Rapid Sand Casting Process of Cylinder Head Based on Numerical Simulation

1. Introduction and Research Significance

In the 21st century, the Chinese automotive industry is experiencing vigorous development and has become a pillar industry of the national economy. However, the industry still faces challenges including unreasonable industrial structure, low technological level, and weak independent research and development capabilities. One of the key bottlenecks restricting the improvement of independent R&D capabilities is the lack of rapid manufacturing methods and related common technology platforms. Automotive components exhibit characteristics such as complex structures, high load-bearing requirements, stringent dimensional accuracy, and harsh working conditions. Driven by rapid global economic development, there is also a requirement for faster product updates and shorter production cycles to adapt to flexible and changing market demands. Although China is the largest producer of castings globally, the foundry conditions are relatively underdeveloped, making it difficult for the casting mold industry to adapt to the current situation, thus presenting urgent problems for the Chinese foundry industry to solve.

The engine cylinder head is one of the most complex and critical components in an engine, requiring enterprises to possess specialized casting technology for its development and production. Traditional development methods for cylinder heads involve trial production and modification using wooden or metal patterns, leading to long development cycles and high costs. A typical development cycle for a cylinder head lasts 6-8 months, with gravity mold development costs around one million yuan per set. These traditional development approaches severely restrict the improvement of enterprise R&D capabilities and bring enormous development costs, failing to adapt to the rapid upgrading of automotive engines and the urgent need for industrialization of key components.

Sand casting is the most widely used casting technology in the foundry industry. Rapid sand casting technology employs rapid prototype parts instead of traditional metal or wooden patterns, and combines rapid casting process CAD systems for mold design along with traditional casting techniques to rapidly produce castings. SLA (Stereolithography Apparatus) technology is a relatively mature light-curing prototype technology. Using SLA prototypes to create patterns and core boxes, combined with traditional sand mold splitting, assembly, and other processes, forms a complete method for producing rapid sand casting molds. Since SLA patterns and core boxes are reusable in the SLA-based rapid sand casting process, costs are reduced and casting quality is improved. Therefore, rapid sand casting based on SLA prototypes is particularly suitable for automotive castings with complex shapes requiring sand cores, such as cylinder blocks, cylinder heads, intake and exhaust manifolds, and similar sand casting parts.

This research uses a certain type of automotive engine cylinder head as an example, adopts the above rapid sand casting process route to design the mold, and utilizes the professional casting CAE analysis software PROCAST to inversely determine the heat transfer coefficient—a key process parameter in sand casting. Several design schemes for the entire filling and solidification process are simulated, and the optimal gating system and riser structure are determined, providing guidance for the design of actual cylinder head gravity casting molds. This research effectively shortens mold design time and reduces dependence on traditional empirical design, offering high reference value for the development of new products and the production of other single-piece and small-batch parts, especially those categorized as sand casting parts.

2. Rapid Sand Casting Process and Cylinder Head Modeling

2.1 Rapid Sand Casting Process Flow

Rapid sand casting technology involves using a casting process CAD system for process parameter settings, sand core design, gating system design, riser design, and other steps based on the three-dimensional model of the casting. The SLA rapid prototype parts are then used as patterns, combined with the excellent molding capability of resin self-hardening sand, to directly produce the external mold and sand cores. This process offers advantages including short development cycles and higher precision compared to traditional sand casting in single-piece and small-batch production or new product development. The specific process steps include: 3D modeling of the casting → casting process design using CAD system → rapid prototyping of the pattern (SLA) → mold assembly and core making → pouring → post-processing and inspection.

2.2 Three-dimensional Modeling of the Cylinder Head

For this research, the three-dimensional model of the engine cylinder head was created using Unigraphics NX 8.0 software. UG NX is a next-generation digital product developed by Siemens PLM Software, which is the most widely used enterprise application and provides a fully associative integrated CAD/CAM/CAE application suite. The cylinder head casting blank produced by sand casting has a casting material of ZL105 aluminum alloy, with overall dimensions of 426 mm × 200 mm × 131 mm, a volume of 4581 cm³, and a total weight of approximately 12.4 kg. The casting belongs to a thin-walled box-type part with a minimum wall thickness of 4 mm. For single-piece manual molding, the dimensional tolerance grade is 10CT. The engine cylinder head is a medium-sized box-type part that serves as the reference part for assembling other components within the box. The main structure consists of different shapes of cavities enclosed by uniform thin walls, with numerous holes on the cavity walls for accommodating and supporting purposes, along with reinforcing ribs, bosses, recesses, casting fillets, and draft angles. The internal structure of the engine cylinder head is complex, and its structural dimensional accuracy closely relates to the assembly and use of other components. Therefore, the product must guarantee the dimensions and positional accuracy of eight intake ports and four exhaust ports, requiring precise sand core design and positioning.

