In the context of global manufacturing transformation, the foundry industry faces the dual pressure of technological upgrading and environmental sustainability. The machine tool spindle box is undoubtedly the core functional component of a machine tool, and its manufacturing quality directly determines the overall precision and service life of the entire machine tool system. Through my focused research on this critical casting, I have systematically investigated the rapid sand casting process and sand mold molding technology specifically tailored for the machine tool spindle box. My work combines advanced numerical simulation techniques with experimental validation, aiming to provide a reliable technical reference for the application of rapid sand mold forming technology in the field of machine tool castings.
Research Background and Industrial Significance
The casting industry serves as the foundation of modern manufacturing, playing an indispensable role in aerospace, transportation, marine engineering, and heavy machinery sectors. According to the latest available data, global casting production has shown a steady upward trend since 2010, with particularly impressive growth observed in the Chinese foundry sector. By 2022, the annual casting output in China reached approximately 51.95 million tons, accounting for more than half of the global total production. However, despite this numerical advantage, the traditional casting industry is confronted with significant challenges including outdated technology, energy inefficiency, and environmental pollution concerns. The transformation towards a more specialized, large-scale, intelligent, and cleaner casting industry has become an inevitable trend for future development.
When examining the machine tool spindle box specifically, this component serves as the central hub for power transmission and speed control in machine tools. Its casting quality is particularly critical because any internal defects can severely compromise the machining accuracy and vibration resistance of the entire machine tool system. The complexity of this casting lies in its intricate internal structure, the significant variation in wall thickness between the box body and the guide rail portion, and the multiple locations where thermal nodes form naturally during solidification. These structural characteristics make the machine tool spindle box highly susceptible to casting defects including shrinkage cavities, micro-porosity, and gas porosity.
Literature Review of Related Technologies
Sand Mold Rapid Prototyping Technology
The rapid prototyping of sand molds has evolved significantly through two main technical routes: additive manufacturing and CNC subtractive machining of sand molds. In the international context, the German company Actech pioneered the digitized mold manufacturing revolution as early as the 1990s with its CNC sand mold machining centers, successfully applied in the production of marine propellers and aero-engine casings. This innovation dramatically reduced the development cycle of complex prototype castings from 45 days to just 7 days. Similarly, the collaborative research between Audi and the Dutch Institute of Technology established a robotic sand mold milling system capable of processing molds up to 3.0 m × 2.2 m × 0.6 m, providing an efficient solution for automotive structural components.
In the United States, researchers at Pennsylvania State University systematically investigated the effect of alloy freezing range on cast aluminum alloys produced through 3D sand-printed molds. Their groundbreaking findings demonstrated a 10 % improvement in flexural strength and a 25 % reduction in porosity-related casting defects compared to conventional mold approaches. Meanwhile, research conducted at the MSMP Laboratory in France revealed that increasing the 3D-printed sand mold wall thickness from 5 mm to 30 mm resulted in solidification rates enhancement of 17 % and 18.6 % respectively, enabling the formation of finer microstructures in silicon alloy castings.
Within China, the China Academy of Machinery Science and Technology (CAMSC) established the core technological framework for patternless casting, emphasizing the digital material design, intelligent forming equipment, and multi-physics field coupling optimization. Significant progress has also been made in the research of multi-material composite sand molds. Researchers found that incorporating a suitable percentage of zircon sand and chromite sand particles could substantially enhance the mold performance and improve the microstructure of high-end complex castings. The Ningxia Kocel Group pioneered the integration of additive manufacturing, digital twin, and intelligent production lines, enabling the fully independent development of casting-grade coated sand materials and multi-physical field coupled process packages.
Casting Numerical Simulation Technology
Numerical simulation of casting processes has evolved from a purely academic pursuit to an essential production tool. Historically, the first casting simulation was conducted at General Motors Corporation in 1965 to analyze the temperature field in a turbine housing during mold filling. With the rapid advancement of computational capabilities during the 1990s, commercial software packages including ProCAST, FLOW-3D, and MAGMA Soft emerged, providing engineers with robust platforms for predicting solidification behavior and casting defects before physical trials.
