CN107844852A - A kind of shrinkage defect Forecasting Methodology for simulating steel-casting sand casting process - Google Patents
A kind of shrinkage defect Forecasting Methodology for simulating steel-casting sand casting process Download PDFInfo
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Abstract
The present invention relates to a kind of shrinkage defect Forecasting Methodology for simulating steel-casting sand casting process, it is the shrinkage defect for steel-casting sand casting process, simulation and forecast is carried out before actual casting, is advantageous to that casting flaw is predicted and reduced in actual casting;Program is write by development platform of VC++, computer operation is carried out, draws prediction result, show the distribution situation of shrinkage defect in steel-casting sand casting, this Forecasting Methodology is few using equipment, and computational methods are general, reasonable, analog result is accurate, is adapted to the prediction of steel-casting sand casting shrinkage defect.
Description
Technical field
The present invention relates to a kind of shrinkage defect Forecasting Methodology for simulating steel-casting sand casting process, belong to steel-casting sand mold
The technical field of casting flaw prediction.
Background technology
Sand casting is to obtain anticipated shape, the casting method of size after molten metal flows into casting mold solidification;Technical process is
Molten metal flows into running channel by cast gate, until being full of whole die cavity, obtains being expected casting after cooled and solidified.
In casting solidification process, feeding of some regions due to not obtaining molten metal forms scattered and tiny hole
Hole, referred to as shrinkage porosite;This will reduce the mechanical property of casting, have a strong impact on the quality of casting;Shrinkage porosite in metal liquid solidification process
Formation is a complicated process, it is necessary to show its whole process formed, accurate prediction casting with the method for numbered analog simulation
Steel part metal liquid solidification process forms the distribution of shrinkage porosite, and reason is provided for optimize technique, mold design and prevention, reduction casting defect
By foundation.
The content of the invention
Goal of the invention
The purpose of the present invention is to be directed to the situation that shrinkage defect is produced in steel-casting sand casting process, for steel-casting sand
Mold casting process of setting feature, calculated by founding mathematical models and program, form contracting in process of setting to cylinder casting
The distribution of pine is predicted, and is optimize technique, is reduced Shrinkage Porosity defect and is provided theoretical foundation.
Technical scheme
(1) cylinder cast steel casting is obtained
1. prepare sand mold casting mold
Prepare cylinder wooden model and be molded;With sand paper polishing wooden model surface, make any surface finish;Using cylindric wooden model as shaping mould
Type, sand mold mould is made with furan resin-sand, and fixed by mold frame, zirconium oxide filter screen is set in sand mold mould cast gate, it is standby
With;
2. melting prepares steel metal liquation
Cast steel 5.2kg ± 0.1kg is placed in melting kettle, is heated to 1600 DEG C ± 2 DEG C, degasification, removes the gred, temperature drop
It is stand-by to 1550 DEG C ± 2 DEG C;
3. sand casting process
Steel metal liquation is injected into mould gate, molten metal enters mold cavity and fills type;
4. cooling and taking-up casting
After cast, sand mold mould is placed in natural air and is cooled to 25 DEG C;Sand mold mould is opened, takes out cylinder casting
Part;
5. clear up cast(ing) surface
Cast(ing) surface is cleared up with metallic brush, with mechanically cutting casting remainder, with sand paper polishing cast(ing) surface, casting is molded;
(2) shrinkage defect forecast model is established
The computation model of shrinkage defect prediction is established, is comprised the following steps that:
1. establish threedimensional model, particle it is discrete and initialization
3D solid is established first with modeling software, it is then discrete to molten metal progress particle in casting mold, die cavity, if
The initial parameter of particle is put, is comprised the following steps that:
1) foundation of 3D solid
With 3 d modeling software establish casting mold, in die cavity molten metal threedimensional model;
2) particle is discrete and sets the initial parameter of particle
3 d modeling software exports 3D solid, discrete by particle, determines particle initial position;According to particle types not
Together, the initial pressure of setting different attribute particle, density, viscosity, temperature, thermal conductivity factor, specific heat capacity, time step, and provide
