Optimization of Billet Tube Mold Designs for High-Speed Continuous Casting

Abstract

Endless rolling urgently requires an increase in the casting speed of continuous casting. For the continuous casting process of a high-casting-speed billet, the heat flux of the mold would be much higher, requiring a stronger cooling performance and longer mold life to match the high-speed casting. Mold material, thickness, and slot structure have a great influence on the casting speed. To design a more efficient billet casting mold, a three-dimensional thermal-stress-coupled analysis model of a 150 mm × 150 mm mold was established in this research to analyze the thermal state of a mold with high casting speed; in addition, the material, thickness, and water slot structure, which pertain to the mold cooling performance, were also studied. The results show that the billet mold of Cu-Ag with a thinner thickness and right-corner water slot is better in terms of casting speed. Regarding the material, the Cu-Ag mold has a higher thermal conductivity efficiency; its hot surface temperature is 4.89 °C lower, its equivalent stress is 7 MPa lower, and its longitudinal deformation is 0.0023% lower compared with the deoxidized phosphorus copper mold. Regarding the thickness, the thinner mold has a 60.76 °C lower hot surface temperature, its equivalent stress is 340 MPa lower, and its longitudinal deformation is 0.0443% lower compared with the thicker mold. For the water slot structure, the mold with the right-angled water slot has a 2.895 °C lower hot surface temperature, its equivalent stress is 37 MPa lower, and its longitudinal deformation is 0.0039% lower compared with the mold with a rounded-corner water slot.

1. Introduction

High-efficiency continuous casting is becoming more and more important in the development of continuous casting technology. This means that the strand quality and the casting speed should both be higher. As the casting speed increases, the heat flux in the mold would increase, the mold temperature would increase, and the thermal stress of the mold would also increase. These increases would disrupt the original balance of the mold and induce deformation and cracks in the mold, which would reduce the mold life [1,2,3]. Therefore, the mold’s cooling performance has a direct impact on continuous casting production.

In the actual production process, the copper wall of the mold has complex interfacial heat transfer and thermal deformation problems, and can withstand a high heat load; so, the higher casting speed presents a great challenge to the cooling performance and service life of the mold. At the same time, when the casting speed is higher, the fluctuation of the molten steel–mold flux interface in the mold is intensified, the consumption of mold flux is reduced, and the stability and uniformity of the mold flux film between mold and shell are reduced. This results in an uneven heat transfer in the mold, which would increase the frictional resistance and enhance the tendency of the solidified shell to crack or break internally [4,5,6,7].

For the billet, the casting speed becomes higher and higher, leading to more and more requirements in the design of a billet mold. To meet the demands of billet production with a high casting speed, the copper mold tube should be continuously optimized and developed based on specific process requirements. For example, mold performance could be improved by extending the length, adjusting the cooling water supply parameters, and changing the mold vibration mode. However, fundamentally, the design of a mold with excellent heat transfer performance and good service life, according to the actual process requirements, is key to ensuring the quality of the billet and the high efficiency of continuous casting production [8,9].

To enhance the durability of the mold used in continuous casting, several researchers have conducted studies on the thermal and mechanical behavior of the mold. Gorbatyuk S M et al. [10] studied the inner wall coating of the mold. They found that the 0.5~0.6 mm Ni-Cr coating on the inner wall of the mold can reduce the loss of the inner wall and prolong the service life of the mold. Liao et al. [11] increased the thickness of the copper tube of the mold from 13.25 mm to 16 mm and changed the material from TP2 to CuAg. The mold strength increased by 20%, and the 0.09 mm Cr coating was upgraded to a 0.12–0.16 mm Ni-Co-Cr composite coating. In this study, the conflict between the wear resistance of the coating and the bond strength of the substrate was resolved. Meng X N et al. [12] studied the thermal behavior of a slab cooling structure using Ansys FEA software. They found that the temperature distribution of the hot surface was mainly controlled by the cooling structure and the heat transfer conditions. For the center of the hot surface, when the copper plate thickness increased by 5 mm and the nickel layer thickness increased by 1 mm, the maximum surface temperature increased by 30 °C and 15 °C, respectively; when the depth of the water slot increased by 2 mm, the surface temperature without the nickel layer reduced by 10 °C, and the surface temperatures of the nickel layers adjacent to and far from the exit of the mold decreased by 7 °C and 5 °C, respectively. Li Q ZH et al. [13] improved the design of the inner cavity of the 140 mm × 140 mm billet mold. After the improvement, the casting speed of the new mold increased by 0.3~0.6 m/min, the average tapping temperature decreased by 29 °C, the quality of the billet further improved, and the heat dissipation capacity increased by about 83.7%.

