A device and method for measuring dynamic bulk shrinkage-expansion characteristics of a metal melt throughout the entire cooling process

Abstract

A kind of metal melt cooling whole process body shrinkage-expansion characteristic measuring device.The measuring device adopts vertical measuring mode, the positive pressure between test bar and cavity is reduced, so that the friction between metal melt cooling process and inner wall of mould is reduced to the greatest extent, so that the measurement result is more accurate.The dynamic body shrinkage-expansion characteristics of metal melt cooling whole process can be accurately measured by temperature-density correspondence, and the measuring method has important significance for the accurate control of casting quality and size in the field of metal casting.

Description

Technical Field

[0001] This invention belongs to the field of casting, and in particular relates to a device and method for measuring the dynamic shrinkage-expansion characteristics of casting alloy melt during the entire cooling process. Background Technology

[0002] Cast alloys (such as cast steel and cast iron) undergo plastic deformation, internal stress, and cracks during the cooling process from liquid to room temperature. This is closely related to the contraction and expansion during the cooling process of liquid metal. Taking cast steel as an example, molten steel undergoes three consecutive contraction processes when cooling to room temperature: liquid contraction, solidification contraction, and solid-state contraction. Volumetric contraction is the sum of the contractions in these three stages. Cast iron, during solidification, not only experiences contraction but also volume expansion due to the precipitation of graphite. In particular, ductile iron undergoes volume expansion during the eutectic transformation process due to the precipitation of the graphite phase. Specifically, the cooling process of ductile iron involves three stages: liquid contraction, eutectic expansion, and solid-state contraction. The contraction and expansion characteristics of the casting alloy cooling process directly affect the metallurgical quality. Studying the volumetric contraction-expansion characteristics of casting alloys during cooling is of great significance for improving the metallurgical quality of castings.

[0003] The conventional method for measuring dimensional changes during the cooling process of cast alloys involves measuring the changes in a measuring rod attached to the molten alloy, thereby obtaining the change in linear shrinkage during the solid-state shrinkage process. However, this method cannot fully determine the shrinkage and expansion characteristics of the molten alloy during cooling, such as liquid shrinkage, solidification shrinkage, and eutectic expansion. Furthermore, the measurement of the shrinkage rate during solid-state shrinkage is affected by the friction between the sample and the mold. Therefore, designing a compact, easy-to-operate device capable of accurately measuring the volumetric shrinkage characteristics of molten metal throughout the entire cooling process is of great significance.

[0004] CN108152107A discloses a device for measuring the thermal shrinkage parameters of metallic materials in 3D printing simulation. The device includes a data acquisition and analysis system, a displacement sensor, a slider, a bolt, a thermocouple, and a T-slot. The T-slot holds molten metal, and the slider is located within the T-slot and can slide along it. The bolt is connected to the slider and, during use, extends into the molten metal. As the molten metal solidifies and shrinks, the bolt drives the slider to slide. The displacement sensor is connected to the slider to collect displacement data. The thermocouple is placed within the T-slot to collect temperature change data of the melt within the T-slot. The data acquisition and analysis system is connected to the displacement sensor and the thermocouple, receives and processes the collected temperature and displacement data, and ultimately determines the temperature-displacement relationship curve during metal solidification, thereby characterizing the thermal shrinkage parameters of the metallic material. This device can be used to measure the thermal shrinkage parameters of metals and their alloys.

[0005] CN102661966A discloses a method and apparatus for measuring linear shrinkage rate and thermal stress during metal shrinkage. The sample is melted in situ in a crucible and then solidified, achieving solidification under different cooling conditions. During the cooling process, the sample solidifies uniformly with a low axial temperature gradient, resulting in accurate measured thermal shrinkage curves and thermal stress values. The linear shrinkage rate and thermal stress during solidification can be simultaneously measured using stress sensors and displacement sensors, enabling continuous real-time measurement that corresponds to the actual solidification process. Summary of the Invention

[0006] The purpose of this invention is to provide a method for determining the volumetric shrinkage-expansion characteristics of a molten metal during the entire cooling process. This method can measure the dynamic temperature, dynamic volumetric shrinkage-expansion amount, dynamic volumetric shrinkage-expansion rate, and dynamic shrinkage cavity volume of the sample in the liquid phase, solid-liquid two-phase phase, and solid phase.

