In modern manufacturing, high-precision CNC machine tools are essential, and their accuracy depends heavily on the machining precision and stability of components. This requires machine tool castings to exhibit low casting stresses and excellent dimensional stability. However, bed castings often feature complex structures, such as long guideways and significant wall thickness variations, leading to uneven temperature fields during solidification and cooling. This inhomogeneity can generate thermal stress, phase transformation stress, and structural stress, resulting in deformation that severely impacts dimensional accuracy and retention. Despite this, recent research on residual stress and dimensional stability in machine tool castings has been limited, with issues like deformation and cracking due to residual stress becoming a common challenge in the foundry industry. Therefore, this study employs JSCCAST casting simulation software to numerically simulate gray iron bed castings for precision turning centers HTC2050 and precision horizontal machining centers HMC50e. Additionally, the blind hole method is used to measure residual stresses in these gray iron bed castings and ductile iron ram box castings, providing preliminary insights into residual stress and deformation in machine tool castings.
Numerical simulation plays a critical role in understanding and optimizing the casting process for machine tool castings. Using JSCCAST software, we can predict flow patterns, identify potential defects like shrinkage porosity, and analyze temperature distributions and solidification sequences. By leveraging temperature field data from solidification calculations, stress computations can forecast internal stresses, deformation amounts, and fracture tendencies in castings. In this study, 3D models of bed castings were created with SolidWorks and exported as STL files. These files were imported into JSCCAST, where computational conditions and material properties were set for comprehensive analysis, including filling, solidification, temperature field, stress, and deformation simulations. This approach allows for a detailed examination of how machine tool castings behave under various conditions, emphasizing the importance of stress control in ensuring quality.
The filling process is a crucial phase in casting, as it influences defect formation and stress development. For instance, in HTC2050 bed castings, the gating system was designed without a choke, resulting in a stable filling process. In contrast, HMC50e bed castings used a horizontal choke design, which led to higher fluid velocities in the runners and increased turbulence tendencies. This design caused air entrainment and poor slag removal, potentially leading to gas porosity and inclusions that contribute to stress imbalances and subsequent deformation during machining. The following equation summarizes the fluid dynamics involved in filling, where the velocity field \( \vec{v} \) and pressure \( p \) are governed by the Navier-Stokes equations:
$$ \rho \left( \frac{\partial \vec{v}}{\partial t} + \vec{v} \cdot \nabla \vec{v} \right) = -\nabla p + \mu \nabla^2 \vec{v} + \vec{f} $$
Here, \( \rho \) is density, \( \mu \) is dynamic viscosity, and \( \vec{f} \) represents body forces. Understanding these dynamics helps in optimizing gating systems to minimize stresses in machine tool castings.
Temperature field and solidification processes are pivotal in determining residual stresses in machine tool castings. Simulations revealed that guideways in bed castings exhibit higher temperature fields compared to other regions, with areas farther from the gating system and thicker sections retaining more heat, increasing the risk of thermal stress. The bottom square holes and flat riser locations cooled rapidly due to higher heat transfer coefficients, while the lower bed guideways solidified slowly. Significant wall thickness variations led to uneven temperature distributions, fostering phase transformation and structural stresses. The heat conduction equation describes this temperature evolution:
$$ \frac{\partial T}{\partial t} = \alpha \nabla^2 T $$
where \( T \) is temperature, \( t \) is time, and \( \alpha \) is thermal diffusivity. This equation highlights how non-uniform cooling can induce stresses in machine tool castings, necessitating careful control during casting.
Defect prediction and stress analysis further elucidate the challenges in machine tool castings. Shrinkage porosity was identified in cross guideways, vertical guideways, and nodal points, where large temperature differences promote contraction stresses. These defects can be mitigated using chills to achieve directional solidification or by leveraging the feeding action of gates. Stress simulations indicated significant bending deformation in cross guideways, with tensile stresses reaching 160–180 MPa and compressive stresses between -70 and -180 MPa. Vertical guideways experienced lower stresses, with tensile stresses of 14–26 MPa and compressive stresses of -27 to -52 MPa, resulting in minimal deformation. The stress-strain relationship can be expressed as:
$$ \sigma = E \epsilon $$
where \( \sigma \) is stress, \( E \) is Young’s modulus, and \( \epsilon \) is strain. This linear elasticity model, though simplified, aids in understanding deformation mechanisms in machine tool castings.
Displacement field simulations for HMC50e bed castings highlighted dimensional changes along different axes. In the width (X) and height (Z) directions, deformation was relatively small, whereas the length (Y) direction showed substantial contraction, particularly near the ends. This anisotropic behavior underscores the need for targeted stress relief treatments to maintain dimensional stability in machine tool castings. The deformation can be quantified using the displacement vector \( \vec{u} \), related to strain via:
$$ \epsilon = \frac{1}{2} \left( \nabla \vec{u} + (\nabla \vec{u})^T \right) $$
This formulation helps in predicting how machine tool castings deform under residual stresses.