Every 6000 time steps are a calculation stages;Casting mold particle is solid wall boundary particle, and border is handled using force method is repelled;
2. establish full pairing searching method
Particle for meeting condition realizes that particle pairing, storage particle to information, comprise the following steps that:
Respectively using the position where particle i as the center of circle, the spheric region using 2 times of smooth length as radius represents particle i
The domain of influence;As particle i and particle j spacing rijNumerical value when being less than or equal to 2 times of smooth length, then it is considered that particle i
Matched with particle j, influences of the particle j to particle i will be considered in follow-up calculate;In the case where meeting matching condition, in order to avoid weight
Compounding pair, the j particles that only search numbering be less than i particles in itself numbering when just complete pairing and store the particle to information;
After the completion of the calculating of each time step, the search, pairing, storage particle of particle are re-started to information;
3. judge the appearance of shrinkage porosite
Steel metal liquid particles temperature reduces, and temperature change can have an impact to the physical parameter of metal liquid particles;Solidified
Latent heat release model is also crucial in journey, is comprised the following steps that:
1) the calculating transitivity parameter processing of particle temperature;
Temperature computation transitivity parameter processing comprises the following steps that:
Temperature change calculating is carried out to all particles, expression is as follows:
In formula:Represent that i particle temperatures change with time rate, CpiRepresent i particle specific heat capacities, ρiRepresent that i particles are close
Degree,Represent that j particles are summed to i particles influence in the domain of influence, N represents the particle number in the domain of influence, mjRepresent particle j
Quality, ρjRepresent the density of j particles, λiRepresent the thermal conductivity factor of i particles, λjRepresent the thermal conductivity factor of j particles, TiRepresent i grains
The temperature value of son, TjRepresent the temperature value of j particles, rijThe distance between i particles and j particles are represented,Represent smooth function
Gradient, represented using index method, Greek alphabet subscript α and β denotation coordination direction;
For particle in die cavity, viscosity, thermal conductivity factor, density and specific heat capacity variation with temperature in calculating process and become
Change, expression is as follows:
The change of viscosity with temperature, relational expression are as follows:
When particle temperature is less than 1137 DEG C, η=1000, η units are pas;When particle temperature is at 1137 DEG C -1503
DEG C when, η=4103.2-2.73T, η units are pas;When particle temperature is at 1503 DEG C -1600 DEG C, η=0.01, η units
For pas;T represents particle temperature, unit DEG C;
The relational expression of thermal conductivity factor and temperature is as follows:
When particle temperature is less than 950 DEG C, λ=33.6-0.008T, λ units are W/ (m DEG C);When particle temperature is 950
At DEG C -1000 DEG C, λ=0.08T-50, λ units are W/ (m DEG C);When particle temperature is at 1000 DEG C -1600 DEG C, λ=
0.015T+15, λ unit are W/ (m DEG C), and T represents particle temperature, unit DEG C;
Between different calculation stages, density with temperature changes, and relational expression is as follows:
When particle temperature is less than 1137 DEG C, ρ=7878, ρ units are kg/m3;When particle temperature is at 1137 DEG C -1503 DEG C
When, ρ=8990-0.9787T, ρ units are kg/m3;When particle temperature is at 1503 DEG C -1600 DEG C, ρ=7520, ρ units are
kg/m3, T expression particle temperatures, unit DEG C;
Specific heat capacity variation with temperature, relational expression are as follows:
When particle temperature is less than or equal to 580 DEG C, Cp=0.6T+452, CpUnit is J/ (kg DEG C);When particle temperature exists
At 580 DEG C -780 DEG C, Cp=1438-1.1T, CpUnit is J/ (kg DEG C);When particle temperature is at 780 DEG C -1400 DEG C, Cp=
0.13T+478.6, CpUnit is J/ (kg DEG C);When particle temperature is at 1400 DEG C -1600 DEG C, Cp=0.9T-600, CpUnit
For J/ (kg DEG C), T represents particle temperature, unit DEG C;
2) calculating of molten metal particle acceleration;
In formula:W represents smooth function, αdFor constant valueRepresent that j particles influence on i particles in the domain of influence
Effect summation, N represent the particle number in the domain of influence, mjRepresent particle j quality, piRepresent particle i pressure value, pjRepresent