[0007] To achieve the above objectives, the present invention discloses a device for measuring the shrinkage-expansion characteristics of a molten metal during the entire cooling process, comprising a metal mold (1), a first three-dimensional displacement measuring instrument (2) disposed above the measuring hole of the metal mold (1), the metal mold (1) being placed on a first weighing platform (21), a first pressure sensor (19) disposed below the first weighing platform (21), a sand mold (26), a sand sample chamber (24) disposed in the center of the metal mold (3), a spiral resistance heater (5) disposed around the sand sample chamber (24), a second three-dimensional displacement measuring instrument (16) disposed above the sand mold (26), the sand mold (26) being placed above a second weighing platform (25), and a second pressure sensor (12) disposed below the second weighing platform (25); the first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the first pressure sensor (19), and the second pressure sensor (12) are respectively connected to a control recorder (6).

[0008] The metal mold (1) includes a metal mold handle (7), a metal mold hinge (8), and a metal mold pin locking mechanism (9) for opening and closing the metal mold. A first metal melt temperature measuring thermocouple (23) is installed at the bottom of the metal sample chamber (4) to measure the temperature of the metal melt in the metal sample chamber (4). A first pressure sensor (19) is used to measure the weight change of the metal melt in the metal sample chamber (4). A first platform stabilizing device (20) is used to maintain the stability of the weighing platform.

[0009] The sand mold (33) inside the sand mold (26) is made by mixing magnesia and water glass and then drying it. The modulus of water glass is M=3.3, and the amount of water glass added is 2-3.5% of the mass of magnesia. A sand mold sample chamber (24) is hollowed out in the center of the sand mold (33). A second metal melt temperature measuring thermocouple (14) is set at the bottom of the sand mold sample chamber (24) to measure the temperature of the metal melt in the sand mold sample chamber (24). A spiral resistance heater (5) is set around the sand mold sample chamber (24) for preheating the sand mold (33). A mold temperature measuring thermocouple (13) is set on the sand mold (33) to measure the preheating temperature of the sand mold (33). A second pressure sensor (12) is set at the bottom of the sand mold (26) to measure the weight change of the metal melt in the sand mold sample chamber (24).

[0010] A first slow-flow groove (31) and a second slow-flow groove (32) are respectively provided above the metal mold (3) and the sand mold (33). The first slow-flow groove (31) is connected to the first pouring cup (30) and the metal mold sample chamber (4), and the second slow-flow groove (32) is connected to the second pouring cup (17) and the sand mold sample chamber (24).

[0011] The control recorder (6) is connected to the first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the spiral resistance heater (5), the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), and the first molten metal temperature measuring thermocouple (23). The control recorder (6) can adjust the preheating temperature of the mold by the spiral resistance heater (5), receive and record the measurement data of the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), the first molten metal temperature measuring thermocouple (23), the first three-dimensional displacement measuring instrument (2), and the second three-dimensional displacement measuring instrument (16), and perform programmed processing to display the dynamic body shrinkage-expansion amount, volume shrinkage-expansion rate, and dynamic shrinkage volume.

[0012] Another aspect of the present invention discloses a method for measuring the volumetric shrinkage-expansion characteristics of a molten metal during the entire cooling process using the above-described apparatus, comprising the following steps:

[0013] a) Check whether the metal mold pin locking mechanism (9) and sand mold pin locking mechanism (29) on the metal mold (1) and sand mold (26) have locked the metal mold. Then turn on the control recorder (6) and the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) to initialize the instrument data.

[0014] b) Use the control recorder (6) to control the spiral resistance heater (5) to preheat the sample chamber to 200°C;

[0015] c) Using a sampling aluminum silicate casting spoon, the molten steel is poured into the first pouring cup (30) and the second pouring cup (17) in turn. The molten iron flows through the slow flow tank into the metal sample chamber (4) and the sand sample chamber (24).

[0016] d) As the molten iron cools to room temperature, the molten metal undergoes three stages: liquid contraction, solidification contraction, and solid contraction (if it is molten iron, it will go through three stages: liquid contraction, eutectic expansion, and solid contraction). During the cooling process of the molten metal, the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) measure the change in the average height of the surface of the molten metal in real time. The second molten metal temperature measuring thermocouple (14) and the first molten metal temperature measuring thermocouple (23) measure the temperature curve of the molten metal. The pressure sensor measures the mass of the molten metal in the metal mold sample chamber (4) and the sand mold sample chamber (24). The data is processed by the control recorder (6) to dynamically display the volume contraction-expansion characteristics of the molten metal during the entire cooling process.

