CN1285900C - Real time detecting method for gas carburization three dimension concentration field of complicate shape workpiece - Google Patents

Abstract

The present invention relates to a method for monitoring the gas carburization of components in complicated shapes in real time. Workpiece surfaces are induced into various shape characteristics. A computer is applied to a local region of minimum volume for calculating the concentration fields of transient state carburization layers in real time. The local region is composed of found workpiece surfaces of corresponding shape characteristics and inner interfaces conforming to a formula disclosed in the specification, namely zero-dispersion flow conditions. The concentration fields of the carburization layers in the local region are replicated to positions of the same shape characteristics on the workpieces for obtaining the concentration fields of the transient state carburization layers of the whole workpieces, and the concentration fields of the three-dimensional transient state carburization layers of the workpieces are obtained. The three-dimensional transient state concentration fields of the workpieces in complicated shapes are synchronously monitored in the process of gas carburization in real time, and the three-dimensional concentration fields of various workpieces processed in the same furnace are simultaneously monitored, so as to ensure that the carburization layers in all positions of components comprehensively conform to technical requirements, so the use reliability of the components is comprehensively improved.

Description

The method of real-time of complicated shape part gas carburization three dimension concentration field

Technical field

The present invention relates to a kind of method of real-time that is used for the thermo-chemical treatment technical field.Particularly a kind of method of real-time of complicated shape part gas carburization three dimension concentration field.

Background technology

Gas carburizing is to use very wide chemical heat treatment process, usually cemented steel is mild carbon steel or low-carbon alloy steel, carburizing rear surface carbon content Cs brings up to the level of high-carbon steel, and because carbon is to the workpiece internal divergence, form the cementation zone of certain depth, concentration of carbon in the cementation zone is progressively reduced to inside by the surface, and the inside of workpiece still keeps original carbon content C _o(this place's carbon content is C to surface carbon content Cs and carburized (case) depth δ in the technical requirement of general carburized parts _δ) all have clear and definite regulation, δ to be meant that carbon content is C in the cementation zone _δThe place is to the distance on surface, C _δIt is with different steel grades and slightly different to look different technical standard, generally between 0.35～0.4%C.Therefore the development of modern manufacturing industry proposes the demand of control infiltration layer concentration field.For different parts, force-bearing situation is different with form during owing to use, and its best cementation zone concentration field is also different.

Existing carbon-potential control technology can only realize the control (infinitely great flat board or infinitely long cylinder) of one dimension concentration field, however the shape of surface of the work the cementation zone concentration field is had a significant effect, this just need with the two dimension or three-dimensional concentration field describe.Through literature search, document " Mathematical Model of Heat Treatmentand Its Computer Simulation " " CHINESE ACADEMY OF ENGINERING " Vol.2 No.2Jun.2004, P.15-20.(heat treated mathematical model and computer simulation thereof) this article has been introduced a kind of gas carburizing computer modeling technique that can reflect the surface of the work shape factor to the concentration field influence, only provided the two-dimensional concentration field analog result of a gear regional area, do not relate to the simulation of three-dimensional concentration field as yet, more fail to provide the analog result of whole part infiltration layer concentration field, yet the shape of part is usually very complicated in the actual production, need describe with three-dimensional concentration field, at present, yet there are no the report that in Gas Carburizing Process, calculates the whole part three-dimensional concentration field in real time, have the situation of several parts with the stove carburizing still more, therefore original technology seems that significant limitation is arranged.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art and defective, propose a kind of method of real-time of complicated shape part gas carburization three dimension concentration field.Make the complex-shaped three-dimensional transient state concentration field of workpiece of its real-time synchronous monitoring in Gas Carburizing Process, monitor the three-dimensional concentration field of the various workpieces of handling with stove simultaneously, the cementation zone of guaranteeing the part different parts meets technical requirement comprehensively, realizes that the part dependability improves comprehensively.

