CN106202809B - A kind of Optimization Prediction method for simulating cast iron sand casting casting cycle - Google Patents

A kind of Optimization Prediction method for simulating cast iron sand casting casting cycle Download PDF

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CN106202809B
CN106202809B CN201610590374.2A CN201610590374A CN106202809B CN 106202809 B CN106202809 B CN 106202809B CN 201610590374 A CN201610590374 A CN 201610590374A CN 106202809 B CN106202809 B CN 106202809B
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牛晓峰
王红霞
王冠乾
胡磊
阎佩雯
马丽莉
黄志伟
侯华
朱明�
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Shanxi Huaxiang group Limited by Share Ltd
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Taiyuan University of Technology
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Abstract

The present invention relates to a kind of Optimization Prediction method for simulating cast iron sand casting casting cycle, it is that slag group moves irregular situation in cavity filling process in sand mold mould for cast iron, slag is rolled into a ball and is predicted with movement locus of the molten metal in sand mold mould in cavity filling process, by establishing model, program calculates, predict slag group movement locus, optimizing pouring system, theoretical foundation is provided to prevent and eliminating casting defect, this optimization calculates, Forecasting Methodology is general rationally, calculating speed is fast, analog result is accurate, it is adapted to prediction of the ironcasting in gravitational casting slag group movement locus, optimizing pouring system, casting is avoided to produce defect, it is slag group movement locus Forecasting Methodology during advanced ferrous metal gravitational casting liquid metal filling.

Description

A kind of Optimization Prediction method for simulating cast iron sand casting casting cycle
Technical field
The present invention relates to a kind of Optimization Prediction method for simulating cast iron sand casting casting cycle, belong to iron casting technique Optimization and the technical field calculated.
Background technology
Cast iron sand casting is that molten metal fills sand mold die cavity under gravity, to form a kind of method of casting, Because molten metal is full of die cavity, referred to as gravitational casting under gravity, its common technology process is that molten metal passes through Sand mold casting nozzle, die cavity is entered by sprue, cross gate, ingate under gravity, until being full of die cavity, obtained after cooling The casting of solidification.
Cast iron can produce slag group in fusion process, can produce oxidation reaction in casting, cavity filling process, form secondary oxygen Slugging group, slag group enter die cavity can cause casting defect, how to grasp and predict ironcasting in casting cycle slag group in metal Flow trace in liquation, reaching pushing off the slag, skimming effect for optimization casting, prevention eliminates casting defect and provides theoretical foundation, this It is an important research topic.
The content of the invention
Goal of the invention
The purpose of the present invention is to be directed to ironcasting sand casting feature, to cast iron in sand mold mould slag group in cavity filling process Movement locus be predicted, calculated by establishing model and program, prediction slag group movement locus, reach gear for optimization casting Slag, skimming effect, prevention and elimination casting defect provide theoretical foundation.
Technical scheme
During cast iron sand casting, under gravity, the Forecasting Methodology of slag group movement locus is as follows：
(1) prefabricated cast-iron crankshaft exemplar
1. preparing automatic modeling crankshaft casting sand mold, Modeling Material uses furan resin-sand, and zirconium oxide filter screen is set at cast gate；
2. melting prepares metal
Cast iron 6kg ± 0.1kg is weighed, is placed in melting kettle, is heated to 1350 DEG C ± 5 DEG C, using carbon trichloride degasification, Then slagging-off, it is stand-by after standing 5min；
3. gravitational casting
By metal it is static after by sand mold cast gate inject sand mold die cavity carry out filling type, stand 30min after filling type；
4. cool down
After casting, sand mold and its interior casting are embedded in fine sand and are cooled to 25 DEG C；
5. automatic modeling crankshaft casting is taken out in die sinking
6. clear up cast(ing) surface
Clear up cast(ing) surface with metallic brush, with mechanically cutting remainder, then polished cast(ing) surface with sand paper, automatic modeling crankshaft casting into Type；
(2) slag group movement locus forecast model is established
Based on smoothed particle method computational methods, the mathematical modeling of particle interphase interaction is established, finds out casting Solid-fluid Two-phase Flow rule in cavity filling process, simulation molten metal slag group flow process；
