阅读说明：本技术 一种测试金属液流动性的方法 (Method for testing fluidity of metal liquid ) 是由 胡聘聘 李妍佳 张楚博 郭丰伟 丁盼 汤鑫 张明军 肖程波 于 2021-09-01 设计创作，主要内容包括：本发明技术方案设计出结构上包含多个非等厚叶片整体涡轮叶盘模拟件模具,制备出同时含有多个不同厚度叶片的整体涡轮叶盘模拟件的精密铸造型壳,浇注后通过观察不同厚度叶片的充型完整性和充型面积来评价金属液的流动性,包括评估同一合金在不同浇注工艺条件下的充型能力,为发动机结构设计提供技术支持。与传统的“螺旋法”相比,该发明技术方案更加接近工程实际,可以更加准确地模拟实际生产过程中零部件精密铸造过程的充型完整性,为评价产品的可制造性提供准确的设计依据。(According to the technical scheme, a mould of the integral turbine blade disc simulation part structurally comprising a plurality of non-uniform-thickness blades is designed, a precision casting shell of the integral turbine blade disc simulation part simultaneously comprising a plurality of blades with different thicknesses is prepared, and after pouring, the fluidity of molten metal is evaluated by observing the filling integrity and the filling area of the blades with different thicknesses, wherein the filling capacity of the same alloy under different pouring process conditions is evaluated, and technical support is provided for the structural design of an engine. Compared with the traditional spiral method, the technical scheme of the invention is closer to the engineering practice, can more accurately simulate the mold filling integrity of the precision casting process of the parts in the practical production process, and provides accurate design basis for evaluating the manufacturability of products.)

1. A method of testing the fluidity of a metal liquid, characterized by: the method comprises the steps of firstly preparing an investment pattern, wherein the investment pattern comprises a cylinder (1), blades (2) with different thicknesses are uniformly distributed around the cylinder (1) along the height vertical direction, then preparing a casting shell (3) by using the investment pattern, thin-wall cavities formed by the blades (2) with different thicknesses are distributed on the periphery of an inner cavity of the casting shell (3), a metal to be tested is cast into the casting shell (3) after being melted, and the filling degree of the metal to be tested in the thin-wall cavities is observed after cooling so as to test or compare the fluidity of the metal to be tested.

2. The method of testing fluidity of metal liquid according to claim 1, wherein: the blade (2) is flat and is coincided with the middle surface parallel to the two surfaces and the section along the central axis of the column body (1).

3. The method of testing fluidity of metal liquid according to claim 2, wherein: the blades (2) are uniformly distributed on the outer circumferential surface of the cylinder (1) at intervals of 20 degrees, each blade (2) is the same as the blades at the rotational symmetry position of 180 degrees, the number of the blades (2) is 18, and the blades are divided into A, B two groups.

4. A method for testing fluidity of metal liquid according to claims 1 and 3, wherein: a, B the width of the blades in the two groups of blades (2) along the radial direction of the cylinder (1) is 50mm, the height along the axial direction of the cylinder (1) is 100mm, and the thickness variation range is 1 mm-5 mm.

5. The method of testing fluidity of metal liquid according to claim 4, wherein:

the thickness of each of the A, B two groups of blades (2) is 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm and 5.0mm in sequence.

6. The method of testing fluidity of metal liquid according to claim 1, wherein: the diameter of the column body (1) is 100mm, and the height of the column body is 100 mm.

7. The method of testing fluidity of metal liquid according to claim 1, wherein: in the preparation process of the shell (3), the used materials, the coating process and the roasting process are unified.

8. The method of testing fluidity of metal liquid according to claim 1, wherein: when the metal to be measured is cast on different shells (3), the heating temperature of the shells, the heat preservation time of the shells, the casting temperature of molten metal, the smelting and casting speed, the smelting vacuum degree, the size of a crucible for casting, the distance between the shells and the crucible and the casting inclination angle are unified.

Technical Field

The invention relates to a method for testing fluidity of metal liquid, belonging to the technical field of precision casting.

