CN104050335A - Thermal-mechanical coupling predication method for thickness of white layer on surface of hard tuned workpiece - Google Patents

Abstract

The invention belongs to the technical field of machining and relates to a thermal-mechanical coupling predication method for the thickness of a white layer on the surface of a hard tuned workpiece. The method includes the following steps that finite element modeling and simulating are performed in the hard tuning process; stress and strain energy data of the machined surface are extracted from a finite element post analysis result, and critical austenite phase change temperature under influences of coupling of stress, strain and alloying elements is calculated; temperature distribution data underneath the machined surface are extracted from the finite element analysis result, and the thickness of the white layer on the surface is predicated according to temperature distribution and the actual critical phase change temperature. A finite element predication model of the thickness of the white layer on the dry hard tuned surface based on the phase change mechanism is provided and not only can predicate the thickness of the phase change white layer on the surface more accurately under the condition that thermal-mechanical coupling factors are considered, but also discloses the internal mechanism of forming the white layer.

Description

The Thermal-mechanical Coupling Forecasting Methodology of the white layer thickness of a kind of hard as-machined workpiece surface

Technical field

The invention belongs to Machining Technology field, relate to the Forecasting Methodology of the white layer thickness of a kind of hard as-machined workpiece surface.

Background technology

In recent years, along with developing rapidly of various advanced manufacturing methods, harden-cutting technology has obtained application more and more widely.The material metamorphic layer that surface integrity particularly forms at machined surface is one of problem of being concerned about most of hard cutting technology field.Owing to often presenting white at optical microscope lower surface metamorphic layer, be conventionally referred to as " white layer ".The microstructure of white layer and thickness thereof are on having important impact in inside workpiece residual stress distribution, frictional behaviour, anti-fatigue ability, serviceable life etc.Dialogue layer thickness carries out quantitative forecast accurately, can choose best cutting parameter combination in the situation that cutting experiment seldom does not even have cutting experiment, obtains optimum surface quality, greatly saves manufacturing cost.

Up to now, the Forecasting Methodology of the hard white layer thickness of cutting surface mainly contains: based on regression Analysis method, set up polynomial forecast model, artificial intelligence approach, based on finite element method, set up forecast model etc.Regretional analysis and artificial intelligence approach need a large amount of experimental datas as input parameter, and can only be applicable to the Cutting Parameter that do experiment is used, and in high-speed cutting situation, the change that forms mechanism because of white layer can cause very large predicated error.Forecast model based on finite element analysis, although possessed certain rationality from Forecasting Methodology, if but by hardness as critical condition, in difference, form under the impact of mechanism, the critical hardness of white layer is not identical yet, therefore, the inherence that hardness criterion can not embody white layer forms mechanism, and cannot realize heat--the coupling of power influence factor.If by temperature as critical condition, along with cutting speed improves, the thermodynamics coupling factors such as violent temperature rise that in alloying element in steel and material deformation process, larger stress and strain and tool wear aggravation cause all can make a significant impact critical phase temperature, in this case, use nominal critical phase temperature can not dope exactly white layer thickness.As can be seen here, the universality of these forecast models is poor at present, can not realize in working angles the high-precision forecast of white layer thickness under different machining conditions.Therefore, must first determine the critical phase temperature under multifactor coupling influence, then set up bleach mutually Re-Li coupling prediction model of layer thickness of stiff cutting surface, this model should Accurate Prediction goes out the thickness of the layer that bleaches mutually, can, in the situation that being coupled thermodynamics influence factor, disclose the inherent mechanism that white layer forms again.

Summary of the invention

The object of the invention is to propose a kind of forecast model of the white layer thickness based on phase-change mechanism, this model can in the situation that having considered Re-Li coupling factor, dope more exactly hard as-machined workpiece surface bleach mutually layer thickness.