[0017] The principle for determining the shrinkage volume of the shrinkage cavity and the shrinkage-expansion of the molten metal is as follows:

[0018] By analyzing the relationship between the temperature and density of molten metal in metal molds and sand molds, the volumetric shrinkage-expansion characteristics of the sample in the sand mold are measured using the density and volume measured in the metal mold as the standard. After the molten metal enters the sample chamber, the first thermocouple, the second thermocouple, and the mold temperature-measuring thermocouple continuously record the temperature changes of the sample. The state of the sample (liquid phase, solid-liquid two-phase, solid phase) is determined based on the cooling curve. A three-dimensional displacement measuring instrument measures the volume change of the sample in the liquid phase, solid-liquid two-phase, and solid phase states in real time. The control recorder processes the collected temperature, mass, and other data in real time and displays the dynamic temperature, dynamic volumetric shrinkage-expansion, dynamic volumetric shrinkage-expansion rate, and dynamic shrinkage cavity volume of the sample. The data processing principle of the control recorder is shown in the following formula:

[0019] Body contraction-expansion:

[0020]

[0021] Body contraction-expansion rate:

[0022]

[0023] Volume of shrinkage cavity:

[0024]

[0025] Where ΔV is the total volumetric contraction-expansion of the molten metal during the entire cooling process, v is the rate of volumetric contraction-expansion of the molten metal during the entire cooling process, Δv is the volume of the shrinkage cavity during the cooling process of the molten metal, the radius of the molten metal is R, and the cross-sectional area of ​​the molten metal is K=πR. 2The initial mass of the metal mold is G0, the mass of the molten metal at temperature T1 during the cooling process is G1, the average height of the upper surface of the molten metal at temperature T1 in the metal mold is N1, the mass of the molten metal at temperature T2 during the cooling process is G2, and the average height of the upper surface of the molten metal at temperature T2 in the metal mold is N2; the initial mass of the sand mold is g0, the mass of the molten metal at temperature T1 during the cooling process is g1, the average height of the upper surface of the molten metal at temperature T1 in the sand mold is n1, and the time is t1; the mass of the molten metal at temperature T2 during the cooling process is g2, the average height of the upper surface of the molten metal at temperature T2 in the sand mold is n2, and the time is t2.

[0026] The beneficial effects of this invention are:

[0027] Compared with the prior art, the present invention has the following outstanding features and significant progress: the volume shrinkage characteristics during the cooling process of molten metal are a very important parameter. (1) The present invention can measure the volume shrinkage-expansion characteristics of molten metal in the liquid phase stage, solid-liquid two-phase stage, and solid phase stage, that is, measure the volume shrinkage-expansion characteristics of molten metal throughout the entire cooling process; (2) The present invention adopts a vertical measurement method, which reduces the positive pressure between the test bar and the mold cavity, thereby greatly reducing the friction between the molten metal and the inner wall of the mold during the cooling process, and the measurement results are more accurate; it is of great significance for the precise control of casting quality and dimensions in the field of metal casting. Attached Figure Description

[0028] Figure 1 This is a front view of the device in this invention;

[0029] Figure 2 This is a top view of the device in this invention;

[0030] Figure 3 This is a curve showing the shrinkage-expansion characteristics of cast steel.

[0031] Figure 4 This is a curve showing the shrinkage-expansion characteristics of cast iron.

[0032] The components include: a metal mold (1), a first three-dimensional displacement measuring instrument (2), a metal mold (3), a metal mold sample chamber (4), a spiral resistance heater (5), a control recorder (6), a metal mold handle (7), a metal mold hinge (8), a metal mold pin locking mechanism (9), a bracket (10), a quartz crucible (11), a second pressure sensor (12), a mold temperature measuring thermocouple (13), a second metal melt temperature measuring thermocouple (14), a horizontal platform (15), a second three-dimensional displacement measuring instrument (16), and a second pouring cup (17). First junction box (18), first pressure sensor (19), first platform stabilizing device (20), first weighing platform (21), second platform stabilizing device (22), first molten metal temperature measuring thermocouple (23), sand mold sample chamber (24), second weighing platform (25), sand mold (26), sand mold handle (27), sand mold hinge (28), sand mold pin locking mechanism (29), first pouring cup (30), first slow flow channel (31), second slow flow channel (32), sand mold (33), second junction box (34). Detailed Implementation