Particlized is carried out to molten metal, slag group and border using computer program, the reserved capacity in calculator memory, entered The attribute configuration of row primary, three kinds of different attribute particles are carried out with the setting of quality, density, initial velocity, viscosity respectively； After configuring particle property, smooth length L is carried out, calculates time step Δ t setting；
1. establish the searching method of interacting particles
The particle of interaction in support region is determined, and is matched, detailed process is as follows：
1) it is 3 times of smooth length L in one layer of zoning upper berth grid, side length of element size, particle is distributed in each In the cell element of grid, and each cell element is numbered；
2) respectively the particle interacted therewith in the support region of each particle is scanned for matching, in search procedure In, only the cell element where than particle, which is numbered, searches for pairing in the range of big cell element, repeat search is avoided, for being matched in support region Successful particle, the number consecutively since numbering 1；
3) after the completion of the calculating of each time step, the pairing of particle is re-started；
2. on the basis of prediction, after preceding 1/2nd time step, to the speed of metal liquid particles and slag granule Degree, position are modified；
Comprise the following steps that：
1) calculating of metal liquid particles and the sub- variable density of slag granule：
According to Continuous plus equation, density calculating is carried out to any metal liquid particles i, by i particle support regions with The quality of its interacting particles and speed difference accumulating operation, obtain metal liquid particles i variable density, expression formula It is as follows：
In formula：ρiParticle i density is represented, t represents the time,The derivative to particle i solution density versus times is represented, ρjThe particle j density interacted therewith in particle i support regions is represented,Represent to mutual with it in i particle support regions The particle weighted sum of effect, N represent the sum with the particle of i particle interactions, m in support regionjRepresent particle j matter Amount, VijParticle i and particle j speed difference is represented,Represent the derivative of smooth function；
For slag granule, keep density constant in calculating process；
2) calculating of active force suffered by metal liquid particles and slag granule：
For metal liquid particles and slag granule, the active force suffered by any i particles is pressure, viscous force, external force, expression Formula is as follows：
Fi=Fp+Fn+Fw
In formula：FiRepresent that particle i is suffered to make a concerted effort, FpRepresent particle i pressures, FnRepresent viscous force suffered by particle i, Fw Represent external force suffered by particle i；
When the particle of interaction is like particle, it is all metal liquid particles or is all slag granule：
In formula：The particle weighted sum to being interacted therewith in i particle support regions is represented, N is represented in support region and i The sum of the particle of particle interaction, mjRepresent particle j quality, pi pjParticle i and j pressure value are represented respectively, are passed through Solving state equation obtains, ρiRepresent particle i density, ρjThe particle j's that expression interacts therewith in particle i support regions Density, ξiParticle i dynamic viscosity coefficients are represented, g represents the acceleration of gravity of particle,Represent the derivative of smooth function, rij Alternate position spike between expression particle, rij 2Represent interparticle distance from square, VijParticle i and particle j speed difference is represented, ∏ represents grain The artificial viscosity of son；
When interacting particles is inhomogeneity particle, metal liquid particles and slag granule, to its pressure phase, viscous force and outer Power is accordingly corrected：
In formula：The particle weighted sum to being interacted therewith in i particle support regions is represented, N is represented in support region and i The sum of the particle of particle interaction, mjRepresent particle j quality, pi pjParticle i and j pressure value are represented respectively, are passed through Solving state equation obtains, and θ is coefficient, value 0.2, ρiRepresent particle i density, ρjRepresent in particle i support regions with Its particle j to interact density, g represent the acceleration of gravity of particle, and K is a constant coefficient, and expression is interaction The parameter of power size, rijAlternate position spike between expression particle, rij 2Represent interparticle distance from square,Represent leading for smooth function Number, ξi、ξjParticle i and j dynamic viscosity coefficient, V are represented respectivelyijRepresent particle i and particle j speed difference；