Technical solution of the present invention flow process as shown in Figure 1, its main thought is by hard working angles is carried out to finite element modeling and simulation, thereby obtain the stress of machined surface in working angles, the distribution of strain energy and temperature, critical phase temperature computing formula under the multifactor coupling influence of deriving according to the present invention the stress obtaining in conjunction with finite element simulation cutting process, strain energy data obtain actual critical phase temperature distribution curve, obtain the intersection point of critical phase temperature curve and machined surface temperature field distribution curve, material on intersection point will undergo phase transition, form white layer, under intersection point, material is correlated with, without white layer, form, therefore, this intersection point is white layer thickness apart from the degree of depth of machined surface, its concrete steps are as follows:

Step 1: hard working angles is carried out to finite element modeling and simulation;

1. set up the finite element model of hard working angles: constitutive model, friction model and the boundary condition of choosing grid dividing mode, material.

2. hard working angles is carried out to finite element analogy.

Step 2: extract stress, the strain energy data of machined surface from the analysis result of finite element preprocessor, the critical austenite phase transformation temperature under calculated stress, strain and alloying element coupling influence;

1. calculate the phase transition temperature after alloying metal affect: from iron-carbon diagram,, under deformation state, ferritic austenite phase transformation temperature is not 727 ℃, the impact of the alloying element being added, the phase transition temperature of material can change.For carbon steel and alloy steel, under rough, austenite critical phase temperature T ₀pressing formula (1) calculates:

T ₀letter in=727-10.7Mn-16.9Ni+29Si+16.9Cr+290As+6.38W (1) formula represents the percentage composition of respective alloy element.

2. calculate the critical austenite phase transformation temperature after affected by stress, Strain-coupled: according to the thermodynamics that balances each other, the factors such as temperature, pressure, strain have conclusive impact to the state of balancing each other, under different pressure and deformation condition, the critical temperature that material undergoes phase transition is different.Working angles is a process that relates to high temperature, high pressure, large strain, must consider stress, the impact of strain on phase transition temperature.

Suppose that, under temperature T and pressure P condition, pure material balances each other and coexists with α phase and β, the chemical potential of this material in two-phase equates, that is:

$G_m^{\mathrm{\α}}=G_m^{\mathrm{\β}}---\left(2\right)$

In formula, for this material at α the chemical potential in mutually, for this material at β the chemical potential in mutually, unit is J/mol.

When temperature becomes T+dT from T, when pressure becomes P+dP from P, a mole enthalpy of phase change for two-phase becomes respectively with under new equilibrium condition, chemical potential should still equate, convolution (2) draws

$d{G}_m^{\mathrm{\α}}={\mathrm{dG}}_m^{\mathrm{\β}}---\left(\text{3}\right)$

The phase transformation for heat absorption type to austenite phase transformation (α → γ) by ferrite, under deformation condition, it is that strain energy just can reach new balance that phase transition process will absorb elastic deformation energy

$\left\{\begin{array}{c}{\mathrm{dG}}_m^{\mathrm{\α}}=-S_m^{\mathrm{\α}}\mathrm{dT}+V_m^{\mathrm{\α}}\mathrm{dP}{+\mathrm{dW}}_S\\ {\mathrm{dG}}_m^{\mathrm{\β}}=-S_m^{\mathrm{\β}}\mathrm{dT}+V_m^{\mathrm{\β}}\mathrm{dP}\end{array}\right.---\left(4\right)$

In formula, S _mfor molar entropy (J/ (mol ℃)), V _mfor molar volume (m ³/ mol), dW _sfor strain energy increment (J/mol).

By formula (3), (4), can be obtained

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_m\mathrm{dP}-{\mathrm{dW}}_s={\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{S}_m\mathrm{dT}---\left(5\right)$

In formula, molar volume increment during for phase transformation; molar entropy increment during for phase transformation.

Due to

$\left\{\begin{array}{c}{G}_m^{\mathrm{\α}}=H_m^{\mathrm{\α}}-{\mathrm{TS}}_m^{\mathrm{\α}}\\ G_m^{\mathrm{\β}}=H_m^{\mathrm{\β}}-{\mathrm{TS}}_m^{\mathrm{\β}}\end{array}\right.---\left(6\right)$

When two-phase generation reversible transition and while reaching balance, there is Δ G=0, therefore when phase transformation balance, molar entropy increment can use formula (7) to represent:

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{S}_m=\frac{{\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m}{T}---\left(7\right)$

In formula, mole enthalpy of phase change increment during for α → β phase transformation, unit is J/mol, and endothermic process is for just, and exothermic process is for negative.