Zhang J F et al. [14] reformed the mold copper tube for the Pangang Group Company Limited. The taper of the 150 mm × 150 mm billet copper tube reduced from 0.8%/m~10%/m to 0.6%/m~0.7%/m, soft water was used as the cooling water, and the temperature of molten steel in tundish reduced to 1525~1545 °C. The improvement extended the service life of the mold, and the amount of molten steel that passes through the copper tube increased from 1000 t to 3500 t. Zhu N et al. [15] optimized and improved the taper of the mold copper plate, the performance of the flux powder, and the superheat of the molten steel for Nanjing Iron and Steel Co., Ltd, China. After this improvement, the service life of the mold copper plate doubled, the life of the wide side copper plate increased by 295, and the life of the narrow side copper plate increased by 349. The purpose of reducing the production cost and improving the production efficiency was realized. L. Moro et al. [16] studied the durability of a 165 mm × 165 mm mold copper tube by combining Ansys finite element software and an experiment. They found that the permanent displacement of the copper tube was approximately 0.075 mm. Wang J. ZH et al. [17] addressed the serious problem of the casting billet de-squaring, distortion, and even steel leakage of copper tubes in the mold of the Xuan Gang continuous casting machine. Through the improvement of the mold coating, taper, and optimization of the production process, the increase in mold life from the original 10,000 min to the current 22,000 min not only ensures the production rhythm but also reduces the cost.

Pei X et al. [18] analyzed the heat transfer performance of five different kinds of mold cooling structures. They found that the complex structure of water seams and water slot has a better cooling effect; this water slot configuration would take 5.58% more heat away and the maximum temperature would be reduced to 196 °C. At a casting speed of 6.5 m/min, the temperature distribution of the copper tubes would be more uniform. Liu Z X et al. [19] used Ansys FEA software to study the influence of different cooling processes on the heat transfer behavior in the mold of high-speed thin slab continuous casting. They found that the maximum temperature of the hot surface of the copper wall was reduced by 117 °C and the maximum temperature of the cold surface was reduced by 24 °C with the top-down water supply method. The service life of the copper tube was effectively extended under high thermal shock. Liu X Y et al. [20] used the combination of Ansys FEA and experiment to optimize the size of the mold water slot, the quality of the cooling water, and the superheat of the molten steel. As a result, the rhomboidity rate of the shell was reduced to 0.24%, the break-out rate was reduced to 0.08%, and the average pass rate of the copper tube was increased by 24.88%. Mold loss was reduced, and mold life was improved. Janik M et al. [3] used the finite element method (FEM) and the commercial software Ansys to analyze the three-dimensional temperature field in the billet mold during the continuous casting of low carbon steel. They calculated that the thickness of the shell at the outlet of the mold is 9.07 mm and the thickness of the shell is 9.58 mm when the liquid phase content is 30%. To reduce the occurrence of breakout, it is necessary to modify the casting parameters.

Extensive research has been conducted on the coating, taper, and water slot configuration of the mold, but less attention has been paid to the material, wall thickness, and water slot configuration of the billet mold. So, this paper aims to enhance the heat transfer efficiency and service life of molds by optimizing their material, wall thickness, and water slot configuration. A three-dimensional finite element thermal stress indirect coupling model of a copper wall mold was developed using Ansys software. Through the comparison of the temperature field, stress field, and thermal deformation situation, an effective theoretical basis was provided for testing the rationality of the design.

2. Material and Methods

Currently, in the continuous casting production process, the main material of billet mold is deoxidized phosphorus copper, the main material of bloom mold is Cu-Ag, and the main material of slab is Cu-Cr-Zr. Because the Cu-Cr-Zr material strength is higher, Cu-Ag material has high strength and good thermal conductivity. With the development of high casting speed, the requirements for the strength and thermal conductivity of the mold are getting higher and higher. Therefore, this paper selects deoxidized phosphorus copper and Cu-Ag materials for simulation analysis, with a view to obtain a mold material with better heat transfer performance and more stable mechanical properties under the condition of high casting speed.

In this paper, the section size of the 150 mm × 150 mm billet mold was taken as the research object. By comparing and analyzing the molds with different materials, wall thicknesses, and water slot configurations, a better mold design was obtained. Figure 1 shows the basic design of a 1/4 billet thin-walled mold.