3) after 1/2nd time steps before, to metal liquid particles and slag granule carries out speed and position is repaiied Just, comprise the following steps that：
Density, pressure, viscous force, external force, the value of making a concerted effort of metal liquid particles and slag granule are obtained, and then tries to achieve acceleration Degree；After 1/2nd time steps before, the speed and position of metal liquid particles and slag granule are corrected as follows：
Metal liquid particles and slag granule existThe erection rate value at moment adds equal to its velocity amplitude at the n moment Acceleration is multiplied by half time step, and metal liquid particles and slag granule existThe correction position value at moment is equal to Its n moment positional value plus itsThe erection rate value at moment is multiplied by half time step, wherein n tables Show the current calculating moment；
3. after a time step, the speed of metal liquid particles and slag granule, position are calculated；
Metal liquid particles and slag granule the velocity amplitude of n+ time Δts be equal to itsThe erection rate at moment Value be multiplied by two subtract its velocity amplitude at the n moment, metal liquid particles and slag granule n+ time Δts positional value be equal to secondly Correction position value again subtracts its positional value at the n moment, and wherein n represents current and calculates the moment；
After the completion of one time step calculates, the search pairing and the calculating of particle rapidity, position of particle are re-started, directly Die cavity extremely is full of, and obtains the movement locus that slag group is flowed with molten metal；
The movement locus prediction of bent axle iron casting gravitational casting slag group is completed by computer program, and computer program is such as Under：Programming is carried out by development platform of VC++：
4. prediction result
When molten metal and slag group are separated into particle, number of particles is 1000108, and numerical simulation result shows there is slag Group enters cast-internal, according to analog result, optimization casting system design, slag trap is designed, by simulating calculating, slag group again It is distributed in slag trap, is introduced into casting.
Beneficial effect
The present invention has obvious advance compared with background technology, is directed to based on Smoothed Particle Hydrodynamics computational methods Ironcasting gravitational casting slag group simulates with the Solid-fluid Two-phase Flow of molten metal flowing, can effectively simulate the motion of slag group Track, it is predicted before casting, casting system optimization design is carried out according to result of calculation, can effectively avoids slag group from entering casting Inside, it can prevent, reduce and eliminate casting defect in actual casting；By being manufactured experimently to automatic modeling crankshaft casting, and it is based on smooth particle Dynamics calculation method establishes the mathematical modeling of particle interphase interaction, simulates solid-liquid two-phase flow in bent axle casting cycle and flows State, program is write by development platform of computer VS2010, carries out Computing, draws prediction conclusion, shows bent axle weight The track and distribution situation that slag is rolled into a ball in power casting, this Forecasting Methodology is few using equipment, and computational methods are general, reasonable, calculating speed It hurry up, analog result is accurate, is adapted to the movement locus prediction of iron casting gravitational casting slag group, so as to optimize casting system, this Forecasting Methodology is applied to the movement locus prediction of ferrous metal gravitational casting slag group and casting system optimization.
Brief description of the drawings
Fig. 1 is cast-iron crankshaft casting front view
Fig. 2 is cast-iron crankshaft casting top view
Fig. 3 is cast-iron crankshaft casting side view
Fig. 4 is cast-iron crankshaft casting sand mold as-cast condition figure
Shown in figure, list of numerals is as follows：
1. iron casting, 2. longitudinal axis, 3. transverse axis, 4. sand molds, 5. casting gates, 6.L shape die cavities, 7. metals.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described：
It is cast-iron crankshaft casting structure figure shown in Fig. 1,2,3, bent axle generally L-shaped is stepped, by 3 groups of the longitudinal axis 2, transverse axis Into the longitudinal axis 2 and transverse axis 3 are orthogonal, are connected as a single entity.
It is cast-iron crankshaft casting sand mold as-cast condition figure shown in Fig. 4, sand mold 4 is rectangle, and top is provided with casting gate 5, casting Mouth 5 is directed at L-shaped die cavities 6, and connects, and is metal 7 in L-shaped die cavity 6, is cast-iron crankshaft casting after metal cooling.