The present invention is achieved by the following technical solutions, the numerical value of each moment furnace temperature of computer real-time acquisition and Carbon Potential Inside Furnace will be used in the Gas Carburizing Process, initial conditions as this moment carburized parts three-dimensional concentration field of real-time calculating, adopt local to decompose and composition algorithm, surface of the work is reduced shape features, from surface that workpiece is found out the respective shapes feature with meet $\frac{\∂C}{\∂n}=0$ Promptly the minimum volume local that internal interface constituted of zero diffuse flow condition carries out the three-dimensional cementation zone concentration field calculating of real-time transient state, and the cementation zone concentration field of local copied on the position that has identical shaped feature on the workpiece, try to achieve the transient state cementation zone concentration field of whole work-piece, obtain complicated shape part or various workpieces at this three-dimensional transient state cementation zone concentration field constantly.

Concrete steps of the present invention are as follows:

1. appliance computer carries out real-time sampling to Carbon Potential Inside Furnace and furnace temperature;

2. judge the shape factor feature of concrete workpiece: surface of the work is divided into: plane, different curvature curved surface, seamed edge, corner angle, interior angle, exterior angle, cutting edge, chamfering, rounding, 11 kinds of shape facilities of the flank of tooth and the face of cylinder;

3. determine from workpiece find out by the surface with one of these shape facilities with meet $\frac{\∂C}{\∂n}=0,$ The i.e. minimum volume local that internal interface constituted of zero diffuse flow;

4. in complex-shaped part Gas Carburizing Process, read gas phase carbon potential and furnace temperature in each cementing furnace constantly, find the solution and determine the cementation zone concentration field in the local and check whether all inner boundaries meet by computer data acquisition system $\frac{\∂C}{\∂n}=0,$ Do not recomputate after then the interface being adjusted if meet;

5. all meet at the local of confirming all cementation zone concentration fields $\frac{\∂C}{\∂n}=0$ Internal boundary condition after, concentration field result of calculation with local, by symmetrical mapping, rotational angle and shift method, copy on the position that has mutually same shape on the workpiece, the set of the local concentration field by all difformity features on the workpiece, thus transient state cementation zone concentration field in the infiltration layer of whole work-piece surface tried to achieve;

6. the three-dimensional transient state concentration field of the workpiece that computing machine is obtained with the isoconcentration face of cementation zone concentration field or the isoconcentration line on the section or the CONCENTRATION DISTRIBUTION cloud atlas on the section or perpendicular in four kinds of modes of the concentration profile of difformity figuratrix direction one or more, with diagram or be presented on the computer screen in real time with digital form; Perhaps export the three-dimensional concentration field analog result with printout or digital communication method, realize the monitoring of complicated shape part gas carburizing or three-dimensional transient state concentration field analog result directly is passed to control module by computing machine.

By computing machine transient state concentration field and the complicated shape part gas carburizing layer concentration field that calculates required to compare, control the termination of controlled cementation zone concentration field.

Described cementation zone concentration field calculates according to diffusion second law, and setting D is an isotropy, and D is the function of temperature and concentration of carbon:

Under one-dimensional case: $D\frac{{\∂}^{2}C}{{\∂x}^2}=\frac{\∂C}{\∂\mathrm{\τ}}---\left(1\right)$

Under two-dimensional case: $D\frac{{\∂}^{2}C}{{\∂x}^2}+D\frac{{\∂}^{2}C}{{\∂y}^2}=\frac{\∂C}{\∂\mathrm{\τ}}---\left(2\right)$

Under three-dimensional situation: $D\frac{{\∂}^{2}C}{{\∂x}^2}+D\frac{{\∂}^{2}C}{{\∂y}^2}+D\frac{{\∂}^{2}C}{{\∂z}^2}=\frac{\∂C}{\∂\mathrm{\τ}}---\left(3\right)$

Boundary condition is:

X in the formula _b, y _b, z _bBe positioned on the border,

Be respectively surperficial outer normal and x, y, the angle between the z coordinate axis, Cg are the gas phase carbon potentials, and Cs is the surface of the work concentration of carbon,

Starting condition is: C (x, y, z, 0)=C ₀(5).

