In modern industrial applications, gear shaft systems are critical components in power transmission, widely used in aerospace, energy, marine, chemical, and automotive sectors. However, as these systems operate under high-speed, heavy-load, and high-precision conditions, they often experience significant vibration and noise due to meshing impacts, misalignment, and wear. These issues not only reduce operational efficiency and lifespan but also contribute to environmental noise pollution. Traditional vibration control methods, such as gear structure optimization or passive damping elements like damping rings, have limitations in terms of cost, complexity, and narrow frequency bandwidth. To address these challenges, we developed a novel Integral Damping Gear (IDG) that integrates damping mechanisms directly into the gear structure. This study focuses on evaluating the effectiveness of IDG with different damping liquid viscosities in controlling vibration and noise in gear shaft systems. Through experimental analysis, we demonstrate that IDG significantly enhances damping, leading to reduced vibration amplitudes and noise levels, thereby ensuring smoother operation of gear shaft assemblies.
The IDG design incorporates an elastic region, a damping region, O-ring seals, a damping liquid cavity, and sealing end caps. This structure allows the gear to function as both a power transmission element and a damping device. When the gear shaft system operates, meshing-induced vibrations are transmitted to the elastic region of the IDG, which compresses the damping liquid in the cavity. This compression generates damping forces that dissipate vibrational energy. The damping liquid used in this study is dimethyl silicone oil, selected for its stable viscosity-temperature characteristics and low fluidity, which ensure consistent performance across varying operational conditions. The overall damping of the system can be modeled as the sum of the damping contributions from the IDG and the bearings, as expressed by the equation: $$c_{\text{system}} = c_{\text{IDG}} + c_{\text{bearing}}$$ where \(c_{\text{IDG}} \geq c_{\text{bearing}}\). This relationship highlights that the IDG substantially increases the system’s damping, making it more effective in vibration control compared to conventional gear shaft setups.
To validate the performance of IDG, we constructed an experimental test rig consisting of a single-stage spur gear system. The gear shaft arrangement included a driving shaft and a driven shaft, both supported by bearing housings. The gears were made of 45 steel, with key parameters detailed in Table 1. We tested three different viscosities of silicone oil as damping liquids: \(1 \times 10^{-3} \, \text{m}^2/\text{s}\), \(5 \times 10^{-3} \, \text{m}^2/\text{s}\), and \(1 \times 10^{-2} \, \text{m}^2/\text{s}\). The test conditions maintained a constant temperature of 25°C to minimize viscosity variations. Vibration and noise data were acquired using accelerometers mounted on the bearing housings in the horizontal direction and a microphone sensor for noise measurement. Data collection was performed using an NI data acquisition system with NI9234 cards, covering a speed range of 500 to 1500 rpm. The experimental procedure involved comparing the vibration and noise levels of a standard spur gear system with those of the IDG system under different damping liquid viscosities.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Driving Gear Teeth (\(z_1\)) | 50 | Pressure Angle (\(\alpha\)) | 20° |
| Driven Gear Teeth (\(z_2\)) | 25 | Gear Width (\(b_1\)) | 20 mm |
| Gear Ratio (\(i\)) | 1/2 | Theoretical Center Distance (\(d\)) | 75 mm |
| Module (\(m\)) | 2 mm | — | — |
The vibration control efficacy of IDG was assessed across the speed range of 500 to 1500 rpm. The results, summarized in Table 2 and depicted in graphical form, show that IDG with higher damping liquid viscosity consistently reduced vibration amplitudes on both the driving and driven gear shafts. For instance, at a viscosity of \(1 \times 10^{-3} \, \text{m}^2/\text{s}\), the average vibration reduction was 29.1% on the driving shaft and 38.2% on the driven shaft. As viscosity increased to \(5 \times 10^{-3} \, \text{m}^2/\text{s}\), the reductions improved to 40.4% and 43.3%, respectively. At the maximum viscosity of \(1 \times 10^{-2} \, \text{m}^2/\text{s}\), the average vibration reduction reached 64.4% for the driving shaft and 50.8% for the driven shaft. This trend indicates that higher damping liquid viscosity enhances the energy dissipation capacity of the IDG, leading to more effective vibration suppression in the gear shaft system. The relationship between viscosity and vibration reduction can be further analyzed using the damping coefficient model: $$\zeta = \frac{c}{2\sqrt{m k}}$$ where \(\zeta\) is the damping ratio, \(c\) is the damping coefficient, \(m\) is the mass, and \(k\) is the stiffness. Higher viscosity increases \(c\), thereby raising \(\zeta\) and improving vibration control.
