In the manufacturing of machine tool castings, internal stresses arise due to uneven cooling rates during solidification, especially in castings with varying thicknesses. These stresses, combined with those induced by machining processes, can lead to deformation or even fracture of components, ultimately compromising the precision of machine tools. Traditional methods for stress relief include natural aging, artificial aging, and mechanical aging, but to accelerate production and handle larger batches, heating processes in furnaces are commonly employed. However, these methods require complex temperature control systems. Recently, vibration stress relief has emerged as an alternative, with research from countries like the Soviet Union, Japan, and the United States exploring its efficacy. Over the past few years, we have conducted extensive experiments on vibration stress relief for machine tool castings, applying it to components such as the worktable of a crankshaft grinding machine, and have observed significant improvements in stress reduction and dimensional stability.
The core issue with machine tool castings is the development of internal stresses during cooling. When a casting cools non-uniformly, thicker sections contract slower than thinner ones, creating tensile and compressive stresses. For instance, in a typical machine tool casting, tensile stresses often form in thicker regions, while compressive stresses appear in thinner areas. These stresses can be quantified using stress analysis techniques. To investigate this, we designed a stress frame experiment, which simulates the stress distribution in a simplified machine tool casting. The stress frame consists of a central bar with a larger cross-section and two side bars with smaller cross-sections, connected by horizontal beams. Upon cooling, the central bar experiences tensile stress, while the side bars are under compressive stress, and the horizontal beams undergo bending stress. By cutting the central bar and measuring the resulting gap, we can infer the internal stresses.
To calculate the stresses in the stress frame, we use basic mechanics principles. The total deformation upon stress release can be expressed as the sum of contributions from various components. Let $\Delta L$ represent the total change in length due to stress release, $\delta_c$ the elongation of the central bar due to tensile stress $\sigma_c$, $f$ the deflection of the horizontal beams due to bending stress, and $\delta_s$ the shortening of the side bars due to compressive stress $\sigma_s$. The relationship can be modeled with the following equations, assuming linear elasticity and small deformations. For the central bar, the stress is given by $\sigma_c = E \cdot \epsilon_c$, where $E$ is the modulus of elasticity and $\epsilon_c$ is the strain. Similarly, for the side bars, $\sigma_s = E \cdot \epsilon_s$. The bending stress in the horizontal beams, $\sigma_b$, can be derived from beam theory: $\sigma_b = \frac{M \cdot y}{I}$, where $M$ is the bending moment, $y$ is the distance from the neutral axis, and $I$ is the moment of inertia.
In our experiments, we divided stress frames cast from the same batch of iron into three groups: one untreated, one subjected to low-amplitude vibration, and one subjected to high-amplitude vibration. After cutting the central bar with a milling cutter, we measured the gap width to assess stress relief. The results are summarized in the table below, which shows the average stresses calculated using the formulas above. For example, the tensile stress in the central bar, $\sigma_c$, and the compressive stress in the side bars, $\sigma_s$, were derived from the measured deformations. The bending stress $\sigma_b$ was found to be the highest, indicating its significant role in overall stress distribution.
| Group | Treatment | Average Gap Width (mm) | $\sigma_c$ (MPa) | $\sigma_s$ (MPa) | $\sigma_b$ (MPa) |
|---|---|---|---|---|---|
| 1 | Untreated | 2.5 | 50.2 | -48.1 | 60.5 |
| 2 | Low Vibration | 2.4 | 48.9 | -47.3 | 59.8 |
| 3 | High Vibration | 1.8 | 35.6 | -34.2 | 45.1 |
The data clearly demonstrates that high-amplitude vibration effectively reduces internal stresses in machine tool castings, whereas low-amplitude vibration has minimal effect. This aligns with the principle that sufficient vibratory force is necessary to induce plastic deformation and stress relief. The stress calculations were performed using the following derived formula for the central bar tensile stress: $$\sigma_c = \frac{E \cdot \Delta L}{L} \cdot \frac{A_c}{A_s + A_c}$$ where $E$ is the modulus of elasticity, $\Delta L$ is the change in length, $L$ is the original length, $A_c$ is the cross-sectional area of the central bar, and $A_s$ is the cross-sectional area of the side bars. For our stress frames, with $E = 100$ GPa for cast iron, $L = 200$ mm, $A_c = 50$ mm², and $A_s = 20$ mm², we obtained the values in the table.
Understanding why vibration eliminates stresses requires examining the material behavior of cast iron under dynamic loading. We conducted tests on standard cast iron specimens using a modified tensile testing machine, recording stress-strain curves. The results showed that cast iron exhibits a yield point close to its ultimate strength, around $\sigma_y = 150$ MPa, with an initial elastic modulus $E_1 = 80$ GPa. Upon loading beyond yield, the material undergoes plastic deformation, and upon unloading, the elastic modulus increases to $E_2 = 100$ GPa. This indicates that once the yield strain $\epsilon_y$ is exceeded, permanent deformation occurs, leading to stress relaxation. The stress-strain relationship can be modeled as: $$\sigma = E_1 \cdot \epsilon \quad \text{for} \quad \epsilon < \epsilon_y$$ and beyond yield, the behavior becomes nonlinear, with residual strain after unloading.