Background

The precision casting high-temperature alloy has the advantages of net forming, low cost, high efficiency and the like, and is widely applied to the field of aeroengines and gas turbines to prepare parts such as turbine blades, guide blades, integral turbine blade discs, guide guides, casings, nozzles and the like which work at high temperature and high pressure. With the improvement of the thrust-weight ratio of an aeroengine, the structure of a high-temperature alloy precision casting is more and more complex, the alloy system is more and more abundant, and the evaluation on the fluidity of the alloy and the evaluation on the casting and filling capacity are more and more important. However, the conventional casting fluidity evaluation is mostly based on cast steel, cast iron, aluminum alloy, magnesium alloy, copper alloy and the like, and the applicability to precision casting high-temperature alloy of vacuum induction melting is not strong, so that the evaluation of the fluidity and the shell mold filling capability of the high-temperature alloy is in a development lag state. The research on the fluidity test of the metal liquid of the precision casting high-temperature alloy is limited, no uniform industrial specification exists, and the fluidity and the mold filling capacity of the high-temperature alloy are lack of data support, so that the test is performed based on experience and a trial and error mode in the traditional engine material selection and structure design and precision casting process design, higher test cost is brought, and the test period is prolonged. In order to reduce the development cost of an engine and shorten the design verification period, a quantitative test method is urgently needed to be formed and popularized and applied in the aspect of high-temperature alloy fluidity, and quantitative data support is provided for the design of high-temperature alloy precision castings such as turbine disks, blades and casings of the engine.

Disclosure of Invention

The invention provides a method for testing the fluidity of metal liquid, which is designed and provided aiming at the prior art, and aims to provide a practical and effective quantitative evaluation basis for the casting fluidity and the mold filling capacity of the high-temperature alloy by the method, and form a data support with practical engineering guidance significance in the processes of material research and development, engine structure design and precision casting process design of the high-temperature alloy.

The purpose of the invention is realized by the following technical scheme:

the method for testing the fluidity of the metal liquid comprises the steps of firstly preparing an investment pattern which comprises a cylinder 1, uniformly distributing blades 2 with different thicknesses around the cylinder 1 along the height vertical direction as shown in figure 1, then preparing a casting shell 3 by using the investment pattern, distributing thin-wall cavities formed by the blades 2 with different thicknesses around the inner cavity of the shell 3 as shown in figure 2, casting the molten metal to be tested into the shell 3, and observing the filling degree of the metal to be tested in the thin-wall cavities after cooling so as to test or compare the fluidity of the metal to be tested.

In implementation, the blades 2 are flat plates, and the middle surfaces parallel to the two surfaces are overlapped with the cross sections along the central axis of the column body 1, so that molten metal can be stably and uniformly injected into each blade at the same time.

In implementation, the blades 2 are uniformly distributed on the outer circumferential surface of the column body 1 at intervals of 20 degrees, and each blade 2 is the same as the blade at the rotational symmetric position of 180 degrees, so that the test error caused by uneven shell placement or uneven pouring is avoided; the number of the blades 2 is 18, and the blades are divided into A, B two groups.

Further, the A, B two sets of blades 2 have a width of 50mm along the radial direction of the column 1, a height of 100mm along the axial direction of the column 1, and a thickness variation range of 1 mm-5 mm.

Further, the thickness of each of the A, B two groups of blades 2 is 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm and 5.0mm in sequence.

In practice, the column 1 has a diameter of 100mm and a height of 100 mm.

In the implementation, in the preparation process of the shell 3, in order to ensure the reliability of the evaluation result, parameters influencing the fluidity of the metal liquid, such as used materials, a coating process, a roasting process and the like, are unified, so that shells with consistent quality are prepared.

In the implementation, when the metal to be measured is cast on different shells 3, in order to ensure the reliability of the evaluation result, all parameters influencing the fluidity of the metal liquid, such as the heating temperature of the shells, the heat preservation time of the shells, the pouring temperature of the metal liquid, the melting and pouring speed, the melting vacuum degree, the size of the crucible for pouring, the distance between the shells and the crucible, the pouring inclination angle and the like, are unified, and the consistency of the melting and pouring is ensured. Preferably, the pouring is carried out in an automatic pouring mode, so that test errors caused by differences of pouring methods of operators are eliminated.

