1. Introduction
Semi-autogenous mills play a crucial role in the mining industry, being widely used for crushing and grinding various ores. The cylinder liner of a semi-autogenous mill is a key component that directly impacts the mill’s performance and service life. It is subjected to intense impact and friction from ore blocks and grinding media during operation, which requires it to have excellent impact resistance and wear resistance. The casting quality of the liner is closely related to its service life. Defects such as shrinkage porosity and shrinkage cavity in the liner can significantly reduce its mechanical properties and service life, leading to increased maintenance costs and production interruptions. Therefore, improving the casting process of semi-autogenous mill cylinder liners is of great significance for enhancing the efficiency and economy of the mining industry.
2. The Role and Importance of Semi-autogenous Mill Cylinder Liners
2.1 Functions of Cylinder Liners
Cylinder liners in semi-autogenous mills have two main functions. Firstly, they protect the mill cylinder from being eroded by ore pulp and directly impacted by steel balls. The harsh working environment inside the mill, with high – speed collisions of ore and steel balls, would quickly damage the cylinder without the protection of the liner. Secondly, the raised lifting bars on the liner can continuously lift the grinding media and materials, enabling them to fall and cascade, which is essential for the crushing and grinding of materials.
2.2 Impact on Mill Performance
The quality of the cylinder liner has a direct impact on the performance of the semi-autogenous mill. A well – cast liner with high – quality material and proper design can improve the grinding efficiency of the mill. For example, a liner with less wear and tear can maintain its shape and surface integrity, ensuring that the grinding media and materials are effectively lifted and distributed, which in turn enhances the crushing and grinding effect. On the contrary, a liner with defects such as shrinkage porosity and shrinkage cavity may have reduced mechanical strength. This can lead to premature failure, such as fatigue wear and fracture, increasing the frequency of liner replacement and affecting the continuous operation of the mill.
3. Problems with the Original Casting Process
3.1 Liner Structure and Material
The semi-autogenous mill cylinder liner studied in this paper has a contour size of 1180mm x 470mm x 340mm. Its quality attributes are shown in Table 1.
| Volume (\(cm^{3}\)) | Curved Surface Area (\(cm^{2}\)) | Density (\(kg\cdot cm^{-3}\)) | Mass (kg) | |
|---|---|---|---|---|
| Liner Casting | \(9.27\times10^{4}\) | \(2.03\times10^{4}\) | \(7.82\times10^{-3}\) | \(7.25\times10^{2}\) |
| Table 1. Quality attributes of linings |
The liner is made of chromium – molybdenum alloy steel, and its chemical composition is presented in Table 2.
| Element | C | Si | Mn | P | S | Cr | Mo | Cu |
|---|---|---|---|---|---|---|---|---|
| Content (%) | – | – | – | – | – | – | – | – |
| Table 2. Chemical composition of chromium – molybdenum alloy steel |
The liquidus temperature of this alloy steel is 1476°C, and the solidus temperature is 1117°C.
3.2 Simulation Analysis of the Original Casting Process
The original casting process of the liner is shown in Figure 2. The metal liquid is introduced from the end face of the liner casting, and the open riser is set between the casting and the inner runner. The pouring temperature of the liner casting is 1530°C, and the ambient temperature is 20°C.
The simulation analysis using ProCAST software shows several problems. In the filling process, as shown in Figure 3, when the metal liquid flows into the mold cavity through the inner runner, it has the minimum potential energy and the maximum kinetic energy when approaching the end of the mold. Then it collides with the end of the mold, which may cause the EVA film and the coating layer that maintain the negative pressure state of the mold to fall off, reducing the vacuum degree of the mold and potentially resulting in mold collapse. Moreover, the metal liquid may experience backflow and flow pulsation, which is prone to gas entrapment.
In the solidification process, as the cooling time increases, the liner casting gradually solidifies from the outer edge to the thick – walled center. When the solidification reaches a certain stage, the feeding channel of the casting shrinks and narrows, and the feeding effect of the riser on the casting deteriorates. Finally, the feeding channel is blocked by the solidified metal, and the open riser loses its feeding function on the casting, resulting in the formation of isolated liquid – phase areas inside the casting. This is predicted to cause shrinkage porosity and shrinkage cavity defects. The distribution of shrinkage porosity and shrinkage cavity in the casting is shown in Figure 4. The simulation results are consistent with the actual defects found in the castings produced by the V – process foundry.
