Abstract:
The numerical simulation of the sintering temperature field in titanium alloy investment casting shells. The thermal conductivity, density, and specific heat capacity of the shell materials were measured, providing parameter support for the numerical simulation. A solver for investment casting shell sintering was developed by reversing the traditional solidification cooling theory, and a heating model for the high-temperature sintering process of the shell was established to simulate the heating and cooling processes. Based on the geometric modeling of the casting, the automatic generation of shell geometric modeling was realized. Taking a complex thin-walled skeleton shell for titanium alloy casting as the research object, the temperature variation law during the sintering process was simulated and analyzed. The results indicate that the established shell sintering model gives a better description of the variation law of sintering temperature.
1. Introduction
Investment casting, also known as lost-wax casting, involves processes such as wax pressing, wax trimming, tree assembly, slurry dipping, wax melting, pouring, and post-processing [1]. As each process progresses, the dimensional deviations generated in each process continue to accumulate and propagate backward. Excessive dimensional deviations in any process can result in significant differences between the final cast part dimensions and the design dimensions [2]. Shell preparation is a critical process in investment casting because its inner surface directly contacts the alloy liquid, significantly impacting the dimensional accuracy, surface roughness, and internal quality of the cast part [3]. Therefore, a high-performance shell is crucial for obtaining high-quality cast parts.
The shell sintering process involves phase changes, microstructure evolution, and mechanical property changes in the shell material, making it difficult to grasp the variation laws. The development of numerical simulation technology has provided a new direction for studying the shell sintering process [4-7]. However, there are still few reports on numerical simulations of the shell sintering process, and the lack of material parameters related to the shell increases the difficulty of simulating this process.
This study measured the material parameters of the shell before and after sintering, developed a simulation solver for the sintering temperature field of investment casting based on the reverse transformation of solidification cooling theory, automatically generated the shell geometric model based on the casting geometric model, and conducted numerical simulations of the sintering temperature field of the shell for a large and complex thin-walled skeleton casting made of titanium alloy. The overall temperature variation law of the sintered shell was obtained, providing thermal boundary conditions for stress and deformation simulations.
2. Measurement of Shell Material Parameters
The shell is a complex multiphase system composed of refractory materials and binders. During the high-temperature sintering process, its physical parameters change with temperature, and the material properties inside the shell also change due to high-temperature conditions, resulting in different material parameters before and after sintering. To ensure the accuracy of the simulation, the material parameters of the shell before and after sintering were measured separately to obtain two sets of material properties varying with temperature for subsequent numerical simulation of the temperature field. The shell material used in this study consisted of Y2O3, ZrO2, SiO2, and bauxite.
Table 1: Material Composition of the Shell
| Material | Composition |
|---|---|
| Refractory Material | Y2O3, ZrO2, SiO2 |
| Binder | Aluminous Clay |
2.1 Measurement of Material Properties Before Sintering
The shell before sintering is relatively weak and brittle. Therefore, the sample size for the pre-sintered shell cannot be too small, and excessive thinness can easily lead to the shell being directly broken by the cutting tool during sampling. Additionally, the shell is a heterogeneous multiphase material containing impurities such as sand grains. During sampling, it should be avoided that the end face contains obvious impurities, which may cause significant errors between the measured data and the actual data.
The thermal conductivity of the pre-sintered shell was measured using a Hot Disk TPS 2500 S tester with a sample size of 40 mm × 40 mm × 10 mm and a measurement temperature range of 20-1000 °C, meeting the ISO 22007-2 standard.
2.2 Measurement of Material Properties After Sintering
After sintering, the shell has sufficient strength, allowing for more precise dimensions and thicknesses during sampling. Most of the measurement methods for the material parameters of the post-sintered shell are the same as those for the pre-sintered shell, but due to differences in strength, some parameters require different testing methods.
The thermal diffusivity of the shell was measured using the laser thermal conductivity method, and the final thermal conductivity was obtained by multiplying the specific heat capacity and density. An LFA457 laser thermal conductivity analyzer was used with a test temperature range of 20-1000 °C.
