Method for predicting maximum size of spherical inclusions in bearing steel

Abstract

The invention provides a method for predicting the maximum size of spherical inclusions in bearing steel, which comprises the following steps of: randomly cutting a plurality of groups of inclusion samples at the half radius of a rolled material, carrying out heat treatment on the samples, and carrying out size measurement on the spherical inclusions; counting the measured data, and calculating the maximum threshold value and the minimum threshold value of the data; establishing a prediction model based on probability regression, performing ascending order arrangement on the data, inputting the data into the prediction model, and calculating corresponding parameters, probabilities and cumulative probabilities through the prediction model; solving values of a positioning parameter delta ML and a scale parameter lambda ML of an extreme value distribution function based on a maximum likelihood method through planning and summation of an SOLVER function by utilizing the calculated extreme value distribution parameter; and calculating data points on the optimal average line by utilizing the obtained values of delta ML and lambda ML and combining a reduction variable, and measuring 95% confidence interval of each data point to obtain the maximum distribution state of the inclusions.

Description

Technical Field

[0001] The present invention relates to the technical field of iron and steel metallurgy, and in particular, to a method for predicting the maximum size of spherical inclusions in bearing steel. Background Art

[0002] With the improvement of domestic smelting process level, the metallurgical quality level of bearing steel has been further improved. For the inspection of inclusions in bearing steel, only 6 specimens are inspected, and each specimen has a small volume. The rating is carried out according to standards such as GB / T 18254 and GB / T 10561. Due to the small number of samples (only 6 specimens are inspected for each heat), and each specimen has a small volume and the inspection is only for one plane, it is difficult to find large-size inclusions in the steel, and it is impossible to inspect all the steel to obtain detailed inclusion information. Therefore, it is necessary to evaluate the situation of the largest non-metallic inclusions in the steel through a specific method, and use the known data to deduce the unknown data to realize the research on the size of the inclusions. Summary of the Invention

[0003] In view of the above-mentioned technical problems, a method for predicting the maximum size of spherical inclusions in bearing steel is provided. The present invention mainly uses a specific statistical method to establish a special prediction analysis model, and uses the known data to deduce the unknown data to speculate the size of the largest spherical inclusions in the steel.

[0004] The technical means adopted by the present invention are as follows:

[0005] A method for predicting the maximum size of spherical inclusions in bearing steel, comprising:

[0006] S1. Randomly cut multiple groups of inclusion specimens at the mid-radius of the rolled material, heat-treat the specimens, and measure the sizes of the spherical inclusions;

[0007] S2. Statistically analyze the data measured in S1, and calculate the maximum limit value and the minimum limit value of the data;

[0008] S3. Establish a prediction model based on probability regression, arrange the data in ascending order, input it into the prediction model, and calculate the corresponding parameters, probabilities, and cumulative probabilities through the prediction model;

[0009] S4. Use the extreme value distribution parameters calculated in S3, and solve the location parameter δ of the extreme value distribution function based on the maximum likelihood method through the planning summation SOLVER function ML and the scale parameter λ ML values;

[0010] S5. Use the δ ML and λ ML values obtained in S4, combine the reduction variables to calculate the data points on the optimal average line, and determine the 95% confidence interval of each data point to obtain the maximum distribution state of the inclusions.

[0011] Furthermore, when the specimen is heat-treated, quenching and tempering are required. After reaching the heating temperature for quenching, it is held for a certain time, and then tempered using a coolant. After the heat treatment operation, the specimen is polished and inspected, magnified for observation, and the size of the spherical inclusions in the specimen is measured.

[0012] Furthermore, the method for calculating the maximum and minimum boundary values of the calculated data is as follows:

[0013] Maximum boundary value = (Maximum value - Average value) / Standard deviation; Minimum boundary value = (Average value - Minimum value) / Standard deviation.

[0014] Furthermore, the prediction model is used to calculate the parameters, probability, and cumulative probability of spherical inclusions, including:

[0015] The reduced variable Red.Va r is calculated as follows:

[0016] Red.Var = -ln(-lnP)

[0017] P = 1 / (1 + n)

[0018] where P is the probability of each inclusion detection value appearing, and n is the number of inclusion detection values;

[0019] The probability density LL i is calculated as follows:

[0020]

[0021] where N represents the number of inclusion inspections; LL is the sum of probability densities:

[0022]

[0023] where λ represents the location parameter of the extreme value distribution function, equivalent to the starting inclusion size; δ represents the scale parameter of the extreme value distribution function; x i represents the length of each inclusion detection.