And after the pouring is finished, cleaning the shell, counting the filling integrity of the blade, and calculating the filling area percentage of the incomplete blade to evaluate the flowability. Counting the number of the thinnest blades with complete filling as an integral part of fluidity, counting the number of the blades without complete filling as '0', counting the percentage of the filling area of the thickest blades with incomplete filling as a first decimal part of fluidity, counting the percentage of the filling area of the second thickest blades with incomplete filling as a second decimal part of fluidity, analogizing, then superposing, and evaluating the fluidity. (according to the experimental accuracy requirement, the evaluation after decimal point can be carried out, for example, if the thinnest filled leaf is 4#, the integral part is counted as 4, if the filling area of the 5# leaf accounts for 82% of the whole leaf, then 0.82 is added, if the filling area of the 6# leaf accounts for 71% of the whole area, then 0.071 is added, if the filling area of the 7# leaf accounts for 55% of the whole area, then 0.0055 is added, if the filling area of the 8 th leaf accounts for 45% of the whole area, then 0.00045 … … is added, and so on

In order to eliminate errors caused by uneven metal flow during casting, two symmetrical parts are calculated respectively during evaluation, and the average value of the two parts is taken as the fluidity of the alloy to be tested. The fluidity of the alloy is 0 when all the blades can not be filled, and the fluidity of the alloy is 9 when all the blades can be filled completely, and the higher the measured value is, the higher the fluidity of the alloy is.

The method can be used for evaluating the fluidity of a certain alloy under the conditions of a specific shell and a smelting and pouring process, can also be used for evaluating the fluidity of the same alloy under the conditions of different shells or smelting and pouring processes, provides a basis for the structural design of an engine, and can also be used for guiding the precise casting shell and the smelting and pouring process to be formulated according to the fluidity evaluation result after the structural design of the high-temperature alloy precise casting is finished.

Aiming at an integral turbine blade disc of an aircraft engine, the technical scheme of the invention designs an integral turbine blade disc simulation piece mold structurally comprising a plurality of non-uniform-thickness blades, prepares a precision casting shell of the integral turbine blade disc simulation piece simultaneously comprising a plurality of blades with different thicknesses, and evaluates the fluidity of molten metal by observing the filling integrity and the filling area of the blades with different thicknesses after pouring, including evaluating the filling capacity of the same alloy under different pouring process conditions and providing technical support for the structural design of the engine. Compared with the traditional spiral method, the technical scheme of the invention is closer to the engineering practice, can more accurately simulate the mold filling integrity of the precision casting process of the parts in the practical production process, and provides accurate design basis for evaluating the manufacturability of products.

Drawings

FIG. 1 is a schematic structural diagram of the investment pattern in the method of the present invention

FIG. 2 is a schematic view of the structure of the shell in the method of the present invention

Detailed Description

The technical scheme of the invention is further detailed in the following by combining the drawings and implementation:

example 1:

in order to evaluate the fluidity of the K4169 superalloy molten metal under normal casting conditions, a dummy for evaluating the fluidity of the precision cast superalloy molten metal was designed according to the claims, and then a ceramic shell was prepared using a standard alternating shell-and-shell process, with a shell thickness of 7 and a half, followed by melt casting. Putting the shell into a furnace at room temperature during smelting and casting, heating to 1150 ℃ at the speed of 30 ℃/min, and then preserving heat for 20 min; the casting temperature of the molten metal is 150 ℃ above the liquidus; the blanking weight is 15Kg, and an M-22 crucible is adopted for pouring; controlling the pouring time to be 1.5S; the casting vacuum degree is 0.2 Pa. And (5) cleaning shells and calculating after pouring. Through observation and calculation, in the A group of blades, 1-8 # blades are completely filled, and the filling area of the 9# blade accounts for 62% of the area of the whole blade, and the fluidity calculation process based on the A group of blades is as follows: the thinnest blade with complete filling is the No. 8 blade, so the integral part is taken as 8; the thickest blade with incomplete filling is a No. 9 blade, the filling area of the blade accounts for 62% of the whole blade area, so that the count is 0.62, and the fluidity A is 8+0.62 is 8.62; in the B group of blades, 1-8 # blades are all completely filled, and the filling area of 9# blades accounts for 68% of the area of the whole blade, so that the fluidity calculation process based on the B group of blades is as follows: the thinnest blade with complete filling is the No. 8 blade, so the integral part is taken as 8; the thickest blade with incomplete filling is a No. 9 blade, the filling area of the blade occupies 68% of the whole blade area, so that the count is 0.68, and the fluidity B is 8+0.68 which is 8.68; finally, the average values of the groups a and B were obtained, and the average fluidity was (8.62+8.68)/2 was 8.65. The fluidity of the K4169 alloy under this process condition was 8.65.

