CN100495007C - A Finite Element Based Shrinkage Cavity Defect Prediction Method for Ductile Iron Castings - Google Patents

Abstract

The invention discloses nodular iron casting shrinkage hole failure prediction method based on finite element. It adopts finite element processing simulation ProCAST to analyze nodular iron casting to gain cavity fill and temperature field analysis document, calculate unite solid phase ratio, volume, and eutectic expansion rate, search sealed and isolated areas, calculate whole volume changed value and output, and judge the shrink defects. The invention can process quantification forecast for nodular iron casting shrinkage-hole defect, and offer exact forecast reference for engineering production.

Description

A Finite Element Based Shrinkage Cavity Defect Prediction Method for Ductile Iron Castings

technical field

The invention relates to a method for predicting shrinkage cavity defects of metal materials, in particular to a method for predicting shrinkage cavity defects of ductile iron castings based on finite element technology.

Background technique

The solidification process of ductile iron has both liquid contraction, solidification contraction and graphitization expansion, so the solidification process of ductile iron is actually the result of dynamic superposition of contraction and expansion, so the prediction of shrinkage cavity defects in ductile iron castings is more accurate than that in the solidification process It is more complicated to only consider the solidification shrinkage of cast steel and aluminum castings. The existing shrinkage cavity prediction methods for ductile iron castings are difficult to reflect the dynamic superposition of shrinkage and expansion during the solidification process of ductile iron castings, and most of them only consider graphitization expansion and do not consider the cavity expansion of the mold. Therefore, for ductile iron castings The shrinkage cavity prediction accuracy cannot be guaranteed.

In "Solidification Simulation and Shrinkage Defect Prediction of Iron Mold Sand-Coated Ductile Iron Castings" (Author: Liang Zuojian, Li Guilai, etc., 2001 (5) "Special Casting and Non-ferrous Alloys" -25-27), by establishing the iron mold sand-coated casting solidification process The mathematical model of the simulation uses the dynamic expansion and contraction method (DECAM) and the K·G/√R criterion to predict the shrinkage defects of ductile iron castings, but the prediction accuracy of the defects is not high.

In the patent JP19980122126 19980501 "Solidification Analysis Method for Casting Products" (publication number JP11314152, date of publication: November 16, 1999), in the patent text, a computer and an analysis model composed of many units are used for solidification analysis of castings, and each non- The solid phase shrinkage when the solid phase region is split and the shrinkage volume from the solidification shrinkage are based on the finite difference analysis method, but the graphitization expansion and the cavity expansion caused by the solidification process of ductile iron castings are not considered.

In the patent JP20050121506 20050419 "solidification analysis method" (publication number JP2005329465, date of publication: December 02, 2005), the disclosed analysis method is to calculate the shrinkage of each unit according to the difference of the solid phase ratio of adjacent units, which is only Most of the shrinkage can be estimated, but it is difficult to predict the shrinkage cavity accurately and quantitatively.

Contents of the invention

The purpose of the present invention is to provide a method for predicting shrinkage cavity defects of ductile iron castings based on finite elements, which fully considers the influence of graphitization expansion and cavity expansion in the solidification process of ductile iron castings, and solves the problem of existing prediction methods on ductile iron castings. The problem of poor prediction accuracy of shrinkage cavity defects.

The technical solution adopted in the present invention is a method for predicting shrinkage cavity defects of ductile iron castings based on finite elements, using the breadth-first search method of graphs to process massive finite element data technology in the process of casting process analysis, and calculating from The formation mechanism of the microstructure considers the influence of graphitization expansion and cavity expansion dynamically. By inputting the temperature field results and casting geometry files, setting control parameters and calculation parameters, and performing closed area search, isolated area search, and total cavity expansion calculation, the final result is To obtain the volume change value of the isolated area, the method comprises the following steps:

Step 1. Use finite element-based commercial process simulation ProCAST to conduct mold filling and temperature field analysis on ductile iron castings, obtain the temperature field file and geometry file within the selected step range of the casting, and use viewcast to convert the temperature field file and geometry file The output is a common finite element temperature file format and a geometry file format;