2.1. Major Assumptions

The model is symmetrical. Therefore, the 1/4 mold three-dimensional model was used to simulate the temperature field, stress field, and thermal deformation situation of the copper wall of the mold. The basic assumptions of the model are as follows:

(1)

The thermal and mechanical properties of the mold copper walls are isotropic. The effect of temperature on the physical properties of the copper wall was neglected and treated as an approximate constant.

(2)

Compared with the casting speed, the longitudinal heat transfer in the casting direction was neglected.

(3)

The heat transfer between the outer wall of the mold and the cooling water was considered to be stable; the cooling water has no nucleate boiling. The cooling water temperature changes linearly along the height of the mold, and the temperature is equal at the same height.

(4)

The top and bottom of the mold were set to be insulated.

(5)

The copper wall of the mold was set to an elastoplastic model.

Based on the above assumptions, this paper simulated the temperature field, stress field, and thermal deformation of the mold copper wall.

2.2. Geometric Model

The cold surface of the model has a water slot with a width of 15.5 mm and a depth of 8 mm, as shown in Figure 2. The water slot and the mold were divided by the same grid, using a hexahedral meshing form, as shown in Figure 3.

2.3. Heat Transfer Model

In this paper, the heat flux density was solved by using specific coefficients [21], as shown in Equations (1) and (2):

$$\mathrm{q}={\mathrm{A}}_0-{\mathrm{B}}_0\sqrt{{\mathrm{l}}_{\mathrm{z}}/\mathrm{v}}$$

(1)

In Equation (1), $\mathrm{q}$ is the heat flux density between casting blank and mold, $\mathrm{M}\mathrm{W}/{\mathrm{m}}^2$; ${\mathrm{l}}_{\mathrm{z}}$ is the distance from any point on the inner wall of the mold to the meniscus, m; and $\mathrm{v}$ is the casting speed, $\mathrm{m}/\mathrm{s}$. ${\mathrm{A}}_0$ is constantly measured for different equipment and casting conditions. In this paper, ${\mathrm{A}}_0$ = 2.688 $\mathrm{M}\mathrm{W}/{\mathrm{m}}^2$.

$${\mathrm{B}}_0=\left(\mathrm{L}\mathrm{h}{\mathrm{A}}_0-{\mathrm{c}}_{\mathrm{w}}\mathrm{W}{\mathsf{\rho }}_{\mathrm{w}}∆\mathrm{T}\right)\frac{3{\mathrm{v}}^{1/2}}{2\mathrm{L}{\mathrm{h}}^{3/2}}$$

(2)

In Equation (2), ${\mathrm{B}}_0$ is constantly measured for different equipment and casting conditions, $\mathrm{M}\mathrm{W}/{\mathrm{m}}^2{\mathrm{s}}^{1/2}$; $\mathrm{L}$ is the perimeter of the mold cavity, m; $\mathrm{h}$ is the effective length of the mold, m; ${\mathrm{c}}_{\mathrm{w}}$ is the specific heat of cooling water, $\mathrm{J}·{\mathrm{K}\mathrm{g}}^{-1}·{°\mathrm{C}}^{-1}$; $\mathrm{W}$ is cooling water flow, ${\mathrm{m}}^3·\mathrm{s}$; ${\mathsf{\rho }}_{\mathrm{w}}$ is the cooling water density, $\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$; and $∆\mathrm{T}$ is the temperature difference of cooling water, °C.

There is convective heat transfer between the water slot and the cooling water. The convective heat transfer coefficient is obtained by Equation (3) [22,23]:

$${\mathrm{h}}_{\mathrm{w}}=0.023\frac{{\mathsf{\lambda }}_{\mathrm{W}}}{{\mathrm{D}}_{\mathrm{W}}}{\left(\frac{{\mathsf{\rho }}_{\mathrm{W}}{\mathrm{v}}_{\mathrm{W}}{\mathrm{D}}_{\mathrm{W}}}{{\mathsf{\mu }}_{\mathrm{W}}}\right)}^{0.8}{\left(\frac{{\mathrm{c}}_{\mathrm{W}}{\mathsf{\mu }}_{\mathrm{W}}}{{\mathsf{\lambda }}_{\mathrm{W}}}\right)}^{0.4}$$

(3)

In Equation (3), ${\mathrm{h}}_{\mathrm{w}}$ is the heat transfer coefficient between the cold surface of the mold copper tube and the cooling water, ${\mathrm{m}}^2·°\mathrm{C}/\mathrm{W}$; ${\mathsf{\lambda }}_{\mathrm{W}}$ is the thermal conductivity of cooling water, $\mathrm{W}·{\mathrm{m}}^{-1}·{°\mathrm{C}}^{-1}$; ${\mathrm{D}}_{\mathrm{W}}$ is the hydraulic diameter, m; ${\mathrm{v}}_{\mathrm{W}}$ is the cooling water flow rate, m/s; and ${\mathsf{\mu }}_{\mathrm{W}}$ is the viscosity of the cooling water, Pa∙s.