[0024] Furthermore, for the location parameter δ ML and the scale parameter λ ML , the maximum value distribution parameters δ mom and λ mom are calculated using the average inclusion length value and the standard deviation as the initial calculation values:

[0025]

[0026] where Sde v is the standard deviation of inclusion length;

[0027]

[0028] Among them, is the arithmetic mean of the inclusions;

[0029] Use the SOLVER function to plan the summation and solve for δ ML and λ ML values.

[0030] Furthermore, the calculation method of the data points on the optimal average line is as follows:

[0031] x i = δ ML (Red.Var) + λ ML

[0032] Measure the 95% confidence interval points of each data point:

[0033]

[0034] 95% CL = ±2SE(x)

[0035] Among them, SE(x) is the standard deviation of any inclusion with a length of x calculated by the maximum likelihood method, and 95% CL represents the 95% confidence interval of the inclusion size;

[0036]

[0037] Among them, x low represents the predicted minimum inclusion length, and x hig represents the predicted maximum inclusion length, obtaining the maximum distribution state of the inclusions.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] A method for predicting the maximum size of spherical inclusions in bearing steel proposed by the present invention randomly cuts multiple groups of inclusion specimens at half of the radius of the rolled material, heat-treats the specimens, and measures the sizes of the spherical inclusions; statistically processes the measured data, and calculates the maximum and minimum limit values of the data; establishes a prediction model based on probability regression, sorts the data in ascending order, inputs it into the prediction model, and calculates the corresponding parameters, probabilities, and cumulative probabilities through the prediction model; uses the calculated extreme value distribution parameters to solve the location parameter and scale parameter values of the extreme value distribution function based on the maximum likelihood method through the SOLVER function of the planned summation; combines the reduced variables to calculate the data points on the optimal average line, and measures the 95% confidence interval of each data point to obtain the maximum distribution state of the inclusions. The present invention can deduce unknown data from known data and infer the maximum size of spherical inclusions in steel.

[0040] Based on the above reasons, the present invention can be widely promoted in the fields of iron and steel metallurgy and the like. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0042] Figure 1 It is a flowchart of the method for predicting the maximum size of spherical inclusions in bearing steel of the present invention.

[0043] Figure 2 It is a schematic diagram of the sampling position of the metallographic specimen processing and inspection sample in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0045] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0046] As Figure 1 shown, the present invention provides a method for predicting the maximum size of spherical inclusions in bearing steel, including:

[0047] S1. Randomly cut multiple groups of inclusion specimens at half of the radius of the rolled material, heat-treat the specimens, and measure the sizes of the spherical inclusions;

[0048] In specific implementation, as a preferred implementation manner of the present invention, when the specimen is heat-treated, quenching and tempering are required. After reaching the heating temperature for quenching, it is held for a certain time, and then tempered using a coolant; after the specimen undergoes the heat treatment operation, it is polished and inspected, magnified for observation, and the sizes of the spherical inclusions in the specimen are measured.

[0049] S2. Statistically analyze the data measured in S1, and calculate the maximum limit value and the minimum limit value of the data;

[0050] In specific implementation, as a preferred implementation manner of the present invention, the method for calculating the maximum limit value and the minimum limit value of the data is as follows:

[0051] Maximum limit value = (Maximum value - Average value) / Standard deviation. Minimum limit value = (Average value - Minimum value) / Standard deviation.

[0052] S3. Establish a prediction model based on probability regression, arrange the data in ascending order, input it into the prediction model, and calculate the corresponding parameters, probabilities, and cumulative probabilities through the prediction model;

[0053] In specific implementation, as a preferred implementation manner of the present invention, the prediction model is used to calculate the parameters, probabilities, and cumulative probabilities of spherical inclusions, including:

[0054] The calculation method of the reduced variable Red.Var is as follows:

[0055] Red.Var = -ln(-lnP)

[0056] P = 1 / (1 + n)

[0057] where P is the probability of the occurrence of each inclusion detection value, and n is the number of inclusion detection values;

[0058] The probability density LL i is calculated as follows:

[0059]

[0060] where N represents the number of inclusion inspections; LL is the sum of probability densities:

[0061]

[0062] where λ represents the location parameter of the extreme value distribution function, which is equivalent to the starting inclusion size; δ represents the scale parameter of the extreme value distribution function, 1 / δ is equivalent to the slope of the distribution curve, representing the growth rate, and the larger δ is, the faster the growth; x i represents the length of each inclusion detection.

