CN103617354A - Universal fitting calculation method of steel hardenability - Google Patents

Abstract

The invention relates to a universal fitting calculation method of steel hardenability and belongs to the technical field of steel hardenability calculation. The method includes: using a non-linear fitting method to build a common relation of the hardenability coefficient and the end hardenability, using a support vector machine method to build the relation between alloy elements and grain size number with the hardenability coefficient, and combining common methods to enhance algorithm adaptability. The method has the advantages that the method is wide in algorithm application range and high in adaptability, and steel hardenability prediction precision can be increased effectively.

Description

A kind of general the Fitting Calculation method of quenching degree of steel

Technical field

The invention belongs to iron and steel quenching degree computing technique field, particularly relate to a kind of general the Fitting Calculation method of quenching degree of steel.

Background technology

The quenching degree of steel is to characterize the characteristic that obtains martensite ability when steel quench, and it is to provide the performance of steel and a significant data of planing machine part, and conventional quenching degree computing method mainly contain several below at present.The one, ideal noise diode scaling method: this is a kind of conversion method at the beginning of the forties, it is by calculating the ideal critical diameter of quenching degree, then utilize water-cooled end hardness and ending quenching hardness ratio table amplification Er Lai， U.S. SAE J406-2009 standard and domestic GB/T5216-2004 standard all to describe this algorithm in detail; The 2nd, Just fitting formula method: EJust proposes a kind of computing formula in l968, american car industry association has also proposed respectively computing formula to low middle carbon (alloy) steel on this basis.This formula is to have done after numerical transformation by alloy element, utilizes the method for regression equation calculation to obtain; The 3rd, remaining cypress sea formula: when this formula in the industry cycle calculates quenching degree, frequency of utilization is also higher, and it is to rely on professional standing and experience to carry out statistical study widely on the basis of Just formula to carry out obtaining after nonlinear fitting improvement.

Though it is many to calculate the method for quenching degree, these methods exist the shortcomings such as precision of prediction is low, narrow application range, not yet have so far in addition a kind of general approximating method or computation model, all can not solve the computational problem of all steel grade quenching degree.

Summary of the invention

A kind of general the Fitting Calculation method of quenching degree that the object of the present invention is to provide steel, has overcome the shortcomings such as above-mentioned precision of prediction is low, narrow application range; Be applicable to the general matching of quenching degree and the calculating of basic, normal, high carbon steel; Can adapt to the matching that all steel grade quenching degree is calculated.

Method of the present invention comprises that use non-linear fitting method is set up the universal relation formula of hardenability coefficient and ending quenching hardness, use support vector machine method is set up the relation of alloying element and grain size number and hardenability coefficient, in conjunction with conventional method, strengthened three aspects such as algorithm adaptability.This computing method scope of application is wider, and adaptive faculty is stronger, can effectively improve prediction of hardenability precision.

The processing step of the technical solution adopted in the present invention comprises three parts: the relation of using nonlinear method matching ending quenching hardness and hardenability coefficient, use the relation between support vector machine method matching hardenability coefficient and alloying element and grain size, in conjunction with general algorithmic method, when data qualification does not possess, strengthen algorithm applicability.

Described hardenability coefficient can characterize the characteristic that obtains martensite ability when steel quench, with end-to-end distance from size irrelevant.

The one, use non-linear fitting method to set up the universal relation formula of hardenability coefficient and ending quenching hardness, it according to as follows:

The hardness of middle surface hardening steel almost just starts to decline from initiating terminal;

The hardness of high hardenability steel remains unchanged in one segment distance of end, and after surpassing certain distance, just starts to decline;

No matter high surface hardening steel, when distance is tending towards infinity, finally can obtain a comparatively stable hardness;

If end quenching distance is x, hardness distribution density is J (x), has when x=0, obtains highest hardness J _max; When x → ∞, obtain minimum hardness J _min.Obtain now a general fitting formula:

J(x)=AU(x)+J _min

Satisfy condition:

J(x)| _x=0=J _max

$\underset{x\→\∞}{\lim }J\left(x\right)=J_{\min }$

After bringing formula into, can obtain:

$U\left(x\right)=\frac{J\left(x\right)-J_{\min }}{J_{\max }-J_{\min }}$

Following formula meets feature above-mentioned:

$\frac{\mathrm{dU}\left(x\right)}{\mathrm{dx}}={-\mathrm{kx}}^n{U}^m\left(x\right),$ K ≠ 0 wherein, 0≤x< ∞;

With upper integral, can calculate, expression formula is:

$U^{1-m}=\frac{k(m-1)}{n+1}{x}^{n+1}+C$

The experimental data of utilizing GB/T5216-2004 national standard to provide, and adopt trial method to select successively at random m and n, calculate

and x ⁿ⁺¹value, with scatter diagram, check whether meet linear relationship, by calculating, find to work as n=1, during m=2, the scatter diagram of painting meets linear relationship most.