Step 2. Calculate the unit solid phase ratio of each finite element according to the corresponding relationship between temperature and solid phase ratio, and calculate the unit volume from the geometry file according to the unit coordinates, and calculate the eutectic transition according to the chemical composition of the casting Expansion rate;

Step 3. Use the finite element algorithm to process the initial step T=1, where T is the step size. According to the unit solid phase ratio of each finite element calculated above, combine the geometry file data to close the above solid phase ratio field Area search, in the unit of interconnected solid phase rate less than the critical solid phase rate in the casting, the area surrounded by the solid phase rate isosurface is the closed area;

Step 4. Search the isolated area in the closed area obtained by the above search, each closed area corresponds to the corresponding isolated area, and use the method of unit expansion until all the isolated area units belong to a certain isolated area, and search the isolated area at the same time For the boundary elements in contact with the outer surface of the casting, the total cavity expansion value is calculated according to the total surface area of the boundary elements;

Step 5. Go to the next calculation step T=n+1 for looping, where T is the step size, search for the closed area and isolated area of this step, if the isolated area of the previous step derives a new isolated area, then the new isolated area is Number the isolated area, and calculate the volume change and cavity expansion value of the isolated area at the same time, according to this method, until the search of all calculation steps is completed;

Step 6. Calculate the volume change of the searched isolated area according to the total cavity expansion value, unit volume value and eutectic expansion rate calculated above, and output the volume change value of the isolated area. According to the volume change value and The volume of the isolated area and the position of the isolated area can be used to quantitatively judge the shrinkage defects of the casting.

The present invention is also characterized in that:

Closed area search uses the breadth-first search method of graphs to establish a set of methods for searching closed areas, which can accurately and quickly record the size, location and inheritance relationship of closed areas, and proceed according to the following steps:

(1) Firstly, when t=0, assign the number of the closed area to all casting units: -1;

(2) When t=n, all units are judged, the solidification state number of fis>fsc unit is 1, and the solidification state number of fis<fsc unit is 0, fis is the solid fraction of i unit, and fsc is The critical solid fraction of the alloy, the unit of fis>fsc means that the unit has no feeding ability;

(3) Start searching from the highest point of the casting, if the state number of unit V(i, j, k) is 0, use this unit as the search starting unit, and mark this unit as the visited unit;

(4) Visit each unit adjacent to V(i, j, k), if the unit has been visited, then no further processing; otherwise, determine whether the solid phase rate of the unit is less than the critical solid phase rate, If it is less than, store the unit in the array arr[0]. If it is greater than the critical solid phase rate, it means that it has solidified and will not be processed. Search all adjacent units in turn, and record the unvisited unit in the array arr[0] ]middle;

(5) Take out the unvisited unit V(i, j, k) from the array arr[0] sequentially, as the initial search unit, search according to the method in step (4), and record the units less than the critical solid phase ratio To arr[1], until the units recorded in arr[0] are searched;

(6) Take the unvisited unit V(1, j, k) sequentially from the array arr[1], as the initial search unit, search according to the method in step (4), and record the units less than the critical solid phase ratio To arr[0], arr[0] has been cleared before use, until the units recorded in arr[0] have been searched, then skip to (5), and execute repeatedly until the search is completed;

(7) Repeat (3), sequentially assign closed area numbers 2, 3, ..., until t=n, the closed area numbers of all units are not -1;

(8) Repeat steps (1) to (4) at time t _n+1 .

The isolated region search is to let the closed regions existing in the casting carry out mesh expansion in turn. Each closed region can only expand one layer of mesh each time. At the same time, it is stipulated that the mesh that has been expanded into a certain closed region cannot be expanded into other regions. Closed area until all meshes with a solid fraction greater than the critical solid fraction but less than 1 have been divided.