[0063] S4. Using the extreme value distribution parameters calculated in S3, solve for the location parameter δ of the extreme value distribution function based on the maximum likelihood method through the Solver function for planning summation. ML and the scale parameter λ ML values;

[0064] In specific implementation, as a preferred implementation manner of the present invention, the location parameter δ ML and the scale parameter λ ML , use the average inclusion length value and standard deviation to calculate the maximum value distribution parameters δ mom and λ mom as the initial calculated values:

[0065]

[0066] where Sde v is the standard deviation of the inclusion length;

[0067]

[0068] where is the arithmetic mean of the inclusions;

[0069] Use the Solver function to plan summation to solve for the values of δ ML and λ ML values.

[0070] S5. Using the values of δ ML and λ ML obtained in S4, combine the reduced variables to calculate the data points on the optimal average line, and measure the 95% confidence interval of each data point to obtain the maximum distribution state of the inclusions.

[0071] In specific implementation, as a preferred implementation manner of the present invention, the calculation method of the data points on the optimal average line is as follows:

[0072] x i = δ ML (Red.Var)+λ ML

[0073] Measure the 95% confidence interval points of each data point:

[0074]

[0075] 95% CL = ±2SE(x)

[0076] where SE(x) is the standard deviation of any inclusion with a length of x calculated by the maximum likelihood method, and 95% CL represents the 95% confidence interval of the inclusion size;

[0077]

[0078] Among them, x low represents the predicted minimum inclusion length, and x hig represents the predicted maximum inclusion length.

[0079] In implementation, when the collected data points follow a certain distribution, their maximum and minimum values follow a specific distribution, that is, the probability density function of the maximum inclusion characteristic value measured on a specific area or volume, so as to obtain the maximum distribution state of inclusions.

[0080] Embodiment

[0081] As Figure 1 shown, the present invention provides a method for predicting the maximum size of spherical inclusions in bearing steel. In order to fully predict the maximum size of spherical inclusions in bearing steel in this embodiment, a total of 18 metallographic specimens are selected as the basic prediction data. The 18 metallographic specimens are sampled according to GB / T 18254, 6 pieces per heat, and each specimen is taken from different billets of steel. This prediction method is based on certain assumptions, that is, the specimens of 3 heats are taken from the same smelting state and rolling state.

[0082] In the specimen processing and inspection stage, inclusion specimens are randomly cut at the position of half of the radius of the rolled material. The specimen size is 10 mm × 20 mm (rolling direction), and the inspected area is 200 mm 2 , and the sampling and processing positions of the metallographic specimens of non-metallic inclusions are as Figure 2 shown.

[0083] The non-metallic inclusion specimens are quenched and tempered according to the heat treatment system. The quenching heating temperature is 820 °C - 850 °C, the quenching heating time is 1.5 min for heat preservation, the coolant is oil, the tempering temperature is 150 °C ± 10 °C, and the tempering time is 1 h - 2 h. After each specimen's polished surface is inspected, it is observed at a magnification of 100 times, and the evaluation method is carried out according to Method A in GB / T 10561. The inspection and rating measure the size of spherical inclusions in the steel.

[0084] Take the metallographic specimens of 3 heats of bearing steel hot-rolled materials and carry out heat treatment, processing, sample preparation and rating according to the standard requirements. The inspected area ≥ 160 mm 2 . The rating results are shown in Table 1.

[0085] Table 1 Sizes (μm) of spherical inclusions in metallographic specimens of 3 heats of bearing steel hot-rolled materials

[0086] Heat number Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Heat number 1 2.77 3.65 5.16 5.89 6.55 8.45 Heat number 2 3.26 3.92 5.16 6.2 6.55 8.6 Heat number 3 3.44 4.65 5.44 6.34 7.44 11.44

[0087] Perform quantity statistics, calculation of the maximum value, minimum value, and standard deviation on the 18 input data, calculate the maximum limit value and minimum limit value of this set of data, and record the final data in the prediction table of the maximum size of spherical inclusions, as shown in Table 2.