2.3 Casting Process Design

Based on the casting process requirements, the casting process CAD system developed by the laboratory was used for the casting process design of the cylinder head. The design process includes casting process analysis, parting surface setting, material addition, sand core design, gating system design, riser design, exhaust system design, as well as casting process parameters such as machining allowance and casting shrinkage.

According to the structural characteristics of the engine cylinder head, the sand cores can be divided into: (a) lower left oil gallery core, (b) lower right oil gallery core, (c) water jacket sand core, (d) upper oil gallery core, (e) intake port sand core, and (f) exhaust port sand core. In rapid sand gravity casting, the sand cores vary in shape and require high strength, all manufactured using the shell core process. To ensure core quality, the surface is coated with water-based alcohol coating to prevent sand inclusion defects during mold filling. The lower left and right oil gallery cores are placed on the bottom core. The intake port sand core and exhaust port sand core are positioned relative to other sand cores through core print left and right positioning blocks. The middle layer is the water jacket sand core connected to the lower oil gallery cores as a whole, while the upper oil gallery core is installed and positioned on the mold using three-point positioning. Core rods are used as support structures in slender sections of each sand core to ensure strength.

The design of the gating system is crucial for guiding the molten metal into the mold cavity. The rationality of the gating system design relates to whether the molten metal can smoothly fill the mold cavity and whether defects such as sand erosion, gas entrapment, and turbulence occur during the filling process. The design principles include: smooth and continuous filling of molten metal without direct impact on cores; controlling the flow direction and sequence during filling to ensure clear and complete casting contours; filling the cavity within an appropriate time to avoid defects such as sand inclusion and cold shut; and providing slag retention and overflow capacity with simplicity and reliability.

Three different pouring positions were determined for this design: unilateral top injection, symmetrical top injection, and unilateral bottom injection. The unilateral top injection system has four ingates distributed at the top of the casting. The pouring time can be calculated as:

$$ t = 3\sqrt{G_{件}} + \delta \times 3\sqrt[3]{G_{件}} $$

The total ingate cross-sectional area is calculated using:

$$ A_{内} = \frac{G_L}{\rho_L \mu t \sqrt{2g h_p}} $$

where \( G_L \) is the total mass of molten metal flowing through the choke area, \( \rho_L \) is the density of molten metal, \( \mu \) is the flow loss coefficient, \( t \) is the pouring time, \( g \) is gravitational acceleration, and \( h_p \) is the average static pressure head. An open gating system was adopted with a cross-section ratio of \( A_{直}:A_{横}:A_{内} = 1:2:4 \). The designed runner cross-section dimensions and various gating system parameters for the three schemes are summarized in Table 1.

Riser design employs the modulus method. According to the Chvorinov formula, the solidification times of the casting and riser are:

$$ M = \frac{V}{A} $$

$$ T_c = \left(\frac{M_c}{K_c}\right)^2, \quad T_r = \left(\frac{M_r}{K_r}\right)^2 $$

Based on the feeding shrinkage characteristics of the casting, standard waist-shaped top open risers were selected, located in the upper mold. Two types of risers were set according to the position, shape, and volume of the feeding area.

3. Numerical Simulation Pre-processing

3.1 Mesh Generation

For the numerical simulation, ProCAST’s mesh generation module MeshCAST was used. The models were exported from UG NX 8.0 in a universal format that MeshCAST can recognize. ProCAST uses tetrahedral elements for meshing. The basic mesh division experience requires that the element length generally be 1/2 to 1/3 of the minimum wall thickness. For Scheme 1, the casting was divided into a total of 107,385 nodes and 471,675 elements; Scheme 2 had 107,035 nodes and 470,289 elements; Scheme 3 had 115,990 nodes and 508,256 elements. Mesh quality evaluation was performed using three criteria: dihedral angle, radius ratio, and edge length ratio. The ideal mesh consists of regular tetrahedral elements, with dihedral angles approaching 60°, radius ratio approaching 1, and edge length ratio approaching 1. After smoothing and optimization, the mesh quality met the computational requirements without singular triangles.