The calculation method of the total cavity expansion value is as follows:

Assuming that the solidification speed of the casting shell unit corresponding to the isolated area is roughly similar, and the effect of each unit on the expansion of the cavity is roughly equal, assuming that there are N casting shell units, and the volume of the unit is Ve(i), then the shell unit i The expression of cavity expansion caused by the increase of solid phase ratio from 0.7 to 1.0 is:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; V</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Assuming that the expansion of the cavity caused by the shell unit has a linear relationship with the increase of its solid phase rate, then when the isolated region is formed, if the solid phase rate of unit i is fs(i), then the unit will cause △Vm from this moment to complete solidification (i) the cavity is enlarged,

fs(i)≤0.7 △Vm(i)＝Vm(i) (2)

fs(i)>0.7 $\mathrm{\&Delta;}{V}_m\left(i\right)=\frac{1.0-f_{\mathrm{the\; s}}\left(i\right)}{1.0-0.7}.V_m\left(i\right)---\left(3\right)$

Calculate △Vm(i) for all shell elements and accumulate them to get:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

This is the total cavity expansion value of the isolated area from the formation to the end of solidification.

The present invention has the following advantages:

1. In the calculation of the solidification process of ductile iron castings, the present invention adopts the dynamic consideration of the influence of graphitization expansion and cavity expansion from the microstructure formation mechanism, and can accurately predict the size and position of shrinkage cavity defects in ductile iron castings. Shrinkage cavity defects provide quantitative prediction, thereby providing support for optimizing casting process design and guiding process practice.

2. The present invention uses the finite element algorithm to search the isolated area during the dynamic superposition process of shrinkage and expansion during the solidification process of ductile iron castings, and obtains the volume change of the isolated area, which can better describe complex molds than the commonly used finite difference algorithm The mold wall, so as to calculate the cavity expansion value more accurately.

3. The present invention uses the breadth-first search method of graphs to process massive finite element data in the process of casting process analysis, which greatly improves the calculation speed and calculation accuracy, saves time for casting process analysis, and shortens the casting process design cycle.

Description of drawings

Fig. 1 is a schematic flow sheet of the inventive method;

Figure 2 is a sample casting process diagram;

Figure 3 is a diagram of the closed area formed during the solidification of the sample;

Figure 4 is the actual anatomical diagram of the sample.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The prediction method of the present invention adopts the breadth-first search method of graphs to process massive finite element data technology in the process of casting process analysis, and dynamically considers the influence of graphitization expansion and cavity expansion from the formation mechanism of microstructure in the calculation of solidification process, through Input the temperature field results and casting geometry files calculated by the commercial finite element software ProCAST, set control parameters and calculation parameters, and output the result files after calculation, which can show the position and size of shrinkage cavity formation in ductile iron castings, so as to achieve prediction The purpose of shrinkage defects. First, use ProCAST software to obtain the temperature field file and geometry file within the selected step range of the casting; then calculate the solid phase ratio of each finite element element according to the corresponding relationship between temperature and solid phase ratio; at the same time, calculate from the geometric file according to the unit coordinates Calculate the unit volume; calculate the eutectic expansion rate during eutectic transformation by inputting the chemical composition of ductile iron; then process the initial step, and use the solid phase rate value to judge whether the initial closed area is formed. Once the closed area is formed, use the unit The method of expansion calculates the initial isolated area, and searches for the boundary elements in contact between the isolated area and the outer surface of the casting, calculates the total cavity expansion value according to the total surface area of the boundary elements, and then transfers to the next simulation step, and performs a cycle to search for this step closed and isolated areas. If a new isolated area is derived from the isolated area of the previous step, number the new isolated area, and calculate the volume change and cavity expansion of the isolated area at the same time; in this way, until the calculation of all calculation steps is completed, Obtain the number and volume change value of the final isolated area. In this process, although each step of calculation needs to search the closed area, the search of the closed area does not need to be carried out at every step, only when the closed area derives a new closed area, the search of the closed area is required, so It greatly saves the simulation time and improves the program efficiency. After completing the isolated area search for all calculation steps, output the isolated area search results and statistical data in the form of a report, output the volume change value of the isolated area, the volume of the isolated area when it starts to form, and the position of the isolated area, thus To quantitatively determine whether there is a shrinkage defect.