In commercial Application, adopt finite element method or method of finite difference to find the solution.Computing method itself are ripe, problem is that wanting the necessary condition of the variation of real-time monitoring infiltration layer concentration field in the carburizing production run of a reality is enough to lack the time of finishing a concentration field calculating, makes calculating can catch up with the beat that concentration field changes in the production run.Wherein the calculated amount of one-dimensional problem is less, can finish the calculating of an one dimension concentration field with present Industrial Control Computer in less than 1 second time, thereby can use the real-time monitoring that common industrial computer or personal computer are realized the one dimension concentration field at present.Yet the influence of considering the surface configuration factor just must be calculated two dimension and three-dimensional concentration field, be respectively the quadratic power and the three cubed multiple of workpiece size its computing time, for example for the miniature parts of 50 * a 50 * 50mm, be more than 2500 times of one dimension the computing time of two dimension, be more than 125000 times of one dimension three-dimensional computing time, and can run in the actual production than much bigger size of this example and much complicated shape.The computer speed of Industrial Control Computer also is difficult to satisfy, present Industry Control computer that Here it is can only realize the reason that the concentration field online in real time of the single component of one dimension concentration field or simple shape is monitored, the approach that overcomes this defective of original technology has two, the first improves the arithmetic speed of Industrial Control Computer with the multiple that becomes the order of magnitude, this just must increase substantially its cost, and it two is to manage to reduce significantly calculated amount.The present invention adopts a kind of technology in back.

The present invention extracts the shape factor that some have feature from various complicated shape piece surfaces, only need be in a concrete part to having some regional areas of character shape factor, appliance computer carries out concentration field and calculates, and the result of calculation of regional area copied to by computing machine have identical shaped superficial layer on the workpiece, just can reflect whole part infiltration layer concentration field, thereby to become order of magnitude multiple to reduce computing time, realize the real time on-line monitoring that three-dimensional concentration field changes under the multiple shape factor, also can be implemented in the monitoring in real time synchronously of the concentration field of several difformity workpiece of carburizing in the same heat.

To carry out result of calculation in full accord with result of calculation of whole volume while of workpiece in order to guarantee from integral body to extract regional area, must be with meeting $\frac{\∂C}{\∂n}=0$ Inner boundary and meet the zone (abbreviation local) of the local calculation that outside surface with certain feature forms, Concentration gradient for the normal direction of inner boundary.This inner boundary also can be described as " zero diffuse flow " border, that is to say the internal interface that does not have diffuse elements to flow on its normal direction.

The local of described cementation zone concentration field all meets $\frac{\∂C}{\∂n}=0$ Internal boundary condition have: the 1. shape plane of symmetry; 2. concentration of carbon still remains the original concentration of carbon C of steel after the carburizing ₀Internal interface; 3. with the infiltration layer concentration field in the perpendicular interface of concentration of carbon contour surface, can judge and carry out the tentative calculation correction then whether checking meets C according to experience for wherein back two kinds _In=C ₀Or it is not vertical with the concentration contour surface.

Meet $\frac{\∂C}{\∂n}=0$ Promptly the concrete grammar of the minimum volume local that internal interface constituted of zero diffuse flow condition is:

1) with outer face surface at a distance of the internal interface of m δ, δ is carbon-coating degree of depth mm, apart from the plane of plane surface m δ and apart from curved surface along radius-of-curvature direction m δ curved inner surface;

2) curved surface and Plane intersects be in in-plane apart from the distance of handing over transversal for the inner plane of m δ place and Surface Vertical and on curved surface the arc length of distance friendship transversal be the face of m δ place and Surface Vertical, as with the perpendicular interface of the contour surface of concentration of carbon;

3) apart from the plane of interior angle m δ place perpendicular to the surface.

Wherein Coefficient m is selected in 1～2.5.