| Gear Shaft | \(1 \times 10^{-3} \, \text{m}^2/\text{s}\) | \(5 \times 10^{-3} \, \text{m}^2/\text{s}\) | \(1 \times 10^{-2} \, \text{m}^2/\text{s}\) |
|---|---|---|---|
| Driving Shaft | 29.1% | 40.4% | 64.4% |
| Driven Shaft | 38.2% | 43.3% | 50.8% |
Time-frequency analysis of vibration data at 1200 rpm provided deeper insights into the IDG’s performance. The time-domain waveforms revealed that IDG significantly mitigated impact vibrations, with reductions in peak amplitudes as viscosity increased. Specifically, for the driving gear shaft, vibration reductions were 19.3%, 26.2%, and 55.1% for viscosities of \(1 \times 10^{-3} \, \text{m}^2/\text{s}\), \(5 \times 10^{-3} \, \text{m}^2/\text{s}\), and \(1 \times 10^{-2} \, \text{m}^2/\text{s}\), respectively. Similarly, for the driven gear shaft, reductions were 34.1%, 38.4%, and 45.2%. The frequency-domain spectra, analyzed using Fast Fourier Transform (FFT), showed that IDG effectively suppressed meshing frequency components and sidebands associated with modulation phenomena. For example, at the driving shaft, the vibration amplitudes at key frequency bands (e.g., 460–520 Hz, 950–1010 Hz, and 1460–1520 Hz) were reduced by up to 74.0%, 79.5%, and 82.8% with the highest viscosity IDG, as detailed in Table 3. This suppression of dominant frequencies underscores the IDG’s ability to dampen gear shaft vibrations across a broad frequency range, reducing the risk of resonance and fatigue failure.
| Frequency Band | Standard Gear Amplitude (g) | \(1 \times 10^{-3} \, \text{m}^2/\text{s}\) Reduction | \(5 \times 10^{-3} \, \text{m}^2/\text{s}\) Reduction | \(1 \times 10^{-2} \, \text{m}^2/\text{s}\) Reduction |
|---|---|---|---|---|
| 460–520 Hz | 0.10696 | 17.5% | 59.0% | 74.0% |
| 950–1010 Hz | 0.04468 | 42.0% | 64.9% | 79.5% |
| 1460–1520 Hz | 0.12525 | 35.1% | 50.6% | 82.8% |
Noise reduction measurements further confirmed the benefits of IDG. As shown in Table 4, the IDG system with damping liquid viscosity of \(1 \times 10^{-3} \, \text{m}^2/\text{s}\) achieved an average noise reduction of 3.2 dB(A), with a maximum reduction of 6.2 dB(A). At \(5 \times 10^{-3} \, \text{m}^2/\text{s}\), the average reduction increased to 4.6 dB(A), peaking at 7.4 dB(A). The highest viscosity of \(1 \times 10^{-2} \, \text{m}^2/\text{s}\) yielded an average noise reduction of 5.9 dB(A) and a maximum reduction of 7.6 dB(A). These results align with the vibration data, demonstrating that enhanced damping in the gear shaft system directly correlates with lower acoustic emissions. The noise reduction can be modeled using the sound pressure level equation: $$L_p = 20 \log_{10} \left( \frac{p}{p_0} \right)$$ where \(L_p\) is the sound pressure level in dB, \(p\) is the measured sound pressure, and \(p_0\) is the reference pressure. By reducing vibration-induced sound pressures, IDG effectively lowers \(L_p\), contributing to a quieter operating environment.
| Speed (rpm) | \(1 \times 10^{-3} \, \text{m}^2/\text{s}\) Reduction (dB(A)) | \(5 \times 10^{-3} \, \text{m}^2/\text{s}\) Reduction (dB(A)) | \(1 \times 10^{-2} \, \text{m}^2/\text{s}\) Reduction (dB(A)) |
|---|---|---|---|
| 500 | 4.5 | 5.1 | 6.3 |
| 600 | 3.8 | 4.9 | 6.5 |
| 700 | 1.0 | 2.9 | 6.3 |
| 800 | 0.3 | 1.9 | 5.1 |
| 900 | 1.7 | 3.3 | 5.8 |
| 1000 | 2.1 | 3.2 | 4.8 |
| 1100 | 2.5 | 4.0 | 4.7 |
| 1200 | 2.6 | 4.6 | 4.8 |
| 1300 | 5.0 | 6.3 | 6.4 |
| 1400 | 5.1 | 6.7 | 6.8 |
| 1500 | 6.2 | 7.4 | 7.6 |
In conclusion, our experimental study demonstrates that the novel Integral Damping Gear (IDG) effectively controls vibration and noise in gear shaft systems. The key findings are: (1) IDG with higher damping liquid viscosities significantly reduces vibration amplitudes, with average reductions exceeding 50% at the maximum viscosity tested; (2) Time-frequency analyses confirm that IDG mitigates impact vibrations and suppresses meshing frequency components, leading to smoother gear shaft operation; (3) Noise levels are substantially lowered, with reductions up to 7.6 dB(A), highlighting the dual benefits of vibration and acoustic control. The IDG design offers a practical solution for enhancing the reliability and performance of gear shaft systems in various industrial applications. Future work could explore optimizing the IDG geometry and damping liquid properties for specific operational conditions to further improve gear shaft dynamics.