CN102274947B - Forecasting method for shrinkage cavity porosity of aluminum alloy low-pressure casting - Google Patents

Abstract

The invention relates to a forecasting method for shrinkage cavity porosity of aluminum alloy low-pressure casting. For overcoming the phenomenon and the shortcoming of the shrinkage cavity porosity of the aluminum alloy low-pressure casting, the method is used for forecasting before casting, thereby being contribute to preventing, reducing and eliminating the phenomenon of the shrinkage cavity porosity in a practical casting process. The forecasting method comprises the following steps: manufacturing a dumbbell-shaped casting piece and adopting a dynamic isolated multiple molten pool judgment, an insolated molten pool equivalent liquid-level decreasing method and a low-pressure feeding method, thereby establishing a calculation model for the shrinkage cavity porosity; programming by taking computer VC++ as a development platform; and performing computer arithmetic, thereby acquiring a forecasting result and providing a theoretical quantized data for the distribution, size and position of the phenomenon of the shrinkage cavity porosity of the aluminum alloy low-pressure casting. The forecasting accuracy is 99%. The forecasting method has the advantages that the adopted equipment is less, the calculation method is general and reasonable, the calculation speed is high and the simulated result is accurate. The forecasting method is an ideal forecasting method for the shrinkage cavity porosity of the aluminum alloy low-pressure casting. The forecasting method is also suitable for forecasting the defects of magnesium alloy/ferrous metal low-pressure casting.

Description

A kind of Shrinkage Prediction method of aluminum alloy low-pressure casting

Technical field

The present invention relates to a kind of Shrinkage Prediction method of aluminum alloy low-pressure casting, belong to the FORECAST AND PREVENTION of low-pressure casting process defective and the technical field of calculating.

Background technology

Low pressure casting is under pressure filling die cavity of liquid metal, to form a kind of method of foundry goods, because used pressure is compared low with pressure casting, be referred to as low pressure casting, its common technology process is: pass into dry pressurized air in airtight crucible, molten metal enters die cavity along stalk by cast gate under the effect of gaseous tension, and the gaseous tension on the liquid level in the maintenance crucible, until foundry goods solidifies fully, after removing the gaseous tension on the molten metal liquid level, the metal that does not solidify in the stalk flows back to crucible has namely finished low pressure casting.

In low pressure casting, because technique arranges improper easy generation shrinkage cavity shrinkage porosity phenomenon, become a large defective of foundry goods, also will reduce the mechanical property of foundry goods, aluminium alloy is one of the most frequently used casting alloy, how to grasp and predict the shrinkage cavity shrinkage porosity phenomenon of the low die casting of aluminium alloy, providing theoretical foundation for the shrinkage cavity shrinkage porosity of prevent and avoid foundry goods is an important research topic.

Summary of the invention

Goal of the invention

The objective of the invention is for the low pressure casting characteristics, shrinkage cavity shrinkage porosity phenomenon in the low die casting of aluminium alloy is predicted, calculate by setting up model and program, prediction foundry goods internal shrinkage shrinkage porosite position, quantity and size are for eliminating and preventing foundry goods shrinkage cavity shrinkage porosity phenomenon that theoretical foundation is provided.

Technical scheme

Shrinkage Prediction method in the aluminum alloy low-pressure casting foundry goods is as follows:

(1) prefabricated aluminium alloy dumb bell sample

1. prepare dumbbell shaped foundry goods sand mold, Modeling Material adopts furan resin-sand, and the cast gate place arranges the zirconia filter screen;

2. prepare molten aluminium alloy

Take by weighing aluminium alloy 6kg ± 0.1kg, place melting kettle, be heated to 730 ℃ ± 5 ℃, adopt the carbon trichloride degasification, subsequently slagging-off, leave standstill 5min after the molten aluminium alloy temperature be down to 700 ℃ ± 5 ℃, stand-by;

3. low pressure casting

The pressurized air of drying is passed in the close crucible, molten aluminium alloy injects the sand mold die cavity along stalk by cast gate and fills type under the effect of gaseous tension, filling time 5s, mold filling pressure 9.88KPa, investing time 10s, crust pressure 9.88KPa, dwell time 300s, dwell pressure 19.88KPa;

4. cooling

After the cast, place natural air to be cooled to 25 ℃ sand mold;

5. unpack and take out foundry goods

Open sand mold, take out the dumbbell shaped foundry goods;