The inner boundary of gear determines that principle is: 1. along the profile depth of the tooth inside surface for m δ place; 2. apart from the inner plane of side m δ; 3. the plane of symmetry of tooth top width and the 4. plane of symmetry of teeth groove.Wherein Coefficient m is selected in 1～2.5.The selection of inner boundary that has the local of little fillet is handled by above-mentioned curved surface and Plane intersects method.

The calculation control zone of other shape face can be inferred according to above principle.

Prior art is with the infiltration layer concentration field of infinitely great flat board or infinitely long cylinder workpiece, usually with practical work piece, particularly there is difference in the infiltration layer CONCENTRATION DISTRIBUTION of complicated shape part, therefore can't monitor in real time to the cementation zone of diverse location on the part and with the cementation zone of different workpieces in the stove, can't make comprehensive judgement the carburized parts quality.The inventive method can be tried to achieve whole complicated shape part different parts and with the three-dimensional transient state concentration field of the multiple part of stove, can be guaranteed the carburizing quality and the reappearance of whole furnaceman's part, so substantive the progress arranged.

Description of drawings

Fig. 1 infiltration layer concentration of carbon curvature of field line distribution schematic diagram

Fig. 2 embodiment 1,25 * 50 * 200mm workpiece synoptic diagram

Fig. 3 embodiment 2, step workpiece synoptic diagram

Fig. 4 embodiment 3, semicircle curved surface slab workpiece synoptic diagram

Fig. 5 embodiment 4, the automobile gear synoptic diagram

Fig. 6 embodiment 5, axle sleeve workpiece synoptic diagram

Embodiment

Content in conjunction with the inventive method provides following examples:

Embodiment 1: as shown in Figure 2, workpiece size is 25 * 50 * 200mm, material 20Cr, and cementation zone requires degree of depth δ=1mm, and infiltration layer concentration of carbon field meets the distribution of Fig. 1 curve 2.

Is that 2.5mm and the face parallel with the surface and the plane of symmetry of corner angle all meet in edges and corners apart from drift angle a $\frac{\∂C}{\∂n}=0$ Condition, therefore get a zonule abcdef that Fig. 2 shows and carry out three-dimensional concentration field and calculate the concentration field that can reflect on the whole work-piece different surfaces.Because the concentration field of second half abc ' d ' ef of corner angle zone is can being duplicated according to the concentration field of abcdef automatically by computing machine of symmetry, the concentration field in other several corner angle zone also is consistent with abcdef on the workpiece, and width is that concentration field is identical on concentration field and the cdef face in the zone of 2.5mm on 12 seamed edges on the workpiece, and in full accord greater than the CONCENTRATION DISTRIBUTION and the CONCENTRATION DISTRIBUTION on the ef of all surface upper edge degree of depth of 2.5mm on six surfaces apart from the border, so only need press to workpiece shown in Figure 2 $\frac{\∂C}{\∂n}=0$ Internal interface take out only account for the workpiece cumulative volume about 40,000/ regional area, carry out concentration field with finite element method and calculate the concentration field that can extrapolate any part on the workpiece according to its result.

Cut apart and calculate the carbonization concentration field of finding the solution by above, fixed inner boundary all meet $\frac{\∂C}{\∂n}=0.$

Use above-mentioned method to the real-time synchronous monitoring of complex-shaped part gas carburization three dimension transient state concentration field.Can monitor each regional carburizing process of difformity workpiece in real time, carburized (case) depth and infiltration layer concentration of carbon be distributed all meet the requirements, and on computer display screens, show or printout.

Embodiment 2: the step workpiece, as shown in Figure 3, and size AB=FE=GH=100mm, BC=150mm, DE=FG=AH=50mm, material 20CrMnTi, cementation zone requires degree of depth δ=1.2mm, and the infiltration layer concentration of carbon meets the distribution of Fig. 1 curve 1.

In order to consider the influence of interior angle shape factor, need the concentration field of the local abcdefgh of interior angle of calculating H point proximal side near.

