This article presents a comprehensive configuration design and performance analysis of an inter-axle limited slip differential with face gears. Tables and diagrams are utilized to summarize key information and enhance readability.
1. Overview
To address the limitations of existing inter-axle limited slip differentials, such as limited slip capability, complex configurations, and processing difficulties, a novel design for an inter-axle limited slip differential with face gears is proposed. This design leverages the advantages of face gears, including low cost, high load capacity, and axial force transmission only.
2. Key Components and Structure
The main components of the face gear inter-axle limited slip differential are shown in Table 1.
| Component | Description |
|---|---|
| Power Input Shaft | Transmits power to the differential |
| Integral Planet Carrier | Supports and rotates the planetary gears |
| Planetary Gears | Distribute torque between the front and rear axles |
| Front Face Gear | Engages with planetary gears and transmits torque to the front axle |
| Rear Face Gear | Engages with planetary gears and transmits torque to the rear axle |
| Friction Plates | Provide limiting slip functionality by transferring torque |
| Output Front Axle | Connects to the front wheels |
| Output Rear Axle | Connects to the rear wheels |
3. Operational Principles
3.1 Differential Motion Characteristics
The angular velocity relationships among the integral planet carrier (ω0), front face gear (ω1), and rear face gear (ω2) are governed by:
ω0=52ω1+53ω2
3.2 Torque Characteristics
During steady-state driving, the input torque (T0) is distributed to the front and rear axles (T1 and T2) based on the gear ratios. During wheel slip, the friction plates engage to transfer torque and limit slip.
4. Mathematical Models
4.1 Mechanical Model
The mechanical model is illustrated, including torque relationships and moments acting on the friction plates.
4.2 Friction Plate Model
The torque capacity of the friction plates (Tf) is governed by:
Tf=2.3n(Fs+2Tctanα3mz)μRo2−Ri2Ro3−Ri3
Where:
- Fs is the preset axial force on the friction plates.
- Tc is the face gear meshing torque.
- α is the gear pressure angle.
- z and m are the gear teeth number and module, respectively.
- μ is the friction coefficient.
- n is the number of friction surfaces.
- Ro and Ri are the outer and inner radii of the friction plates.
4.3 Locking Coefficient Model
The locking coefficient (K) is used to evaluate the slip-limiting performance, with K = T1/T2.
5. Simulation Models
5.1 Face Gear Tooth Surface Model
The tooth surface of the face gears is modeled using mathematical equations and Matlab software. The assembled model in SolidWorks.
5.2 Adams Virtual Prototype Model
The assembled model from SolidWorks is imported into Adams for simulation. Constraints, drivers, and loads are applied to simulate different driving conditions.
6. Simulation Analysis
6.1 Straight and Steady Driving on a Good Road
Simulations are conducted for speeds of 10, 20, and 40 km/h. The torque distribution and speed curves confirm that the design torque distribution ratio of 40:60 is achieved.
6.2 Straight Driving on a Dual-adhesion Coefficient Road
Simulations are performed for driving on a dual-adhesion coefficient road with one axle slipping. The torque distribution, speed curves, and friction torque of the friction plates are analyzed.
Table 2: Vehicle Parameters for Simulation
| Parameter | Value |
|---|---|
| Vehicle Mass | 2000 kg |
| Wheel Radius | 0.325 m |
| Front/Rear Axle Load Ratio | 54:55 |
| Axle Differential Ratio | 2.514 |
7. Conclusion
The proposed face gear inter-axle limited slip differential demonstrates superior slip-limiting performance and design feasibility. The simulation results validate the theoretical analysis and provide a basis for further research and application.