6. clear up cast(ing) surface

Clear up cast(ing) surface, mechanically cutting remainder, sand papering with metallic brush, the moulding of dumbbell shaped foundry goods;

(2) set up the Shrinkage Prediction model

Adopt dynamic Isolated multiple melts criterion, isolate melts equivalence liquid level descent method and low pressure feeding method to set up the computation model of shrinkage cavity shrinkage porosity;

1. adopt computer program that the dumbbell shaped foundry goods is carried out mesh generation, grid number is 18000, obtains Finite Difference Meshes, leaves in the calculator memory; It is discrete that Fourier Heat Conduction partial differential equation in the process of setting is carried out the implicit expression finite difference, adopts computer program accounting temperature field; Adopt the temperature recovery method to process the heat that latent heat discharges;

2. dynamically the Isolated multiple melts method is judged

Adopt dynamic Isolated multiple melts method search foundry goods not solidified connection foundry goods unit in process of setting, set up the computation model basis;

1) when current calculating, whole 18000 grid cells of foundry goods are searched for judgement, the unit solid rate is set the molten bath greater than the unit of the critical solid rate of alloy be numbered 0, the unit solid rate is set the molten bath less than the unit of the critical solid rate of alloy be numbered-1;

2) traversal calculator memory medium casting total-grid unit, an optional molten bath is numbered-1 foundry goods grid cell and carries out isolate melts and judge, give molten bath numbering 1 with this element, then begin six adjacent unit, to seek liquid unit from this element, if its right sided cell is liquid unit, then begin to continue to seek new molten bath in its six adjacent unit from right sided cell and be numbered-1 liquid unit, seek so successively, seek out all connected units, these unit must be in same isolate melts, give the molten bath for these unit and are numbered 1;

3) repeat second step, give successively molten bath numbering 2,3 ..., traversal calculator memory medium casting total-grid unit is not until all the molten bath of unit numbering is till-1;

4) constantly repeat three steps of the first step to the in next one calculating

Dynamically the Isolated multiple melts method can be determined each molten bath number and unit molten bath of living in situation constantly in the process of setting, shrinks for gravity, and by computer program, the molten bath is searched for to lowest part from internal memory medium casting unit highest point; For low pressure casting, by computer program, the molten bath is searched for to highest point from internal memory medium casting unit lowest part;

3. equivalent liquid level amount of contraction method

Equivalence liquid level amount of contraction method is quantitatively to calculate position, shape, the size that shrinkage cavity shrinkage porosity occurs in the casting solidification process, and the volumetric contraction when liquid phase is only considered in the feeding of setting molten metal to solid transformation is not considered the impact of expanding with heat and contract with cold; Set when the solid rate of unit reaches critical solid rate this element forfeiture feeding capacity;

The concrete steps that the equivalence level surface method calculates shrinkage cavity shrinkage porosity are as follows:

The body shrinkage factor was when 1) unit became solid phase from liquid phase

$\mathrm{\β}=\frac{{\mathrm{\ρ}}_S-{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_L}---\left(I\right)$

In the formula: β represents solidification shrinkage rate, ρ _SThe expression solid Density, ρ _LThe expression density of liquid phase;

2) volume shrinkage mass of grid cell in a time step is expressed as

ΔV _j＝β(Δf _Lj)V _j (II)

In the formula: j represents grid cell numbering, Δ V _jExpression is numbered the volume shrinkage mass of unit in a time step of j, Δ f _LjExpression is numbered the liquid fraction changing value of j unit, V _jExpression is numbered the volume of the unit of j, β (Δ f _Lj) V _jResult of calculation represents the volume shrinkage mass of grid cell in a time step;

3) in a time step, the molten bath volume shrinkage mass is expressed as

$\mathrm{\Δ}{V}_P=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{V}_j=\mathrm{\β}\left(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{f}_{\mathrm{Lj}}\right)V_j---\left(\mathrm{III}\right)$

In the formula: p represents the molten bath numbering, and m represents to occur in the p molten bath in the time step number of the grid cell of solid-liquid transformation, Δ V _PThe total volume shrinkage mass in expression p molten bath,

The expression summation,

Result of calculation represents the molten bath volume shrinkage mass;

4) relatively be numbered top middle unit, the molten bath solid rate of p less than unit volume sum and the Δ V of the critical solid rate of alloy _PSize, two kinds of situations appear:

Situation 1: if V _k〉=Δ V _P

In the formula: k represents reticulate layer in the molten bath, V _kExpression is numbered in the molten bath of p in the top i.e. k layer unit solid rate less than the unit volume sum of the critical solid rate of alloy, liquid level still is in the k layer grid, for the unit of unit solid rate less than the critical solid rate of alloy, its unit liquid measure reduces, and unit liquid measure volume can be expressed as

$V_{\mathrm{jk}}=V_{\mathrm{jk}}-\frac{\mathrm{\Δ}{V}_P}{N_k}---\left(\mathrm{IV}\right)$

In the formula: V _JkRepresent that the k layer is numbered the liquid volume of j unit, N _kRepresent that k layer unit solid rate is less than the unit number of the critical solid rate of alloy;

Situation 2: if V _k＜Δ V _P

The unit solid rate becomes dummy cell less than the unit of the critical solid rate of alloy in the k layer, liquid level decline one deck, and the unit solid rate further reduces less than its metal liquid measure of unit of the critical solid rate of alloy in the k-1 layer, and k-1 layer unit liquid measure becomes:

$V_{\mathrm{jk}-1}=V_{\mathrm{jk}-1}-\frac{\mathrm{\Δ}{V}_P-V_k}{N_{k-1}}---\left(V\right)$

In the formula: V _Jk-1Represent that the k-1 layer is numbered the liquid volume of j unit, N _K-1Represent that k-1 layer unit solid rate is less than the unit number of the critical solid rate of alloy;

Be not enough to feeding if can be used for the liquid sum of feeding in k layer and the k-1 layer, then liquid level will drop to the k-2 layer, and disposal route is consistent;

All the other molten bath disposal routes are consistent;

4. the variation of pressure lower critical solid rate

Pressure is selected influential to critical solid rate, pressure and critical solid rate relation are as follows:

1) when pressure 0 to p ' _mBetween the time, the critical solid rate of alloy can be seen in alignment, its equation is:

f _sc＝k′p′+b (VI)

In the formula: p ' expression pressure, p ' _mThe expression critical pressure value, f _ScThe critical solid rate of expression alloy, k ' and b represent two parameters, its value size is determined by experiment;

2) when pressure greater than p ' _mThe time, the variation of critical solid rate is slower, and so long regard it as a horizontal line and process this moment;

5. low pressure liquid level amount of contraction method

According to the low pressure casting characteristics, the upwards feeding of serving as reasons down of its feeding state, adopt low pressure liquid level amount of contraction method to calculate the size of shrink defects, before calculating, do following hypothesis: the volumetric contraction when liquid phase is only considered in the molten metal feeding to solid transformation, do not consider the impact of expanding with heat and contract with cold; When the solid rate of unit reaches critical solid rate, this element forfeiture feeding capacity; Under low-pressure state, molten metal only solidifies under the impact of low pressure, does not consider the impact of gravity;

Concrete steps are as follows:

The body shrinkage factor was when 1) unit became solid phase from liquid phase

$\mathrm{\β}=\frac{{\mathrm{\ρ}}_S-{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_L}---\left(\mathrm{VII}\right)$

2) volume shrinkage mass of grid cell in a time step is expressed as

ΔV _j＝β(Δf _Lj)V _j (VIII)

3) in a time step, the molten bath volume shrinkage mass is expressed as

$\mathrm{\Δ}{V}_P=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{V}_j=\mathrm{\β}\left(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{f}_{\mathrm{Lj}}\right)V_j---\left(\mathrm{IX}\right)$

4) relatively be numbered in the molten bath lowermost layer of p the unit solid rate less than unit volume sum and the Δ V of the critical solid rate of alloy _PSize, two kinds of situations appear:

Situation 1: if V _{K "}〉=Δ V _P

" reticulate layer in the expression molten bath, V in the formula: k _{K "}Expression is numbered in the molten bath of p lowermost layer namely in k " the unit solid rate is less than the unit volume sum of the critical solid rate of alloy in the layer; liquid level still is in k " the layer grid, for the unit of unit solid rate less than the critical solid rate of alloy, its unit liquid measure reduces, and unit liquid measure volume can be expressed as

$V_{{\mathrm{jk}}^{\′\′}}=V_{{\mathrm{jk}}^{\′\′}}-\frac{\mathrm{\Δ}{V}_P}{N_{k^{\′\′}}}---\left(X\right)$