Temperature field solution boundary conditions: (1) the inner wall of the mold model was applied with heat flux; (2) the water slot part was applied with convective heat transfer coefficient; (3) the inlet and outlet directions of the cooling water were set to be lower in and higher out, and the temperature difference of the cooling water was set to be 8 °C; (4) the rest was set to adiabatic.

2.4. Stress Model

In actual production, the mold copper wall material must meet the thermal elastic–plastic deformation in the casting process. The thermal elastic–plastic stress–strain equation of the mold copper wall is expressed as Equation (4) [22,23]:

$${\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}=2{\mathrm{L}}_1{\mathsf{\epsilon }}_{\mathrm{i}\mathrm{j}}+{\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}\left[{\mathrm{L}}_2{\mathsf{\epsilon }}_{\mathrm{k}\mathrm{k}}-\left(2{\mathrm{L}}_1+3{\mathrm{L}}_2\right)\mathsf{\beta }\mathsf{\Delta }\mathrm{T}\right]$$

(4)

In Equation (4), ${\mathsf{\sigma }}_{\mathrm{i}\mathrm{j}}$ is stress, Pa; ${\mathsf{\epsilon }}_{\mathrm{i}\mathrm{j}}$ is strain; ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ are Lamé coefficients; ${\mathsf{\epsilon }}_{\mathrm{k}\mathrm{k}}$ is node-positive strain; $\mathsf{\beta }$ is the coefficient of thermal expansion, ${°\mathrm{C}}^{-1}$; $\mathsf{\Delta }\mathrm{T}$ is the temperature variation, °C; and ${\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}$ is the Kronecker function. Among them, the stress and strain of the mold copper wall include elastic, plastic, and thermal strain, as shown in Equations (5)–(8):

$${\mathsf{\epsilon }}_{\mathrm{i}\mathrm{j}}={\mathsf{\epsilon }}_{\mathrm{e}}+{\mathsf{\epsilon }}_{\mathrm{p}}+{\mathsf{\epsilon }}_{\mathrm{t}}$$

(5)

$${\mathsf{\epsilon }}_{\mathrm{t}}={\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}\mathsf{\beta }\mathsf{\Delta }\mathrm{T}$$

(6)

$${\mathsf{\epsilon }}_{\mathrm{p}}=\frac{\sqrt{3}}{2}\frac{{\mathsf{\epsilon }}_0}{\mathsf{\Phi }\left({\mathsf{\epsilon }}_0\right)}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}$$

(7)

$$\Phi \left({\mathsf{\epsilon }}_0\right)={\sigma }_y+\frac{\mathrm{E}\cdot {\mathrm{E}}_{\mathrm{t}}}{\mathrm{E}-{\mathrm{E}}_{\mathrm{t}}}{\mathsf{\epsilon }}_0$$

(8)

In Equations (5)–(8), ${\mathsf{\epsilon }}_{\mathrm{e}}$, ${\mathsf{\epsilon }}_{\mathrm{p}}$, and ${\mathsf{\epsilon }}_{\mathrm{t}}$ are elastic, plastic, and thermal strains, respectively; ${\epsilon }_0$ is the effective strain; ${\mathrm{S}}_{\mathrm{i}\mathrm{j}}$ is skew tensor; $\mathrm{E}$ is Young’s modulus, Pa; ${\mathrm{E}}_{\mathrm{t}}$ is the linear hardening modulus, Pa; and ${\sigma }_y$ is yield strength, Pa.

Stress field solution boundary conditions: (1) the non-water slot area of the cold surface of the mold was fixed; (2) the symmetry surface of the mold model was fixed; (3) the top surface of the mold was fixed, and the bottom surface was free from constraint; (4) the area from the meniscus to the lower mouth of the mold was subjected to static pressure of molten steel; (5) the cold surface water slot area of the mold was subjected to cooling water pressure; (6) the thermal load of mold copper wall was given by the temperature field.