Bringing formula (5) into can obtain

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_m\mathrm{dP}-{\mathrm{dW}}_S=\frac{{\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m}{T}\mathrm{dT}---\left(8\right)$

To above formula both sides integration,

${\∫\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_m\mathrm{dP}-{\∫\mathrm{dW}}_S=\∫\frac{{\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m}{T}\mathrm{dT}---\left(9\right)$

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_m(P-P_0)-(W_S-W_0)={\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m\·\ln \frac{T}{T_0}---\left(10\right)$

In formula, W ₀strain energy while not deforming for workpiece before cutting, P ₀for the stress that before cutting, workpiece is subject to, T ₀for the phase transition temperature of the workpiece material under alloying metal affect before cut, therefore there is P ₀=0, W ₀=0.

Therefore,

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_{m}P-W_S={\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m\·\ln \frac{T}{T_0}---\left(11\right)$

Obtain stress P and strain energy W _sunder impact, the critical phase temperature of α → β phase transformation:

$T=T_0\exp \left(\frac{{\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{V}_m\·P-W_S}{{\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\β}}{H}_m}\right)---\left(12\right)$

In formula, T is at stress P and strain energy W _sphase transition temperature under effect; T ₀for being subject to the phase transition temperature (formula (1)) of the workpiece material under alloying metal affect before cut; for molar volume increment (m ³/ mol); mole enthalpy of phase change increment (J/mol) during for α → β phase transformation, endothermic process be on the occasion of, exothermic process is negative value; P is stress (Pa), W _sfor strain energy (J/mol), the two can extract from the preprocessor of working angles finite element analysis.

While 3. changing due to the geometric parameter of cutter, the maximum temperature that workpiece machined surface bears, location of maximum stress are different, and the position that most probable undergoes phase transition is also thereupon different.Wear of the tool flank has a significant impact the Temperature Distribution of workpiece machined surface, therefore the present invention is in two kinds of situation:

1) when cutter is without wear of the tool flank, the maximum temperature that workpiece machining surface place is subject to and maximum stress are below point of a knife, phase transformation most probable occurs herein, therefore for calculating stress, the strain energy of phase transition temperature and all extracting from point of a knife below for calculating the workpiece temperature data of white layer thickness;

2) when cutter has wear of the tool flank, the maximum temperature that now workpiece machining surface bears is not or not point of a knife place, but at the end of major flank wear land, for predicting that the data such as temperature, stress, strain energy of white layer thickness all extract below wear of the tool flank end of tape.

Step 3: extract the temperature profile data of machined surface below from the analysis result of finite element preprocessor, according to Temperature Distribution and actual critical phase temperature caluclate table colourless layer thickness;

First from finite element analysis result, extract in the machined surface of point of a knife below or wear of the tool flank end below each node along the temperature distribution history of depth direction, then calculate the critical austenite phase transformation temperature after multifactor coupling influence, obtain the actual transformation temperature curve of each node of the machined surface below point of a knife or below wear of the tool flank end, the intersection point of these two temperature curves is the thickness of the white layer in surface apart from the degree of depth of machined surface, see Fig. 2, its concrete forecasting process diagram as shown in Figure 3, wherein, while extracting the temperature distribution history of workpiece machining surface and below thereof, be divided into and have tool wear and without two kinds of situations of tool wear.

Effect of the present invention and benefit are: the computing method that the present invention proposes multifactor coupling influence lower critical phase transition temperature, set up the finite element prediction model of the white layer thickness of stiff cutting surface based on phase-change mechanism, this model can dope more exactly the thickness of the surperficial layer that bleaches mutually in the situation that having considered Re-Li coupling factor.Adopt the method, not only can effectively improve working (machining) efficiency and surface quality, for further formulating and optimizing the theoretical foundation that harden-cutting parameter provides science, actual production practice is had to great using value simultaneously.