The application of computational fluid dynamics and finite element methods in casting simulation allows the prediction of various casting defects including shrinkage cavities, gas porosity, inclusions, and hot tearing. Numerical studies at the University of Padova demonstrated remarkable accuracy in predicting oxide-related defects in gravity die-cast aluminum alloys, with simulation results showing excellent consistency with experimental observations. Similar validations were performed at Cairo University for high-pressure die-casting processes, where air entrapment porosity was correctly predicted. Additionally, research at the Central Iron and Steel Research Institute in China thoroughly investigated the motion trajectories of inclusions in horizontal centrifugal casting, developing models for defect control that were experimentally verified.
The use of ProCAST software specifically has become the gold standard in many foundry enterprises due to its coupled non-linear thermodynamic solving algorithms. Chinese studies have demonstrated the capability of ProCAST to predict shrinkages in complex aluminum alloy wheel hubs and eliminate hot tearing defects in turbine blades by controlling solidification stress evolution. The work of aero-engine material research institutes further validated that optimized ProCAST simulations effectively prevent the formation of large-scale shrinkage cavities in alloy impeller castings.
Design Analysis and Mold Development for the Spindle Box
Analysis of Structural Characteristics and Casting Difficulties
I chose the machine tool spindle box as my research subject because it represents a class of typical complex castings used in vertical machining centers. The selected spindle box has a net weight of approximately 217 kg, with the overall profile dimensions of 670 mm × 600 mm × 331 mm. An outstanding challenge is presented by the maximum wall thickness of up to 75 mm located in the guide rail section, while the minimum wall thickness is only 20 mm in the box shell structure. This dramatic variation in wall thickness creates severe non-uniform cooling conditions, which promotes the formation of isolated liquid regions and hot spots that become preferential sites for shrinkage defects.
The spindle box material was determined to be HT300 gray cast iron, which offers excellent wear resistance, vibration damping capacity, and good machinability, making it well suited for machine tool structures. The measured liquidus and solidus temperatures of HT300 are approximately 1242.3 ℃ and 1146.1 ℃, respectively. The chemical composition in weight percentages is summarized below:
| Element | C | S | P | Mn | Si |
| Content range | 2.9–3.2 | ≤ 0.12 | ≤ 0.15 | 0.5–1.4 | 1.0–2.5 |
Concerning the casting difficulties, I identified several critical factors. First, the internal shaft holes designed for supporting the spindle and gear system integrate with the external box wall, creating multiple thermal nodes and discontinuities in wall thickness. Second, the guide rail section, after lightweight design optimization, contains four recessed grooves with dramatically varying wall thicknesses that significantly increase the risk of shrinkage defects. Third, the notable physical difference between the 75 mm thick guide rail section and the 20 mm thick box shell causes substantial temperature gradients that impair sequential solidification and increase the danger of macro-segregation and localized shrinkage porosity.
Sand Mold Design Principles and Implementation
According to the technical requirements of sand mold rapid forming, my design approach incorporates both sand mold printing and CNC machining characteristics. A crucial aspect is the precise calculation of the casting contraction allowance. The linear contraction coefficient K is determined by:
$$K = \frac{L_0 – L_1}{L_0} \times 100\%$$
where L0 represents the mold cavity dimension in millimeters and L1 is the final casting dimension in millimeters. A contraction ratio of 1 % was selected based on the actual production condition of gray iron castings. For all machining surfaces, I assigned a machining allowance of 4 mm, while for small shaft holes with diameters below 40 mm, I specified that they be produced by subsequent machining operations.
Using the NX 12.0 software with its mold wizard module, I developed the sand mold by the surface parting method, which enables effective separation of complex geometric features. The selected base surface for the parting was the top surface of the guide rail, which ensures no dimensional interference during core assembly and facilitates sand removal from internal cavities. An 80 mm sand mold margin was established around the casting as a contiguous buffer layer. The finalized design divided the mold into three distinct components: the upper mold, the lower mold, and the sand core. The upper mold has a relatively simple geometry with no undercuts, whereas the lower mold contains the lead screw nut mounting holes and deep internal recesses. This arrangement led me to determine that the upper mold was more suitable for CNC machining, while the sand core and lower mold could be best manufactured by sand printing.
Gating System Design and Calculation
The gating system is important for the soundness of the final casting because it controls the flow pattern, filling time, and thermal gradients during the mold filling process. I considered the principles of gating system design, including that the liquid metal should fill the cavity within a reasonable time, maintain laminar flow to avoid gas entrainment, and minimize thermal erosion on the mold walls. For the HT300 cast iron, I chose a semi-closed gating system because it balances the advantages of pressure-fed and open systems, providing good slag retaining capability with reduced tendency for splashing at high flow rates.