Claims (2)

  1. A kind of 1. Optimization Prediction method for simulating cast iron sand casting casting cycle, it is characterised in that：
    During cast iron sand casting, under gravity, the Forecasting Methodology of slag group movement locus is as follows：
    (1) the prefabricated cast-iron crankshaft exemplars of
    1. preparing automatic modeling crankshaft casting sand mold, Modeling Material uses furan resin-sand, and zirconium oxide filter screen is set at cast gate；
    2. melting prepares metal
    Cast iron 6kg ± 0.1kg is weighed, is placed in melting kettle, is heated to 1350 DEG C ± 5 DEG C, using carbon trichloride degasification, then Slagging-off, it is stand-by after standing 5min；
    3. gravitational casting
    By metal it is static after by sand mold cast gate inject sand mold die cavity carry out filling type, stand 30min after filling type；
    4. cool down
    After casting, sand mold and its interior casting are embedded in fine sand and are cooled to 25 DEG C；
    5. automatic modeling crankshaft casting is taken out in die sinking
    6. clear up cast(ing) surface
    Cast(ing) surface is cleared up with metallic brush, with mechanically cutting remainder, is then molded with sand paper polishing cast(ing) surface, automatic modeling crankshaft casting；
    (2) establishes slag group movement locus forecast model
    Based on smoothed particle method computational methods, the mathematical modeling of particle interphase interaction is established, finds out casting filling During Solid-fluid Two-phase Flow rule, simulation molten metal slag group flow process；
    Particlized is carried out to molten metal, slag group and border using computer program, the reserved capacity in calculator memory, carried out just The attribute configuration of beginning particle, three kinds of different attribute particles are carried out with the setting of quality, density, initial velocity, viscosity respectively；Configuration After particle property, carry out smooth length L and calculate, time step Δ t setting；
    1. establish the searching method of interacting particles
    The particle of interaction in support region is determined, and is matched, detailed process is as follows：
    1) it is 3 times of smooth length L in one layer of zoning upper berth grid, side length of element size, particle is distributed in each grid Cell element in, and each cell element is numbered；
    2) respectively the particle interacted therewith in the support region of each particle is scanned for matching, in search procedure, only The cell element where than particle, which is numbered, searches for pairing in the range of big cell element, repeat search is avoided, for successful matching in support region Particle, the number consecutively since numbering 1；
    3) after the completion of the calculating of each time step, the pairing of particle is re-started；
    2. on the basis of prediction, after preceding 1/2nd time step, to the speed of metal liquid particles and slag granule, position Put and be modified；
    Comprise the following steps that：
    1) calculating of metal liquid particles and the sub- variable density of slag granule：
    According to Continuous plus equation, density calculating is carried out to any metal liquid particles i, by i particle support regions with its phase The quality of interaction particle and speed difference accumulating operation, metal liquid particles i variable density is obtained, expression formula is such as Under：
    <mrow> <mfrac> <mrow> <msub> <mi>d&amp;rho;</mi> <mi>i</mi> </msub> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <munderover> <mo>&amp;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>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    In formula：ρiParticle i density is represented, t represents the time,Represent the derivative to particle i solution density versus times, ρjTable Show the particle j interacted therewith in particle i support regions density,Represent to being interacted therewith in i particle support regions Particle weighted sum, N represents the sum with the particles of i particle interactions, m in support regionjRepresent particle j quality, Vij Particle i and particle j speed difference is represented,Represent the derivative of smooth function；
    For slag granule, keep density constant in calculating process；
    2) calculating of active force suffered by metal liquid particles and slag granule：
    For metal liquid particles and slag granule, the active force suffered by any i particles is pressure, viscous force, external force, and expression formula is such as Under：
    Fi=Fp+Fn+Fw
    In formula：FiRepresent that particle i is suffered to make a concerted effort, FpRepresent particle i pressures, FnRepresent viscous force suffered by particle i, FwRepresent grain External force suffered by sub- i；
    When the particle of interaction is like particle, it is all metal liquid particles or is all slag granule：
    <mrow> <msub> <mi>F</mi> <mi>p</mi> </msub> <mo>=</mo> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <mo>+</mo> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>&amp;Pi;</mo> <mo>&amp;rsqb;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>F</mi> <mi>n</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>F</mi> <mi>w</mi> </msub> <mo>=</mo> <mi>g</mi> <munderover> <mo>&amp;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> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    In formula：The particle weighted sum to being interacted therewith in i particle support regions is represented, N is represented in support region and i particles The sum of the particle of interaction, mjRepresent particle j quality, pi pjParticle i and j pressure value are represented respectively, pass through solution State equation obtains, ρiRepresent particle i density, ρjThe particle j density interacted therewith in particle i support regions is represented, ξiParticle i dynamic viscosity coefficients are represented, g represents the acceleration of gravity of particle,Represent the derivative of smooth function, rijRepresent grain Alternate position spike between son, rij 2Represent interparticle distance from square, VijParticle i and particle j speed difference is represented, Π represents the people of particle Work viscosity；