Accompanying drawing explanation

Accompanying drawing 1 is the process flow diagram of the white layer thickness Thermal-mechanical Coupling of hard as-machined workpiece surface Forecasting Methodology.

Accompanying drawing 2 is to obtain white layer thickness according to temperature distribution history and actual transformation temperature curve intersection point.

Accompanying drawing 3 is the diagrams of white layer thickness forecast model.

Accompanying drawing 4 is extracting positions of cutter temperature, stress, strain energy during without wear of the tool flank.

Accompanying drawing 5 is extracting positions of cutter temperature, stress, strain energy while having wear of the tool flank.

Accompanying drawing 6 is the predicted value of model in the present invention and the comparison of Umbrello model predication value and experiment value (situation that has negative chamfered edge).

Accompanying drawing 7 is the predicted value of model in the present invention and the comparison of Ramesh model predication value and experiment value (without the situation of negative chamfered edge).

Accompanying drawing 8 is embodiment of the present invention experiment photos.

Accompanying drawing 9 is comparisons that under different machining conditions, the present invention predicts the outcome with embodiment experimental result.

Embodiment

The present invention be take GCr15 hardened steel as example, sets up the Thermal-mechanical Coupling Forecasting Methodology of the white layer thickness in surface.Below in conjunction with technical scheme of the present invention and accompanying drawing, describe specific embodiment of the invention step and embodiment in detail.

Step 1: the hard working angles of GCr15 is carried out to finite element modeling and simulation.

1. set up the finite element model of working angles: constitutive model, friction model and the boundary condition of choosing grid dividing mode, material, wherein grid is divided and is adopted adaptive mesh partitioning technology, constitutive model is selected Johnson-Cook (JC) model, and Johnson-Cook equation is suc as formula shown in (13):

$\stackrel{\‾}{\mathrm{\σ}}=[A+{\mathrm{B\ϵ}}^n][1+C\ln \left(\frac{\stackrel{\·}{\mathrm{\ϵ}}}{{\stackrel{\·}{\mathrm{\ϵ}}}_0}\right)][1-{\left(\frac{T-T_r}{T_m-T_r}\right)}^m]---\left(13\right)$

In formula, for equivalent stress, ε is plastic strain, for plastic strain rate, for with reference to rate of strain; T _rfor reference temperature, be generally room temperature, T _mfor temperature of fusion; A, B, n exosyndrome material strain hardening item coefficient, A is initial yield stress (MPa), and B is hardening modulus, and n is work hardening index; C is for characterizing a rate of strain strengthening coefficient (MPa); M is thermal softening coefficient.For GCr15 hardened steel, in constitutive model, the selection of parameters is as shown in table 1.

The J-C constitutive parameter of table 1 GCr15 (HRC62)

Friction model adopts the Colomb model of revising, shown in (14):

In formula, τ _ffor surface of contact friction stree, μ is sliding area friction factor, σ _nfor the normal stress on surface of contact, τ _pcritical shear yield strength for workpiece.

Boundary condition adopts the cutter fixing mode of workpiece of at the uniform velocity advancing, and the initial temperature that cutter and workpiece are set is 20 ℃.

2. GCr15 steel working angles is carried out to finite element analogy;

Step 2: extract stress, the strain energy of machined surface from finite element analysis result, the austenite phase transformation temperature under calculated stress, strain and alloying element coupling influence;

1. the alloy content of GCr15 steel is as shown in table 2, by austenite critical phase temperature T under table 2 and rough ₀computing formula (formula (1)), can be in the temperature of GCr15 bearing steel material generation austenite phase transformation under rough:

T ₀＝727-10.7×0.35-16.9×0.06+29×0.25+16.9×1.5＝754.8℃

The chemical composition of table 2 GCr15 hardened steel (HRC62)

2. stress, Strain-coupled affect the critical austenite phase transformation temperature of rear GCr15 hardened steel.The phase transformation that cutting GCr15 hardened steel occurs is mainly austenite phase transformation (α → γ). adopt the Δ H of pure iron _mvalue 920.5J/ (mol).By the molal weight (55.85g/mol) of iron, ferritic density (7.571g/cm ³) and austenitic density (7.633g/cm ³), molar volume increment that can be when being changed mutually to γ mutually by α be shown below:

${\mathrm{\Δ}}_{\mathrm{\α}}^{\mathrm{\γ}}{V}_m=\frac{55.85}{7.633}-\frac{55.85}{7.571}=-0.06{\mathrm{cm}}^3/\mathrm{mol}$

Utilize formula (12) to draw, during cutting GCr15 hardened bearing steel, the austenite phase transformation temperature under alloying element, stress, Strain-coupled impact is:

$T=754.8\×\exp \left(\frac{-0.06\×{10}^{-6}\×P-W_S}{920.5}\right)$

In formula, W _scan from finite element analysis result, directly extract with P, the two is in time and the amount constantly changing along workpiece depth direction, and its extracting mode can be divided into Fig. 4, two kinds of modes of Fig. 5 according to the difference of processing conditions.

Step 3: extract the Temperature Distribution of machined surface below from finite element analysis result, according to the white layer thickness of Temperature Distribution and actual transformation temperature prediction surface, and contrast and checking with experimental result predicting the outcome.

Feasible in the white layer thickness theory for prediction model that the present invention sets up, but whether actual prediction result accurately also needs to verify by specific embodiment.

Experiment cutter for same is selected wimet YD201 clip type blade, tool orthogonal rake-10 °, 6 ° of relief angles.Workpiece material is GCr15 bearing steel, and its chemical element content is as shown in table 2, and workpiece hardness is HRC62, and metallographic structure is acicular martensite, carbonide and a small amount of retained austenite.Workpiece is diameter of phi 90mm, the cylindric test specimen of wall thickness 2.5mm, and cutting way adopts end face Dry Turning.

Adopt experiments of single factor, each cutting only changes a cutting parameter, and the selection range of cutting speed is 50m/min～600m/min, and rear knife face grinds rubstrip in advance, and wear extent is respectively 0mm, 0.1mm and 0.2mm.During cutting of hardened steel, in order to increase the edge strength of cutter, at cutter rake face, grind in advance negative chamfered edge, be of a size of-30 ° * 0.2mm.After each experiment, from workpiece machined surface, cut sample, through grinding, polishing and corrosion, make metallographic specimen, use SEM to observe White layer, measure white layer thickness.

People [the Umbrello D such as the predicted value of model and Umbrello, Ramesh in the present invention, Jawahir I.S.Numerical modeling of the nfluence of process parameters and workpiece hardness on white layer formation in AISI52100steel[J] .International Journal of Advanced Manufacturing Technology, 2009,44:955-968; Ramesh A, Melkote S N, Allard L F, et al.Analysis of white layers formed in hard turning of AISI52100steel[J] .Materials Science and Engineering A, 2005,390:88-97] predicted value of institute's established model and the comparing result of experiment value as shown in Figure 6 and Figure 7, wherein, Fig. 6 is that cutter has the contrast in the situation of negative chamfered edge, and Fig. 7 is that cutter is without the contrast in the situation of negative chamfered edge.Fig. 8 is the SEM photo of workpiece machined surface section words spoken by an actor from offstage layer in specific embodiment.In the situation that having tool wear, the contrast of the experiment value recording in the predicted value of model and specific embodiment in the present invention as shown in Figure 9.