Wherein the length of ab, df and cg cd, fg, eh is 2.5 δ (m=2.5), the length of side of ad and bc is 1.25 δ (m=1.25), the size of the size of its volume and concentration field calculated amount and corner angle near zone is in the same order of magnitude, and concentration field in abc ' d ' ef ' g ' h and abcdefgh are the concentration fields of the workpiece interior angle opposite side of symmetry, they also are symmetrical, bcghg ' c ' face just can correctly be reflected the influence of interior angle shape factor to CONCENTRATION DISTRIBUTION in the hope of the concentration field of interior angle line near zone along interior linea angulata direction transfer.

The carbonization concentration distributional analysis of interior angle H shape factor local exists everywhere this step workpiece: H, H ', F and F ', the carbonization concentration distributional analysis of the corner angle local shown in the embodiment 1 exists 12 places: A, A ', B, B ', C, C ', D, D ', E, E ', G and G ' to this step workpiece, seamed edge processing etc. also with

Embodiment 1 is identical.

Find the solution the carbonization concentration field of this workpiece by the present invention, fixed inner boundary all meet $\frac{\∂C}{\∂n}=0.$

Use above-mentioned method to the real-time synchronous monitoring of complex-shaped part gas carburization three dimension transient state concentration field.Can monitor each regional carburizing process of difformity workpiece in real time, carburized (case) depth and infiltration layer concentration of carbon be distributed all meet the requirements, and on computer display screens, show or printout.

Embodiment 3: semicircle curved surface thick-plate parts workpiece shown in Figure 4, AC=BD=A ' C '=B ' D '=400mm, AA '=BB '=CC '=DD '=50mm, radius R=100mm, material 15Cr, cementation zone requires degree of depth δ=1.5mm, and the infiltration layer concentration of carbon meets the distribution of Fig. 1 curve 3.

Processing for plane, corner angle, seamed edge is identical with embodiment 1.Double round surface seamed edge and straight flange seamed edge crossover sites inner edge interface processing are as follows: 1. apart from the inner plane of plane surface 2.5 δ mm, 2. apart from the negative camber of curved surface along radius-of-curvature direction 2.5 δ mm, 3. be the inner edge interface of 1.25 δ mm places and Surface Vertical at in-plane apart from handing over transversal, 4. the arc length apart from the friendship transversal is the inner edge interfaces vertical with positive camber, 1.25 δ mm places on curved surface.The octahedron of Gou Chenging is for calculating local like this, and this local has 4: E, F, G, and H.Semicircle curved portion seamed edge inner edge interface processing is as follows: 1. 1. and 2. press with inner plane and negative camber above-mentioned and 2., 3. 4. the semicircle curved surface plane of symmetry presses the above-mentioned inner edge interface of 4. determining, the bent hexahedron of Gou Chenging is for calculating local like this.This local also has 4.Removing the outer regional concentration of carbon of curved surface seamed edge on the semicircle curved surface distributes identical from surperficial 2.5 δ mm inner edge interfaces with seamed edge.

Calculate the carbonization concentration field find the solution this workpiece by above cutting apart, fixed inner boundary all meet $\frac{\∂C}{\∂n}=0.$

Use above-mentioned method to the real-time synchronous monitoring of complex-shaped part gas carburization three dimension transient state concentration field.Can monitor each regional carburizing process of difformity workpiece in real time, carburized (case) depth and infiltration layer concentration of carbon be distributed all meet the requirements, and on computer display screens, show or printout.

4: one automobile gear m=3 of embodiment, Z=40, pitch diameter 120mm, gear thickness 30mm, material 20CrMo, cementation zone requires degree of depth δ=0.8～1.0mm, and the infiltration layer concentration of carbon meets the distribution of Fig. 1 curve 2.Illustrating in Fig. 5 of a tooth of gear.

It is as follows that local inner edge interface processing is calculated by tooth portion: 1. along the inside surface of flank profil lateral surface vertical range 2.5 δ mm, 2. along the inner plane of tooth outerplanar apart from 2.5 δ mm, 3. the plane of symmetry of addendum width central authorities, 4. the plane of symmetry of space width central authorities, the calculating local of Gou Chenging is totally 80 like this, but appliance computer duplicates.