Particle j pressure value, ρiRepresent particle i density, ρjParticle j density is represented, g represents the acceleration of gravity of particle, ηiWith
ηjParticle i and particle j dynamic viscosity coefficients are represented respectively,Particle i and particle j speed difference is represented, is represented using index method,
Greek alphabet subscript α and β denotation coordination direction, R represent the ratio of interparticle distance and smooth length;
The calculating of above formula needs to calculate particle pressure value p, and pressure value p calculation expressions are as follows:
In formula:p0Represent pressure initial value, ρ0Particle initial density is represented, γ is constant, and g represents acceleration of gravity, H tables
Show casting height;
In same calculation stages, rate of change of the density is tried to achieve by following formula, and expression is as follows:
In formula:Represent that particle i density changes with time rate,Represent that j particles influence to make on i particles in the domain of influence
With summation, N represents the particle number in the domain of influence, mjParticle j quality is represented,Particle i and particle j speed difference is represented,
Represented using index method, Greek alphabet subscript α and β denotation coordination direction;
3) latent heat is handled
The latent heat discharged when molten metal is solidified is used to compensate the temperature reduction caused by heat transfer, when molten metal grain
When sub- temperature value is between liquidus curve and solidus, revised temperature valueCalculation formula is as follows:
Work as TL≤ToAt≤1600 DEG C:
Work as To< TLWhen:
In formula:Represent current time revised temperature value, TcThe temperature value before current time amendment is represented, L is represented
The latent heat of solidification of molten metal, CpRepresent specific heat capacity, ToRepresent the temperature value of last moment, TsRepresent solidus temperature, TLLiquidus curve
Temperature;
4) for particle in die cavity, in the domain of influence, it is calculated as follows process:
In formula:TiRepresent particle i temperature value, TjRepresent particle j temperature value, rijRepresent interparticle distance, ToRepresent particle
I is in the temperature value of last moment, T·Temperature values of the particle i at current time is represented, if particle temperature is in liquidus curve and solid phase
Temperature value after correcting is taken when between line, Δ t represents time step, if TgWith CrRatio be less than 0.8, judgement there is shrinkage porosite;
4. passing through a time step, the temperature, speed, position of particle are updated, comprised the following steps that:
1) particle changes with time rate in the temperature value that the temperature value at current time etc. is carved for the moment thereon plus temperature
Time step is multiplied by, when molten metal particle temperature is between liquidus curve and solidus, carries out temperature value amendment;
2) molten metal particle speed and location updating are as follows:
Metal liquid particles are taken the opportunity spacer step in the velocity amplitude that the velocity amplitude at current time etc. is carved for the moment thereon plus acceleration
It is long;Metal liquid particles are multiplied by time step in the positional value that the positional value at current time etc. is carved for the moment thereon plus acceleration
Square multiplied by with
After the completion of one time step calculates, re-start search, pairing and the particle temperature of particle, speed, position and
The calculating of physical parameter, terminate until calculating;
The shrinkage defect Forecasting Methodology of steel-casting sand casting process is completed by computer program, using VC++ as development platform
Programming is carried out, calculation procedure is as follows:
(3) prediction result
Numerical simulation result shows that shrinkage defect occurs in cylinder casting, is coincide with measured result.
Beneficial effect:
The present invention has obvious advance compared with background technology, is that the shrinkage porosite for being directed to steel-casting sand casting process lacks
Fall into, simulation and forecast is carried out before actual casting, be advantageous to that casting flaw is predicted and reduced in actual casting;Using VC++ to open
Hair platform writes program, carries out computer operation, draws prediction result, shows the distribution of shrinkage defect in steel-casting sand casting
Situation, this Forecasting Methodology is few using equipment, and computational methods are general, reasonable, and analog result is accurate, is adapted to steel-casting sand casting contracting
Loose failure prediction.