4. Intelligent Design of the New Casting Process
4.1 Development of the Casting Process Intelligent Design Software
Based on the production conditions of the V – process foundry, a 《Casting Process Intelligent Design (Steel Casting)》 software was independently developed using the Basic language. This software provides one – stop services for the gating system design, riser design, and chill design of liner castings. It offers various shapes of open risers and exothermic risers, such as cylindrical, frustum – shaped, and frustum – waist – shaped, to meet different design requirements.
4.2 Intelligent Design of the Gating System
4.2.1 Calculation of Pouring Time
The design of the gating system for V – process casting follows the principle of “seeking speed while ensuring stability”. To reduce the baking time of the EVA film on the upper surface of the mold cavity during the pouring process and avoid a decrease in the negative pressure in the mold, the pouring time needs to be shortened as much as possible. The pouring time t is calculated by the formula \(t = S_{1}\sqrt[3]{\delta G_{L}}\). For this liner casting, considering the weight and thickness of the casting, the total mass of the metal liquid in the mold \(G_{L}\) is initially determined to be 2150kg (two pieces per box), and the average wall thickness \(\delta\) of the casting is taken as 150mm. By looking up the table, the coefficient \(S_{1}\) is selected as 1.1. Then the pouring time t is calculated as follows: \(t = 1.1\sqrt[3]{150\times2150}\approx75s\)
4.2.2 Calculation of the Sprue Hole Cross – sectional Area
First, the pouring speed v is calculated as \(v=\frac{G_{L}}{t}=\frac{2150}{75}\approx29kg/s\). Considering the opening degree of the sprue hole plug head during pouring, the sprue hole pouring speed \(v_{sprue}\) should be 1.3 times the required pouring speed of the casting, so \(v_{sprue}=1.3\times29 = 37.7kg/s\approx38kg/s\). The cross – sectional area of the sprue hole \(A_{sprue}\) is calculated by the formula \(v_{sprue}=\mu A_{sprue}\rho_{L}\sqrt{2gH_{0}}\). After calculation, \(A_{sprue}\approx24cm^{2}\), and the diameter of the sprue hole \(d\approx55mm\).
4.2.3 Calculation of the Cross – sectional Areas of Each Unit
For bottom – pouring with an open gating system, the general ratio of the cross – sectional areas of each unit is \(\sum A_{sprue}:\sum A_{straight}:\sum A_{runner}:\sum A_{ingate}=1.0:(1.8 – 2.0):(1.8 – 2.0):(2.0 – 2.5)\). In V – process casting, to alleviate heat concentration and reduce the melt flow rate, the total cross – sectional area of the ingate is increased by about 30% compared with ordinary sand casting. So the ratio of the cross – sectional areas of each unit is adjusted to \(\sum A_{sprue}:\sum A_{straight}:\sum A_{runner}:\sum A_{ingate}=1:1.8:2:3\). Accordingly, \(\sum A_{straight}=44cm^{2}\), \(\sum A_{runner}=48cm^{2}\), and \(\sum A_{ingate}=72cm^{2}\). The gating system is designed as shown in Figure 5. The straight runner is designed as a tapered shape to prevent the formation of a low – pressure liquid – flow area at the bottom, which could suck in air and cause casting defects. A pouring basin is designed at the lower end of the straight runner to buffer the impact of the liquid flow. The cross – section of the runner is designed as a trapezoid, and its length is appropriately extended to collect slag. The ingate is introduced at the parting surface of the liner casting to combine the advantages of top – pouring and bottom – pouring, and its cross – section is designed as a semi – circle.