[0033] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0034] Example 1

[0035] A device for measuring the shrinkage-expansion characteristics of a molten metal during the cooling process includes a metal mold (1), a first three-dimensional displacement measuring instrument (2) positioned above the measuring hole of the metal mold (1), the metal mold (1) being placed on a first weighing platform (21), a first pressure sensor (19) being positioned below the first weighing platform (21), a sand mold (26), a sand sample chamber (24) being positioned at the center of the metal mold (3), a spiral resistance heater (5) being positioned around the sand sample chamber (24), a second three-dimensional displacement measuring instrument (16) being positioned above the sand mold (26), the sand mold (26) being positioned above a second weighing platform (25), and a second pressure sensor (12) being positioned below the second weighing platform (25); the first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the first pressure sensor (19), and the second pressure sensor (12) are respectively connected to a control recorder (6).

[0036] The metal mold (1) includes a metal mold handle (7), a metal mold hinge (8), and a metal mold pin locking mechanism (9) for opening and closing the metal mold. A first metal melt temperature measuring thermocouple (23) is installed at the bottom of the metal sample chamber (4) to measure the temperature of the metal melt in the metal sample chamber (4). A first pressure sensor (19) is used to measure the weight change of the metal melt in the metal sample chamber (4). A first platform stabilizing device (20) is used to maintain the stability of the weighing platform.

[0037] The sand mold (33) inside the sand mold (26) is made by mixing magnesia and water glass and then drying it. The modulus of water glass is M=3.3, and the amount of water glass added is 2-3.5% of the mass of magnesia. A sand mold sample chamber (24) is hollowed out in the center of the sand mold (33). A second metal melt temperature measuring thermocouple (14) is set at the bottom of the sand mold sample chamber (24) to measure the temperature of the metal melt in the sand mold sample chamber (24). A spiral resistance heater (5) is set around the sand mold sample chamber (24) for preheating the sand mold (33). A mold temperature measuring thermocouple (13) is set on the sand mold (33) to measure the preheating temperature of the sand mold (33). A second pressure sensor (12) is set at the bottom of the sand mold (26) to measure the weight change of the metal melt in the sand mold sample chamber (24).

[0038] A first slow-flow groove (31) and a second slow-flow groove (32) are respectively provided above the metal mold (3) and the sand mold (33). The first slow-flow groove (31) is connected to the first pouring cup (30) and the metal mold sample chamber (4), and the second slow-flow groove (32) is connected to the second pouring cup (17) and the sand mold sample chamber (24).

[0039] The control recorder (6) is connected to the first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the spiral resistance heater (5), the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), and the first molten metal temperature measuring thermocouple (23). The control recorder (6) can adjust the preheating temperature of the mold by the spiral resistance heater (5), receive and record the measurement data of the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), the first molten metal temperature measuring thermocouple (23), the first three-dimensional displacement measuring instrument (2), and the second three-dimensional displacement measuring instrument (16), and perform programmed processing to display the dynamic body shrinkage-expansion amount, volume shrinkage-expansion rate, and dynamic shrinkage volume.

[0040] Example 2

[0041] The method for determining the shrinkage characteristics of molten metal during the entire cooling process using the apparatus described in Example 1 includes the following steps:

[0042] a) Check whether the metal mold pin locking mechanism (9) and sand mold pin locking mechanism (29) on the metal mold (1) and sand mold (26) have locked the metal mold. Then turn on the control recorder (6) and the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) to initialize the instrument data.

[0043] b) Use the control recorder (6) to control the spiral resistance heater (5) to preheat the sample chamber to 200°C;

[0044] c) Using a sampling aluminum silicate casting spoon, the molten metal is poured into the first pouring cup (30) and the second pouring cup (17) in succession. The molten metal flows through the slow flow tank into the metal sample chamber (4) and the sand sample chamber (24).

[0045] d) As the molten metal cools to room temperature, it undergoes three stages: liquid contraction, solidification contraction, and solid contraction (for molten iron, it will undergo three stages: liquid contraction, eutectic expansion, and solid contraction). During the cooling process, the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) measure the change in the average height of the molten metal surface in real time. The second molten metal temperature measuring thermocouple (14) and the first molten metal temperature measuring thermocouple (23) measure the temperature curve of the molten metal. The pressure sensor measures the mass of the molten metal in the metal mold sample chamber (4) and the sand mold sample chamber (24). The data is processed by the control recorder (6) to dynamically display the volumetric contraction-expansion characteristics of the molten metal throughout the cooling process. The volumetric contraction-expansion curve of the molten steel during the entire cooling process is shown in the figure. Figure 3 The volumetric contraction-expansion curves for the entire cooling process of molten iron are shown below. Figure 4 .