Brief description of the drawings
Fig. 1, cylinder casting front view
Fig. 2, cylinder casting top view
Fig. 3, cylinder casting side view
Fig. 4, steel-casting cylinder casting sand mold as-cast condition figure
Shown in figure, list of numerals is as follows:
1st, upper cylinder, 2, lower cylinder, 3, mold frame, 4, sand mold mould, 5, zirconium oxide cast gate, the 6, first folding
Frame, the 7, second movable rack, the 8, the 3rd movable rack, the 9, the 4th movable rack, 10, upper cylinder die cavity, 11, lower cylinder die cavity, 12,
Molten metal.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described:
It is cylinder casting structure figure shown in Fig. 1,2,3, each portion position, annexation are correct, and upper cylinder 1 is small
Diameter end, lower cylinder 2 are larger diameter end.
It is cylinder casting sand mold as-cast condition figure shown in Fig. 3, each portion position, annexation are correct.
Outside is mold frame 3, and is consolidated by the first movable rack 6, the second movable rack 7, the 3rd movable rack 8, the 4th movable rack 9
It is fixed;It is sand mold mould 4 in mold frame 3, the internal upper part of sand mold mould 4 is upper cylinder die cavity 10, interior bottom is lower cylinder type
Chamber 11;The upper middle position of mold frame 3 is provided with zirconium oxide cast gate 5, the upper cylinder die cavity 10 of the bottom of zirconium oxide cast gate 5 connection,
Lower cylinder die cavity 11;Type is filled by steel metal liquation 12 in upper cylinder die cavity 10, lower cylinder die cavity 11.
Claims (2)
- A kind of 1. shrinkage defect Forecasting Methodology for simulating steel-casting sand casting process, it is characterised in that:(1) cylinder cast steel casting is obtained1. prepare sand mold casting moldPrepare cylinder wooden model and be molded;With sand paper polishing wooden model surface, make any surface finish;Using cylindric wooden model as forming model, Sand mold mould is made with furan resin-sand, and is fixed by mold frame, zirconium oxide filter screen is set in sand mold mould cast gate, it is standby;2. melting prepares steel metal liquationCast steel 5.2kg ± 0.1kg is placed in melting kettle, is heated to 1600 DEG C ± 2 DEG C, degasification is removed the gred, and temperature is down to It is 1550 DEG C ± 2 DEG C, stand-by;3. sand casting processSteel metal liquation is injected into mould gate, molten metal enters mold cavity and fills type;4. cooling and taking-up castingAfter cast, sand mold mould is placed in natural air and is cooled to 25 DEG C;Sand mold mould is opened, takes out cylinder casting;5. clear up cast(ing) surfaceCast(ing) surface is cleared up with metallic brush, with mechanically cutting casting remainder, with sand paper polishing cast(ing) surface, casting is molded;(2) shrinkage defect forecast model is establishedThe computation model of shrinkage defect prediction is established, is comprised the following steps that:1. establish threedimensional model, particle it is discrete and initialization3D solid is established first with modeling software, it is then discrete to molten metal progress particle in casting mold, die cavity, grain is set The initial parameter of son, is comprised the following steps that:1) foundation of 3D solidWith 3 d modeling software establish casting mold, in die cavity molten metal threedimensional model;2) particle is discrete and sets the initial parameter of particle3 d modeling software exports 3D solid, discrete by particle, determines particle initial position;It is different according to particle types, Initial pressure, density, viscosity, temperature, thermal conductivity factor, the specific heat of different attribute particle are setHold, time step, and provide that every 6000 time steps are a calculation stages;Casting mold particle is solid wall boundary particle, Border is handled using force method is repelled;2. establish full pairing searching methodParticle for meeting condition realizes that particle pairing, storage particle to information, comprise the following steps that:Respectively using the position where particle i as the center of circle, the spheric region using 2 times of smooth length as radius represents particle i shadow Ring domain;As particle i and particle j spacing rijNumerical value when being less than or equal to 2 times of smooth length, then it is considered that particle i and grain Sub- j matchings, will consider influences of the particle j to particle i in follow-up calculate;In the case where meeting matching condition, in order to