As shown in Figure 1, the method includes the following steps:

Step 1. Use the finite element-based commercial process simulation software ProCAST to analyze the filling and temperature field of ductile iron castings, obtain the temperature field file and geometry file, and use the visualization module viewcast of ProCAST software to output the temperature field file and geometry file as General finite element temperature file format and geometry file format such as patran or ideas, this file format is a readable text file;

Step 2. Calculate the unit solid phase ratio of each finite element according to the corresponding relationship between temperature and solid phase ratio, and calculate the unit volume from the geometry file according to the unit coordinates, and calculate the eutectic transition according to the chemical composition of the casting Expansion rate;

The eutectic expansion rate can be calculated by inputting the chemical composition of ductile iron and referring to the eutectic solidification curve of ductile iron.

Step 3. Use the finite element algorithm to process the initial step T=1, where T is the step size. According to the unit solid phase ratio of each finite element calculated above, combine the geometry file data to close the above solid phase ratio field Area search, using the breadth-first search method of the graph, can automatically find out the units in the casting whose interconnected solid phase ratio is less than the critical solid phase ratio, and stipulate that the solid phase ratio (critical solid phase ratio) when the feeding molten iron stops flowing is 0.7 , the area surrounded by the solid fraction isosurface is the closed area;

The present invention uses the breadth-first search method of the graph to search the closed area, and establishes a set of methods for searching the closed area, which can accurately and quickly record the size and position of the closed area, as well as the inheritance relationship. Here, a single closed area is searched, The search speed is greatly improved, and all units that meet the conditions can be searched, and there will be no missed search. The specific search method is as follows:

(1) Firstly, when t=0, assign the number of the closed area to all casting units: -1;

(2) When t=n, all units are judged, the solidification state number of fis>fsc unit is 1, and the solidification state number of fis<fsc unit is 0, fis is the solid fraction of i unit, and fsc is The critical solid fraction of the alloy, the unit of fis>fsc means that the unit has no feeding ability;

(3) Start searching from the highest point of the casting (generally the riser), if the state number of the unit V(i, j, k) is 0, use this unit as the starting unit of the search, and mark this unit as the visited unit ;

(4) Visit each unit adjacent to V(i, j, k), if the unit has been visited, then no further processing; otherwise, determine whether the solid phase rate of the unit is less than the critical solid phase rate, If it is less than, store the unit in the array arr[0]. If it is greater than the critical solid phase rate, it means that it has solidified and will not be processed. Search all adjacent units in turn, and record the unvisited unit in the array arr[0] ]middle;

(5) Take out the unvisited unit V(i, j, k) from the array arr[0] sequentially, as the initial search unit, search according to the method in step (4), and record the units less than the critical solid phase ratio To arr[1], until the units recorded in arr[0] are searched;

(6) Take the unvisited unit V(1, j, k) sequentially from the array arr[1], as the initial search unit, search according to the method in step (4), and record the units less than the critical solid phase ratio To arr[0], arr[0] has been cleared before use, until the units recorded in arr[0] have been searched, then skip to (5), and execute repeatedly until the search is completed;

(7) Repeat (3), sequentially assign closed area numbers 2, 3, ..., until t=n, the closed area numbers of all units are not -1;

(8) Repeat steps (1) to (4) at time t _n+1 .

Step 4. Search for the isolated area in the closed area obtained by the above search, and search for the boundary elements in contact with the outer surface of the casting at the same time, and calculate the total cavity expansion value according to the total surface area of the boundary elements;

The isolated area refers to the space area where the solid phase rate of the closed area and its surroundings is greater than the critical solid phase rate but less than 1 when the closed area is just formed. It is difficult to reasonably divide the space region whose solid phase ratio is greater than the critical solid phase ratio but less than 1 by the method of searching isolated regions of ductile iron castings. Since nodular cast iron is solidified in a paste state, in general, when a closed area is formed, the space area with a solid phase rate greater than the critical solid phase rate but less than 1 exists in a large range, and the gradient of the solid phase rate in the area is small, and the distance between the closed area and the closed area The difference in the solid phase ratio between different places is not obvious, which also causes great difficulties for the reasonable division of the isolated area. For this reason, the isolated area can be divided according to the nearest principle: that is, for a unit whose solid phase rate is greater than the critical solid phase rate but less than 1, its volume change will be the closest to which closed area. If an area has the greatest influence, then it should be classified as this area. However, in order to accurately evaluate which closed area is closest to each unit with a solid phase ratio greater than the critical solid phase ratio but less than 1, the shortest distance from the unit to each closed area must be obtained, which requires a lot of calculation work. In order to avoid a large amount of calculation, the present invention uses the following method to search for isolated regions:

Let the closed areas existing in the casting undergo grid expansion in turn, and each closed area can only expand one layer of grid each time, and it is stipulated that the grid that has been expanded into a certain closed area cannot be expanded into other closed areas until All the meshes whose solid phase ratio is greater than the critical solid phase ratio but less than 1 are divided. This method will not cause large calculation errors when the mesh size of the casting is not large, and can meet the accuracy required by actual engineering.

The calculation method of the total cavity expansion value is as follows:

The cavity expansion value Vm due to the expansion of the casting shell is: △t×casting surface area, where △t is the distance that the casting surface moves outward due to the expansion of the casting shell. This value can be determined through experiments. In Vm, the feeding channel is closed The part that occurs later is recorded as △Vm, and △Vm will directly enter the calculation of the net volume change of the isolated area.

The calculation method of ΔVm is as follows:

Except for the outer sharp corner and cold iron, the solidification speed of the shell unit of the casting part corresponding to the isolated area is roughly close. Assuming that the solidification speed of the casting shell unit corresponding to the isolated area is roughly similar, the effect of each unit on the expansion of the cavity The effect is roughly equivalent. Assuming that there are N casting shell units in total, and the volume of the unit is Ve(i), then the cavity expansion caused by the solid phase ratio of shell unit i increasing from 0.7 to 1.0 can be expressed as for:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; V</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Assuming that the expansion of the cavity caused by the shell unit has a linear relationship with the increase of its solid phase rate, then when the isolated region is formed, if the solid phase rate of unit i is fs(i), then the unit will cause △Vm from this moment to complete solidification (i) the cavity is enlarged,

fs(i)≤0.7 △Vm(i)=Vm(i) (2)

fs(i)>0.7 $\mathrm{\&Delta;}{V}_m\left(i\right)=\frac{1.0-f_{\mathrm{the\; s}}\left(i\right)}{1.0-0.7}.V_m\left(i\right)---\left(3\right)$

Calculate △Vm(i) for all shell elements, and then accumulate, get:

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

This is the cavity expansion value from the formation of the isolated area to the end of solidification.

In order to calculate the cavity expansion more accurately, the total cavity expansion value caused by the expansion of the casting shell can be calculated as the surface area of the casting shell contained in the isolated area × Δt when the first closed area of the casting is just formed.

For the isolated area derived from the initial isolated area one or more times, the cavity expansion from its formation to the end of solidification can also be calculated according to the above method. Each shell unit of the derived isolated area must be the shell unit of the upper-level isolated area, and the expansion of the cavity caused by the increase of the solid phase ratio from 0.7 to 1 is unchanged, but the solid phase of the shell unit at this time The rate has only increased. Therefore, the cavity expansion caused by each unit of the shell of the derived isolated area from the formation to the end of solidification is calculated by formulas (3) and (4), and the sum is the total cavity expansion value of the derived area from the formation to the end of solidification.

Step 5, then turn to the next calculation step T=n+1 for looping, search for the closed area and isolated area of this step, if a new isolated area is derived from the isolated area of the previous step length, then carry out the new isolated area Number, calculate the volume change and cavity expansion value of the isolated area at the same time; follow this method until the search of all calculation steps is completed.

Step 6. Calculate the volume change of the searched isolated region based on the total cavity expansion value, unit volume value and eutectic expansion rate calculated above, and output the volume change value of the isolated region and the volume when the isolated region begins to form The quantity and the position of the isolated area can be used to quantitatively judge whether there is a shrinkage defect.