In the formula: V _{Jk "}" layer is numbered the liquid volume of j unit, N to represent k _{K "}" layer unit solid rate is less than the unit number of the critical solid rate of alloy to represent k;

Situation 2: if V _{K "}＜Δ V _P

K " in the layer unit solid rate less than the unit of the critical solid rate of alloy become dummy cell, liquid level rising one deck, k " the unit solid rate further reduces k less than its metal liquid measure of unit of the critical solid rate of alloy in+1 layer "+1 layer of unit liquid measure becomes:

$V_{{\mathrm{jk}}^{\′\′}+1}=V_{{\mathrm{jk}}^{\′\′}+1}-\frac{\mathrm{\Δ}{V}_P-V_{k^{\′\′}}}{N_{k^{\′\′}+1}}---\left(\mathrm{XI}\right)$

In the formula: V _{Jk "+1}Represent k "+1 layer of liquid volume that is numbered the j unit, N _{K "+1}"+1 layer of unit solid rate is less than the unit number of the critical solid rate of alloy to represent k;

Be not enough to feeding if can be used for the liquid sum of feeding among the k " layer and k "+1 layer, then liquid level will rise to k "+2 layers, disposal route is consistent;

All the other molten bath disposal routes are consistent;

6. the Shrinkage Prediction of aluminum alloy low-pressure casting is finished by computer program, and computer program is as follows: carry out programming take VC++ as development platform:

7. predict the outcome

During the Finite Difference Meshes subdivision, the size of mesh opening of dumbbell shaped foundry goods is 4mm * 4mm * 4mm, and dumbbell shaped foundry goods cumulative volume is 1152cm ³, numerical simulation result shows that shrinkage cavity shrinkage porosity has appearred in cast top, volume is 1.715cm ³, owing to be connected with stalk, shrinkage porosity defect of contraction cavity does not appear in the foundry goods bottom, analog result and measured result are in full accord.

Beneficial effect

The present invention has obvious advance compared with prior art, shrinkage cavity shrinkage porosity phenomenon and the drawback that exists for aluminum alloy low-pressure casting, before casting, predict, be conducive in actual casting, prevent, reduce and eliminate the shrinkage cavity shrinkage porosity phenomenon, by preparation dumbbell shaped foundry goods, adopt dynamic Isolated multiple melts to judge, isolate melts equivalence liquid level descent method and low pressure feeding method are set up the computation model of shrinkage cavity shrinkage porosity, take computing machine VC++ as the development platform coding, carry out Computing, draw prediction conclusion, make the distribution situation of the shrinkage cavity shrinkage porosity phenomenon of aluminum alloy low-pressure casting, size, there is a theoretic quantized data position, predictablity rate is 99%, this Forecasting Methodology uses equipment few, computing method are general, rationally, computing velocity is fast, and analog result is accurate, be the Shrinkage Prediction method of very good aluminum alloy low-pressure casting, this Forecasting Methodology also can be used for magnesium alloy, the low pressure casting failure prediction of ferrous metal.

Description of drawings

Fig. 1 is aluminium alloy dumbbell shaped foundry goods front view

Fig. 2 is aluminium alloy dumbbell shaped foundry goods vertical view

Fig. 3 is aluminium alloy dumbbell shaped foundry goods side view

Fig. 4 is dumbbell shaped foundry goods mesh generation figure

Fig. 5 is the constitutional diagram of dumbbell shaped foundry goods low pressure casting

Shown in the figure, list of numerals is as follows:

L, dumbbell length, L ₁, left bell length, L ₂, right bell length, L ₃, be neck length, H ₁, the dumbbell height, H ₂, the height of neck, H ₃, neck width.

1. dumbbell molding flask, 2. dumbbell die cavity, 3. sandbox frame, 4. sandbox frame, 5. sandbox frame, 6. sandbox frame, 7. sprue channel open, 8. aluminum alloy melt, 9. left bell, 10. right bell, 11. necks.

Embodiment

The present invention will be further described below in conjunction with accompanying drawing:

Shown in Fig. 1,2,3, be dumbbell shaped casting structure figure, the dumbbell shaped foundry goods is left and right sides bell symmetrical structure, and the centre is neck 11, and neck 11 left sides are left bell 9, and neck 11 right sides are right bell 10, and left bell, right bell shape, size are identical with volume, and its length is with L, L ₁, L ₂Expression, its height, width H ₁, H ₂, H ₃Expression, its volume is 1152cm ³

Shown in Figure 4, be dumbbell shaped foundry goods mesh generation figure.