Two candidate gating schemes were designed: an intermediate-pouring system with ingates positioned at the mid-height of the casting, and a bottom-pouring system with ingates located at the base of the guide rail. The pouring time was initially computed using the empirical equation applicable to cast iron:
$$\tau = \sqrt[3]{G} + \sqrt{G}$$
where G is the total pouring mass in kilograms. For this spindle box, the initial pouring time is approximately 21 seconds. To verify that the liquid metal rise velocity in the mold cavity meets the critical requirements, I calculated the rise velocity according to:
$$v = \frac{C}{\tau}$$
and verified that 21 seconds is in compliance with the minimum allowable rise velocity based on the average wall thickness of 10–40 mm. I subsequently modified the flow coefficient based on factors including pouring temperature, number of gates, and mold permeability. The final chosen values of the relevant parameters and computed cross-sectional areas for the gating system are summarized in the two tables below for the two arranged configurations:
| Scheme | μ | H0 (mm) | P (mm) | Hp (mm) | S_inner (cm²) | S_cross (cm²) | S_sprue (cm²) |
| Intermediate | 0.47 | 229 | 141 | 199 | 15.25 | 22.88 | 18.30 |
| Bottom | 0.52 | 359 | 331 | 193.5 | 13.98 | 20.85 | 16.68 |
The relationship between the average pressure head and the geometric parameters was defined as follows:
$$H_p = H_0 – \frac{P^2}{2C}$$
with the parameters defined as: H0 being the pressure head above the choke, C the total cavity height, and P the cavity height above the choke. For the bottom-gating system, since the choke is at the base, P equals C, and the formula simplifies accordingly. The runner and ingate dimensions follow the functional cross-section area hierarchy Sinner : Scross : Ssprue = 1 : 1.5 : 1.2. Based on these calculations, the three-dimensional models for both gating schemes were created using NX 12.0.
Numerical Simulation of Mold Filling and Solidification
Governing Equations and Mathematical Models
For the numerical simulation of the casting process, the transient fluid flow and heat transfer must be properly described by the equations of conservation of mass, momentum, and energy. For the incompressible flow of liquid metal, the continuity equation is written as:
$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$
The Navier-Stokes equations, in the vector form and for a Newtonian fluid, are expressed as:
$$\rho \frac{D\mathbf{V}}{Dt} = \mu \nabla^2 \mathbf{V} – \nabla P + \rho \mathbf{G}$$
where ρ is the fluid density, μ is the dynamic viscosity, P is the pressure, and G denotes the gravitational acceleration. The energy conservation equation is given by:
$$\frac{\partial (\rho c_p T)}{\partial t} + \frac{\partial (\rho c_p u T)}{\partial x} + \frac{\partial (\rho c_p v T)}{\partial y} + \frac{\partial (\rho c_p w T)}{\partial z} = \frac{\partial}{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right)$$
where T represents temperature, cp is the specific heat at constant pressure, and λ is the thermal conductivity. The transport of the free surface in the mold filling simulation is governed by the volume-of-fluid (VOF) function F:
$$\frac{\partial F}{\partial t} + u \frac{\partial F}{\partial x} + v \frac{\partial F}{\partial y} + w \frac{\partial F}{\partial z} = 0$$
For solidification, the latent heat release, thermal diffusive transfer, and the micro-porosity predictive Niyama criterion were used to assess the local shrinkage conditions:
$$Niyama = \frac{G}{\sqrt{v_c}}$$
where G is the local thermal gradient and vc is the cooling rate. Small values of the Niyama parameter indicate susceptibility to micro-porosity formation.
Mesh Independence Verification
I began the simulation campaign with a mesh independence analysis to determine the optimum element size that balances computational efficiency and numerical accuracy. Using the ProCAST Visual-Mesh module, I generated a computational grid for the complete mold assembly, which includes the upper mold, the lower mold, the sand core, and the cast metal domain. The mesh statistics evaluation is summarized in the following table:
| Case | Mold max. spacing (mm) | Casting max. spacing (mm) | Surface mesh | Volume mesh (×10⁶) | Casting porosity (%) |
| 1 | 10 | 8 | 168,785 | 2.43 | 37.05 |
| 2 | 8 | 6 | 277,501 | 5.02 | 37.63 |
| 3 | 6 | 4 | 449,216 | 7.20 | 38.83 |
| 4 | 4 | 2 | 653,113 | 11.87 | 38.86 |
From this analysis, I can confirm that when the volume mesh count increased from 7.20 million to 11.87 million, the predicted porosity changed only marginally from 38.83 % to 38.86 %. This confirmed that Case 3 was the optimal choice for all subsequent calculations, achieving a satisfactory balance between accuracy and computational cost.