By Fig. 6, can be obtained, when cutting speed v=92m/min, in the present invention, the relative error of the predicted value of model is about 11.4%; When v=183m/min, the relative error that in the present invention, the relative error of the predicted value of model is about 2%, Umbrello model predication value is about 22%; When v=274m/min, the relative error that in the present invention, the relative error of the predicted value of model is about 5.3%, Umbrello model predication value is about 18.4%.Can obtain thus, in the present invention, the precision of prediction of model is higher than the precision of prediction of Umbrello forecast model.From Fig. 7, can obtain, as speed of feed f=0.127mm/rev, during cutting speed v=213m/min, the relative error that in the present invention, the relative error of model predication value is about 45%, Ramesh model predication value is about 45%; Work as f=0.127mm/rev, during v=274m/min, the relative error that in the present invention, the relative error of the predicted value of model is about 21.9%, Ramesh model predication value is about 3%; Work as f=0.178mm/rev, during v=274m/min, the relative error that in the present invention, the relative error of the predicted value of model is about 50%, Ramesh model predication value is about 12.5%.Can obtain thus, in the present invention, the precision of prediction of model is lower than the precision of prediction of Ramesh model.As seen from Figure 8, cutting GCr15 Hardened Steel Workpiece surface has formed White layer clearly, white layer thickness 10-20 μ m, and, there is significant difference with workpiece substrate tissue in the serious refinement of crystal grain, illustrates that phase transformation may occur in white layer.By Fig. 9, can be obtained, as tool abrasion VB=0.2mm, during v=50m/min, in the present invention, the relative error of the predicted value of model is about 8.7%; Work as VB=0.2mm, during v=236m/min, in the present invention, the relative error of the predicted value of model is about 8%; Work as VB=0.2mm, during v=420m/min, in the present invention, the relative error of the predicted value of model is about 4%; Work as VB=0.1mm, during v=50m/min, in the present invention, the relative error of the predicted value of model is about 7.7%, the goodness of fit of the experiment value that in the present invention, the predicted value of model and specific embodiment measure is higher, its relative error is controlled in 10%, and, when tool wear and cutting speed when larger the precision of predicted value higher.Can obtain thus, in the situation that cutter has negative chamfered edge or wear of the tool flank, in the present invention, the predicted value of model and the experiment value goodness of fit are higher; When cutter is during without the cutting of negative chamfered edge or non-negative rake, the forecast model in the present invention has relatively large error.In the model of Ramesh, a counter stress is derived on the impact of phase transition temperature, the impact of strain is not considered, and the impact of stress and strain is not coupled together, therefore, the model of Ramesh is only applicable to cutter without negative chamfered edge or the cutting of non-negative rake, the situation that Thermal-mechanical Coupling is insufficient, cutting deformation is relatively little.The forecast model that the present invention proposes is based on phase-change mechanism, when if cutter has negative chamfered edge, negative rake, wear of the tool flank, along with the raising of cutting speed, in cut, workpiece deformation is larger, and the rubbing action between interface is violent, the heat in metal cutting producing is more, Thermal-mechanical Coupling is more abundant, more than workpiece machining surface temperature more easily reaches phase transition temperature, thereby undergoes phase transition, therefore the forecast model that, the present invention proposes is applicable to the prevailing hard working angles of Thermal-mechanical Coupling factor.

Claims (1)

1. a Thermal-mechanical Coupling Forecasting Methodology for the white layer thickness of hard as-machined workpiece surface, is characterized in that, comprises the following steps:

Step 1, carries out finite element modeling and simulation to hard working angles; Comprise the following steps:

(1) set up the finite element model of hard working angles: constitutive model, friction model and the boundary condition of choosing grid dividing mode, material;

(2) hard working angles is carried out to finite element analogy;

Step 2 is extracted stress, the strain energy data of machined surface, the critical austenite phase transformation temperature under calculated stress, strain and alloying element coupling influence from the analysis result of finite element preprocessor; According to T ₀=727-10.7Mn-16.9Ni+29Si+16.9Cr+290As+6.38W calculates the austenite critical phase temperature under alloying metal affect, foundation austenite phase transformation temperature under calculated stress, strain impact, wherein, T is at stress P and strain energy W _sphase transition temperature under effect; T ₀for being subject to the phase transition temperature of the workpiece material under alloying metal affect before cut; for molar volume increment (m ³/ mol); mole enthalpy of phase change increment (J/mol) during for α → γ phase transformation, endothermic process be on the occasion of, exothermic process is negative value; P is stress (Pa), W _sfor strain energy (J/mol);

Step 3 is extracted the temperature profile data of machined surface below, according to Temperature Distribution and actual critical phase temperature caluclate table colourless layer thickness from the analysis result of finite element preprocessor; First from finite element analysis result, extract the temperature distribution history of workpiece machining surface and below thereof and the actual transformation temperature curve of machined surface and below thereof, the intersection point of these two temperature curves is white layer thickness apart from the degree of depth of machined surface.