avoid repeating to match somebody with somebody It is right, the j particles that only search numbering be less than i particles in itself numbering when just complete pairing and store the particle to information;Every After the completion of individual time step calculates, the search, pairing, storage particle of particle are re-started to information;3. judge the appearance of shrinkage porositeSteel metal liquid particles temperature reduces, and temperature change can have an impact to the physical parameter of metal liquid particles;In process of setting Latent heat release model is also crucial, is comprised the following steps that:1) the calculating transitivity parameter processing of particle temperature;Temperature computation transitivity parameter processing comprises the following steps that:Temperature change calculating is carried out to all particles, expression is as follows:<mrow> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>C</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>&rho;</mi> <mi>i</mi> </msub> </mrow> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msub> <mi>m</mi> <mi>j</mi> </msub> <msub> <mi>&rho;</mi> <mi>j</mi> </msub> </mfrac> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <msub> <mi>&lambda;</mi> <mi>j</mi> </msub> </mrow> <mrow> <msub> <mi>&lambda;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&lambda;</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>j</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&alpha;</mi> </msubsup> </mrow> </mfrac> </mrow>In formula:Represent that i particle temperatures change with time rate, CpiRepresent i particle specific heat capacities, ρiI particle densities are represented, Represent that j particles are summed to i particles influence in the domain of influence, N represents the particle number in the domain of influence, mjRepresent particle j matter Amount, ρjRepresent the density of j particles, λiRepresent the thermal conductivity factor of i particles, λjRepresent the thermal conductivity factor of j particles, TiRepresent i particles Temperature value, TjRepresent the temperature value of j particles, rijThe distance between i particles and j particles are represented,Smooth function gradient is represented, Represented using index method, Greek alphabet subscript α and β denotation coordination direction;For particle in die cavity, viscosity, thermal conductivity factor, density and specific heat capacity variation with temperature in calculating process and change, have Body expression formula is as follows:The change of viscosity with temperature, relational expression are as follows:When particle temperature is less than 1137 DEG C, η=1000, η units are pas;When particle temperature is at 1137 DEG C -1503 DEG C, η =4103.2-2.73T, η unit are pas;When particle temperature is at 1503 DEG C -1600 DEG C, η=0.01, η units are pas; T represents particle temperature, unit DEG C;The relational expression of thermal conductivity factor and temperature is as follows:When particle temperature is less than 950 DEG C, λ=33.6-0.008T, λ units are W/ (m DEG C);When particle temperature 950 DEG C- At 1000 DEG C, λ=0.08T-50, λ units are W/ (m DEG C);When particle temperature is at 1000 DEG C -1600 DEG C, λ=0.015T+ 15, λ units are W/ (m DEG C), and T represents particle temperature, unit DEG C;Between different calculation stages, density with temperature changes, and relational expression is as follows:When particle temperature is less than 1137 DEG C, ρ=7878, ρ units are kg/m3;When particle temperature is at 1137 DEG C -1503 DEG C, ρ= 8990-0.9787T, ρ unit are kg/m3;When particle temperature is at 1503 DEG C -1600 DEG C, ρ=7520, ρ units are kg/m3, T tables Show particle temperature, unit DEG C;Specific heat capacity variation with temperature, relational expression are as follows:When particle temperature is less than or equal to 580 DEG C, Cp=0.6T+452, CpUnit is J/ (kg DEG C);When particle temperature is 580 At DEG C -780 DEG C, Cp=1438-1.1T, CpUnit is J/ (kg DEG C);When particle temperature is at 780 DEG C -1400 DEG C, Cp= 0.13T+478.6, CpUnit is J/ (kg DEG C);When particle temperature is at 1400 DEG C -1600 DEG C, Cp=0.9T-600, CpUnit For J/ (kg DEG C), T represents particle temperature, unit DEG C;2) calculating of molten metal particle