Intermediate-Pouring Scheme Simulation
The material properties assigned in the simulation were: casting metal as EN-GJL-300, mold material as Silica Sand, initial casting temperature of 1340 ℃, pouring time of 21 seconds, and mold temperature of 24 ℃. The interfacial heat transfer coefficient between the casting and the silica sand mold was defined as 500 W/(m²·K).
The filling process analysis revealed that when the filling time was 6.34 s, the mold cavity had reached 31.6 % full, with stable metal front advancement and no sign of splashing or air entrainment. By 13.54 s, the filling rate was 67.4 %, and the metal started to enter the guide rail section, with a smooth and flat metal surface observed. At 19.69 s, the cavity was 98 % full. However, examining the solidification temperatures indicated that the thin external walls of the box had already started to solidify at this point, while the internal regions around the shaft support holes were still in the liquid state.
The solidification process was assessed at multiple time steps. At 194.39 s, the solid fraction was 21.7 %. At 534.39 s, the solid fraction was 51 %, and I observed that the thin box walls had completely solidified, effectively isolating the liquid pools around the shaft holes and trapping them as isolated liquid regions. This phenomenon eliminated the feeding channels to these regions, which combined with the relatively early solidification of the riser, caused the formation of significant shrinkage defects. The final porosity distribution showed the maximum casting defects concentrated in the areas of the guide rail grooves and the interior shaft support locations, precisely as I had anticipated from the structural analysis.
Bottom-Pouring Scheme Simulation
For the bottom-gating configuration, I aimed to exploit the different heat transfer characteristics of various sand materials. The lower mold was assigned Chromite Sand with a higher heat exchange coefficient of 900 W/(m²·K), whereas the upper mold and the core were of Silica Sand with 500 W/(m²·K). The interface between Chromite Sand and Silica Sand was set to 200 W/(m²·K).
The filling stage progressed very smoothly from the bottom gate upward, with a flat and stable liquid metal level observed during the entire 21-second filling. The temperature field, however, showed that while the bottom guide rail began to lose heat quickly due to the chromite sand, the upper thin box walls still solidified prematurely. This was primarily due to the rapid cooling through the thin walls, preventing the risers from feeding the interior hot spots. The final output of this simulation showed a distributed pattern of casting defects, centered on the guide rail grooves and the box interior. The maximum porosity was higher than that of the intermediate-gating configuration, proving the superiority of the intermediate-pouring layout for this particular casting geometry.
Optimization of Casting Process
Based on the initial simulation findings, I proceeded with the measure of applying insulation risers and chills. The insulation risers were designed to maintain liquid metal temperature for an extended feeding duration, while the chills were placed on the thick wall sections and around the internal shaft holes to accelerate local cooling and avoid the formation of isolated liquid islands. The optimized configuration for the intermediate-pouring scheme involved four insulation risers at the main hot spots and two additional risers for the secondary thicker sections. Chills were inserted on the shaft hole interiors.
| Interface | Heat Transfer Coefficient (W/(m²·K)) |
| Casting – Silica Sand | 500 |
| Casting – Chill | 2000 |
| Chill – Silica Sand | 300 |
| Insulating Riser – Silica Sand | 100 |
I monitored the temperature curves at five characteristic points located across the casting. These point temperature histories demonstrated a distinct trend of progressive solidification from the bottom to the top, with point 1, located on the thin lower box, cooling rapidly, while point 5, located near the insulation riser, retained the highest temperature for extended periods. The casting defect map after optimization demonstrated that the shrinkage cavities and micro-shrinkage had been successfully eliminated. The maximum porosity of the casting was now 1.358 %, a value below the industrial safety margin of 2 %.