4.3 Intelligent Design of the Open Exothermic Riser
4.3.1 Calculation of the Volume Shrinkage Rate of Molten Steel during Solidification
The molten steel in the mold experiences three interrelated shrinkage stages during the cooling process from the pouring temperature to room temperature: liquid shrinkage, solidification shrinkage, and solid shrinkage. The volume shrinkage rate \(\varepsilon\) of molten steel during liquid shrinkage is mainly affected by alloy composition and pouring temperature. For chromium – molybdenum alloy steel, the volume shrinkage rate \(\varepsilon\) is calculated by the formula \(\varepsilon = 1.9943+7.459w_{c}-4.73w_{c}^{2}+\sum K_{i}w_{i}+K_{T}(T_{P}-T_{L})\). After calculation, the volume shrinkage rate \(\varepsilon\) of the chromium – molybdenum steel molten steel is 5.81%.
4.3.2 Calculation of the Size of the Open Exothermic Riser
The size of the open exothermic riser is calculated using the analytical method (cubic equation). By equating the actual modulus of the riser at the end of solidification \(M_{R}’\) and the actual modulus of the fed casting \(M_{C}’\), and through a series of mathematical derivations, the formula for calculating the equivalent diameter d of the riser is obtained: \(d=\sqrt[3]{A + B+\sqrt{2AB + B^{2}}}+\sqrt[3]{A + B-\sqrt{2AB + B^{2}}}+\sqrt[3]{A}\) For this liner casting, after substituting the relevant parameters, the equivalent diameter d of the exothermic riser is calculated to be 25cm, and the height h of the riser is \(h = f_{1}\cdot d=1.5\times25 = 37.5cm\). An HLFM – C – S300 type open exothermic riser is selected, with a heating energy of \(1650kJ\cdot kg^{-1}\), an ignition temperature of 1200°C, and a heating time of 240s.
4.4 Determination of the Riser Placement Position
The placement position of the riser is crucial for eliminating shrinkage porosity and shrinkage cavity defects in the casting. The traditional view is that to improve the feeding efficiency of the riser, the riser should be placed at the position with the largest modulus of the casting. However, practical production shows that directly placing the riser at the position with the largest modulus may lead to the generation of contact hot spots. Only by placing the riser slightly 偏离 the position with the largest modulus of the casting can the shrinkage porosity and shrinkage cavity defects in the casting be effectively eliminated.
To accurately obtain the modulus distribution of each part of the casting, the Chvorinov thermal modulus is used as the modulus of the casting. For a semi – infinite large flat – plate sand casting, the relationship between the solidification layer thickness S and the solidification time \(t_{sol}\) is \(S=\frac{2}{\sqrt{\pi}}\left(\frac{T_{all,sol}-T_{mold,ini}}{\rho_{al,sol}\cdot\Delta H_{al}}\right)\left(k_{mold,ini}\cdot\rho_{mold,ini}\cdot C_{p,mold,ini}\right)^{1/2}\left(t_{sol}\right)^{1/2}\). This relationship is extended to complex – shaped castings, and the Chvorinov theorem \(M=\frac{V}{A}\approx S\) is obtained.
By using the ProCAST numerical simulation system to analyze the casting process of the liner casting (excluding the riser) and substituting the relevant parameters into the Chvorinov thermal modulus calculation formula, the distribution cloud diagram of the Chvorinov thermal modulus of the liner casting is obtained, as shown in Figure 6. It can be seen that the maximum value of the thermal modulus of the casting is 3.9cm, and the distribution law is that the thermal modulus gradually increases from the outer edge of the liner to the center. Therefore, the open exothermic riser is determined to be set near the center of the upper surface of the base plate.
5. Simulation Analysis of the New Casting Process
The ProCAST numerical simulation software is used to analyze the new casting process of the liner casting. Since two pieces are cast in one box and they are approximately symmetric, to improve the accuracy of the numerical simulation operation while avoiding a significant increase in the amount of calculation, a symmetric plane is set in the middle of the model, and half of the model is used for simulation analysis.
In the filling process, as shown in Figure 8, the metal liquid flows into the mold cavity quickly and stably through the gating system. When the metal liquid approaches the end of the mold, the flow velocity is 0.5 – 0.7m/s. Then it collides slightly with the end of the mold, and the backflow occurs with an unobvious liquid – flow stratification. The overall flow of the metal liquid in the mold cavity is gentle during the filling process, and the free liquid surface rises steadily without disturbance, effectively avoiding oxidation inclusions caused by the disturbance and overflow of the metal liquid in the mold cavity.