acceleration;<mrow> <mi>W</mi> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&alpha;</mi> <mi>d</mi> </msub> <mo>&times;</mo> <mrow> <mo>(</mo> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mo>-</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>R</mi> <mn>3</mn> </msup> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&le;</mo> <mi>R</mi> <mo><</mo> <mn>1</mn> <mo>;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&alpha;</mi> <mi>d</mi> </msub> <mo>&times;</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <msup> <mrow> <mo>(</mo> <mn>2</mn> <mo>-</mo> <mi>R</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>1</mn> <mo>&le;</mo> <mi>R</mi> <mo><</mo> <mn>2</mn> <mo>;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow><mrow> <mfrac> <mrow> <msubsup> <mi>dv</mi> <mi>i</mi> <mi>&alpha;</mi> </msubsup> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mfrac> <mrow> <msub> <mi>&eta;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&eta;</mi> <mi>j</mi> </msub> </mrow> <mrow> <msub> <mi>&rho;</mi> <mi>i</mi> </msub> <msub> <mi>&rho;</mi> <mi>j</mi> </msub> </mrow> </mfrac> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>&beta;</mi> </msubsup> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>R</mi> </mrow> </mfrac> <mo>-</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <mrow> <msub> <mi>&rho;</mi> <mi>i</mi> </msub> <msub> <mi>&rho;</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mi>&alpha;</mi> </msubsup> </mrow> </mfrac> <mo>+</mo> <mi>g</mi> </mrow>In formula:W represents smooth function, αdFor constant value Represent that j particles are asked i particle influences in the domain of influence With, the particle number in the N expression domains of influence, mjRepresent particle j quality, piRepresent particle i pressure value, pjRepresent particle j's Pressure value, ρiRepresent particle i density, ρjParticle j density is represented, g represents the acceleration of gravity of particle, ηiAnd ηjTable respectively Show particle i and particle j dynamic viscosity coefficients,Particle i and particle j speed difference is represented, is represented using index method, Greek alphabet Subscript α and β denotation coordination direction, R represent the ratio of interparticle distance and smooth length;The calculating of above formula needs to calculate particle pressure value p, and pressure value p calculation expressions are as follows:<mrow> <mi>p</mi> <mo>=</mo> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>&lsqb;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mi>&rho;</mi> <msub> <mi>&rho;</mi> <mn>0</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mi>&gamma;</mi> </msup> <mo>-</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow><mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mn>30</mn> <mn>2</mn> </msup> <msub> <mi>gH&rho;</mi> <mn>0</mn> </msub> </mrow> <mi>&gamma;</mi> </mfrac> </mrow>In formula:p0Represent pressure initial value, ρ0Particle initial density is represented, γ is constant, and g represents acceleration of gravity, and H represents casting Part height;In same calculation stages, rate of change of the density is tried to achieve by following formula, and expression is as follows:<mrow> <mfrac> <mrow> <msub> <mi>d&rho;</mi> <mi>i</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mi>&beta;</mi> </msubsup> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&part;</mo> <msub> <msup> <mi>x</mi> <mi>&beta;</mi> </msup> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>In formula:Represent that particle i density changes with time rate,Represent that j particles are asked i particle influences in the domain of influence With, the particle number in the N expression domains of influence, mjParticle j quality is represented,Particle i and particle j speed difference is represented, is used Index method expression, Greek alphabet subscript α and β denotation coordination direction;3) latent heat is handledThe latent heat discharged when molten metal is solidified is used to compensate the temperature reduction caused by heat transfer, when metal liquid particles temperature When angle value is between liquidus curve and solidus, revised temperature valueCalculation formula is as follows:Work as TL≤ToAt≤1600 DEG C:<mrow> <msubsup> <mi>T</mi> <mi>c</mi> <mo>*</mo> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>+</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo><</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> <mo>-</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <mfrac> <msub> <mi>C</mi> <mi>p</mi> </msub> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mo>+</mo> <mfrac> <mi>L</mi> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> <mo>-</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> <mo>&le;</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>&le;</mo> <msub> <mi>T</mi> <mi>L</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>Work