Existing stating on other planes except that above-mentioned and the curved surface treatment principle.

Calculate the carbonization concentration field find the solution this workpiece by above cutting apart, fixed inner boundary all meet $\frac{\∂C}{\∂n}=0.$

Use above-mentioned method to the real-time synchronous monitoring of complex-shaped part gas carburization three dimension transient state concentration field.Can monitor each regional carburizing process of difformity workpiece in real time, carburized (case) depth and infiltration layer concentration of carbon be distributed all meet the requirements, and on computer display screens, show or printout.

Embodiment 5: large-scale axle sleeve d=50mm, D ₁=180mm, D ₂=300mm, h ₁=80mm, h ₂=140mm.1 * 45 ° of part inside and outside circle chamfering, axle sleeve external diameter variation place rounding 1mm.Material is 40Cr, has excellent abrasive resistance to carry out gas carburizing in order to require the surface, and effective case depth δ=1.2mm, infiltration layer concentration of carbon press CONCENTRATION DISTRIBUTION 2 among Fig. 1.Attention: because material heart portion carbon content is 0.40%, m gets 1 here.

Circular property at parts of edges and corners inner edge interface processing is as follows: 1. apart from the inner plane of plane surface 1.2mm (being m=1); 2. the inner cylinder of distance circle outer surface of column 1.2mm (being m=1); 3. the radial plane of 30 ° in the angle of cut and 1. inner plane and the 2. crossing inner boundary plane of inside surface.1 * 45 ° of part inside and outside circle chamfering is because m δ=1 * 1.2=1.2mm herein, so can not deal with.

Rounding inside corner position inner edge interface processing is as follows: 1. apart from the inner plane of plane surface 1.2mm; 2. distance D ₁The inside surface of the periphery 1.2mm of=180mm; 3. the radial plane of 30 ° in the angle of cut and 1. inner plane and the 2. crossing inner boundary plane of inside surface.Part inside and outside circle chamfering 1mm is suitable with depth of penetration, also can not deal with.

Calculate the carbonization concentration field find the solution this workpiece by above cutting apart, fixed inner boundary all meet $\frac{\∂C}{\∂n}=0.$

Use above-mentioned method to the real-time synchronous monitoring of complex-shaped part gas carburization three dimension transient state concentration field.Can monitor each regional carburizing process of difformity workpiece in real time, carburized (case) depth and infiltration layer concentration of carbon be distributed all meet the requirements, and on computer display screens, show or printout.

Claims (5)

1, a kind of method of real-time of complicated shape part gas carburization three dimension concentration field, it is characterized in that, the numerical value of each moment furnace temperature of computer real-time acquisition and Carbon Potential Inside Furnace will be used in the Gas Carburizing Process, initial conditions as this moment carburized parts three-dimensional concentration field of real-time calculating, adopt local to decompose and composition algorithm, surface of the work is reduced shape features, from surface that workpiece is found out the respective shapes feature with meet $\frac{\∂C}{\∂n}=0$ Promptly the minimum volume local that internal interface constituted of zero diffuse flow condition carries out the three-dimensional cementation zone concentration field calculating of real-time transient state, and the cementation zone concentration field of local copied on the position that has identical shaped feature on the workpiece, try to achieve the transient state cementation zone concentration field of whole work-piece, obtain complicated shape part or various workpieces at this three-dimensional transient state cementation zone concentration field constantly.