3. Numerical Simulation of the Sintering Temperature Field
3.1 Heat Transfer Model
Temperature is an important factor affecting shell deformation during sintering. Before calculating and analyzing shell stress and deformation, it is necessary to simulate and calculate the temperature field during shell sintering. Therefore, a related heat transfer model needs to be established as the theoretical basis for numerical simulation. The heat transfer modes involved in the shell sintering process mainly include thermal conduction, convection, and radiation.
3.1.1 Thermal Conduction
Thermal conduction is the primary heat transfer mode in solids, essentially the thermal motion of a large number of molecules inside the object. In investment casting, there is a temperature difference between the internal and external temperatures of the shell, resulting in thermal conduction during solidification. At the same time, the temperature of the molten metal inside the shell constantly changes over time, so the heat transfer between the molten metal and the shell is a non-steady-state heat conduction phenomenon.
The mathematical expression for the differential equation of three-dimensional unsteady heat conduction in the Cartesian coordinate system is:
Where ρ is density, cp is specific heat capacity at constant pressure, λ is thermal conductivity, Q is the heat source term, T is temperature, t is time, and x, y, z represent three-dimensional space.
3.1.2 Thermal Convection
Thermal convection is the heat transfer mode within fluids, generated by uneven temperature distribution inside the fluid. During the sintering process of titanium alloy investment casting shells, convection heat transfer mainly occurs between the outer surface of the sintering furnace and the air during the cooling stage as the shell cools down with the furnace. Newton’s cooling formula is used to describe thermal convection:
q = h(Tf – Tw)
Where h is the convective heat transfer coefficient, Tf is the fluid temperature, and Tw is the wall temperature.
3.1.3 Thermal Radiation
All objects with temperature emit electromagnetic waves outward, and this heat transfer mode is called thermal radiation. During the investment casting process, thermal radiation mainly occurs between the outer surface of the sintering furnace and the air, as well as between the outer layer of the shell and the inner surface of the sintering furnace. Stefan-Boltzmann’s law is used to describe the thermal radiation process:
q = εσ0Ts4
Where ε is the blackbody radiation coefficient, σ0 is the Stefan-Boltzmann constant (5.67×10-8 W/(m2⋅K4)), and Ts is the thermodynamic temperature of the object.
3.2 Reverse Heating Theory
Shell sintering is a crucial step in the investment casting process, particularly for titanium alloys. It involves placing the dewaxed shell into a sintering furnace for high-temperature sintering. The sintering furnace, equipped with thermocouples, typically heats the shell from three sides: the upper surface and two lateral sides.
The traditional approach focuses on the cooling and solidification process of the casting. However, in the context of shell sintering, the reverse heating theory is applied. This theory transforms the traditional metal solidification cooling process into a heating process for the shell. Instead of considering the metal-mold interface and air as the primary heat exchange media, the shell (formerly the “mold” in casting terms) becomes the subject of study, and the heating furnace simulates the air that can assign arbitrary temperatures.
During the sintering process, the shell undergoes a series of temperature changes. Initially, a temperature curve for the heating and holding process is set on the sintering furnace. Key parameters include heating time, holding time, holding temperature, and cooling time with the furnace. These parameters significantly impact the shell’s strength and surface quality after sintering.
The implementation of the reverse heating theory in software involves several steps:
- Setting the Temperature Curve: The sintering furnace’s temperature curve is predefined, simulating the heating environment.
- Heat Exchange Simulation: The software simulates the heat exchange between the shell (now considered the “casting” in this reverse scenario) and the air (represented by the sintering furnace’s set temperature).
- Heating and Holding: The shell is heated to the desired sintering temperature and held there for a specified duration to ensure complete sintering.
- Furnace Cooling: After the holding stage, to prevent cracking due to sudden temperature changes, the shell is cooled to room temperature along with the furnace. This is simulated by adjusting the air temperature in the software back to room temperature and continuing the heat exchange process.
By applying the reverse heating theory, researchers can simulate the entire sintering process of the shell, from heating and holding to cooling. This approach provides insights into the shell’s temperature variations during sintering, which are crucial for predicting potential stress deformations and optimizing the sintering process.
In summary, the reverse heating theory allows for a comprehensive simulation of the shell sintering process, transforming the traditional cooling-based solidification theory into a heating-based approach tailored for shell sintering. This method ensures accurate prediction of temperature changes within the