As a key component in precision gear manufacturing, internal gear grinding machines play a critical role in achieving high-quality gear profiles. The grinding head, which houses the spindle and grinding wheel, directly influences machining accuracy. In this study, we investigate the vibration characteristics of the grinding head through finite element analysis and experimental validation. The objective is to optimize the design for enhanced dynamic performance, which is crucial for internal gear manufacturers aiming to produce high-precision internal gears. Vibration-induced errors can lead to significant quality issues in internal gears, making this research vital for advancing manufacturing processes.
The grinding head assembly consists of several components, including the grinding wheel frame, electric spindle, spindle support, and connecting base. The compact design is necessary to accommodate the internal diameter constraints of the gears being processed. For internal gear manufacturers, ensuring the rigidity and stability of the grinding head is paramount to maintain the tolerances required for internal gears. We developed a detailed 3D model of the grinding head to simulate its behavior under operational conditions. The model incorporates materials such as 45 steel for the grinding wheel frame and QT450-10 for the connecting base, reflecting typical choices in the industry for internal gears production.
To analyze the dynamic characteristics, we established a finite element model using ANSYS Workbench. The model was meshed with hexahedral elements, resulting in 121,435 nodes and 36,446 elements. This allowed us to perform a prestressed modal analysis, which considers the effects of operational loads on vibration behavior. The grinding force, a primary source of excitation, was calculated based on the spindle power and grinding parameters. The tangential grinding force \( F_t \) and normal grinding force \( F_n \) are derived from the following equations, which are essential for internal gear manufacturers to optimize their processes:
$$ F_t = \frac{60P_w}{2\pi n R} $$
where \( P_w \) is the spindle power (4 kW), \( n \) is the grinding wheel speed (6,000 rpm), and \( R \) is the grinding wheel radius (67.5 mm). The ratio of normal to tangential force is typically in the range of 1.9 to 2.6; we used \( F_n / F_t = 2.6 \) for conservative design. This yielded \( F_t = 94 \, \text{N} \) and \( F_n = 245 \, \text{N} \). The static analysis showed a maximum stress of 2.1137 MPa and a deformation of 3.43 μm, indicating that the structure is within safe limits for internal gears machining.
The modal analysis under prestress revealed the natural frequencies and mode shapes of the grinding head. The first six natural frequencies are summarized in Table 1, which provides insights into the dynamic behavior that internal gear manufacturers must consider to avoid resonance. The mode shapes primarily involved bending deformations in the X and Y directions, highlighting potential weak areas in the design.
| Mode | Frequency (Hz) |
|---|---|
| 1 | 280.9 |
| 2 | 311.5 |
| 3 | 423.7 |
| 4 | 659.91 |
| 5 | 1052.6 |
| 6 | 1160 |
To improve the dynamic performance, we focused on optimizing the grinding wheel frame, a critical component for internal gear manufacturers. Parameterization was applied to key dimensions, such as the length, width, and height of weight-reduction grooves. The design variables and their ranges are listed in Table 2, which served as the basis for sensitivity analysis. This step is crucial for identifying parameters that most influence mass, stress, and displacement in the context of internal gears production.
| Variable | Original Value (mm) | Range (mm) |
|---|---|---|
| P1 | 15 | 10–20 |
| P2 | 20 | 15–25 |
| P3 | 125 | 115–140 |
| P4 | 50 | 45–55 |
| P5 | 23 | 18–28 |
| P6 | 155 | 140–170 |
Sensitivity analysis indicated that parameters P1 and P4 had the highest impact on total deformation and stress. For instance, increasing P1 and P4 led to higher displacement and stress, while P4 and P5 significantly affected mass. Using response surface optimization, we generated three candidate designs and selected the one with the lowest mass, stress, and deformation. The optimized values are shown in Table 3, which resulted in a 4.97% increase in the first natural frequency, enhancing the grinding head’s resistance to vibration for internal gears applications.
| Variable | Optimized Value (mm) | Final Value (mm) |
|---|---|---|
| P1 | 10.415 | 11 |
| P2 | 20.786 | 21 |
| P3 | 131.55 | 132 |
| P4 | 21.285 | 21 |
| P5 | 61.032 | 61 |
| P6 | 160.05 | 160 |
Experimental validation was conducted on a YK7350NF internal gear grinding machine to assess the vibration characteristics under actual grinding conditions. We set up a test platform with accelerometers and a data acquisition system, sampling at 2,000 Hz. Three operating conditions were tested, varying spindle speed and grinding depth, as detailed in Table 4. These conditions simulate real-world scenarios faced by internal gear manufacturers when producing internal gears.
| Condition | Spindle Speed (rpm) | Grinding Depth (mm) |
|---|---|---|
| 1 | 4800 | 0.01 |
| 2 | 4800 | 0.02 |
| 3 | 6000 | 0.02 |
The frequency domain analysis of vibration signals revealed peaks near the spindle rotation frequency and natural frequencies. For example, in Condition 1, peaks at 85 Hz in the X-direction and 82.5 Hz in the Y-direction corresponded to the spindle frequency of 80 Hz, indicating forced vibration. The relationship between spindle frequency \( f \) and speed \( n \) is given by:
$$ f = \frac{n}{60} $$
where \( n \) is in rpm. In Condition 2, similar peaks were observed at 77.5 Hz, with higher amplitudes due to increased grinding depth. This underscores the importance of controlling process parameters for internal gear manufacturers to minimize vibrations in internal gears. Condition 3, with a higher spindle speed of 6,000 rpm, showed peaks at 100 Hz and 110 Hz, close to the optimized natural frequencies, leading to resonant vibrations.
The experimental results demonstrate that low-frequency vibrations are more pronounced and are often excited by spindle speeds nearing the grinding head’s natural frequencies. Additionally, elastic deformation of the grinding wheel shaft under load contributes to chatter, which can affect the surface quality of internal gears. To mitigate these issues, internal gear manufacturers should optimize grinding parameters, such as speed and depth, and consider structural enhancements based on dynamic analysis.
In conclusion, this study provides a comprehensive analysis of the vibration characteristics in grinding heads for internal gear grinding machines. Through finite element simulation and experimental testing, we identified key factors influencing vibration and proposed an optimized design that improves dynamic performance. The findings offer valuable insights for internal gear manufacturers seeking to enhance the precision and efficiency of internal gears production. Future work could explore advanced materials or active vibration control systems to further reduce vibrations in high-speed grinding applications.