3.2 Virtual Mold Setting

To avoid excessively large computation tasks, ProCAST can simulate molds without actual mesh division using a virtual mold approach. The virtual mold requires defining the mold dimensions (a rectangular box along x, y, z directions), mold material, and the interfacial heat transfer coefficients between various parts of the casting and the mold. The calculation time depends only on the number of mesh elements of the casting itself. The mold boundary conditions outside the defined box are treated as adiabatic boundaries. A sufficiently large box was defined to avoid significant errors.

3.3 Boundary Conditions and Material Parameters

The casting material is ZL105 aluminum alloy, an Al-Si-Mg system alloy with good casting performance, high strength, and good thermoplasticity. The liquidus temperature of ZL105 alloy is 622°C, and the solidus temperature is 536°C. The mold materials (upper mold, lower mold, and sand cores) all use phenolic urethane resin sand based on silica sand. The temperature-dependent thermophysical properties of ZL105 aluminum alloy are shown in the following equations and tables. The solid fraction can be expressed as:

$$ f_s = \begin{cases} 1, & T \leq T_s \\ \frac{T_L – T}{T_L – T_s}, & T_s < T < T_L \\ 0, & T \geq T_L \end{cases} $$

The density, enthalpy, and thermal conductivity of ZL105 aluminum alloy as functions of temperature are given in Table 2. Table 3 lists the reference initial conditions and boundary conditions used in the simulation.

4. Inverse Determination of Interfacial Heat Transfer Coefficient

4.1 Experimental Design

The accuracy of numerical simulation depends significantly on the boundary conditions, among which the interfacial heat transfer coefficient (IHTC) at the solidifying interface plays a decisive role. The IHTC is affected by various factors during the casting process, such as spatial temperature, atmospheric pressure, casting and mold materials, initial mold temperature, and interface coatings, making accurate experimental determination very difficult. In this research, the interfacial heat transfer coefficient between ZL105 aluminum alloy and resin sand mold was determined using an inverse method based on Beck’s nonlinear estimation technique combined with experimentally measured temperature data.

To ensure reasonable computation time and improve efficiency, the experimental model was simplified to a two-dimensional axisymmetric problem. The experimental casting was a standard cylindrical symmetric structure with dimensions of 300 mm × 200 mm. The model was simplified to a single interface between the casting and sand mold, neglecting external environmental interference factors. Thermal insulation materials (asbestos) were used at the pouring cup and bottom end to minimize direct heat dissipation from the casting to the air. The molten metal was quickly poured from the top, followed by covering with an insulating asbestos layer. The measurement points included TC1 (1 mm from the interface in the casting), and TC2, TC3, TC4, TC5 in the sand mold at distances of 5 mm, 10 mm, 15 mm, and 20 mm from the interface, respectively.

4.2 Mathematical Model for Inverse Determination

The interfacial heat transfer coefficient is defined as the amount of heat passing through the casting-mold interface per unit area, unit time, and unit temperature difference, expressed as:

$$ h(t) = \frac{q(t)}{T_1 – T_2} $$

where \( h(t) \) is the IHTC, \( q(t) \) is the heat flux at the interface, \( T_1 \) is the casting surface temperature, and \( T_2 \) is the mold surface temperature. The heat conduction equation in cylindrical coordinates was simplified to a one-dimensional form:

$$ \frac{\partial T}{\partial t} = \alpha \left( \frac{1}{r} \frac{\partial T}{\partial r} + \frac{\partial^2 T}{\partial r^2} \right) $$