[0046] Figure 3 The figure shows the volume shrinkage-expansion curve of the steel. The two dashed lines in the figure correspond to the solidus temperature and liquidus temperature of the cast steel, respectively. The AB segment of the curve is the volume shrinkage-expansion curve of the liquid phase region, which shows linear shrinkage. The BC segment is the volume shrinkage-expansion curve of the solid-liquid two-phase region (solidification stage), which shows nonlinear shrinkage. The CD segment is the volume shrinkage-expansion curve of the solid phase region. The curve inflection in the solid phase region is due to the volume expansion of the sample caused by phase transformation. Figure 4 The volumetric shrinkage-expansion curves of the molten iron are shown. The two dashed lines correspond to the solidus temperature and liquidus temperature of the molten iron, respectively. The EF segment of the curve is the volumetric shrinkage-expansion curve of the liquid phase region, where linear shrinkage occurs. The FG segment is the volumetric shrinkage-expansion curve of the solid-liquid two-phase region (solidification stage), where the curve inflection occurs due to eutectic expansion. The GH segment is the volumetric shrinkage-expansion curve of the solid phase region, where the curve inflection occurs due to the volume expansion of the sample caused by phase transformation.

[0047] The above embodiments are illustrative examples of the present invention and are not intended to limit the scope of protection of the present invention. All other technical solutions obtained by those skilled in the art based on the described embodiments without inventive effort are within the scope of protection of the present invention.

Claims

1. A device for measuring the shrinkage-expansion characteristics of a molten metal during the entire cooling process, comprising a metal mold (1), a first three-dimensional displacement measuring instrument (2) disposed above the measuring hole of the metal mold (1), the metal mold (1) being placed on a first weighing platform (21), a first pressure sensor (19) being disposed below the first weighing platform (21), a metal mold (3) being placed inside the metal mold (1), a sand mold (33) being placed inside a sand mold (26), a metal sample chamber (4) being disposed in the center of the metal mold (3), and a sand mold (33) being disposed in the center of the sand mold (33). A sand mold sample chamber (24) is set in the center, and a spiral resistance heater (5) is set around the sand mold sample chamber (24). A second three-dimensional displacement measuring instrument (16) is set above the sand mold (26). The sand mold (26) is placed above the second weighing platform (25). A second pressure sensor (12) is set below the second weighing platform (25). The first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the first pressure sensor (19), and the second pressure sensor (12) are respectively connected to the control recorder (6). A second molten metal temperature measuring thermocouple (14) is installed at the bottom of the sand mold sample chamber (24) to measure the temperature of the molten metal in the sand mold sample chamber (24). A spiral resistance heater (5) is installed around the sand mold sample chamber (24) for preheating the sand mold (33). A mold temperature measuring thermocouple (13) is installed on the sand mold (33) to measure the preheating temperature of the sand mold (33). A second pressure sensor (12) is installed at the bottom of the sand mold (26) to measure the weight change of the molten metal in the sand mold sample chamber (24). The metal mold (3) and the sand mold (33) are respectively provided with a first slow flow groove (31) and a second slow flow groove (32). The first slow flow groove (31) is connected to the first pouring cup (30) and the metal mold sample chamber (4), and the second slow flow groove (32) is connected to the second pouring cup (17) and the sand mold sample chamber (24). The metal mold (1) includes a metal mold handle (7), a metal mold hinge (8), and a metal mold pin locking mechanism (9) for opening and closing the metal mold. A first metal melt temperature measuring thermocouple (23) is installed at the bottom of the metal sample chamber (4) to measure the temperature of the metal melt in the metal sample chamber (4). A first pressure sensor (19) is used to measure the weight change of the metal melt in the metal sample chamber (4). A first platform stabilizing device (20) is used to maintain the stability of the weighing platform.

2. The measuring device as described in claim 1, characterized in that... The sand mold (33) inside the sand mold (26) is made by mixing magnesia and water glass and then drying it. The water glass modulus M = 3.3 and the amount of water glass added is 2-3.5 wt% of the mass of magnesia. A sand mold sample chamber (24) is hollowed out in the center of the sand mold (33).