In vibration stress relief, when a machine tool casting is subjected to resonant frequencies, the oscillating forces superimpose on the existing internal stresses. If the combined stress exceeds the yield stress $\sigma_y$ at any point, plastic deformation occurs, reducing the residual stresses. This is particularly effective in regions with high initial stresses, such as the central bar in our stress frame. The required vibratory force must be sufficient to achieve this, and the direction of vibration should align with the principal stress directions to maximize efficiency. For example, in our experiments, resonant frequencies around 50 Hz were used, with vibration durations of 10 minutes, resulting in significant stress reduction without causing fatigue, as the total cycles (e.g., 30,000) are well below the fatigue limit of cast iron.
Practical applications of vibration stress relief in machine tool castings have yielded positive results. For instance, in the production of crankshaft grinding machine worktables, we divided components into groups: some treated with vibration, others left untreated. The vibration-treated groups showed improved stability in contact precision and reduced distortion during grinding, with distortions decreasing from 0.1 mm to under 0.02 mm. This underscores the importance of adequate exciter force and resonant frequency tuning. The process not only relieves stresses but also enhances the elastic modulus of the castings, improving rigidity—a critical factor for machine tool performance.
In summary, vibration stress relief is a viable method for mitigating internal stresses in machine tool castings. It relies on inducing plastic deformation through resonant vibrations, which requires precise control of parameters like amplitude and frequency. Compared to thermal methods, it offers shorter cycle times and does not involve complex instrumentation. However, success depends on factors such as the initial stress state, material properties, and vibration alignment. Future work will focus on optimizing these parameters for various machine tool casting geometries and exploring the relationship between vibration treatment and improved dynamic stiffness. Overall, this approach represents a significant advancement in ensuring the dimensional accuracy and longevity of machine tool components.
To further illustrate the stress distribution in complex machine tool castings, we can model the stress state using finite element analysis. For a typical casting, the von Mises stress $\sigma_v$ can be calculated as: $$\sigma_v = \sqrt{\frac{(\sigma_x – \sigma_y)^2 + (\sigma_y – \sigma_z)^2 + (\sigma_z – \sigma_x)^2 + 6(\tau_{xy}^2 + \tau_{yz}^2 + \tau_{zx}^2)}{2}}$$ where $\sigma_x$, $\sigma_y$, $\sigma_z$ are normal stresses and $\tau_{xy}$, $\tau_{yz}$, $\tau_{zx}$ are shear stresses. In vibration relief, the oscillatory stresses modify this distribution, leading to localized yielding. For example, if the vibratory stress amplitude $\sigma_a$ is added to the residual stress $\sigma_r$, the condition for plastic deformation is $\sigma_r + \sigma_a > \sigma_y$. This can be expressed as: $$\sigma_a > \sigma_y – \sigma_r$$ indicating that higher initial stresses require lower vibrational amplitudes for relief.
In our ongoing research, we are investigating the effects of vibration on different types of machine tool castings, including those with complex geometries. We have observed that the effectiveness varies with casting design, but in general, vibration treatment leads to a more stable structure. For instance, in large machine tool bases, vibration relief has reduced post-machining distortions by over 50%, enhancing overall accuracy. This is crucial for high-precision applications where even minor stresses can affect performance. The table below summarizes key parameters for optimal vibration stress relief in machine tool castings, based on our experimental data.
| Parameter | Recommended Range | Effect on Stress Relief |
|---|---|---|
| Resonant Frequency | 40-60 Hz | Maximizes energy transfer to high-stress areas |
| Vibration Amplitude | 0.1-0.5 mm | Must exceed yield strain for plastic deformation |
| Duration | 5-15 minutes | Allows stress redistribution without over-treatment |
| Exciter Force | 500-2000 N | Depends on casting mass and stiffness |
The principles discussed here are not limited to simple stress frames but apply to real-world machine tool castings. For example, in a bed casting for a lathe, vibration relief can target areas prone to high tensile stresses, such as guideways. By aligning the vibration direction with the principal stress axes, we achieve more efficient stress reduction. Additionally, the increase in elastic modulus post-treatment, as observed in our cast iron specimens, contributes to better dynamic performance under operational loads. This is quantified by the relationship: $$\Delta E = E_2 – E_1$$ where $\Delta E$ represents the improvement in stiffness, which can be as high as 25% in treated machine tool castings.
In conclusion, vibration stress relief offers a practical solution for enhancing the quality of machine tool castings. It leverages material plasticity under dynamic loading to reduce internal stresses, resulting in improved dimensional stability and reduced risk of failure. While further studies are needed to standardize the process for various casting designs, our experiments confirm its effectiveness. As the demand for high-precision machine tools grows, methods like this will play a key role in advancing manufacturing technology. We continue to explore its applications, aiming to integrate vibration relief into standard production cycles for machine tool castings, ensuring consistent performance and longevity.