The equivalent optimization for the bottom-pouring scheme also increased porosity to an acceptable level of 1.685 %, but this was still inferior to the intermediate-gating design. The optimized bottom-pouring scheme used the same heat exchange coefficient framework as the intermediate design, with the lower mold made of Chromite Sand. Although pushing the porosity down to the threshold, distributed casting defects were still present in higher concentration than with the intermediate design. Based on this detailed comparison, I concluded that the intermediate-gating system provided the best quality for this machine tool spindle box.
Optimization of Casting Process Parameters by RSM and Genetic Algorithm
Evaluation of Casting Quality
The measure of porosity effectively determines the casting quality. The porosity η is defined based on density measurements as follows:
$$\eta = \frac{\rho_m – \rho_a}{\rho_m} \times 100\%$$
where ρm is the density of the pore-free reference material and ρa is the apparent density of the actual casting including its internal pores.
Single-Factor Experiments
Using the intermediate-gating optimized scheme as the baseline, I launched a series of single-factor numerical experiments to explore the influence of three key parameters: pouring temperature, pouring time, and mold temperature. The purpose of this stage was to identify the main-effect trends and set the parameter ranges for more complex response surface studies.
For the variation of mold temperature, I held the pouring temperature at 1380 ℃ and the pouring time at 22 seconds. The mold temperature was varied from 22 ℃ to 28 ℃. The results are tabulated below:
| Mold temperature (℃) | 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| Porosity (%) | 1.386 | 1.362 | 1.353 | 1.345 | 1.343 | 1.353 | 1.359 |
I observed that porosity decreases as the mold temperature increases from 22 ℃ to 26 ℃, reaching a minimum at approximately 26 ℃. This behavior is explained by the enhanced flowability of the liquid metal at a higher mold temperature which enables better filling of the thin recesses and easier escape of trapped gases. Beyond 26 ℃, the melt becomes too fluid for its own good, leading to turbulence and air entrapment, which increases the porosity level.
For the influence of pouring temperature, I fixed the mold temperature at 26 ℃ and the pouring time at 22 seconds. The pouring temperature was varied between 1340 ℃ and 1400 ℃, and the results are given below:
| Pouring temperature (℃) | 1340 | 1350 | 1360 | 1370 | 1380 | 1390 | 1400 |
| Porosity (%) | 1.366 | 1.346 | 1.316 | 1.321 | 1.343 | 1.352 | 1.358 |
The optimum is located at approximately 1360 ℃. At lower temperatures the metal freezes prematurely causing cold shuts and gas trapping, while at higher temperatures, excessive superheating increases the gas solubility in the liquid and promotes defects during the subsequent degassing stage.
For the pouring time, with a pouring temperature of 1360 ℃ and a mold temperature of 26 ℃, I varied the time from 20 to 26 seconds, with the results shown below:
| Pouring time (s) | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
| Porosity (%) | 1.342 | 1.336 | 1.316 | 1.308 | 1.323 | 1.328 | 1.338 |
I found the optimum pouring time to be approximately 23 seconds. A shorter time of 20 seconds leads to turbulent filling, whereas a longer time causes slow cooling of the melt front and consequent cold-lap defects.
Response Surface Methodology Experiment
Based on the single-factor results, the three design variables and their ranges were defined as follows: pouring temperature A between 1340 ℃ and 1380 ℃, pouring time B between 21 s and 25 s, and mold temperature C between 24 ℃ and 28 ℃. I used the Box-Behnken experimental design of Design-Expert software to construct a total of 17 simulation runs. The experimental matrix and the resulting porosity values are summarized below:
| Run | A (℃) | B (s) | C (℃) | η (%) |
| 1 | 1360 | 21 | 24 | 1.310 |
| 2 | 1360 | 23 | 26 | 1.307 |
| 3 | 1360 | 23 | 26 | 1.306 |
| 4 | 1340 | 21 | 26 | 1.346 |
| 5 | 1360 | 23 | 26 | 1.305 |
| 6 | 1360 | 23 | 26 | 1.311 |
| 7 | 1360 | 25 | 28 | 1.325 |
| 8 | 1340 | 25 | 26 | 1.350 |
| 9 | 1380 | 21 | 26 | 1.371 |
| 10 | 1380 | 23 | 28 | 1.360 |
| 11 | 1380 | 25 | 26 | 1.352 |
| 12 | 1340 | 23 | 24 | 1.341 |
| 13 | 1360 | 25 | 24 | 1.315 |
| 14 | 1360 | 21 | 28 | 1.338 |
| 15 | 1360 | 23 | 26 | 1.308 |