The inverse method uses the finite difference method to estimate the temperature field. The initial and boundary conditions are:

$$ q = q(t), \quad T(r,0) = Q(r,0), \quad T(l,t) = Q(l,t) $$

The finite difference equations for the surface node and internal nodes are given by:

$$ T_i^{p+1} = T_i^p(1 – 2F_0) + T_{i+1}^p F_0 \left(1 – \frac{\Delta r}{2r}\right) + \frac{2q k \Delta t}{\Delta r} \quad (i=1) $$

$$ T_i^{p+1} = T_{i-1}^p F_0 \left(1 + \frac{\Delta r}{2r}\right) + T_i^p(1 – 2F_0) + T_{i+1}^p F_0 \left(1 – \frac{\Delta r}{2r}\right) \quad (i=2,3,…) $$

The Fourier number is constrained as:

$$ F_0 = \frac{\alpha \Delta t}{\Delta r^2} = \frac{k \Delta t}{c \rho \Delta r^2} \leq 0.5 $$

The sensitivity coefficient is calculated as:

$$ X_{i,j} = \frac{T_{i+j-1}^p – T_{i+j-1}^p}{\partial q} $$

The heat flux correction is iteratively computed using:

$$ \Delta q^p = \frac{\sum_{j=1}^{m} \sum_{i=1}^{u} X_{i,j}^{p} (Y_i – T_{i,j}^{p-1})}{\sum_{j=1}^{m} \sum_{i=1}^{u} (X_{i,j}^{p})^2} $$

$$ q_{corr}^p = q^p + \Delta q^p $$

The iteration is terminated when the convergence criterion is satisfied:

$$ \left| \frac{\Delta q}{q} \right| \leq \varepsilon $$

4.3 Experimental Results and IHTC Determination

The temperature cooling curves of ZL105 aluminum alloy in phenolic urethane resin sand mold were measured. The casting surface temperature and center temperature initially decreased rapidly, while the mold temperature increased sharply. As the temperature difference narrowed, the rate of change became more gradual. During the first 60 seconds, the casting center temperature decreased significantly from 690°C to 635°C. From 60 to 300 seconds, the temperature decreased more gradually to 611°C. Subsequently, the cooling rate became even slower until the solidus temperature was reached at approximately 2300 seconds. The mold temperature at 5 mm from the interface reached a maximum of about 570°C at 300 seconds, then slowly decreased. At 5000 seconds, the temperatures at distances of 5 mm, 10 mm, 15 mm, and 20 mm from the interface were 384°C, 353°C, 346°C, and 326°C, respectively.

Using the inverse method with time and distance intervals of 1 s and 1 mm, respectively, the estimated heat flux showed a significant increase during the initial stage (0-60 s) reaching a maximum of 256000 W/m², followed by a rapid decrease to 4300 W/m² at 500 s, and then a gradual decline. The IHTC between ZL105 aluminum alloy and the phenolic urethane resin sand mold was calculated, and the relationship between IHTC and casting surface temperature is shown in Table 4.

At the initial casting temperature of 690°C, the IHTC was 811 W/(m²·K), decreasing to 790 W/(m²·K) at the liquidus temperature. During the mushy zone, the IHTC decreased rapidly, reaching 310 W/(m²·K) at the end of solidification. During subsequent cooling, the IHTC stabilized at approximately 230 W/(m²·K). The inverse-determined IHTC was validated by comparing measured and simulated temperature profiles, with maximum error of approximately 11°C, confirming the reliability of the results. This provides a reference for future simulations of ZL105 aluminum alloy in phenolic urethane resin sand molds.

5. Numerical Simulation Results and Analysis

5.1 Unilateral Top Injection Scheme

The filling process of the cylinder head with the first scheme (unilateral top injection) was analyzed. The results show that the molten metal can successfully fill the mold cavity without cold shut defects, with a total filling time of approximately 15.7 seconds. During the initial filling stage, the molten metal enters the mold cavity through multiple ingates dispersed to avoid direct sand erosion. After 8 seconds of filling, the bottom layer of molten metal is at approximately the same level and then rises slowly and steadily until the cavity is filled, with no obvious gas entrapment observed. However, the filling time distribution for different positions at the same horizontal level is uneven in the initial stage due to the unilateral gating arrangement. Positions closer to the ingate fill faster initially, while at higher levels the filling times become more uniform.