as To< TLWhen:<mrow> <msubsup> <mi>T</mi> <mi>c</mi> <mo>*</mo> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>+</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo><</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> <mo>-</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <mfrac> <msub> <mi>C</mi> <mi>p</mi> </msub> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mo>+</mo> <mfrac> <mi>L</mi> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> </mrow> </mfrac> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mi>S</mi> </msub> <mo>-</mo> <mfrac> <mi>L</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mfrac> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> <mrow> <msub> <mi>T</mi> <mi>L</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>S</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>&le;</mo> <msub> <mi>T</mi> <mi>L</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>In formula:Represent current time revised temperature value, TcThe temperature value before current time amendment is represented, L represents molten metal Latent heat of solidification, CpRepresent specific heat capacity, ToRepresent the temperature value of last moment, TsRepresent solidus temperature, TLLiquidus temperature;4) for particle in die cavity, in the domain of influence, it is calculated as follows process:<mrow> <msub> <mi>T</mi> <mi>g</mi> </msub> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mi>j</mi> </msub> </mrow> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mi>C</mi> <mi>r</mi> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>-</mo> <msup> <mi>T</mi> <mo>&CenterDot;</mo> </msup> </mrow> <mrow> <mi>&Delta;</mi> <mi>t</mi> </mrow> </mfrac> </msqrt> </mrow>In formula:TiRepresent particle i temperature value, TjRepresent particle j temperature value, rijRepresent interparticle distance, ToRepresent that particle i exists The temperature value of last moment, T·Represent temperature values of the particle i at current time, if particle temperature be in liquidus curve and solidus it Between when take amendment after temperature value, Δ t represent time step, if TgWith CrRatio be less than 0.8, judgement there is shrinkage porosite;4. passing through a time step, the temperature, speed, position of particle are updated, comprised the following steps that:1) particle is multiplied by the temperature value that the temperature value at current time etc. is carved for the moment thereon plus the temperature rate of changing with time Time step, when molten metal particle temperature is between liquidus curve and solidus, carry out temperature value amendment;2) molten metal particle speed and location updating are as follows:Metal liquid particles multiply time step in the velocity amplitude that the velocity amplitude at current time etc. is carved for the moment thereon plus acceleration;Gold In the positional value at current time etc., the positional value at quarter adds square that acceleration is multiplied by time step to category liquid particles for the moment thereon Multiplied by withAfter the completion of one time step calculates, search, pairing and particle temperature, speed, position and the physical property of particle are re-started The calculating of parameter, terminate until calculating;The shrinkage defect Forecasting Methodology of steel-casting sand casting process is completed by computer program, is carried out by development platform of VC++ Programming;(3) prediction resultNumerical simulation result shows that shrinkage defect occurs in cylinder casting, is coincide with measured result.
- 2. a kind of shrinkage defect Forecasting Methodology of simulation steel-casting sand casting process according to claims 1, it is special Sign is:Steel-casting cylinder sand casting state is:Outside is mold frame (3), and is opened by the first movable rack (6), second It is fixed to close frame (7), the 3rd movable rack (8), the 4th movable rack (9);It is sand mold mould (4) in mold frame (3), sand mold mould (4) internal upper part be upper cylinder die cavity (10), interior bottom be lower cylinder die cavity (11);The upper middle position of mold frame 3 is set There are zirconium oxide cast gate (5), the upper cylinder die cavity (10) of zirconium oxide cast gate (5) bottom connection, lower cylinder die cavity (11);Upper cylinder Type is filled by steel metal liquation (12) in build chamber (10), lower cylinder die cavity (11).
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