediction, a two-factor, five-level test is established. Response surface analysis is performed using Designexpert software, and a linear regression equation is fitted. The equation is then optimized using a multi-objective function in Matlab's genetic algorithm toolbox. The results are verified, and the following conclusions are drawn:

[0115] First, a crankshaft hardness failure risk assessment and early warning model was established based on the normal distribution theory. By looking up the table through the normal distribution, the K value was found to be 1.04. The analysis of the crankshaft hardness produced by different furnace numbers showed that the error range between the theoretical early warning value and the actual early warning value was within 3%, which met the error requirements for failure risk assessment. The failure early warning value was successfully set, which played an early warning and inspection role in the crankshaft production tempering process.

[0116] Second: A CCD center composite test was established to fit the linear regression equation between various mechanical properties and quenching and tempering temperatures. The response surface optimization model shows that the various mechanical properties are clearly layered on the response surface projection surface. Combining the 3D surface model and the projection surface, the process range that meets the three performance requirements is quenching temperature: 835~850℃, tempering temperature: 590~620℃.

[0117] The heat treatment process obtained after multi-objective optimization using the Matlab genetic algorithm toolbox was selected from point 1. The process is quenching at 845.6℃ + tempering at 616.9℃, with a hardness of 32.0 HRC, tensile strength of 988.1 MPa, and yield strength of 826.2 MPa. All mechanical properties meet the target requirements, and the heat treatment process range is within the range obtained from the response surface methodology. Experimental verification of the optimization results showed a strength reduction of 3.33%, which is far less than the 7.25% hardness reduction, meeting the target requirements. While reducing hardness, the tensile strength was slightly reduced, while the reduction of area and elongation at fracture both slightly increased, indicating that the product exhibits good impact toughness and fatigue strength under this target process. The metallographic grade is relatively higher, and the clarity and uniformity of the microstructure are superior to the initial process.

Claims

1. A method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts, characterized in that: After obtaining crankshaft data from different batches of production, an early warning assessment of crankshafts from different batches of production is conducted based on the normal distribution theory of risk quantification assessment. This results in the establishment of crankshaft hardness field finite element analysis models and tempering mechanical property prediction models for crankshafts from different batches of production. Composite experiments are then conducted at different tempering process centers using these models. Linear regression equations for tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature are fitted based on the response surface characteristics. The linear regression equations are then optimized using a Matlab genetic algorithm to obtain standard equations. The evaluation process is completed by comparing the standard equations with the actual crankshaft data from different batches of production. A finite element analysis model of crankshaft hardness field and a prediction model of tempering mechanical properties were established respectively. A composite data center experiment was conducted using these models. The process of fitting linear regression equations for tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature based on the response surface characteristics is as follows: Based on the principle of central composite design combined with single-factor variable experiments of quenching and tempering, a quantitative assessment model for crankshaft hardness failure risk was established using a two-factor, five-level design method. The results were verified based on this model. Quenching temperature and tempering temperature were represented by T1 and T2, respectively, and variable levels were represented by -2, -1, 0, 1, and 2, forming a two-factor, five-level experimental design code. The average value of the two-factor, five-level experimental design code was calculated using hardness simulation and tempering performance prediction formulas. A two-dimensional multivariate fitting was designed using Design Expert software, and a significance test was performed. The fitted equation and the actual temperature formula are as follows: HRC=-7125.0142959912+10.816882183927T1+8.5991954023188T2+0.00 024999999997561T1T2-0.006517241379313T1²-0.0072672413793098T2² Rm=-110415.65775901+164.88793103504T1+138.16172413843T2+0.005999999999396T1T2-0.10003448275874T1²-0.11803448275862T2² Re=-81624.416379443+209.7697988507T1-18.019137930769T2+0.0014999999997T1T2-0.12501724137927T1²+0.01248275862068T2²; The above calculations show that, based on the response surface optimization of the tempering mechanical property prediction model, the various mechanical properties are clearly layered on the response surface projection plane. Combining the 3D surface model and the projection plane, the process range that meets the performance requirements of tempering hardness, tensile strength, yield strength, quenching temperature, and tempering temperature is obtained.

2. The method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts according to claim 1, characterized in that: After obtaining crankshaft data from different batches of production, the process of conducting early warning assessments of crankshafts from different batches based on the normal distribution theory of risk quantification assessment is as follows: The crankshaft data is processed using a normal distribution assessment to select hardness values ​​that conform to a normal distribution as target samples. The expected value μ of the target samples is calculated, and the data points are assessed within a specific interval according to the Chebyshev inequality. The probability P within which k is a constant. Given the standard deviation of crankshaft data, determine the interval corresponding to the probability P for hardness testing during the crankshaft manufacturing process. This represents the reliable fluctuation range of crankshaft hardness. and These are respectively used as the lower and upper limits for hardness warning; The calculation process for the warning value is as follows: According to the normal distribution theory, the boundary value is calculated when the data X conforms to a general normal distribution, i.e. The probability that the data in the sample falls within the interval is calculated using the following formula: （5-1） Standardize this type of general normal distribution, let Therefore, we can conclude that: （5-2） Further simplification yields: （5-3） When the data is in ( In the middle, substituting the two endpoints into the above formula, we get: （5-4） in The standard deviation of the data. For mathematical expectation, The hardness data follows a standard normal distribution function, with a probability P of 70%. Calculate the standard deviation of the data using SPASS software and mathematical expectation Afterwards, according to When the hardness is 0.85, the k value is found to be 1.04 by referring to the table, from which the theoretical lower limit of hardness warning can be calculated. and the theoretical warning upper limit of hardness ; When the P value is 70%, the lower limit of the actual warning is 15% of the hardness data sorted by size, and the upper limit of the actual warning is 85%.

3. The method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts according to claim 2, characterized in that: After calculating the lower and upper limits of the hardness warning based on the normal distribution theory, the crankshaft hardness data is evaluated. When the crankshaft hardness data is in the non-corner area, the surface crankshaft hardness is in a safe state. When the crankshaft hardness data is in the corner area, it indicates that the crankshaft hardness is outside the warning value, and the furnace process where the crankshaft is located is in a warning failure state.

4. The method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts according to claim 1, characterized in that: The standard equation was obtained by optimizing the linear regression equation using a Matlab genetic algorithm. The evaluation process was then completed by comparing the standard equation with crankshaft data from different furnace production batches. After determining the optimal ranges for various mechanical properties, quenching temperature, and tempering temperature of the crankshaft, and considering the inhibitory relationship between multiple objectives, the multi-objective optimization of the crankshaft's mechanical properties and heat treatment process were completed using the GA toolbox in MATLAB's genetic algorithm. That is, the minimum value of the function is the optimal value, so the tensile strength and yield strength settings need to be set with opposite values. Therefore, the multi-objective optimization function is obtained as follows: （5-5） In the above formula, Hardness For tensile strength, Yield strength; The above function can be solved using the GA solver in the Matlab Genetic Algorithm Toolbox.

5. The method for evaluating the quenching and tempering of 42CrMo quenched and tempered steel crankshafts according to claim 4, characterized in that: The Matlab genetic algorithm optimizes the objective function using the Pareto method to ensure that all mechanical properties meet the target requirements. At the same time, it ensures that the heat treatment process range is within the range of the results obtained from the response surface. The optimization results are experimentally verified. When the hardness is reduced and the tensile strength is slightly reduced, the reduction of area and elongation after fracture are slightly increased. This indicates that the crankshaft has good impact toughness and fatigue strength, a relatively higher metallographic grade, and the clarity and uniformity of the microstructure are better than the initial process.

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