For the solidification process, the temperature field evolution was examined at various times. Early in solidification, the casting can form sequential solidification toward the ingate direction, with the ingate region maintaining the highest temperature, providing feeding conditions. However, after approximately 120 seconds, the riser region starts to solidify while the bottom of the casting still contains liquid-solid coexistence regions, meaning the riser cannot adequately feed the casting. The solid fraction evolution in the riser cross-section revealed that after 45 s, the solid fraction in the ingate and riser reaches about 40%, providing good feeding. However, at 125 s, the solidification rate at the bottom of the ingate reaches 85%, while the center of the thick sections has only 45% solid fraction, creating an isolated liquid region that inevitably leads to shrinkage porosity and shrinkage cavities. The simulation predicted three significant shrinkage cavity regions in the lower-middle thick sections near the ingate, consistent with the isolated liquid regions observed in the solid fraction analysis.

5.2 Symmetrical Top Injection Scheme

The second scheme utilized eight symmetrically arranged top ingates. The filling time was approximately 14 seconds. Due to the dispersed ingate arrangement, the initial filling rate was relatively low, with only 10% filling at 4 s and 25% at 8 s. The entire filling process appeared smoother compared to the first scheme. However, the runner system is longer, causing more significant temperature decrease of the molten metal and potential for slag inclusion defects. The filling time distribution for positions at the same horizontal level showed more significant differences compared to the first scheme, which could potentially lead to oxidation and gas entrapment defects.

During solidification, the initial stage follows sequential solidification with good feeding. The temperature gradient analysis and solid fraction evolution in the riser cross-section showed that at 45 s, the casting begins to form closed high-temperature regions, and the riser cannot provide adequate feeding. At 125 s, isolated liquid regions still appear but are smaller than in the first scheme. After 240 s, the bottom regions still have about 70% solid fraction, suggesting defects are likely in the isolated liquid regions. The predicted shrinkage cavity and porosity distribution showed one larger shrinkage defect at the bottom near the ingate, but the total defect volume was reduced compared to the first scheme. The solid fraction profiles for both schemes are compared in Table 5.

5.3 Unilateral Bottom Injection Scheme

The third scheme employed a unilateral bottom injection gating system. The filling process analysis showed that this scheme achieves smooth filling with a total filling time of approximately 15.4 seconds. At 2 s, the molten metal begins filling the casting; at 5 s, 15% is filled; at 8 s, 40% is filled; at 11 s, 70% is filled; and filling completes at 16 s. The filling rate is appropriately slow at the initial stage to avoid sand erosion and gas entrapment, stable in the middle stage with uniform liquid level rise, and the final stage accommodates the reduction in filling rate due to gravity and pouring pressure, yet still successfully completes the riser filling without needing to increase the static pressure head height. The filling time distribution shows that after 15% filling, the filling times at the same horizontal level are basically consistent, providing very stable filling that effectively avoids defects such as inclusions, turbulence, and oxidation compared to the first two schemes.

For solidification analysis, the temperature field at different times showed that the casting follows sequential solidification throughout the entire process. At 46 s, the riser region exhibits obvious feeding. At 126 s, the casting interior temperature is higher than the edges, but the ingate and runner metal temperature remains higher than the thick sections of the casting. Even at 236 s, while the casting has essentially completely solidified, the ingate still maintains a liquid-solid two-phase region, indicating excellent feeding capability of the gating and riser system. The solid fraction evolution showed that during 45-240 s, the casting solidifies according to the sequential solidification principle, with adequate feeding of thick sections by the riser for upper regions and by the ingate for lower thick sections that were difficult to feed in the first two schemes. The entire casting does not form obvious isolated liquid regions. The shrinkage prediction showed only uniformly dispersed micro-porosity within the casting, representing the highest quality among the three schemes.

The comprehensive comparison of the three gating system designs is presented in Table 6.

Based on the numerical simulation analysis, the unilateral bottom injection scheme was selected as the optimal design. The pouring temperature was determined to be approximately 690°C with a pouring speed of 0.22 m/s, which ensures smooth filling without turbulence or discontinuity, accurately reflects the temperature field evolution, and minimizes casting defects. These optimized parameters significantly reduce production costs and improve efficiency for producing sand casting parts.

6. Rapid Sand Casting Experimental Production

6.1 Mold Assembly and Sand Core Installation

Based on the optimized design, the three-dimensional exploded diagram of the sand mold assembly was created. The sand core design considers core print positioning and smooth installation and removal, combined with the parting surface of the SLA prototype. The external mold is designed layer by layer from bottom plate to top. The mold assembly was completed, followed by mold finishing, assembly, cleaning, and coating processes.