Residual stress measurements using the blind hole method provided empirical data on stress levels in machine tool castings. This technique involves attaching strain gauges, drilling a small hole (1.5 mm diameter, 2 mm depth) at the center, and calculating residual stresses from the released strains. The equipment included a ZDL-II residual stress drilling device, YC-III stress meter, and specialized strain gauges. Measurements were taken on gray iron bed castings shaken out at 200°C and 500°C, as well as on ductile iron ram box castings before and after rough machining. The results, summarized in Table 1, show that residual stresses are predominantly compressive due to the casting geometry, aligning with simulation predictions. Lower shakeout temperatures reduced residual stresses, whereas rough machining increased them significantly, highlighting the sensitivity of machine tool castings to processing conditions.
| Point | Gray Iron HMC50e (200°C Shakeout) σ₁ | σ₂ | σₓₓ | σᵧᵧ | Gray Iron HTC2050 (500°C Shakeout) σ₁ | σ₂ | σₓₓ | σᵧᵧ | Ductile Iron Ram Box (Before Machining) σ₁ | σ₂ | σₓₓ | σᵧᵧ | Ductile Iron Ram Box (After Machining) σ₁ | σ₂ | σₓₓ | σᵧᵧ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | -60.9 | -75.9 | -62.6 | -74.2 | -151 | -172.9 | -160.0 | -164.2 | 46.8 | 6.1 | 6.4 | 46.5 | -131.2 | -130.7 | -30.3 | -110.4 |
| 2 | -1.40 | -95.7 | -51.7 | -45.3 | -93.1 | -139.6 | -134.0 | -98.6 | 37.8 | 24.0 | 34.6 | 27.2 | -156.3 | -153.2 | -110.4 | -105.3 |
| 3 | -7.90 | -52.7 | -49.6 | -11.0 | -55.3 | -91.40 | -65.10 | -81.5 | 54.9 | 37.7 | 40.5 | 52.1 | -156.5 | -155.0 | -105.3 | -105.3 |
| 4 | -19.7 | -63.1 | -25.2 | -57.5 | -26.4 | -91.60 | -83.60 | -34.4 | 39.1 | -65.5 | 23.8 | -50.2 | – | – | – | – |
| 5 | -49.0 | -66.8 | -49.2 | -66.6 | -78.40 | -71.40 | -73.0 | -25.8 | -59.1 | -25.8 | -59.1 | -29.8 | – | – | – | – |
| 6 | -56.1 | -65.2 | -62.2 | -59.1 | -109.2 | -91.30 | -42.1 | -30.5 | -65.5 | -51.4 | -44.5 | -107.3 | – | – | – | – |
The data in Table 1 illustrates that gray iron machine tool castings exhibit higher residual stresses compared to ductile iron variants. For example, maximum residual stresses were -95.7 MPa at 200°C shakeout and -172.9 MPa at 500°C, emphasizing the benefit of lower shakeout temperatures. In ductile iron ram box castings, stresses increased from -65.5 MPa before machining to -156.5 MPa after rough machining, indicating that mechanical processing introduces additional stresses. This aligns with the general formula for residual stress relief, often modeled as:
$$ \sigma_r = \sigma_0 e^{-k t} $$
where \( \sigma_r \) is residual stress, \( \sigma_0 \) is initial stress, \( k \) is a material constant, and \( t \) is time. However, in practice, factors like machining parameters and material heterogeneity complicate this for machine tool castings.
To further analyze the stress distribution in machine tool castings, we can consider the von Mises stress criterion, which combines principal stresses to assess yield behavior:
$$ \sigma_v = \sqrt{ \frac{ (\sigma_1 – \sigma_2)^2 + (\sigma_2 – \sigma_3)^2 + (\sigma_3 – \sigma_1)^2 }{2} } $$
This criterion helps in identifying critical regions where stress concentrations may lead to failure in machine tool castings. For instance, in cross guideways, high von Mises stresses correlate with observed deformations, necessitating post-casting treatments like aging to relieve stresses.
In conclusion, this study demonstrates the effectiveness of numerical simulation and experimental measurements in addressing residual stress and deformation in machine tool castings. Key findings include the superiority of non-choke gating designs for stable filling, the impact of uneven temperature fields on stress generation, and the significant deformation in the length direction of bed castings. Residual stress measurements confirm that gray iron machine tool castings have higher stresses than ductile iron ones, and lower shakeout temperatures reduce these stresses. However, rough machining exacerbates residual stresses, highlighting the need for integrated stress management strategies. Future work could explore advanced heat treatments and real-time monitoring to further enhance the quality and durability of machine tool castings, ensuring they meet the demanding standards of modern manufacturing.
Overall, the interplay between simulation and experimentation provides a robust framework for optimizing machine tool castings. By continuously refining these approaches, we can mitigate stress-related issues, improve dimensional stability, and extend the service life of these critical components. The insights gained here underscore the importance of a holistic approach to stress control in machine tool castings, combining theoretical models with practical validations to achieve superior performance in industrial applications.