The present invention calculates the volume change in the solidification process of ductile iron castings. For castings with complex shapes, the closed area initially generated during the solidification process often splits into multiple closed areas as the solidification process proceeds, that is, several closed areas are derived from one closed area. a closed area. Similarly, derivation relations also exist in isolated areas. The present invention judges the shrinkage defect based on the net volume change of the isolated region that is no longer split.

In order to improve the simulation accuracy of the solidification process of ductile iron and achieve the purpose of quantitatively and accurately predicting the shrinkage cavity defects of ductile iron castings, the present invention deduces the dynamic search process of solidification and shrinkage of ductile iron from the aspect of solidification and crystallization, by analyzing the temperature field calculated by commercial software Data processing solves the problem of analyzing and judging defects in process simulation, and provides an exact prediction basis for actual engineering production.

The following provides an example of applying the method of the present invention to test samples.

Fig. 2 shows the sample pouring process diagram for verification, for these samples, there is a closed liquid phase region as shown in Fig. 3 in the solidification process, and the calculation of the volume change of these isolated regions is applied by the method of the present invention , the volume change of the isolated area for sample a is -0.83×10 ^-6 m ³ , and the volume change of the isolated area for sample b is -0.26×10 ^-6 m ³ , it can be seen that both samples a and b will appear Shrinkage cavity defect, and the size of the defect is a larger than b, and for the sample C whose volume change is 0.12×10 ^-6 m ³ , there will be no shrinkage cavity defect, which is consistent with the result of the actual casting sample, as shown in Figure 4 As shown, it better reflects the shrinkage cavity of the sample.

Claims (4)

1. nodular iron casting shrinkage cavity defect Forecasting Methodology based on finite element, the BFS (Breadth First Search) method of employing figure is handled the magnanimity finite element data technique in the Casting Technological Analysis process, in calculating, process of setting forms the influence that mechanism considers that dynamically graphitization expansion and die cavity enlarge from microstructure, by input temp field result and how much files of foundry goods, controlled variable and calculating parameter are set, carry out closed area search, isolated region search and total die cavity and enlarge calculating, finally draw isolated region volume change value, it is characterized in that this method may further comprise the steps:

Step 1, employing are filled type and temperature field analysis based on the commercial processing simulation ProCAST of finite element to nodular iron casting, obtain temperature field file and how much files in the selected step-length scope of this foundry goods, and temperature field file and how much files are output as common finite element temperature file layout and how much file layouts with viewcast;

Step 2, calculate the unit solid rate of each finite element, go out unit volume by how much files according to the unit coordinate Calculation simultaneously, the eutectic expansivity when calculating eutectic transformation according to the chemical constitution of this foundry goods according to the corresponding relation of temperature and solid rate;

Step 3, employing finite element algorithm are handled initial step T=1, wherein T is a step-length, the unit solid rate of each finite element that draws according to aforementioned calculation, carry out the closed area search in conjunction with the solid rate field that the geometry file data constitutes the unit solid rate by above-mentioned each finite element, in the unit of the solid rate that is interconnected in the foundry goods less than critical solid rate, be the closed area by this solid rate contour surface area surrounded that is interconnected;

Step 4, in the closed area that above-mentioned search obtains, carry out isolated region search, the all corresponding corresponding isolated region in each closed area, utilize the way of unit expansion, all belong to some isolated regions up to all isolated region unit, the boundary element that contacts with cast outer surface of searching isolated zone simultaneously calculates total die cavity expansion value according to the total surface area of boundary element;

Step 5, change the next step T=n+1 that calculates over to and circulate, wherein T is a step-length, search for the closed area and the isolated region in this step, if the isolated region that previous step is long derives from the isolated region that makes new advances, then new isolated region is numbered, calculate the volume change and the die cavity expansion value of this isolated region simultaneously, according to said method, up to finishing the search that all calculate the step;

Step 6, the total die cavity expansion value, unit volume value and the eutectic expansivity that draw according to aforementioned calculation are carried out the calculating of volume change to the isolated region that search obtains, and with isolated region volume change value output, the volume when beginning to form according to this volume change value and isolated region, the position of isolated region can be carried out quantification to the shrink defects of this foundry goods and be judged.