Shown in Figure 5, be the constitutional diagram of dumbbell shaped foundry goods low pressure casting, each position, annexation want correct, according to the order of sequence operation, molding flask 1 is rectangle, and periphery is sandbox frame 3,4,5,6, adopts upper, middle and lower three box structures, utilize top box deadweight and foundary weight method fastening, inside is dumbbell shaped die cavity 2, and during cast, aluminum alloy melt 8 enters die cavity 2 by sprue channel open 7, and filling, form the low pressure casting state.

Claims (2)

1. the Shrinkage Prediction method of an aluminum alloy low-pressure casting is characterized in that:

Shrinkage Prediction method in the aluminum alloy low-pressure casting foundry goods is as follows:

1. prefabricated aluminium alloy dumb bell sample

1. prepare dumbbell shaped foundry goods sand mold, Modeling Material adopts furan resin-sand, and the cast gate place arranges the zirconia filter screen;

2. prepare molten aluminium alloy

Take by weighing aluminium alloy 6kg ± 0.1kg, place melting kettle, be heated to 730 ℃ ± 5 ℃, adopt the carbon trichloride degasification, subsequently slagging-off, leave standstill 5min after the molten aluminium alloy temperature be down to 700 ℃ ± 5 ℃, stand-by;

3. low pressure casting

The pressurized air of drying is passed in the close crucible, molten aluminium alloy injects the sand mold die cavity along stalk by cast gate and fills type under the effect of gaseous tension, filling time 5s, mold filling pressure 9.88KPa, investing time 10s, crust pressure 9.88KPa, dwell time 300s, dwell pressure 19.88KPa;

4. cooling

After the cast, place natural air to be cooled to 25 ℃ sand mold;

5. unpack and take out foundry goods

Open sand mold, take out the dumbbell shaped foundry goods;

6. clear up cast(ing) surface

Clear up cast(ing) surface, mechanically cutting remainder, sand papering with metallic brush, the moulding of dumbbell shaped foundry goods;

2. set up the Shrinkage Prediction model

Adopt dynamic Isolated multiple melts criterion, isolate melts equivalence liquid level descent method and low pressure feeding method to set up the computation model of shrinkage cavity shrinkage porosity;

1. adopt computer program that the dumbbell shaped foundry goods is carried out mesh generation, grid number is 18000, obtains Finite Difference Meshes, leaves in the calculator memory; It is discrete that Fourier Heat Conduction partial differential equation in the process of setting is carried out the implicit expression finite difference, adopts computer program accounting temperature field; Adopt the temperature recovery method to process the heat that latent heat discharges;

2. dynamically the Isolated multiple melts method is judged

Adopt dynamic Isolated multiple melts method search foundry goods not solidified connection foundry goods unit in process of setting, set up the computation model basis;

1) when current calculating, whole 18000 grid cells of foundry goods are searched for judgement, the unit solid rate is set the molten bath greater than the unit of the critical solid rate of alloy be numbered 0, the unit solid rate is set the molten bath less than the unit of the critical solid rate of alloy be numbered-1;

2) traversal calculator memory medium casting total-grid unit, an optional molten bath is numbered-1 foundry goods grid cell and carries out isolate melts and judge, give molten bath numbering 1 with this element, then begin six adjacent unit, to seek liquid unit from this element, if its right sided cell is liquid unit, then begin to continue to seek new molten bath in its six adjacent unit from right sided cell and be numbered-1 liquid unit, seek so successively, seek out all connected units, these unit must be in same isolate melts, give the molten bath for these unit and are numbered 1;

3) repeat second step, give successively molten bath numbering 2,3 ..., traversal calculator memory medium casting total-grid unit is not until all the molten bath of unit numbering is till-1;

4) constantly repeat three steps of the first step to the in next one calculating

Dynamically the Isolated multiple melts method can be determined each molten bath number and unit molten bath of living in situation constantly in the process of setting, shrinks for gravity, and by computer program, the molten bath is searched for to lowest part from internal memory medium casting unit highest point; For low pressure casting, by computer program, the molten bath is searched for to highest point from internal memory medium casting unit lowest part;