2.5. Determination of Physical Parameters

In this study, the thermal–physical parameters of the material itself do not change much under thermal conditions. In addition, in many related studies, the constant values of thermal–physical parameters were selected for research. Therefore, this study cited relevant references for simulation and analysis. The chemical composition and thermal–physical performance parameters of different materials for the copper wall of molds are given in

Table 1. Chemical composition and thermal–physical performance parameters of different materials.

Alloy	Chemical Composition	Thermophysical Properties
		Thermal Conductivity W/m·°C	Specific Heat Capacity J/kg·°C	Recrystallization Temperature °C
Deoxidized phosphorized copper (Deformation 20%)	wt% (Cu) = 99.9% wt% (P) = 0.03% Other components	340	384	300
Silver copper (Cu-Ag)	wt% (Cu) = 99.9% wt% (Ag) = 0.09% wt% (P) = 0.006% Other components	370	381	370

[24].

Though many researchers [25] have studied the mechanical parameters of copper alloys, the composition of the material in this study is different from theirs; so, the mechanical parameters of the material in this study were calculated using Jmatpro software (Jmatpro7.0). It is well known that the material’s Poisson’s ratio parameter does not vary significantly with temperature. Therefore, in this study, Poisson’s ratio of deoxidized phosphorus copper material is 0.34 and Poisson’s ratio of Cu-Ag material is 0.35. The remaining mechanical parameters were calculated using Jmatpro software. Various mechanical parameters vary with temperature, as shown in Figure 4 and Figure 5.

2.6. Simulated Conditions

In this paper, the cooling performance and service life of 150 mm × 150 mm billet mold copper tubes with different configuration designs were simulated at a casting speed of 5.5 m/min, cooling water volume of 150 t/h, down–top water supply, and a cooling water temperature of 8 °C. Through simulation analysis, the optimum design of the mold copper tubes with superior performance was determined.

3. Results and Discussion

In this paper, in order to explore the influence of different mold copper tube designs on its cooling performance and service life under high casting speed, the materials, wall thickness, and water slot configuration of the mold copper tube were simulated and analyzed. The objective was to obtain a copper tube configuration design for the mold that has better heat transfer performance and a longer service life.

3.1. The Influence of Mold Material

Different materials for molds exhibit varying heat transfer performance and mechanical properties. To ensure rapid and uniform cooling of molten steel within the mold, it is crucial to ensure that the mold possesses excellent heat transfer capability and deformation resistance. These requirements are even more stringent in high-speed continuous casting. Consequently, this study explores different mold materials in search of a more suitable material for high-speed continuous casting.

The heat transfer performance and service life of the molds are strongly influenced by the physical properties of different materials. The temperature field cloud atlas of the hot surface of a 15 mm mold copper tube with different material wall thicknesses under the conditions of 5.5 m/min casting speed and 150 t/h cooling water volume is shown in Figure 6. As shown in Figure 6, the temperature of the hot surface of the copper wall rises rapidly from the meniscus to the area 116 mm from the top, reaching the peak temperature of the mold’s hot surface. The temperature gradually decreases from the top 116 mm to the bottom of the mold. The molten steel gradually solidifies in this area, forming a solidified shell. The air gap between the shell shrinkage and the inner wall of the mold leads to a gradual increase in heat transfer resistance, resulting in a gradual decrease in temperature. The mold material plays a critical role in determining the hot surface temperature of the mold during the steel casting process. The simulation results show that the maximum temperature of the deoxidized phosphorus copper material is 151.797 °C and the minimum temperature is 48.361 °C. The maximum temperature of the Cu-Ag material is 146.877 °C and the minimum temperature is 48.318 °C. The maximum temperature of the Cu-Ag mold is lower than that of the deoxidized phosphorus copper material by approximately 4.92 °C. Qi L J et al. [24] studied these two different materials of water seam mold and found that the highest temperature of deoxidized phosphorus copper material was 263.88 °C and the lowest temperature was 63.81 °C; the highest temperature of Cu-Ag material was 241.59 °C and the lowest temperature was 64.43 °C. The water slot mold made of different materials in this study had a lower temperature and were more suitable for high-speed continuous casting production. Considering that the recrystallization temperature of Cu-Ag alloy is 370 °C, the Cu-Ag material mold would be an excellent choice as it provides superior cooling performance and is well-suited for continuous casting requirements.