| 16 | 1340 | 23 | 28 | 1.342 |
| 17 | 1380 | 23 | 24 | 1.332 |
I performed analysis of variance (ANOVA) on these results. The initial regression model revealed that the quadratic term C² was not statistically significant (P > 0.05), so I refined the model by eliminating this term. The resulting regression equation for porosity is:
$$\eta = 1.31 + 0.0045 A – 0.0029 B + 0.0084 C – 0.0058 AB + 0.0067 AC – 0.0045 BC + 0.0346 A^2 + 0.0129 B^2$$
The analysis of variance for the refined model is summarized in the following table:
| Source | Sum of squares | DF | Mean square | F-value | P-value |
| Model | 0.0072 | 8 | 0.0009 | 78.42 | < 0.0001 |
| A | 0.0002 | 1 | 0.0002 | 14.15 | 0.0055 |
| B | 0.0001 | 1 | 0.0001 | 5.78 | 0.0430 |
| C | 0.0006 | 1 | 0.0006 | 49.01 | 0.0001 |
| AB | 0.0001 | 1 | 0.0001 | 11.55 | 0.0094 |
| AC | 0.0002 | 1 | 0.0002 | 15.92 | 0.0040 |
| BC | 0.0001 | 1 | 0.0001 | 7.07 | 0.0288 |
| A² | 0.0051 | 1 | 0.0051 | 442.64 | < 0.0001 |
| B² | 0.0007 | 1 | 0.0007 | 61.32 | < 0.0001 |
| Residual | 0.0001 | 8 | 0.0000 | ||
| Lack of fit | 0.0001 | 4 | 0.0000 | 3.32 | 0.1359 |
| Pure error | 0.0000 | 4 | 5.3 × 10⁻⁶ |
The model’s lack of fit value of P = 0.1359 is not significant, indicating a good fit. The determination coefficient R² was 0.9874, adjusted R² = 0.9748, and predicted R² = 0.9023. These values confirmed the reliability of the regression model. By comparing the F-values, the order of influence of the parameters on the porosity was: mold temperature C > pouring temperature A > pouring time B.
With respect to the model terms, both AC and AB interaction effects are significant. The interaction between pouring temperature and mold temperature showed the strongest influence on porosity, since this combination controls the thermal state of the melt when it contacts the mold. The response surfaces generated from the regression equation further revealed that the porosity has a clear minimum in the interior of the design space, located at a pouring temperature around 1360 ℃ and a mold temperature between 24 and 26 ℃.
Genetic Algorithm Optimization
For the purpose of finding the global optimum process parameters, I used genetic algorithm (GA) optimization methodology. The GA mathematical model was described as:
$$SGA = (C, E, P_0, M, \Phi, \Gamma, \Psi, T)$$
In this formulation, C refers to the individual coding method, E is the fitness function, P0 is the initial population, M is the population size, Φ is the selection operator, Γ is the crossover operator, Ψ is the mutation operator, and T is the termination condition.
The optimization problem was formally stated as:
$$\min \eta(A, B, C)$$
$$1340 \leq A \leq 1380$$
$$21 \leq B \leq 25$$
$$24 \leq C \leq 28$$
I set the population size to 50, applied the roulette wheel selection, single-point crossover with probability 0.8, and non-uniform mutation with probability 0.01. The termination condition was set at a maximum of 60 generations or when the most fit individual remained unchanged for a certain number of consecutive generations. The fitness evolution curve showed converging behavior after 56 iterations, at which point the optimal values were obtained. The GA optimization result was: pouring temperature A = 1360 ℃, pouring time B = 23 s, and mold temperature C = 24 ℃. The minimum predicted porosity was 1.301 %.
I subsequently performed a verification simulation at these optimized parameters. The obtained porosity was 1.306 %, which deviated from the predicted value by only 0.38 %. The optimized processing parameters reduced the porosity by 4.2 % compared to the pre-optimization baseline value of 1.358 % obtained with the initial parameters. This validates the model and optimization effectiveness in reducing casting defects.
Sand Mold Performance and Experimental Verification
Experimental Setup and Materials
To further improve the casting quality, I directed my attention to the properties of the sand mold itself. For the sand mold, I performed experiments with the silicon sand of 70/140 mesh size. The sand was mixed with furan resin and a curing agent. The sand mold performance was characterized by three principal criteria: gas evolution, mechanical strength, and permeability. The equipment used for the tests included a small sand mixer, a specimen preparation machine, and a universal sand strength testing machine. An intelligent gas evolution tester was used for measuring the gas volume.