3. equivalent liquid level amount of contraction method

Equivalence liquid level amount of contraction method is quantitatively to calculate position, shape, the size that shrinkage cavity shrinkage porosity occurs in the casting solidification process, and the volumetric contraction when liquid phase is only considered in the feeding of setting molten metal to solid transformation is not considered the impact of expanding with heat and contract with cold; Set when the solid rate of unit reaches critical solid rate this element forfeiture feeding capacity;

The concrete steps that the equivalence level surface method calculates shrinkage cavity shrinkage porosity are as follows:

The body shrinkage factor was when 1) unit became solid phase from liquid phase

$\mathrm{\β}=\frac{{\mathrm{\ρ}}_S-{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_L}---\left(I\right)$

In the formula: β represents solidification shrinkage rate, ρ _SThe expression solid Density, ρ _LThe expression density of liquid phase;

2) volume shrinkage mass of grid cell in a time step is expressed as

ΔV _j＝β(Δf _Lj)V _j (II)

In the formula: j represents grid cell numbering, Δ V _jExpression is numbered the volume shrinkage mass of unit in a time step of j, Δ f _LjExpression is numbered the liquid fraction changing value of j unit, V _jExpression is numbered the volume of the unit of j, β (Δ f _Lj) V _jResult of calculation represents the volume shrinkage mass of grid cell in a time step;

3) in a time step, the molten bath volume shrinkage mass is expressed as

$\mathrm{\Δ}{V}_P=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{V}_j=\mathrm{\β}\left(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{f}_{\mathrm{Lj}}\right)V_j---\left(\mathrm{III}\right)$

In the formula: p represents the molten bath numbering, and m represents to occur in the p molten bath in the time step number of the grid cell of solid-liquid transformation, Δ V _PThe total volume shrinkage mass in expression p molten bath,

The expression summation,

Result of calculation represents the molten bath volume shrinkage mass;

4) relatively be numbered top middle unit, the molten bath solid rate of p less than unit volume sum and the Δ V of the critical solid rate of alloy _PSize, two kinds of situations appear:

Situation 1: if V _k〉=Δ V _P

In the formula: k represents reticulate layer in the molten bath, V _kExpression is numbered in the molten bath of p in the top i.e. k layer unit solid rate less than the unit volume sum of the critical solid rate of alloy, liquid level still is in the k layer grid, for the unit of unit solid rate less than the critical solid rate of alloy, its unit liquid measure reduces, and unit liquid measure volume can be expressed as

$V_{\mathrm{jk}}=V_{\mathrm{jk}}-\frac{\mathrm{\Δ}{V}_P}{N_k}---\left(\mathrm{IV}\right)$

In the formula: V _JkRepresent that the k layer is numbered the liquid volume of j unit, N _kRepresent that k layer unit solid rate is less than the unit number of the critical solid rate of alloy;

Situation 2: if V _k＜Δ V _P

The unit solid rate becomes dummy cell less than the unit of the critical solid rate of alloy in the k layer, liquid level decline one deck, and the unit solid rate further reduces less than its metal liquid measure of unit of the critical solid rate of alloy in the k-1 layer, and k-1 layer unit liquid measure becomes:

$V_{\mathrm{jk}-1}=V_{\mathrm{jk}-1}-\frac{\mathrm{\Δ}{V}_P-V_k}{N_{k-1}}---\left(V\right)$

In the formula: V _Jk-1Represent that the k-1 layer is numbered the liquid volume of j unit, N _K-1Represent that k-1 layer unit solid rate is less than the unit number of the critical solid rate of alloy;

Be not enough to feeding if can be used for the liquid sum of feeding in k layer and the k-1 layer, then liquid level will drop to the k-2 layer, and disposal route is consistent;

All the other molten bath disposal routes are consistent;

4. the variation of pressure lower critical solid rate

Pressure is selected influential to critical solid rate, pressure and critical solid rate relation are as follows:

1) when pressure is between 0 to p ' m, the critical solid rate of alloy can be seen in alignment, and its equation is:

f _sc＝k′p′+b (VI)

In the formula: p ' expression pressure, p ' _mThe expression critical pressure value, f _ScThe critical solid rate of expression alloy, k ' and b represent two parameters, its value size is determined by experiment;

2) when pressure greater than p ' _mThe time, the variation of critical solid rate is slower, and so long regard it as a horizontal line and process this moment;