3. The measuring device as described in claim 1, characterized in that... The control recorder (6) is connected to the first three-dimensional displacement measuring instrument (2), the second three-dimensional displacement measuring instrument (16), the spiral resistance heater (5), the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), and the first molten metal temperature measuring thermocouple (23). The control recorder (6) can adjust the preheating temperature of the mold by the spiral resistance heater (5), receive and record the measurement data of the mold temperature measuring thermocouple (13), the second molten metal temperature measuring thermocouple (14), the first molten metal temperature measuring thermocouple (23), the first three-dimensional displacement measuring instrument (2), and the second three-dimensional displacement measuring instrument (16), and perform programmed processing to display the dynamic body shrinkage-expansion amount, volume shrinkage-expansion rate, and dynamic shrinkage volume.

4. A method for measuring the volumetric contraction-expansion characteristics of a molten metal during the entire cooling process using the apparatus described in any one of claims 1-3, comprising the following steps: a) Check whether the metal mold pin locking mechanism (9) and sand mold pin locking mechanism (29) on the metal mold (1) and sand mold (26) have locked the metal mold and sand mold. Then turn on the control recorder (6) and the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) to initialize the instrument data. b) Use the control recorder (6) to control the spiral resistance heater (5) to preheat the sample chamber to 200°C; c) Using a sampling aluminum silicate casting spoon, the molten metal is poured into the first pouring cup (30) and the second pouring cup (17) in succession. The molten metal flows through the slow flow tank into the metal sample chamber (4) and the sand sample chamber (24). d) As the molten metal cools to room temperature, it undergoes three stages: liquid contraction, solidification contraction, and solid contraction. During the cooling process, the first three-dimensional displacement measuring instrument (2) and the second three-dimensional displacement measuring instrument (16) measure the change in the average height of the molten metal surface in real time. The second molten metal temperature measuring thermocouple (14) and the first molten metal temperature measuring thermocouple (23) measure the temperature curve of the molten metal. The pressure sensor measures the mass of the molten metal in the metal mold sample chamber (4) and the sand mold sample chamber (24). The data is processed by the control recorder (6) to dynamically display the volume contraction-expansion characteristics of the molten metal throughout the cooling process.

5. The method as described in claim 4, characterized in that... The molten metal described in step d) is molten iron, and its cooling process goes through three stages: liquid contraction, eutectic expansion, and solid contraction.

6. The method as described in claim 4, characterized in that... The formula for calculating the volume contraction-expansion is as follows: Body contraction-expansion: （1） Where ΔV is the volumetric contraction-expansion of the molten metal during the entire cooling process, and the cross-sectional area of ​​the molten metal K = πR 2 The radius of the molten metal is R, the initial mass of the metal mold is G0, the mass of the molten metal at cooling temperature T1 is G1, the average height of the upper surface of the molten metal is N1, the mass of the molten metal at cooling temperature T2 is G2, and the average height of the upper surface of the molten metal is N2; the initial mass of the sand mold is g0, the mass of the molten metal at cooling temperature T1 is g1, and the mass of the molten metal at cooling temperature T2 is g2.

7. The method as described in claim 4, characterized in that... The formula for calculating the rate of body contraction-expansion is as follows: （2） Where v is the rate of contraction-expansion of the molten metal during the entire cooling process, and the cross-sectional area of ​​the molten metal K = πR 2 The radius of the molten metal is R, the initial mass of the metal mold is G0, the mass of the molten metal at temperature T1 during the cooling process is G1, the average height of the upper surface of the molten metal is N1, the mass of the molten metal at temperature T2 during the cooling process is G2, and the average height of the upper surface of the molten metal is N2; the initial mass of the sand mold is g0, the mass of the molten metal at temperature T1 during the cooling process is g1, the time is t2, the mass of the molten metal at temperature T2 during the cooling process is g2, and the time is t1.

8. The method as described in claim 4, characterized in that The formula for calculating the volume of shrinkage cavity is as follows: （3） Where Δv is the volume of the shrinkage cavity during the cooling process of the molten metal, and the cross-sectional area of ​​the molten metal K = πR 2 The radius of the molten metal is R, the initial mass of the metal mold is G0, the mass of the molten metal at temperature T1 during the cooling process is G1, and the average height of the upper surface of the molten metal is N1; the initial mass of the sand mold is g0, the mass of the molten metal at temperature T1 during the cooling process is g1, and the average height of the upper surface of the molten metal at temperature T2 during the cooling process is n2.

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