Example 2:

to evaluate the flowability of the K4169 superalloy metal melt under fine grain casting conditions, a dummy for evaluating the flowability of the precision cast superalloy metal melt was designed according to the claims, followed by the preparation of a ceramic shell with a thickness of 7 and a half layers using a standard alternating shell-making process, followed by melt casting. Putting the shell into a furnace at room temperature during smelting and casting, heating to 1050 ℃ at the speed of 30 ℃/min, and then preserving heat for 20 min; the casting temperature of the molten metal is selected to be 70 ℃ above the liquidus line; the blanking weight is 15Kg, and an M-22 crucible is adopted for pouring; controlling the pouring time to be 1.5S; the casting vacuum degree is 0.2 Pa. And (5) cleaning shells and calculating after pouring. Through observation and calculation, in the A group of blades, 1-6 # blades are completely filled, the filling area of 7# blades accounts for 91% of the whole blade area, the filling area of 8# blades accounts for 75% of the whole blade area, and the filling area of 9# blades accounts for 52% of the whole blade area, so that the fluidity process is calculated based on the A group of blades as follows: the thinnest leaf number with complete filling is 6# leaf, so the integral part is 6; the thickest blade with incomplete filling is a No. 7 blade, and the filling area of the blade accounts for 91 percent of the whole blade area, so that the count is 0.91; the incomplete-filling second-thickness blade is an 8# blade, and the filling area of the incomplete-filling second-thickness blade accounts for 75% of the area of the whole blade, so that the count is 0.075; the incomplete filling third blade thickness is blade # 9, the filling area of which is 52% of the total blade area, so the count is 0.0052, and the fluidity a is 6+0.91+0.075+0.0052 is 6.99. In B group's blade, 1 ~ 6# blade is all filled type complete, 7# blade fills type area and accounts for whole blade area 93%, 8# blade fills type area and accounts for whole blade area 79%, 9# blade fills type area and accounts for whole blade area 55%, then based on B group's blade calculation mobility process as follows: the thinnest leaf number with complete filling is 6# leaf, so the integral part is 6; the thickest blade with incomplete filling is a No. 7 blade, and the filling area of the blade accounts for 89% of the whole blade area, so that the count is 0.89; the second thick blade with incomplete mold filling is an 8# blade, and the mold filling area of the blade accounts for 66% of the whole blade area, so that the count is 0.066; the incomplete-filling third-thickness blade is the 9# blade, the filling area of the incomplete-filling third-thickness blade accounts for 39% of the whole blade area, so the count is 0.0039, and the fluidity B is 6.9599 between 6+0.89+0.066+ 0.0039. Finally, the average values of the groups a and B were obtained, and the average fluidity was (6.99+6.9599)/2 was 6.975. The flowability of the K4169 alloy under the process conditions was 6.975. As can be seen from comparison of examples 1 and 2, the higher the casting temperature is, the higher the molten metal filling ability is under the same conditions.

Example 3:

to evaluate the flowability of the K447A superalloy metal melt under fine grain casting conditions, a dummy block for evaluating the flowability of a precision cast superalloy metal melt was designed according to the claims, followed by the preparation of a ceramic shell with a shell thickness of 7 and a half by standard alternating shell casting process, followed by melt casting. Putting the shell into a furnace at room temperature during smelting and casting, heating to 1050 ℃ at the speed of 30 ℃/min, and then preserving heat for 20 min; the casting temperature of the molten metal is selected to be 70 ℃ above the liquidus line; the blanking weight is 15Kg, and an M-22 crucible is adopted for pouring; controlling the pouring time to be 1.5S; the casting vacuum degree is 0.2 Pa. And (5) cleaning shells and calculating after pouring. Through observation and calculation, in the A group of blades, 1-5 # blades are completely filled, the filling area of the 6# blade accounts for 86% of the whole blade area, the filling area of the 7# blade accounts for 65% of the whole blade area, the filling area of the 8# blade accounts for 12% of the whole blade area, and the 9# blade is not filled completely, so that the fluidity process is calculated based on the A group of blades as follows: the thinnest leaf number which is completely filled is 5# leaf, so that 5 is taken from the integral part; the thickest blade with incomplete filling is a No. 6 blade, and the filling area of the blade accounts for 86 percent of the whole blade area, so that the number is 0.86; the second thick blade with incomplete filling is a No. 7 blade, and the filling area of the second thick blade accounts for 65% of the whole blade area, so that the count is 0.065; the incomplete-filling third-thickness blade is the No. 8 blade, the filling area of the incomplete-filling third-thickness blade accounts for 12% of the whole blade area, so the count is 0.0012, the No. 9 blade is completely not filled, so the count is 0, and the flowability A is 5.9262 which is 5+0.86+0.065+0.0012+ 0. In B group's blade, 1 ~ 5# blade is all filled type complete, 6# blade fills type area and accounts for whole blade area 65%, 7# blade fills type area and accounts for whole blade area 50%, 8# blade fills type area and accounts for whole blade area 23%, 9# blade does not fill the type completely, then based on B group's blade calculation mobility process as follows: the thinnest leaf number which is completely filled is 5# leaf, so that 5 is taken from the integral part; the thickest blade with incomplete filling is a No. 6 blade, and the filling area of the blade accounts for 65 percent of the whole blade area, so that the number is 0.65; the blade with incomplete mold filling and the second thickness is a No. 7 blade, and the mold filling area of the blade accounts for 50 percent of the whole blade area, so the number is 0.050; the incomplete-filling third thick blade is the 8# blade, the filling area of the incomplete-filling third thick blade accounts for 23% of the whole blade area, so the counting number is 0.0023, the 9# blade is completely unfilled, so the counting number is 0, and the fluidity B is 5+0.65+0.050+0.0023+ 0-5.7023. Finally, the average values of the groups a and B were obtained, and the average fluidity was (5.9262+5.7023)/2 was 5.975. The flowability of the K4169 alloy under the process conditions was 5.8142. Comparing example 3 with example 2, it is found that the fluidity of the molten metal of K4169 alloy is better than that of K447A under the same casting conditions.

Example 4:

in order to evaluate the mold filling capacity of molten metal when the alternating shell is used for fine grain casting of K447A superalloy, a simulation piece for evaluating the mold filling capacity of a precision casting shell was designed according to the claims, and then a ceramic shell was prepared by a standard alternating shell casting process, wherein the shell thickness is 7 and a half, and then the melting and pouring are carried out. Putting the shell into a furnace at room temperature during smelting and casting, heating to 1050 ℃ at the speed of 30 ℃/min, and then preserving heat for 20 min; the casting temperature of the molten metal is selected to be 70 ℃ above the liquidus line; the blanking weight is 15Kg, and an M-22 crucible is adopted for pouring; controlling the pouring time to be 1.5S; the casting vacuum degree is 0.2 Pa. And (5) cleaning shells and calculating after pouring. Through observation and calculation, in the A group of blades, 1-5 # blades are completely filled, the 6# blade filling area accounts for 86% of the whole blade area, the 7# blade filling area accounts for 65% of the whole blade area, the 8# blade filling area accounts for 12% of the whole blade area, and the 9# blade is not filled completely, so that the shell filling capacity process is calculated based on the A group of blades as follows: the thinnest leaf number which is completely filled is 5# leaf, so that 5 is taken from the integral part; the thickest blade with incomplete filling is a No. 6 blade, and the filling area of the blade accounts for 86 percent of the whole blade area, so that the number is 0.86; the second thick blade with incomplete filling is a No. 7 blade, and the filling area of the second thick blade accounts for 65% of the whole blade area, so that the count is 0.065; the incomplete-filling third-thickness blade is the No. 8 blade, the filling area of the incomplete-filling third-thickness blade accounts for 12% of the whole blade area, so the count is 0.0012, the No. 9 blade is not filled at all, and the filling capacity A is 5+0.86+0.065+0.0012+0 is 5.9262. In B group's blade, 1 ~ 5# blade is all filled type complete, 6# blade fills type area and accounts for whole blade area 65%, 7# blade fills type area and accounts for whole blade area 50%, 8# blade fills type area and accounts for whole blade area 23%, 9# blade does not fill the type completely, then based on B group's blade calculation fill type ability process as follows: the thinnest leaf number which is completely filled is 5# leaf, so that 5 is taken from the integral part; the thickest blade with incomplete filling is a No. 6 blade, and the filling area of the blade accounts for 65 percent of the whole blade area, so that the number is 0.65; the blade with incomplete mold filling and the second thickness is a No. 7 blade, and the mold filling area of the blade accounts for 50 percent of the whole blade area, so the number is 0.050; the third thick blade with incomplete filling is a No. 8 blade, and the filling area of the third thick blade accounts for 23 percent of the whole blade area, so that the count is 0.0023; the 9# blade is not filled at all, so the count is 0, and the filling capacity B is 5+0.65+0.050+0.0023+0 is 5.7023. Finally, the average filling capacity (5.9262+5.7023)/2 (5.975) can be obtained by averaging the groups a and B. The mold filling capacity of molten metal when the alternating shell is used for the fine-grained casting of K447A superalloy is 5.975.