The temperature curves of the hot surface center and cold surface center for different material molds are shown in Figure 7. It can be observed from Figure 7 that the mold material has little effect on the temperature curves. Due to the cooling water on the cold surface of the mold for cooling, the temperature of the cold surface is much lower than that of the hot surface. The hot surface temperature and cold surface temperature of different material molds are basically the same in the area above the meniscus. However, a significant difference in hot surface temperature appears from below the meniscus to the exit of the mold. The temperature of the hot surface is higher than that of the cold surface, but there is no significant difference in the temperature change trend between the hot surface and the cold surface. The analysis shows that the mold material has a great influence on the hot surface temperature of the copper wall, but it has little effect on the cold surface temperature. The temperature change trend of the hot surface and the cold surface has little relationship with the mold material.

Different materials have different physical properties. Therefore, it is necessary to explore the differences in the magnitude and location of the von Mises equivalent forces in different materials during the continuous casting process. The von Mises equivalent stress cloud atlas of different material mold copper tubes at 5.5 m/min casting speed and 150 t/h cooling water volume are shown in Figure 8. It can be seen from Figure 8 that the von Mises equivalent stress distribution on the inner wall of the copper tube is uniform; the maximum von Mises stress exists near the corner, which is 116 mm away from the upper mouth of the mold. The maximum von Mises equivalent stress of deoxidized phosphorus copper is 263 MPa, and the minimum von Mises equivalent stress is 18 MPa. The maximum von Mises equivalent stress of Cu-Ag material is 256 MPa, and the minimum von Mises equivalent stress is 17.6 MPa. The maximum von Mises equivalent stress of Cu-Ag material is 7 MPa lower than that of deoxidized phosphorus copper material, and the minimum von Mises equivalent stress is 0.4 MPa lower. The results show that the distribution of von Mises equivalent stresses of the two materials is consistent, but the von Mises equivalent stresses of Cu-Ag material are smaller. So, the Cu-Ag mold can have a longer service life than deoxidized phosphor copper in the continuous casting process, which is conducive to the smooth operation of continuous casting production.

The upper end of the tubular mold is generally fixed by a flange, and the surrounding is fixed by a steel plate. In actual production, due to the thermal expansion and cold contraction effects, the copper tube mainly produces longitudinal deformation along the casting direction. The longitudinal displacement cloud atlas of the copper wall of mold with different materials is shown in Figure 9. The longitudinal displacement of the copper wall of different materials is shown in Figure 10. It can be seen from Figure 9 and Figure 10 that due to the fixed reasons, the longitudinal deformation of the mold copper tube gradually increases from top to bottom and reaches its maximum at the outlet of the mold. When the mold is in continuous casting, the maximum longitudinal deformation of the deoxidized phosphorus copper material is 1.085 mm, and the maximum longitudinal deformation of the Cu-Ag material is 1.065 mm. The longitudinal deformation of the silver-coated copper tube is 0.0023% lower than that of the deoxidized phosphorus copper tube. When the mold returns to room temperature, due to the principle of thermal expansion and contraction, the mold copper tube will shrink, and the longitudinal deformation of Cu-Ag material is 4.86 × 10⁻⁵ mm less than that of deoxidized phosphorus copper material. The mold temperature and von-Mises equivalent stress of Cu-Ag material are lower; so, the longitudinal deformation is smaller, which is suitable for high-speed continuous casting production.

3.2. The Influence of Mold Wall Thickness

With different mold thicknesses, the cooling capacity and deformation resistance change accordingly. Different mold wall thicknesses have an important impact on the solidification of molten steel. Therefore, mold wall thickness is an inevitable issue in the mold design process. Appropriate mold wall thickness will play a positive role in the cooling and solidification of molten steel. In the process of high-speed continuous casting, the cooling capacity and deformation resistance of the mold is particularly important. Therefore, in this paper, the simulation analysis of molds with different wall thicknesses is carried out in order to obtain a better mold wall thickness design.

Because the transfer capacity of heat flow along the wall thickness of the mold gradually weakens, cooling capacity and service life vary considerably with mold wall thickness. So, three-dimensional simulations are carried out for different wall thicknesses of the mold to analyze the effect of different wall thicknesses on the temperature field of the mold. The design of a mold with different wall thicknesses is shown in Figure 11. The temperature field cloud atlas of the hot surface of the Cu-Ag mold with a different wall thickness under the conditions of 5.5 m/min casting speed and 150 t/h cooling water volume is shown in Figure 12. Because the wall thickness affects the heat transfer, the hot surface temperature of the thick-walled mold is much higher than that of the thin-walled mold. The maximum temperature of the 25 mm wall thickness mold is 207.64 °C and the minimum temperature is 55.60 °C. The maximum temperature of the 15 mm wall thickness mold is 146.88 °C and the minimum temperature is 48.32 °C. The maximum temperature of the hot surface of the 25 mm wall thickness mold is 60.76 °C higher than that of the 15 mm wall thickness mold and the minimum temperature is 7.28 °C higher. Prior studies [26] found that the mold wall thickened and the temperature increased; when the wall thickness increases by 4 mm, the hot surface temperature increases by about 20~25 °C. The results of this study are consistent with this. Therefore, to ensure the strength and stiffness of the copper tube, the wall thickness of the mold copper tube should be reduced to improve the cooling performance of the mold.