6.2 Selection of Molding Material

Phenolic urethane resin self-hardening sand was selected as the molding material for the rapid sand casting experiments. This material offers advantages of easy compaction, high strength, high precision, and good collapsibility, making it particularly suitable for single-piece and small-batch production. The requirements for the base sand include: high SiO₂ content, round grain shape with a grain shape coefficient less than 1.2, particle size of approximately 40-70 mesh, average fineness appropriate for surface finish, moisture content below 0.2%, clay content below 0.05%, and sand temperature controlled between ambient temperature and 35°C.

Orthogonal experiments were designed to determine the optimal ratio of the two resin components. The experiments used 400 g of sand per batch at room temperature (approximately 25°C) with mixing time of about 2 minutes and demolding time of about 40 minutes. The factor-level table for the orthogonal experiment is shown in Table 7.

The tensile strength test results showed that when Component I (or Component II) is below 0.8% of the sand mass, the requirements cannot be met regardless of the other component. When one component is sufficient and the other is above 1%, basic requirements are achieved. The tensile strength increases with increasing amounts of both components. When Component I is below 2%, the tensile strength increases rapidly; above 2%, the increase slows. Similarly, when Component II is below 2.2%, the tensile strength increases rapidly; above 2.2%, the increase slows. From the perspective of strength requirements for SLA rapid sand casting, when Component I exceeds 2% of the total sand mass, the strength becomes too high, causing difficulty in sand repair and wasting resin material. The ideal condition was determined as Component I:Component II = 1:1 with Component I at 0.8%–1% of the total sand mass, achieving a tensile strength of approximately 1.1 MPa, which satisfies the strength requirements while minimizing material cost.

6.3 Production Results

Following the design specifications, the molding process was completed. The mold finishing, assembly, cleaning, and coating operations were performed, followed by pouring. The production process included the installation of intake and exhaust sand cores, water jacket sand cores, and the complete assembly before pouring. The comparison between qualified and unqualified molding results confirmed the importance of proper resin component ratios. When either component is insufficient, the mold strength is inadequate and cannot meet performance requirements. The qualified aluminum alloy cylinder head castings were successfully produced through this rapid sand casting process, validating the complete technological route. The successful production demonstrates that the process is well-suited for manufacturing complex sand casting parts in single-piece and small-batch quantities.

7. Conclusions and Future Work

This research established a complete and feasible rapid sand casting process route for the engine cylinder head. The key conclusions are summarized as follows:

(1) The three-dimensional model of the cylinder head was successfully created using UG NX 8.0, and the casting process design including gating system, risers, sand cores, and process parameters was completed using the casting process CAD system developed by the laboratory. The integration of CAD modeling and mold design enabled visualization, flexibility, and efficiency in the design process.

(2) The interfacial heat transfer coefficient between ZL105 aluminum alloy and phenolic urethane resin sand mold was determined through inverse analysis of experimentally measured temperature data. The IHTC values were 811 W/(m²·K) above the liquidus temperature (622°C), decreasing rapidly through the mushy zone to 310 W/(m²·K) at the solidus temperature (536°C), and stabilizing at approximately 230 W/(m²·K) during subsequent cooling. The reliability was validated through numerical simulation with a maximum temperature error of approximately 11°C.

(3) The numerical simulation of three different gating systems using ProCAST revealed that the unilateral bottom injection scheme provides the best performance in terms of smooth filling, prevention of sand erosion and gas entrapment, sequential solidification, and minimization of shrinkage defects. The optimized process parameters were determined as pouring temperature of 690°C and pouring speed of 0.22 m/s.

(4) The molding material tests determined that phenolic urethane resin sand with a component ratio of 1:1 and Component I at 0.8%–1% of the total sand mass provides optimal tensile strength, satisfying both strength and cost requirements for rapid sand casting production.

For future work, several aspects deserve further investigation. First, more accurate thermophysical property parameters and boundary conditions should be developed for improved simulation precision. Second, stress analysis during solidification could be incorporated to further optimize mold design. Third, the mold structure could be refined considering actual operational convenience and factory production capabilities.