    When interacting particles is inhomogeneity particle, metal liquid particles and slag granule are sub, and its pressure term, viscous force and external force are entered The corresponding amendment of row：
    <mrow> <msub> <mi>F</mi> <mi>p</mi> </msub> <mo>=</mo> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mo>&amp;lsqb;</mo> <mfrac> <msub> <mi>p</mi> <mi>i</mi> </msub> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <msub> <mi>p</mi> <mi>j</mi> </msub> </mrow> <msubsup> <mi>&amp;rho;</mi> <mi>j</mi> <mn>2</mn> </msubsup> </mfrac> <mo>-</mo> <mfrac> <mrow> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>&amp;rho;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;rho;</mi> <mi>j</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <mo>&amp;rsqb;</mo> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>F</mi> <mi>n</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>4</mn> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>j</mi> </msub> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&amp;xi;</mi> <mi>j</mi> </msub> <mo>)</mo> <msup> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mn>2</mn> </msup> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>F</mi> <mi>w</mi> </msub> <mo>=</mo> <mi>g</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>j</mi> </msub> <mo>+</mo> <mi>K</mi> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>12</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>6</mn> </msup> </mrow> <mo>)</mo> <mfrac> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>2</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <msub> <mi>W</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>
    In formula：The particle weighted sum to being interacted therewith in i particle support regions is represented, N is represented in support region and i particles The sum of the particle of interaction, mjRepresent particle j quality, pi pjParticle i and j pressure value are represented respectively, pass through solution State equation obtains, and θ is coefficient, value 0.2, ρiRepresent particle i density, ρjRepresent in particle i support regions with its phase The particle j of interaction density, g represent the acceleration of gravity of particle, and K is a constant coefficient, and expression is that interaction force is big Small parameter, rijAlternate position spike between expression particle, rij 2Represent interparticle distance from square,The derivative of smooth function is represented, ξi、ξjParticle i and j dynamic viscosity coefficient, V are represented respectivelyijRepresent particle i and particle j speed difference；
    3) after 1/2nd time steps before, metal liquid particles and slag granule are carried out with the amendment of speed and position, Comprise the following steps that：
    Density, pressure, viscous force, external force, the value of making a concerted effort of metal liquid particles and slag granule are obtained, and then tries to achieve acceleration； After preceding 1/2nd time step, the speed and position of metal liquid particles and slag granule are corrected as follows：
    Metal liquid particles and slag granule existThe erection rate value at moment is equal to its velocity amplitude at the n moment plus acceleration Degree is multiplied by half time step, and metal liquid particles and slag granule existThe correction position value at moment is equal to it in n The positional value at moment plus itsThe erection rate value at moment is multiplied by half time step, and wherein n represents current Calculate the moment；
    3. after a time step, the speed of metal liquid particles and slag granule, position are calculated；
    Metal liquid particles and slag granule the velocity amplitude of n+ time Δts be equal to itsThe erection rate value at moment is multiplied by Two subtract its velocity amplitude at the n moment, metal liquid particles and slag granule is equal to secondly repairing again in the positional value of n+ time Δts Positive position value subtracts its positional value at the n moment, and wherein n represents current and calculates the moment；
    After the completion of one time step calculates, the search pairing and the calculating of particle rapidity, position of particle are re-started, until filling Full die cavity, and obtain the movement locus that slag group is flowed with molten metal；
    4. prediction result
    When molten metal and slag group are separated into particle, number of particles is 1000108, and numerical simulation result shows have slag group to enter Enter cast-internal, according to analog result, optimization casting system design, design slag trap, by simulating calculating, the distribution of slag group again Into slag trap, it is introduced into casting.
  2. 2. a kind of Optimization Prediction method for simulating cast iron sand casting casting cycle according to claim 1, its feature exist In：Sand mold mould (4) is rectangle, and top is provided with casting gate (5), casting gate (5) alignment mould L-shaped die cavity (6), and connects, mould It is Cast Iron Melts (7) in tool L-shaped die cavity (6), is cast-iron crankshaft casting after Cast Iron Melts cooling.
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