Described ending quenching hardness and the pass between hardenability coefficient tie up to substitution n=1, and m=2 is as follows to the concrete matching relational expression obtaining after above formula:

$J\left(x\right)=\left\{\begin{array}{c}{J}_{\max },0\&le;x<b\\ \frac{J_{\max }-J_{\min }}{\frac{{(x-b)}^2}{3{(h-b)}^2}+1}+J_{\min },x\&GreaterEqual;b\end{array}\right.---\left(1\right)$

X represents end quenching distance (mm), and J (x) is hardness distribution density, J _maxfor highest hardness (HRC), J _minfor minimum hardness (HRC), b is for obtaining complete martensitic straight length (mm), and h is hardenability coefficient.

The 2nd, use support vector machine method matching hardenability coefficient, obtain the relation between complete martensitic straight length and alloying element and grain size, and set up respectively SVM model for concrete grade of steel and data.

Data use support vector machine matching hardenability coefficient and the method for alloying element and grain size by experiment, if exist under the data sample condition of some applicable to the foundation of any steel grade quenching degree computation model, concrete method is as follows:

(1) prepare the data sample for certain specific grade of steel, this data sample is m * n, and wherein m represents the number of sample, n represent different end-to-end distances from hardness number and the alloying element number of this sample, wherein n >=3;

(2) according to [C] content in each row of data sample and in the industry general computing formula calculate J _max;

J _max=66.5-47.8e ^-4c （2）

(3) according to the different end-to-end distances of each row of data sample from hardness number use Nonlinear Quasi to merge to calculate h, J according to formula (1) _min, b;

(4) to whole sample set, independent variable is made as alloying element and grain size, and dependent variable is respectively h, J _min, b, select ε-SVR algorithm, set C=1000, kernel function type is RBF.Train respectively and use 2 cross validations to obtain better training parameter, preserve training result;

(5) generalization ability of verification model and degree of accuracy, and adjust parameter, preserve the quenching degree computation model of this grade of steel.

The 3rd, in conjunction with general algorithmic method, strengthen algorithm applicability, this Enhancement Method refers to a kind of half-way house of taking when data qualification does not possess.Described data qualification does not possess and refers to following several situation:

1) need a plurality of check data samples under same grade of steel, to form the small sample set of SVM algorithm, if only there are several data, the learning ability of algorithm and generalization ability will weaken greatly;

2) essential three end-to-end distances of every sample from hardness number, if lower than three, cannot simulate h, J according to formula (1) _minand b.

For said circumstances (1), if each grade of steel data sample is very little, can consider to use the quenching degree check data with grade of steel other grades of steel on the same group to join in sample set, enlarged sample capacity;

For situation (2), if the use of the model of institute's matching is the data sample of middle surface hardening steel, can establish b=0, now formula (1) turns to:

$J\left(x\right)=\frac{J_{\max }-J_{\min }}{\frac{x^2}{{3h}^2}+1}+J_{\min }---\left(3\right)$

Now only need two end-to-end distances from hardness number can simulate h and J _min.

If above condition does not all possess, consider that abandoning SVM carries out matching, with following methods, calculate, this algorithm takes full advantage of remaining cypress sea formula and can obtain:

$h=\frac{12}{5+G}\&CenterDot;[\frac{1}{12}M+{\left(\frac{M}{8.5}\right)}^4+1]\&CenterDot;[1+\frac{{25C}^3}{1+{5C}^4}]---\left(4\right)$

b=0.22h-0.34 (5)

In formula, G is grain size number, and M is alloy equivalent, and C is carbon content.The computing formula of last b, with (5), in conjunction with above formula, is brought into the general formula that just obtains a calculating quenching degree in formula (1).

The present invention is the quenching degree feature of data and steel by experiment, uses nonlinear relation to characterize the relation between ending quenching hardness and hardenability coefficient, has universality.

Compared with prior art, the invention has the beneficial effects as follows and set up a kind of general matching relational expression, be applicable to the fit procedure of all grade of steel quenching degree; The method can be set up quenching degree computation model for arbitrary grade of steel in addition, and experimental data shows effectively to improve the quenching degree computational accuracy of steel, and computing method are before greatly improved.

Embodiment

Embodiment comprises following step:

(1) first obtain a set of data samples.This data sample comprises specific alloying element, as C, Mn, Cr etc. and alternative grain size number data, also comprises in addition the hardness number of three different end range points, is made as J ₁, J ₂and J ₃;

(2) by three end-to-end distances in the following formula of x value substitution:

$J\left(x\right)=\left\{\begin{array}{c}{J}_{\max },0\&le;x<b\\ \frac{J_{\max }-J_{\min }}{\frac{{(x-b)}^2}{3{(h-b)}^2}+1}+J_{\min },x\&GreaterEqual;b\end{array}\right.$

Obtain three equatioies, separate Nonlinear System of Equations, can obtain h, J _minand b;

(3) to whole sample set, independent variable is made as alloying element and grain size, and dependent variable is respectively h, J _minand b, select ε-SVR algorithm, set C=1000, kernel function type is RBF.Train respectively and use 2 cross validations to obtain better training parameter, preserve training pattern, obtain the relationship between expression formula of hardenability coefficient and alloying element and grain size.

