Helical gears are critical components in synchronous box-type exciters for mining linear vibrating screens. Their dynamic behavior directly affects the reliability and operational stability of the system. This study investigates the influence of center distance variations on the fatigue life and vibration response of helical gear pairs under complex working conditions.
1. Virtual Prototype Modeling
A multi-body dynamics model was established using ADAMS software, incorporating key parameters:
| Parameter | Symbol | Value |
|---|---|---|
| Normal Module | Mn | 3 mm |
| Number of Teeth | Z | 93 |
| Face Width | B | 100 mm |
| Helix Angle | β | 32.28° |
The meshing force components were calculated using:
$$F_t = \frac{2T}{d}$$
$$F_r = F_t \tan\alpha_n/\cos\beta$$
$$F_a = F_t \tan\beta$$
2. Critical Operating Conditions Analysis
Dynamic center distance fluctuations were observed under four eccentric block positions (0°, 90°, 180°, 270°):
| Position | Max. Contact Stress (MPa) | Equivalent Stress (MPa) |
|---|---|---|
| 0° | 802.90 | 792.30 |
| 90° | 52.09 | 41.83 |
| 180° | 49.37 | 41.34 |
| 270° | 49.79 | 39.95 |
The 0° position showed severe “tooth squeezing” due to reduced center distance, leading to accelerated fatigue failure.
3. Non-standard Center Distance Optimization
Modified center distance was calculated considering optimal backlash:
$$j_{bnmin} = \frac{2}{3}(0.06 + 0.0005a + 0.03m_n) = 0.21\text{ mm}$$
$$a_s = 330.3081\text{ mm}\ (\Delta a = +0.3057\text{ mm})$$
Fatigue life comparison:
| Condition | Minimum Life (Cycles) |
|---|---|
| Standard Center Distance | < 10^6 |
| Non-standard Center Distance | 1.79 × 10^{14} |
4. Dynamic Response Characteristics
Vibration spectrum analysis revealed significant improvements:
$$GMF = \frac{N \times RPM}{60} = \frac{93 \times 750}{60} = 1162.5\text{ Hz}$$
| Frequency Component | Standard (g) | Non-standard (g) |
|---|---|---|
| 1×GMF | 12.5 | 8.2 |
| 2×GMF | 6.8 | 3.1 |
| Sidebands | ±12.5 Hz | None |
5. Conclusion
Non-standard center distance adjustments in helical gear pairs:
1. Eliminate tooth squeezing phenomena
2. Reduce dynamic center distance fluctuations by 32%
3. Decrease vibration acceleration amplitudes by 34-54%
4. Increase fatigue life by 8 orders of magnitude
This research demonstrates that optimized helical gear center distance significantly enhances the operational reliability of vibration screen exciters in mining applications.