Gas Evolution Results
The gas evolution tests were carried out at 850 ℃ on 1 g samples of the mixture. The measured gas volumes are reported below for different concentrations of furan resin and curing agent:
| Resin content | 0.2 % curing | 0.3 % curing | 0.4 % curing | 0.5 % curing | 0.6 % curing |
| 1.7 % | 13.73 | 14.63 | 15.65 | 16.64 | 18.64 |
| 2.4 % | 18.52 | 19.18 | 19.58 | 20.07 | 20.56 |
| 3.1 % | 20.69 | 21.61 | 22.05 | 22.39 | 23.19 |
| 3.8 % | 22.82 | 23.47 | 24.46 | 24.89 | 26.01 |
The gas evolution data demonstrated a strong linear positive correlation with both the resin content and the curing agent content. For and considering the iron casting requirement that the gas evolution should not exceed 20 mL/g, the resin content range of 1.7 % to 2.4 % is acceptable, with the upper range of the curing agent from 0.2 % to 0.4 %. The 2.4 % resin with 0.4 % curing agent combination yields 19.58 mL/g, which remains within the stated boundary.
Mechanical Strength Results
The tensile strength of sand mold specimens was tested with the universal sand strength machine. The eight-shaped specimens were loaded until fracture. The measured tensile strength values are summarized in the following table:
| Resin content | 0.2 % curing | 0.3 % curing | 0.4 % curing | 0.5 % curing | 0.6 % curing |
| 1.7 % | 0.84 | 0.97 | 1.14 | 0.81 | 0.74 |
| 2.4 % | 1.35 | 1.62 | 1.72 | 1.46 | 1.41 |
| 3.1 % | 1.92 | 2.13 | 2.12 | 2.32 | 1.79 |
| 3.8 % | 2.03 | 2.56 | 2.61 | 2.78 | 2.15 |
The tensile strength values generally increase with the increase in resin and curing agent content. When the resin content is at 2.4 %, all tensile strength values were above 1.0 MPa, well exceeding the casting acceptance threshold. Furthermore, the curing agent content around 0.4 % yields the highest tensile strength for this resin level.
For the flexural strength tests, cylindrical specimens of Φ50 mm × 50 mm were used. The data is given below:
| Resin content | 0.2 % curing | 0.3 % curing | 0.4 % curing | 0.5 % curing | 0.6 % curing |
| 1.7 % | 2.23 | 2.56 | 2.67 | 2.33 | 2.08 |
| 2.4 % | 3.58 | 3.87 | 3.93 | 3.71 | 3.53 |
| 3.1 % | 3.97 | 4.08 | 4.16 | 4.31 | 3.72 |
| 3.8 % | 4.13 | 4.34 | 4.42 | 4.54 | 4.05 |
For the 2.4 % resin content, the flexural strength also reaches its highest value at 0.4 % curing agent concentration. Although the 0.4 % curing agent content gives the highest bending strength at 3.93 MPa, I also noticed that the difference between the 0.3 % and 0.4 % variants is only 0.06 MPa, which is quite small. When I examined the 3D-printed specimens made with the 0.4 % curing agent, I observed significant delamination defects in the printed sand mold structure. The sand particles had a stronger tendency to agglomerate and the spreading of the sand layer became more difficult, which resulted in delamination during the printing process. This observation strongly influenced my final choice of curing agent content.
Permeability Test
For the combination of 2.4 % resin content and 0.3 % curing agent content, I also tested the permeability of the sand compact. The measured permeability was 159.9 cm³, which is significantly higher than the typical level of 100 cm³ for conventional sand molds. Good permeability is favorable for the smooth escape of gases during mold filling and solidification, thereby reducing the tendency towards gas-related casting defects.
Sand Mold Production by Additive Manufacturing and CNC Machining
Having selected the optimal parameters, I proceeded to produce the sand mold parts for the spindle box by sand printing. The three-dimensional model was first adjusted to include the optimized riser and chill positions. The STL format was uploaded to the Magics software for model optimization and support design. An LSMP2000 machine was configured with a processing platform of 1000 mm × 2000 mm × 800 mm, and the sand molds were optimally positioned and aligned.