Patent example 5:

in order to evaluate the mold filling capacity of molten metal when a pure corundum shell is used for fine grain casting of K447A high-temperature alloy, a simulation piece for evaluating the mold filling capacity of a precision casting shell is designed according to the claim, then a ceramic shell is prepared by adopting a standard pure corundum shell process, the thickness of the shell is 7 layers and a half, and then smelting and pouring are carried out. Putting the shell into a furnace at room temperature during smelting and casting, heating to 1050 ℃ at the speed of 30 ℃/min, and then preserving heat for 20 min; the casting temperature of the molten metal is selected to be 70 ℃ above the liquidus line; the blanking weight is 15Kg, and an M-22 crucible is adopted for pouring; controlling the pouring time to be 1.5S; the casting vacuum degree is 0.2 Pa. And (5) cleaning shells and calculating after pouring. Through observation and calculation, in the A group of blades, 1-4 # blades are completely filled, the 5# blade filling area accounts for 71% of the whole blade area, the 6# blade filling area accounts for 52% of the whole blade area, the 7# blade filling area accounts for 34% of the whole blade area, the 8# blade filling area accounts for 9% of the whole blade area, and the 9# blade is not filled at all, so that the shell filling capacity calculation process based on the A group of blades is as follows: the thinnest leaf number which is completely filled is 4# leaf, so the integral part is taken as 4; the thickest blade with incomplete filling is a No. 5 blade, and the filling area of the blade accounts for 71 percent of the whole blade area, so that the count is 0.71; the second thick blade with incomplete filling is a No. 6 blade, and the filling area of the second thick blade accounts for 52 percent of the whole blade area, so the count is 0.052; the blade with incomplete filling and the third thickness is a No. 7 blade, and the filling area of the blade accounts for 34 percent of the whole blade area, so the count is 0.0034; the fourth thick blade with incomplete mold filling is a No. 8 blade, and the mold filling area of the fourth thick blade accounts for 9 percent of the whole blade area, so the number is 0.0009; the No. 9 blade is completely unfilled, so the count is 0 and the fill capability A is 4+0.71+0.052+0.0034+0.0009+0 is 4.7663. In the group B blades, 1-4 # blades are all completely filled, the filling area of 5# blades accounts for 31% of the whole blade area, the filling area of 6# blades accounts for 25% of the whole blade area, the filling area of 7# blades accounts for 14% of the whole blade area, the filling area of 8# blades accounts for 5% of the whole blade area, and 9# blades are not filled completely, so that the calculation type shell filling capacity process based on the group B blades is as follows: the thinnest leaf number which is completely filled is 4# leaf, so the integral part is taken as 4; the thickest blade with incomplete filling is a No. 5 blade, and the filling area of the blade accounts for 31 percent of the whole blade area, so that the count is 0.31; the second thick blade with incomplete filling is a No. 6 blade, and the filling area of the second thick blade accounts for 25 percent of the whole blade area, so the number is 0.025; the blade with incomplete filling and the third thickness is a No. 7 blade, and the filling area of the blade accounts for 14 percent of the whole blade area, so that the count is 0.0014; the fourth thick blade with incomplete filling is the No. 8 blade, and the filling area of the fourth thick blade accounts for 5 percent of the whole blade area, so the count is 0.0005; the number 9 leaf is completely unfilled, so the count is 0, and the filling capacity a is 4+0.31+0.025+0.0014+0.0005+0 is 4.3369. Finally, the average filling capacity (4.7663+4.3369)/2 (4.5516) can be obtained by averaging the groups a and B. The molten metal filling capacity of the pure corundum shell for the fine-grain casting of the K447A high-temperature alloy is 4.5516. Comparative examples 4 and 5 can conclude that the air permeability of the alternating shell is better than that of the pure corundum shell.