The temperature curves of the hot surface center and cold surface center of the Cu-Ag material mold with different wall thicknesses are shown in Figure 13. According to Figure 13, it can be clearly concluded that the wall thickness of the mold has a great influence on the overall temperature field of the mold. The temperature of the hot surface and the cold surface of the thick-walled mold is much higher than that of the thin-walled mold. However, the temperature change trend of the two molds is basically the same. This phenomenon shows that while the wall thickness has a great influence on the temperature field of the mold, it has little effect on the temperature change law.

The von Mises equivalent stress cloud atlas of Cu-Ag mold copper tubes with different wall thicknesses at 5.5 m/min casting speed and 150 t/h cooling water volume is shown in Figure 14. It can be obtained from Figure 14 that the maximum von Mises equivalent stress of a 25 mm wall thickness mold copper tube is 601 MPa and the minimum von Mises equivalent stress is 35.80 MPa. The maximum von Mises equivalent stress of a 15 mm wall thickness mold copper tube is 256 MPa, and the minimum von Mises equivalent stress is 17.60 MPa. The von Mises equivalent stress generated by the thick-walled mold is larger. The maximum von Mises stress exists at the corner position 116 mm from the top of the mold. The maximum von Mises equivalent stress is 345 MPa higher than that of the thin wall, and the minimum von Mises equivalent stress is 18.20 MPa higher than that of the thin wall. Therefore, the service life of the thick-walled mold is lower. As the wall thickness of the mold decreases, the thermal stress of the copper tube also decreases. It can be seen that the wall thickness of the mold copper tube should be reduced while ensuring the cooling effect of the mold. On the one hand, it can reduce the cost and production difficulty. On the other hand, it can reduce the deformation damage caused by thermal stress on the mold and improve the life of the mold.

With different wall thicknesses, the temperature field of the mold copper tube is different; so, the longitudinal displacement of the mold is also obvious. The longitudinal displacement cloud atlas of the copper wall of the mold with different wall thicknesses is shown in Figure 15. The longitudinal displacement of the copper walls with different wall thicknesses is shown in Figure 16. According to Figure 15 and Figure 16, under the same materials and the same water slot configuration, the maximum longitudinal displacement of the 25 mm wall thickness mold is 1.463 mm, the maximum longitudinal displacement of the 15 mm wall thickness mold is 1.065 mm, and the maximum longitudinal displacement of the thick-walled mold is 0.0443% higher than that of the thin-walled mold. When the mold returns to room temperature, the longitudinal displacement of the thick-walled mold is 9.875 × 10⁻⁵ mm longer than that of the thin-walled mold.

3.3. The Influence of Mold Water Slot Configuration

The mold primarily transfers heat outward through the flow of cooling water, and in high-speed continuous casting, the cooling water needs to remove more heat. Therefore, the design of the mold water slot configuration is particularly critical. The design of the mold water slot configuration needs to focus on the uniformity of the mold temperature and stress, which is particularly important for the cooling capacity and service life of the mold. Therefore, in this paper, two different types of water slot configurations of the mold are simulated and analyzed, and their temperature field and stress field are explored. Finally, the suitable mold water slot configuration design for high-speed continuous casting is obtained.

Different configurations of the water slot have different cooling effects on the molten steel, and the von Mises equivalent stress on the mold also varies. Therefore, different water slot configurations of the mold have different service lifetimes. The design of different mold water slot configurations is shown in Figure 17. The temperature field cloud atlas of the hot surface of the Cu-Ag material mold with different water slot configurations at a casting speed of 5.5 m/min and a cooling water volume of 150 t/h is shown in Figure 18. The temperature curves of the hot surface center and cold surface center of the Cu-Ag mold with different water slot configurations are shown in Figure 19. It can be seen from Figure 19 that the maximum temperature of the copper tube in the 2 mm rounded water slot is 148.488 °C and the minimum temperature is 48.566 °C. The maximum temperature of the copper tube in the right-angled water slot is 146.877 °C and the minimum temperature is 48.318 °C. The maximum temperature of the 2 mm rounded water slot mold is 2.895 °C higher than that of the right-angled water slot mold, and the minimum temperature is 0.248 °C higher. After the root of the water slot is designed as a rounded corner, the contact area of the cooling water with it decreases—so, the temperature of the 2 mm rounded-corner-type mold increases—but because of the small change in its contact area, the temperature change is also low.

