Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear
Abstract
:1. Introduction
2. Improved TVMS Method for a Spalled Gear
3. Dynamic Modeling of Spur-Gear System
4. Results and Discussion
4.1. Model Validation
4.2. Multi-Spalling TVMS Calculation
4.2.1. Multi-Spalling on Non-Adjacent Teeth Within a Gear
4.2.2. Multi-Spalling on the Same Tooth Within a Gear
4.2.3. Multi-Spalling on Different Gears
4.3. Dynamic Simulation Analysis and Experimental Verification
4.3.1. Experimental Equipment
4.3.2. Multi-Spalling on Adjacent Teeth of the Driving Gear
4.3.3. Multi-Spalling on Different Gears
5. Conclusions
- (1)
- The proposed method can accurately calculate the TVMS of multi-spalling gears. Compared with traditional methods, it offers superior accuracy and greater generality. Therefore, the method shows strong potential for application in gear fault diagnosis.
- (2)
- When two adjacent teeth are spalled, the TVMS experiences a significant reduction. Asymmetric spalling causes a more substantial decrease in TVMS than symmetric spalling, even when the parameters are the same. The effect of multiple spalling teeth on the TVMS depends on the specific spalling parameters. Additionally, spalling on different gears results in eight distinct stiffness components.
- (3)
- The dynamic behavior of a multi-spalling gear system is influenced not only by individual spalling teeth but also by the combined effects of the distribution and degree of spalling. Different spalling modes can significantly change the system’s dynamic behavior. When teeth with spalling faults mesh, the vibration response exhibits more pronounced shocks. The FFT spectrum of the gear system modulates the meshing frequency, incorporating the corresponding rotational frequencies of gears with spalling faults. This study provides a solid foundation for understanding the dynamic behavior of spalled gear systems, revealing their dynamic characteristics and failure mechanisms.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
DOFs | degrees of freedom |
TVMS | time-varying meshing stiffness |
FEM | finite element method |
Hg-Hp | healthy tooth on the gear mesh with healthy tooth on the pinion |
Sg-Hp | spalling tooth on the gear mesh with healthy tooth on the pinion |
Hg-Sp | healthy tooth on the gear mesh with spalling tooth on the pinion |
Sg-Sp | spalling tooth on the gear mesh with spalling tooth on the pinion |
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Parameter | Value |
---|---|
Number of teeth/z1, z2 | 40, 40 |
Module (mm)/m | 3 |
Tooth width (mm)/L | 20 |
Pressure angle (°)/α0 | 20 |
Hub hole radius (mm) | 20, 20 |
Parameter | Value |
---|---|
Number of teeth/z1, z2 | 26, 31 |
Module (mm)/m | 3 |
Teeth width (mm)/L | 25 |
Pressure angle (°)/α0 | 20 |
Mass (kg)/m1, m2 | 0.988, 1.02 |
Backlash (μm)/2b | 40 |
Eccentricity (mm)/ρ1, ρ2 | 1 × 10−3, 2 × 10−3 |
Mass moment of inertia (kg·m2)/I1, I2 | 1.81 × 10−3, 1.87 × 10−3 |
Mass moment of inertia (kg·m2)/Jg, Jp | 2 × 10−3, 2.5 × 10−3 |
Bending stiffness (N·m−1)/ks1, ks2 | 1 × 107, 1.5 × 107 |
Torsional stiffness (N·m−1)/kt1, kt2 | 1.5 × 107, 2 × 107 |
Bearing stiffness (N·m−1)/kx1, ky1, kx2, ky2 | 1 × 108, 1 × 108, 1 × 108, 1 × 108 |
Bearing damping (N·m−1·s−1)/cx1, cy1, cx2, cy2 | 1 × 105, 1 × 105, 1 × 105, 1 × 105 |
0.1 | |
0.05, 0.05 | |
(i = 1, 2, 3, 4) | 0.5 |
Hub hole radius (mm) | 20, 20 |
Spall 1/2/3/4 | |
lmax (mm) | 3/3/3/2 |
hs (mm) | 2/2/2/1 |
p (mm) | 2.5/4/3.2/5.5 |
xcenter (mm) | 40/40/40/41 |
θs (°) | 30/30/30/40 |
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Kong, X.; Yuan, Y.; Sun, S.; Xin, Y.; Meng, Q. Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear. Machines 2025, 13, 299. https://doi.org/10.3390/machines13040299
Kong X, Yuan Y, Sun S, Xin Y, Meng Q. Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear. Machines. 2025; 13(4):299. https://doi.org/10.3390/machines13040299
Chicago/Turabian StyleKong, Xiangxi, Ye Yuan, Shuai Sun, Yi Xin, and Qiang Meng. 2025. "Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear" Machines 13, no. 4: 299. https://doi.org/10.3390/machines13040299
APA StyleKong, X., Yuan, Y., Sun, S., Xin, Y., & Meng, Q. (2025). Time-Varying Meshing Stiffness Calculation and Dynamics Simulation of Multi-Spalling Gear. Machines, 13(4), 299. https://doi.org/10.3390/machines13040299