5. low pressure liquid level amount of contraction method

According to the low pressure casting characteristics, the upwards feeding of serving as reasons down of its feeding state, adopt low pressure liquid level amount of contraction method to calculate the size of shrink defects, before calculating, do following hypothesis: the volumetric contraction when liquid phase is only considered in the molten metal feeding to solid transformation, do not consider the impact of expanding with heat and contract with cold; When the solid rate of unit reaches critical solid rate, this element forfeiture feeding capacity; Under low-pressure state, molten metal only solidifies under the impact of low pressure, does not consider the impact of gravity;

Concrete steps are as follows:

The body shrinkage factor was when 1) unit became solid phase from liquid phase

$\mathrm{\β}=\frac{{\mathrm{\ρ}}_S-{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_L}---\left(\mathrm{VII}\right)$

2) volume shrinkage mass of grid cell in a time step is expressed as

ΔV _j＝β(Δf _Lj)V _j (VIII)

3) in a time step, the molten bath volume shrinkage mass is expressed as

$\mathrm{\Δ}{V}_P=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{V}_j=\mathrm{\β}\left(\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Δ}{f}_{\mathrm{Lj}}\right)V_j---\left(\mathrm{IX}\right)$

4) relatively be numbered in the molten bath lowermost layer of p the unit solid rate less than unit volume sum and the Δ V of the critical solid rate of alloy _PSize, two kinds of situations appear:

Situation 1: if V _{K "}〉=Δ V _P

" reticulate layer in the expression molten bath, V in the formula: k _{K "}Expression is numbered in the molten bath of p lowermost layer namely in k " the unit solid rate is less than the unit volume sum of the critical solid rate of alloy in the layer; liquid level still is in k " the layer grid, for the unit of unit solid rate less than the critical solid rate of alloy, its unit liquid measure reduces, and unit liquid measure volume can be expressed as

$V_{{\mathrm{jk}}^{\′\′}}=V_{{\mathrm{jk}}^{\′\′}}-\frac{\mathrm{\Δ}{V}_P}{N_{k^{\′\′}}}---\left(X\right)$

In the formula: V _{Jk "}" layer is numbered the liquid volume of j unit, N to represent k _{K "}" layer unit solid rate is less than the unit number of the critical solid rate of alloy to represent k;

Situation 2: if V _{K "}＜Δ V _P

K " in the layer unit solid rate less than the unit of the critical solid rate of alloy become dummy cell, liquid level rising one deck, k " the unit solid rate further reduces k less than its metal liquid measure of unit of the critical solid rate of alloy in+1 layer "+1 layer of unit liquid measure becomes:

$V_{{\mathrm{jk}}^{\′\′}+1}=V_{{\mathrm{jk}}^{\′\′}+1}-\frac{\mathrm{\Δ}{V}_P-V_{k^{\′\′}}}{N_{k^{\′\′}+1}}---\left(\mathrm{XI}\right)$

In the formula: V _{Jk "+1}Represent k "+1 layer of liquid volume that is numbered the j unit, N _{K "+1}"+1 layer of unit solid rate is less than the unit number of the critical solid rate of alloy to represent k;

Be not enough to feeding if can be used for the liquid sum of feeding among the k " layer and k "+1 layer, then liquid level will rise to k "+2 layers, disposal route is consistent;

All the other molten bath disposal routes are consistent;

6. the Shrinkage Prediction of aluminum alloy low-pressure casting is finished by computer program, and computer program is as follows: carry out programming take VC++ as development platform:

7. predict the outcome

During the Finite Difference Meshes subdivision, the size of mesh opening of dumbbell shaped foundry goods is 4mm * 4mm * 4mm, and dumbbell shaped foundry goods cumulative volume is 1152cm ³, numerical simulation result shows that shrinkage cavity shrinkage porosity has appearred in cast top, volume is 1.715cm ³, owing to be connected with stalk, shrinkage porosity defect of contraction cavity does not appear in the foundry goods bottom, analog result and measured result are in full accord.

2. the Shrinkage Prediction method of a kind of aluminum alloy low-pressure casting according to claim 1, it is characterized in that: the low pressure casting of dumbbell shaped foundry goods is finished in molding flask, dumbbell molding flask (1) is rectangle, periphery is sandbox frame (3,4,5,6), adopt upper, middle and lower three box structures, utilize top box deadweight and foundary weight method fastening, inside is dumbbell shaped die cavity (2), during cast, aluminum alloy melt (8) enters die cavity (2) by sprue channel open (7), and filling, form the low pressure casting state.

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