2. according to the described Forecasting Methodology of claim 1, it is characterized in that the search of described closed area is the BFS (Breadth First Search) method of employing figure, set up the method for a cover search closed area, can write down size, position and the inheritance of closed area quickly and accurately, carry out according to the following steps:

(1) at first at t _n, give the closed area numbering to all foundry goods unit :-1 at=0 o'clock;

(2) t _nDuring=n, to whole unit judges, with fis〉to decide curdled appearance number be 1 for the unit of fsc, it number is 0 that curdled appearance is decided in the unit of fis＜fsc, fis is the solid rate of i unit, and fsc is the critical solid rate of alloy, fis〉unit of fsc means this element and do not have feeding capacity;

(3) begin search from the foundry goods highest point, if unit V (i, j, state k) number are 0, and this unit as the search start element, and is indicated this unit and is addressed location;

(4) (k) adjacent each unit is if the accessed mistake in this unit so no longer processes for i, j with V in visit; Otherwise, whether the solid rate of judging this unit is less than critical solid rate, if less than, then this unit is deposited in array arr[0] in, if greater than critical solid rate, illustrate to solidify then not deal with, successively the search of all adjacent cells finished, and addressed location is not recorded array arr[0] in;

(5) from array arr[0] take out successively not addressed location V (i, j, k), as initial search unit, search for according to method in the step (4), and less than the unit record of critical solid rate to arr[1], up to arr[0] in all searched the finishing in unit of record;

(6) from array arr[1] take out not addressed location V (i successively, j, k), as initial search unit, search for according to method in the step (4), and handle arrives arr[0 less than the unit record of critical solid rate], arr[0 before using] be cleared, up to arr[1] in all searched the finishing in unit of record, jump to (5) subsequently, carry out repeatedly, finish up to search;

(7) repeat (3), give successively closed area numbering 2,3 ..., when t=n, all the closed area of unit numbering is not-1;

(8) at t _N+1Moment repeating step (1)～(4).

3. according to the described Forecasting Methodology of claim 1, it is characterized in that, the search of described isolated region is to allow the closed area that exists in the foundry goods carry out grid in turn expand, one deck grid can only be expanded in each each closed area, regulation has expanded the grid into a certain closed area simultaneously, can not expand again into other closed areas, till all solid rates have been divided greater than critical solid rate but less than 1 grid.

4. according to the described Forecasting Methodology of claim 1, it is characterized in that the computing method of described total die cavity expansion value are as follows:

The setting rate of supposing the foundry goods outer cover unit corresponding with isolated region is roughly close, it is roughly suitable that each unit enlarges role to die cavity, if total N of foundry goods outer cover unit, the volume of unit is Ve (i), and then the solid rate of outer cover unit i rises to the die cavity that causes 1.0 the process from 0.7 and enlarges expression formula and be:

$V_m\left(i\right)=\frac{V_e\left(i\right)}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{V}_e\left(i\right)}.V_m---\left(1\right)$

Wherein: V _mFor the die cavity expansion value of foundry goods shell expansion generation, generally by test determination; V _m(i) rise to the die cavity expansion value that causes 1.0 the process for the solid rate of foundry goods outer cover unit i from 0.7.

It is linear to suppose that the caused die cavity of outer cover unit enlarges with its solid rate growth, then when isolated region forms, if the solid rate of unit i is f _s(i), then this unit will cause Δ V from this moment to solidifying fully _m(i) die cavity enlarges,

f _s(i)≤0.7 ΔV _m(i)＝V _m(i) (2)

f _s(i)>0.7 ${\mathrm{\&Delta;V}}_m\left(i\right)=\frac{1.0-f_s\left(i\right)}{1.0-0.7}.V_m\left(i\right)---\left(3\right)$

All outer cover units are calculated Δ V _m(i), add up:

${\mathrm{\&Delta;V}}_m=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&Delta;V}}_m\left(i\right)---\left(4\right)$

This promptly this isolated region self-forming to total die cavity expansion value of solidifying end.

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