[0088] Table 2 Prediction Table of the Maximum Size of Spherical Inclusions

[0089]

[0090]

[0091] Continued Table 1

[0092]

[0093]

[0094] According to the prediction probability requirements, select the predicted lengths of the maximum inclusions at different probabilities, as shown in Table 3.

[0095] Table 3 Prediction Table of Inclusion Predicted Lengths at Different Probabilities

[0096]

[0097] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0098] In the above embodiments of the present invention, the descriptions of each embodiment have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0099] In several embodiments provided in the present application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only illustrative. For example, the division of the units can be a logical function division. In actual implementation, there can be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point, the couplings or direct couplings or communication connections shown or discussed with each other can be through some interfaces. The indirect couplings or communication connections of the units or modules can be in an electrical or other form.

[0100] The units described as separate components may or may not be physically separated. The components shown as units may or may not be physical units, that is, they can be located in one place or distributed to multiple units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the maximum size of spherical inclusions in bearing steel, characterized in that: include: S1. Randomly cut multiple groups of inclusion samples at half the radius of the rolled material, heat treat the samples, and measure the size of the spherical inclusions; S2, collect statistics on the data measured in S1, and calculate the maximum limit value and the minimum limit value of the data; S3. Establish a prediction model based on probability regression, arrange the data in ascending order, input the data into the prediction model, and calculate the corresponding parameters, probabilities and cumulative probabilities through the prediction model; S4. Using the extreme value distribution parameters calculated in S3, the location parameter δ of the extreme value distribution function based on the maximum likelihood method is solved by planning and SOLVER function. ML and scale parameter λ ML The value of S5. Using the δ obtained in S4 ML and λ ML The value of is combined with the reduced variables to calculate the data points on the optimal average line, and the 95% confidence interval of each data point is determined to obtain the maximum distribution state of inclusions.

2. The method for predicting the maximum size of spherical inclusions in bearing steel according to claim 1, characterized in that: When the sample is heat treated, it needs to be quenched and tempered. After reaching the heating temperature for quenching, it needs to be kept warm and then tempered with a coolant. After the sample has been heat treated, it needs to be polished and inspected, magnified and observed, and the size of the spherical inclusions in the sample needs to be measured.

3. The method for predicting the maximum size of spherical inclusions in bearing steel according to claim 1, characterized in that: The method for calculating the maximum and minimum limit values ​​of the data is: Maximum limit value = (maximum value - average value) / standard deviation Minimum limit value = (mean value - minimum value) / standard deviation.

4. The method for predicting the maximum size of spherical inclusions in bearing steel according to claim 1, characterized in that: The prediction model is used to calculate the parameters, probability and cumulative probability of spherical inclusions, including: The calculation method of the reduced variable Red.Var is: Red.Var=-ln(-lnP) P = 1 / (1+n) Among them, P is the probability of occurrence of each inclusion detection value, and n is the number of inclusion detection values; The probability density LL i The calculation method is: Where N is the number of inclusions tested; LL is the probability density and: Among them, λ represents the positioning parameter of the extreme value distribution function, which is equivalent to the starting inclusion size; δ represents the scale parameter of the extreme value distribution function; x i Indicates the length of each inclusion detection.

5. The method for predicting the maximum size of spherical inclusions in bearing steel according to claim 1, characterized in that: The positioning parameter δ ML and scale parameter λ ML , using the average length and standard deviation of inclusions to calculate the maximum distribution parameter δ mom and λ mom , as the initial calculated value: Where Sdev is the standard deviation of inclusion length; in, is the arithmetic mean of inclusions; Using the SOLVER function to calculate and solve δ ML and λ ML The value of .

6. The method for predicting the maximum size of spherical inclusions in bearing steel according to claim 1, characterized in that: The method for calculating the data points on the optimal average line is as follows: x i =d ML (Red.Var)+λ ML Determine the 95% confidence interval points for each data point: 95% CL = ± 2 SE (x) Where SE(x) is the standard deviation of any inclusion of length x calculated by the maximum likelihood method, and 95% CL represents the 95% confidence interval of the inclusion size; Among them, x low represents the predicted minimum inclusion length, x hig It indicates the predicted maximum inclusion length and the maximum distribution state of inclusions.

Images