The von Mises equivalent stress cloud atlas of the mold copper tube with different water slot configurations at 5.5 m/min casting speed and 150 t/h cooling water volume is shown in Figure 20. It can be seen from Figure 20 that the distribution of von Mises equivalent stress in the 2 mm rounded water slot mold is consistent with that of the right-angled water slot. The maximum von Mises equivalent stress of the copper tube of the 2 mm rounded water slot mold is 293 MPa, and the minimum von Mises equivalent stress is 17.2 MPa. The maximum von Mises equivalent stress of the copper tube of the right-angled water slot mold is 256 MPa, and the minimum von Mises equivalent stress is 17.6 MPa. The maximum value of the von Mises equivalent stress in the 2 mm rounded-corner water slot mold is 37 MPa higher than that in the right-angled water slot, and the minimum value is 0.4 MPa lower than that in the right-angled water slot. Due to the high temperature of the rounded-corner water slot mold, the von Mises equivalent stress also increases accordingly; so, the right-angled water slot mold has a better cooling effect and higher service life.

The cooling capacity of molds with different water slot configurations varies, resulting in different degrees of longitudinal deformation. The longitudinal displacement cloud atlas of the copper wall of the mold with different water slot configurations is shown in Figure 21. The longitudinal displacement of the copper wall of the mold with different water slot configurations is shown in Figure 22. It can be seen from Figure 21 and Figure 22 that the maximum longitudinal displacement of the copper tube in the 2 mm rounded-corner water slot mold is 1.1 mm, while the maximum longitudinal displacement of the copper tube in the rectangular water slot mold is 1.065 mm. The maximum longitudinal displacement of the 2 mm rounded water slot mold is 0.0039% higher than that of the right-angle type, while the change in longitudinal displacement of the right-angled water slot is lower. When the mold returns to room temperature, the longitudinal displacement of the 2 mm rounded-corner water slot mold is 4.83 × 10⁻⁵ mm longer than that of the rectangular mold. The results show that the service life of the 2 mm rounded mold is worse than that of the right-angle mold. In actual continuous casting production, the right-angle mold has a longer service life.

4. Conclusions

• Comparison with the deoxidized phosphorous copper material mold. For the working state, the Cu-Ag material copper wall exhibited a reduction of 4.92 °C in maximum temperature on its hot surface, as well as a decrease of 7 MPa in maximum von Mises equivalent stress on the copper wall. Additionally, the longitudinal displacement of the copper wall reduced by 0.0023%. When cooling to room temperature, the mold’s longitudinal displacement reduced by 4.86 × 10⁻⁵ m. So, the Cu-Ag material is better suited for the copper tube mold.
• Comparison with the 15 mm wall thickness mold. For the working state, the maximum temperature of the hot surface of the 25 mm wall thickness mold increased by 60.76 °C. Furthermore, the maximum von Mises equivalent stress of the copper wall increased by 340 MPa, and the longitudinal displacement of the copper wall increased by 0.0443%. When cooling to room temperature, the mold’s longitudinal displacement increased by 9.875 × 10⁻⁵ m. So, the thin-walled mold has superior heat transfer performance, prolonged service life, and is ideal for use in continuous casting applications.
• Comparison with the right-angled water slot mold. For the working state, the 2 mm rounded water slot mold exhibited a maximum temperature increase of 2.895 °C on its hot surface. Furthermore, the maximum von Mises equivalent stress of the copper wall increased by 37 MPa, while the longitudinal displacement of the copper wall increased by 0.0039%. When cooling to room temperature, the longitudinal displacement of the mold increased by 4.83 × 10⁻⁵ m. So, the right-angled water slot mold has a more comprehensive effect and better solidification of molten steel in the mold.

Under high-speed casting conditions, all aspects of the performance of the mold need to be improved. In this paper, through the simulation analysis of the mold material, thickness, and slot configuration, we finally determined that the Cu-Ag material with a 15 mm wall thickness and a right-angled slot configuration for the mold is best. It has better heat transfer performance, mechanical properties, and a longer service life. This kind of mold is more in line with the requirements of high-speed casting.