This study proposes a novel vibration damping structure for spur gears by integrating slot-hole features to mitigate meshing-induced vibrations. The design incorporates longitudinal slots and through-holes in the gear teeth, as illustrated below:
1. Dynamic Simulation Methodology
The dynamic behavior of spur gears was analyzed using Adams software with the following key parameters:
| Parameter | Value |
|---|---|
| Module (mm) | 6 |
| Pressure Angle (°) | 20 |
| Number of Teeth | 34 |
| Contact Stiffness (N/mm) | 1.2×105 |
The meshing frequency is calculated as:
$$f_m = \frac{z \cdot n}{60}$$
where \( z \) = number of teeth, \( n \) = rotational speed (r/min).
2. Power Spectrum Analysis
The vibration characteristics were evaluated using correlation power spectrum estimation:
$$r_{\phi}(m) = \frac{1}{N} \sum_{n=0}^{N-1} u_N(n) u_N^*(n – m) \quad |m| \leq N – 1$$
$$S_{\phi}(\omega) = \sum_{m=-M}^{M} r_{\phi}(m) e^{-j\omega m}$$
where \( N \) = total data points, \( M \) = maximum lag index.
3. Orthogonal Experimental Design
A three-factor three-level orthogonal test was conducted to optimize the slot-hole parameters:
| Factor | Level (mm) | ||
|---|---|---|---|
| 1 | 2 | 3 | |
| Slot Width (A) | 0.2 | 0.3 | 0.4 |
| Backlash (B) | 0.2 | 0.07 | -0.03 |
| Hole Diameter (C) | 4 | 6 | 8 |
The signal-to-noise ratio (SNR) for vibration reduction was calculated as:
$$\eta = -10\log \left( \frac{1}{n} \sum_{i=1}^{n} y_i^2 \right)$$
4. Results and Discussion
Key findings from the orthogonal tests:
| Factor | Contribution Rate (%) | F-value |
|---|---|---|
| Slot Width (A) | 0.13 | 1.77 |
| Backlash (B) | 85.84 | 1,189 |
| Hole Diameter (C) | 13.96 | 193.4 |
The optimal parameters for spur gear vibration reduction were determined as:
- Slot width: 0.2 mm
- Backlash: -0.03 mm
- Hole diameter: 4 mm
5. Experimental Verification
Vibration tests under different operating conditions showed:
| Condition | Original | Optimized | Reduction |
|---|---|---|---|
| 780 rpm/150 N·m | 4.776 | 0.777 | 83.7% |
| 1,470 rpm/150 N·m | 0.254 | 0.196 | 22.8% |
The slot-hole structure demonstrated significant vibration reduction capabilities for spur gears, particularly in high-torque conditions. The negative backlash configuration under slot relaxation constraints proved particularly effective in suppressing meshing vibrations.
6. Conclusion
This study establishes that:
- Slot-hole structures reduce spur gear vibration by 20-33% through flexible tooth deformation and stress redistribution
- Backlash contributes 85.84% to vibration characteristics, making it the dominant design factor
- The optimal parameter combination decreases meshing frequency vibrations by 21.1% compared to conventional spur gears
The proposed design methodology provides valuable insights for developing high-precision, low-noise spur gear transmissions in industrial applications.