Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System
Abstract
:1. Introduction
2. Composition of the Transmission System
3. Dynamic Model of the Transmission System
3.1. Dynamic Model
3.2. Calculation of Component Relative Displacements
3.2.1. Relative Displacements between Sun gear and Planet gears
3.2.2. Relative Displacements between the Ring gear and Planet Gears
3.2.3. Relative Displacements between the Carrier and Planet Gears
3.3. Derivation of the Motion Differential Equations
3.3.1. Motion Differential Equation for the Sun Gear, a
3.3.2. Motion Differential Equation for the Planet Gear, mi
3.3.3. Motion Differential Equation for the Ring Gear, d
3.3.4. Motion Differential Equation for the Sun Gear s
3.3.5. Motion Differential Equation for the Planet Gear pi
3.3.6. Motion Differential Equation for the Ring Gear r
3.3.7. Motion Differential Equation for the Carrier, h
3.4. The Definition of LSC
4. Analysis of Dynamic Response Characteristics of the Transmission System
4.1. Dynamic Meshing Forces
4.1.1. Dynamic Meshing Forces under Rated Condition
4.1.2. Effect of External Excitation on Dynamic Meshing Forces
4.2. Analysis of Planet Gear Vibration Displacements
4.2.1. Vibration Displacements of the Planet Gears under Rated Condition
4.2.2. Vibration Displacements of Planet gears under Different Input Torques
4.3. Load-Sharing Coefficients
4.3.1. LSCs under Rated Condition
4.3.2. Dynamic LSCs under External Excitation
4.3.3. Dynamic LSCs under Different Input Torques
5. Model Validation
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Item | Number of Teeth | Angle of Helix (°) | Normal Pressure Angle (°) | Module | Mass (kg) | Moment of Inertia (kg·mm2) |
---|---|---|---|---|---|---|
Sun gear, a | 22 | 20 | 20 | 1.5 | 0.092 | 17.664 |
Planet gear, m | 44 | 20 | 20 | 1.5 | 0.327 | 268.521 |
Ring gear, dL | 110 | 20 | 20 | 1.5 | 0.163 | 1325.860 |
Ring gear, dR | 110 | 20 | 20 | 1.5 | 0.163 | 1325.860 |
Sun gear, s | 55 | 20 | 20 | 1.5 | 0.488 | 525.752 |
Planet gear, p | 27 | 20 | 20 | 1.5 | 0.108 | 35.531 |
Ring gear, rL | 110 | 20 | 20 | 1.5 | 0.163 | 1325.860 |
Ring gear, rR | 110 | 20 | 20 | 1.5 | 0.163 | 1325.860 |
Planet carrier, h | 1.648 | 4946.014 |
Torque (Nm) | Speed (rpm) | |
---|---|---|
Case 1 | 200 | 11,938 |
Case 2 | 300 | 7958 |
Case 3 | 400 | 5968 |
Case 4 | 500 | 4775 |
Case 5 | 600 | 3979 |
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Yue, Z.; Chen, Z.; Qu, J.; Li, Y.; Dzianis, M.; Mo, S.; Yu, G. Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System. Appl. Sci. 2024, 14, 4491. https://doi.org/10.3390/app14114491
Yue Z, Chen Z, Qu J, Li Y, Dzianis M, Mo S, Yu G. Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System. Applied Sciences. 2024; 14(11):4491. https://doi.org/10.3390/app14114491
Chicago/Turabian StyleYue, Zongxiang, Zhaobo Chen, Jianjun Qu, Yang Li, Marmysh Dzianis, Shuai Mo, and Guangbin Yu. 2024. "Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System" Applied Sciences 14, no. 11: 4491. https://doi.org/10.3390/app14114491