In modern manufacturing, gear grinding is a crucial process for achieving high precision in gear production, particularly in internal gear applications. The grinding head, as the core component of gear grinding machines, directly influences machining accuracy and surface quality. However, vibrations during gear profile grinding can lead to issues such as grinding cracks, which compromise gear performance and longevity. This study focuses on the vibration characteristics of an internal gear grinding head, combining finite element analysis with experimental validation to optimize its dynamic performance. By addressing vibration mechanisms, we aim to enhance the reliability of gear grinding processes and minimize defects like grinding cracks.
The grinding head assembly comprises a wheel frame, electric spindle, spindle support, connection seat, bearings, grinding wheel, and belt drive. The electric spindle drives the grinding wheel via a belt, enabling high-speed rotation essential for gear profile grinding. To analyze its behavior, a three-dimensional model was developed and imported into ANSYS Workbench for finite element analysis. Materials were assigned accordingly: 45 steel for the wheel frame, QT450-10 for the connection seat and spindle support, and 20CrMnTi for bearings and shafts. The mesh consisted of 121,435 nodes and 36,446 elements, ensuring accurate simulation of dynamic responses under operational conditions.
Grinding forces play a significant role in inducing vibrations during gear grinding. The tangential grinding force \( F_t \) and normal grinding force \( F_n \) are calculated based on the spindle power and empirical ratios. For an electric spindle with a rated power of 4 kW, grinding wheel radius of 67.5 mm, and speed of 6,000 rpm, the forces are derived as follows:
$$F_t = \frac{60 P_w}{2 \pi n R}$$
where \( P_w = 4000 \, \text{W} \), \( n = 6000 \, \text{r/min} \), and \( R = 0.0675 \, \text{m} \). This yields \( F_t = 94 \, \text{N} \). The normal force is related by \( F_n / F_t = 2.6 \), giving \( F_n = 245 \, \text{N} \). Static analysis under these loads showed a maximum stress of 2.11 MPa and deformation of 3.43 μm, indicating sufficient structural integrity but highlighting potential vibration concerns.
Pre-stressed modal analysis was conducted to determine the natural frequencies and mode shapes of the grinding head. The first six modes were extracted, as summarized in Table 1. The dominant deformations involved bending of the wheel frame and spindle support in the X and Y directions, which are critical for understanding vibration sources in gear grinding operations.
| Mode | Frequency (Hz) | Primary Deformation |
|---|---|---|
| 1 | 280.9 | Y-direction bending of wheel frame |
| 2 | 311.5 | X-direction bending of wheel frame |
| 3 | 423.7 | X-direction bending of spindle support |
| 4 | 659.9 | Z-direction bending of spindle support |
| 5 | 1052.6 | Complex torsional deformation |
| 6 | 1160.0 | Mixed bending and torsion |
To improve dynamic performance, optimization focused on the wheel frame, specifically its weight reduction grooves. Parameters included groove dimensions (length, width, height), with initial values and constraints listed in Table 2. Sensitivity analysis identified key parameters influencing mass, stress, and displacement, guiding the optimization process.
| Parameter | Initial Value (mm) | Range (mm) |
|---|---|---|
| P1 (Groove 1 height) | 15 | 10–20 |
| P2 (Groove 1 width) | 20 | 15–25 |
| P3 (Groove 1 length) | 125 | 115–140 |
| P4 (Groove 2 height) | 23 | 18–28 |
| P5 (Groove 2 width) | 50 | 45–55 |
| P6 (Groove 2 length) | 155 | 140–170 |
Using ANSYS Design Exploration, three candidate designs were evaluated based on minimized mass, stress, and displacement. Candidate 3 was selected for its balanced performance, with parameters adjusted as per Table 3. Post-optimization modal analysis showed increased natural frequencies, particularly the first mode rising by 4.97%, enhancing resistance to vibrations in gear grinding applications.
| Parameter | Initial Value (mm) | Optimized Value (mm) | Change (%) |
|---|---|---|---|
| P1 | 15 | 11 | -26.7 |
| P2 | 20 | 21 | +5.0 |
| P3 | 125 | 132 | +5.6 |
| P4 | 23 | 21 | -8.7 |
| P5 | 50 | 61 | +22.0 |
| P6 | 155 | 160 | +3.2 |
Experimental validation was conducted on a YK7350NF internal gear grinding machine. Vibration signals were acquired using accelerometers and a data acquisition card at 2,000 Hz sampling rate. Three test conditions were defined: Condition 1 (spindle speed 4,800 rpm, grinding depth 0.01 mm), Condition 2 (4,800 rpm, 0.02 mm), and Condition 3 (6,000 rpm, 0.02 mm). Time-domain and frequency-domain analyses revealed vibration peaks near the spindle rotation frequency and natural frequencies, indicating resonant behavior. For instance, in Condition 1, peaks at 85 Hz (X-direction) and 82.5 Hz (Y-direction) correlated with the spindle frequency of 80 Hz, suggesting forced vibrations. Increased grinding depth in Condition 2 amplified vibration amplitudes, underscoring the sensitivity of gear grinding to process parameters.
Vibrations in gear profile grinding can induce grinding cracks, which are surface defects resulting from cyclic loading and thermal stresses. The relationship between vibration amplitude and crack formation is critical; higher vibrations exacerbate stress concentrations, leading to micro-cracks. The following image illustrates typical grinding cracks observed in gear surfaces, highlighting the importance of vibration control.
Frequency-domain analysis for each condition demonstrated that vibrations predominantly occurred at low frequencies, with amplitudes increasing under higher loads and speeds. In Condition 3, peaks at 100 Hz and 110 Hz aligned with the spindle frequency of 100 Hz, confirming excitation near natural modes. The optimized grinding head showed reduced vibration levels, validating the design improvements. Table 4 summarizes the vibration amplitudes under different conditions, emphasizing the impact of operational parameters on gear grinding stability.
| Condition | Spindle Speed (rpm) | Grinding Depth (mm) | Max Amplitude (m/s²) |
|---|---|---|---|
| 1 | 4800 | 0.01 | 0.15 |
| 2 | 4800 | 0.02 | 0.22 |
| 3 | 6000 | 0.02 | 0.28 |
To mitigate vibrations in gear grinding, several strategies are proposed. First, optimizing spindle speeds to avoid natural frequencies reduces resonant excitations. Second, controlling grinding forces through adaptive depth adjustments minimizes dynamic loads. The grinding force model can be extended to include dynamic components:
$$F_d = F_t + \alpha \sin(2\pi f t)$$
where \( F_d \) is the dynamic grinding force, \( \alpha \) is the amplitude of force variation, and \( f \) is the frequency related to spindle rotation. Third, incorporating damping materials into the grinding head assembly can dissipate vibrational energy. Additionally, real-time monitoring of vibration signals during gear profile grinding enables prompt adjustments, preventing the onset of grinding cracks.
In conclusion, this study comprehensively analyzes the vibration characteristics of an internal gear grinding head through finite element simulation and experimental testing. The optimization of the wheel frame improved natural frequencies, reducing vulnerability to vibrations. Experimental results confirmed that vibrations are primarily induced by spindle rotations near resonant frequencies and are exacerbated by increased grinding depths. By implementing the proposed measures, such as speed optimization and force control, the incidence of grinding cracks can be significantly reduced, enhancing the quality and durability of gears produced through gear profile grinding. Future work will explore advanced materials and active vibration control systems to further refine gear grinding processes.