The slicing process was performed with a layer thickness of 0.4 mm, a resolution of 360 DPI, a nozzle width of 1000 pixels, and a contour offset of -0.25 mm. The printing sequence involved the mixing of dry sand with 0.3 % curing agent in the mixing system, and the printing itself was conducted with a resin content of 2.4 %. The print chamber was controlled at a temperature of 22 ℃ and relative humidity of 40 % to ensure the accuracy of the process. After printing, the sand molds were left inside the chamber for 3 to 4 hours to allow sufficient hardening before removal and depowdering.
For the upper mold, I used CNC subtractive machining on the digital patternless casting precision forming machine. The machine has a working area of 3000 mm × 1500 mm × 900 mm and an accuracy of ±0.1 mm per 100 mm. The preparation involved creating a blank, defining cutting tools, and generating tool paths through the NX 12.0 CAM module. The tool parameters I used are listed below:
| Tool number | Type | Diameter | Flutes | Material |
| T1 | Flat end mill | 50 mm | 4 | HSS |
| T2 | Flat end mill | 16 mm | 2 | HSS |
| T3 | Ball end mill | 8 mm | 1 | HSS |
Roughing was performed with the T2 end mill and a depth of cut of 3 mm, and fine machining of the internal small contours was done with the T3 ball-end mill at a depth of cut of 1 mm. After machining, the upper mold was obtained with the required precision and surface quality.
Casting Verification
The final experimental verification consisted of pouring the spindle box according to the optimized parameters. The pouring temperature was maintained at 1360 ℃, the pouring time was 23 seconds, and the mold temperature was at 24 ℃. The actual pouring performance verified the numerical simulation predictions: the mold filling was stable and smooth, and the gas venting was effective. After solidification and cooling, the casting was cleaned and inspected. The spindle box casting presented a complete shape, smooth surface, and accurate dimensions with no obvious casting defects. The achieved quality was sufficient to fulfill the intended functional requirements of the machine tool spindle box.
A panoramic view of the production environment and the crucial automatic pouring line used in the experimental validation stage is captured in the figure below.
Conclusions and Outlook
Through this research, I have drawn the following conclusions:
(1) The rapid sand mold forming technology can be successfully applied to the machine tool spindle box casting. By careful structural analysis and casting process design, both intermediate-pouring and bottom-pouring gating systems were established with optimized parameters. The use of sand mold design based on surface parting method allowed the production of complex cores without any need for traditional wooden patterns.
(2) The ProCAST simulation combined with mesh independence analysis provided reliable predictions of the filling and solidification of the spindle box. The primary casting defects were found to be concentrated in the region of the guide rails and shaft support areas where the wall thickness is non-uniform. The optimized process with insulating risers and chills successfully improved the solidification sequence, effectively eliminated the isolated liquid regions, and reduced the porosity of the casting to around 1.306 %.
(3) The use of response surface methodology and genetic algorithm enabled the efficient optimization of the process parameters. The resulting optimum parameters were pouring temperature of 1360 ℃, pouring time of 23 seconds, and mold temperature of 24 ℃. A comparison of simulation to experimental data demonstrated that the porosity prediction was accurate within a relative error of 0.38 %.
(4) The influence of furan resin and curing agent contents on the sand mold properties was quantified. Based on the constraints of acceptable gas evolution and sufficient mechanical strength, the optimal resin content was found to be 2.4 % and curing agent content 0.3 %. This composition leads to a gas evolution of 19.18 mL/g, tensile strength of 1.62 MPa, flexural strength of 3.87 MPa, and a permeability of 159.9 cm³. The trial production of the spindle box confirmed that this sand mold composition yields excellent mold quality and precise dimensions, and the final casting is functionally adequate.
Regarding the limitations of this study, I acknowledge that the numerical simulation was performed using constant thermophysical material properties. In the future, temperature-dependent properties and solidification kinetics at the dendritic scale should be incorporated for even more accurate predictions. Moreover, the study was limited to silica sand for the mold; future research should investigate the effect of mixed sand materials to further tailor the cooling rates of different casting regions. Finally, the relationship between machining parameters in CNC sand mold production and the ultimate mold quality remains to be investigated, especially with respect to tool wear, cutting speed, and feed rate. These topics offer rich directions for future scientific inquiry in the realm of rapid sand casting technology and casting defects control.