(5), if data sample space is less, uses with the quenching degree check data of grade of steel other grades of steel on the same group and join in sample set, enlarged sample capacity; If every sample only have two each and every one end-to-end distances from hardness number, can establish b=0, use following formula to try to achieve quenching degree:

$J\left(x\right)=\frac{J_{\max }-J_{\min }}{\frac{x^2}{{3h}^2}+1}+J_{\min }$

$h=\frac{12}{5+G}\&CenterDot;[\frac{1}{12}M+{\left(\frac{M}{8.5}\right)}^4+1]\&CenterDot;[1+\frac{{25C}^3}{1+{5C}^4}]$

b=0.22h-0.34。

Claims (1)

1. the general the Fitting Calculation method of the quenching degree of steel, is characterized in that: be applicable to the general matching of quenching degree and the calculating of basic, normal, high carbon steel; Processing step comprises three parts: the relation of using nonlinear method matching ending quenching hardness and hardenability coefficient, use the relation between support vector machine method matching hardenability coefficient and alloying element and grain size, in conjunction with general algorithmic method, when data qualification does not possess, strengthen algorithm applicability;

Described hardenability coefficient can characterize the characteristic that obtains martensite ability when steel quench, with end-to-end distance from size irrelevant;

Described ending quenching hardness and the relation between hardenability coefficient are that data fitting obtains by experiment, and concrete matching relational expression is as follows:

$J\left(x\right)=\left\{\begin{array}{c}{J}_{\max },0\&le;x<b\\ \frac{J_{\max }-J_{\min }}{\frac{{(x-b)}^2}{3{(h-b)}^2}+1}+J_{\min },x\&GreaterEqual;b\end{array}\right.---\left(1\right)$

X represents end quenching distance (mm), and J (x) is hardness distribution density, J _maxfor highest hardness (HRC), J _minfor minimum hardness (HRC), b is for obtaining complete martensitic straight length (mm), and h is hardenability coefficient;

Use support vector machine method matching hardenability coefficient, obtain the relation between complete martensitic straight length and alloying element and grain size number, and set up respectively SVM model for concrete grade of steel and data;

Data use support vector machine matching hardenability coefficient and the method for alloying element and grain size by experiment, if exist under the data sample condition of some applicable to the foundation of any steel grade quenching degree computation model, concrete method is as follows:

(1) prepare the data sample for certain specific grade of steel, this data sample is m * n, and wherein m represents the number of sample, n represent different end-to-end distances from hardness number and the alloying element number of this sample, wherein n >=3;

(2) according to [C] content in each row of data sample and in the industry general computing formula calculate J _max;

J _max=66.5-47.8e ^-4c （2）

(3) according to the different end-to-end distances of each row of data sample from hardness number use Nonlinear Quasi to merge to calculate h, J according to formula (1) _min, b;

(4) to whole sample set, independent variable is made as alloying element and grain size, and dependent variable is respectively h, J _min, b, select ε-SVR algorithm, set C=1000, kernel function type is RBF; Train respectively and use 2 cross validations to obtain better training parameter, preserve training result;

(5) generalization ability of verification model and degree of accuracy, and adjust parameter, preserve the quenching degree computation model of this grade of steel;

Described combination general algorithmic method strengthens algorithm applicability and refer to a kind of half-way house of taking when data qualification does not possess;

Described data qualification does not possess and refers to following several situation:

1) need a plurality of check data samples under same grade of steel, to form the small sample set of SVM algorithm, if only there are several data, the learning ability of algorithm and generalization ability will weaken greatly;

2) essential three end-to-end distances of every sample from hardness number, if lower than three, cannot simulate h, J according to formula (1) _min, b;

For said circumstances 1), if each grade of steel data sample is very little, consider to use the quenching degree check data with grade of steel other grades of steel on the same group to join in sample set enlarged sample capacity;

For situation 2), if the use of the model of institute's matching is the data sample of middle surface hardening steel, establish b=0, now formula (1) turns to:

$J\left(x\right)=\frac{J_{\max }-J_{\min }}{\frac{x^2}{{3h}^2}+1}+J_{\min }---\left(3\right)$

Now only need two end-to-end distances from hardness number can simulate h and J _min;

If above condition does not all possess, consider that abandoning SVM carries out matching, with following methods, calculate, this algorithm has utilized remaining cypress sea formula to obtain:

$h=\frac{12}{5+G}\&CenterDot;[\frac{1}{12}M+{\left(\frac{M}{8.5}\right)}^4+1]\&CenterDot;[1+\frac{{25C}^3}{1+{5C}^4}]---\left(4\right)$

b=0.22h-0.34 (5)

In formula, G is grain size number, and M is alloy equivalent, and C is carbon content; The computing formula of last b, with (5), in conjunction with above formula, is brought into the general formula that just obtains a calculating quenching degree in formula (1).