2, the method for real-time of complicated shape part gas carburization three dimension concentration field according to claim 1 is characterized in that concrete steps are as follows:

1. judge the shape factor feature of concrete workpiece: surface of the work is divided into: plane, different curvature curved surface, seamed edge, corner angle, interior angle, exterior angle, cutting edge, chamfering, rounding, 11 kinds of shape facilities of the flank of tooth and the face of cylinder;

2. in complex-shaped part Gas Carburizing Process, read gas phase carbon potential and furnace temperature in each cementing furnace constantly, find the solution and determine the cementation zone concentration field in the local and check whether all inner boundaries meet by computer data acquisition system $\frac{\∂C}{\∂n}=0,$ Do not recomputate after then the interface being adjusted if meet;

3. all meet at the local of confirming all cementation zone concentration fields $\frac{\∂C}{\∂n}=0$ Internal boundary condition after, concentration field result of calculation with local, by symmetrical mapping, rotational angle and shift method, copy on the position that has mutually same shape on the workpiece, the set of the local concentration field by all difformity features on the workpiece, thus transient state cementation zone concentration field in the infiltration layer of whole work-piece surface tried to achieve;

4. the three-dimensional transient state concentration field of the workpiece that computing machine is obtained with the isoconcentration face of cementation zone concentration field or the isoconcentration line on the section or the CONCENTRATION DISTRIBUTION cloud atlas on the section or perpendicular in four kinds of modes of the concentration profile of difformity figuratrix direction one or more, with diagram or be presented on the computer screen in real time with digital form; Perhaps export the three-dimensional concentration field analog result with printout or digital communication method, realize the monitoring of complicated shape part gas carburizing or three-dimensional transient state concentration field analog result directly is passed to control module by computing machine.

3, according to the method for real-time of claim 1 or 2 described complicated shape part gas carburization three dimension concentration fields, it is characterized in that, described cementation zone concentration field calculates according to diffusion second law, and setting D is an isotropy, and D is the function of temperature and concentration of carbon:

Under one-dimensional case: $D=\frac{{\∂}^{2}C}{{\∂x}^2}=\frac{\∂C}{\∂\mathrm{\τ}}$

Under two-dimensional case: $D\frac{{\∂}^{2}C}{{\∂x}^2}+D\frac{{\∂}^{2}C}{{\∂y}^2}=\frac{\∂C}{\∂\mathrm{\τ}}$

Under three-dimensional situation: $D\frac{{\∂}^{2}C}{\∂x^2}+D\frac{{\∂}^{2}C}{\∂y^2}+D\frac{{\∂}^{2}C}{\∂z^2}=\frac{\∂C}{\∂\mathrm{\τ}}$

Boundary condition is:

X in the formula _b, y _b, z _bBe positioned on the border,

Be respectively surperficial outer normal and x, y, the angle between the z coordinate axis, Cg are the gas phase carbon potentials, and Cs is the surface of the work concentration of carbon,

Starting condition is: and C (x, y, z0)=C ₀

4, the method for real-time of complicated shape part gas carburization three dimension concentration field according to claim 2 is characterized in that the local of described cementation zone concentration field all meets $\frac{\∂C}{\∂n}=0$ Internal boundary condition have: the 1. shape plane of symmetry; 2. concentration of carbon still remains the original concentration of carbon C of steel after the carburizing ₀Internal interface; 3. with the infiltration layer concentration field in the perpendicular interface of concentration of carbon contour surface, judge according to experience and to carry out the tentative calculation correction then whether checking meets C for wherein back two kinds _In=C ₀Or it is not vertical with the concentration contour surface.

5, the method for real-time of complicated shape part gas carburization three dimension concentration field according to claim 1 is characterized in that, meets $\frac{\∂C}{\∂n}=0$ Promptly the concrete grammar of the minimum volume local that internal interface constituted of zero diffuse flow condition is:

1. with the internal interface of outer face surface at a distance of m δ, δ is carbon-coating degree of depth mm, apart from the plane of plane surface m δ and apart from the curved inner surface of curved surface along radius-of-curvature direction m δ;

2. curved surface and Plane intersects be in in-plane apart from the distance of handing over transversal for the inner plane of m δ place and Surface Vertical and on curved surface the arc length of distance friendship transversal be the face of m δ place and Surface Vertical, as with the perpendicular interface of the contour surface of concentration of carbon;

3. apart from the plane of interior angle m δ place perpendicular to the surface;

Described Coefficient m is selected in 1～2.5.

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