In the field of mechanical production, roller conveyor lines play a crucial role in enhancing production efficiency and reducing labor costs. The quality of roller conveyor lines directly affects the quality of mechanical production, and among them, bevel gears play a significant part.
Advantages of Bevel Gear Transmission
Bevel gear transmission is widely used due to its high working efficiency, small footprint, high space utilization, good safety, better durability, and stable transmission. Compared to ordinary gears, the greatest advantage of bevel gears is that they can achieve intersected or staggered shaft movement, making power transmission more straightforward and capable of addressing high-speed and heavy-load transmission issues. However, due to the particularity of their own structure, bevel gears tend to have more obvious shape mutations during fatigue failure, and it is prone to fatigue failure such as gear tooth breakage after repeated loading during the transmission process. Therefore, considering the aspects of cost savings and optimizing the transmission work, it is of great significance to conduct research on the fatigue life of the bevel gear transmission system in the roller conveyor lines.
Previous Studies on Gear Wear and Fatigue Life
Many scholars at home and abroad have conducted studies on the degree of gear wear and fatigue life, achieving abundant results. However, some methods have certain limitations. For example, Xiaohe Deng et al. analyzed and calculated the fatigue life of gears through fatigue experiments on gear materials, but the experiments were rather complex. Youjie Cai et al. studied the bending fatigue stress and fatigue life of few-tooth asymmetric gears. Kong Yiyi et al. analyzed the dynamic characteristics of the gear transmission system with simultaneous crack and wear faults, and proposed an analysis model for tooth profile wear and tooth root crack faults. Lu Yanzhi et al. explored the fatigue life of the spindle bevel gear of the cotton picker, but the mesh division was not detailed enough, resulting in less accurate results. Ning Zhiyuan et al. studied the tooth surface wear and dynamic coupling characteristics of planetary gears, and concluded that the severe deterioration of the tooth meshing conditions was the main cause of the degradation of the planetary gear transmission performance. Ye Nanhai et al. proposed a new calculation method to estimate the fatigue life of bevel gears based on the virtual load spectrum technology, but the practicality of this method awaits verification. Dai Yixiang et al. investigated the fatigue life of the transmission gears of the oil drilling rig, but the model was not precise, and the calculation amount was large.
Establishment of the Finite Element Model of Bevel Gears
In this paper, the transmission bevel gears of a roller conveyor line in an Anshan steel factory were taken as the research object, and a pair of bevel gear transmission models based on the roller transmission system was established according to the tooth surface meshing principle and transmission characteristics of the gears. The core component gears in the established model can be divided into the driving gear and the driven gear, and the specific parameters are shown in Table 1.
| Parameter Name | Parameter Value | |
|---|---|---|
| Driving Gear | Driven Gear | |
| Tooth Number | 20 | 30 |
| Module m | 6 | 6 |
| Pressure Angle | 20 | 20 |
| Tooth Width b/mm | 20 | 20 |
| Yield Strength/MPa | 640 | 640 |
| Tooth Surface Hardness/HBW | 280 | 280 |
| Accuracy Grade | 7 | 7 |
| Roughness R/um | 1.6 | 1.6 |
To establish the bevel gear model, the following steps were taken:
- 3D Model Establishment of Gears: HyperMesh software was used to create a 3D model of bevel gear transmission. When analyzing, only the force conditions during the gear meshing process were considered, without taking into account the time-varying situation. For the convenience of subsequent finite element analysis and calculation, small features such as keyways and gear chamfers were not included in the model.
- Material Settings: 40CrMnMo was selected as the material for the transmission bevel gears, with specific material properties as follows: elastic modulus of 2.09 × 10^5 MPa, Poisson’s ratio of 0.295, density of 7870 kg/m^3, and yield limit of 1050 MPa.
- Mesh Division: To ensure calculation accuracy and shorten the calculation time, C3D8R hexahedral mesh elements were selected. Considering that gear damage mainly occurs in the gear tooth area, the mesh of the gear tooth area of the driving gear and the driven gear was divided more finely, while other parts were divided more coarsely. Finally, the number of divided mesh elements was 58,790, as shown in Figure 1.
- Analysis Step Settings: In order to facilitate the convergence of calculation results, two analysis steps were set. A small load was applied in the first analysis step with a time of 1 second, and the required load was applied in the second analysis step with a time of 5 seconds.
- Definition of Contact Type: Since the contact between gears belongs to non-linearity, the penalty function contact algorithm and the face-to-face contact method were used, which could effectively prevent mutual penetration at the contact parts. The tangential behavior was set as Penalty, with a friction coefficient of 0.05, and the normal behavior was hard contact. Contacts were created for the active tooth surface and the driven tooth surface, as shown in Figure 2.
- Setting of Load and Boundary Conditions: Two points were taken on the axes of the two gears as reference points, and the rotational freedom of the gears around the axes was input, with the freedom in other directions being 0, and all the constraints of the driven gear were set. This made the driven gear only able to rotate through the rotational transmission of the driving gear, and a torque was applied at the coupling point at the center of the driving gear.
Finite Element Analysis of Bevel Gears
Based on the established bevel gear transmission model, a finite element analysis was carried out under common working conditions. In the Anshan steel plant area, the roller conveyor line mainly transports rolled pieces with a weight of approximately 1000 kg, the speed of transporting goods on the conveyor line is about 10 m/s, and the rotational speed of the bevel gears is 20 r/min. When setting the torque, it was first necessary to explore the torque applied to the bevel gears by the roller and the power of the motor of the roller. By analyzing the transportation process of the goods, the time to reach the same speed as the roller was about 0.5 s, and the acceleration of the transported rolled pieces on the roller could be obtained from the definition of acceleration, which was a = 0.33 m/s^2. At the same time, the resultant force of the rolled pieces in the horizontal direction was calculated as follows: F = ma, and the calculated value was F = 3267 N. In the roller transmission, the conveyor belt was simplified as being supported by five rollers, so the horizontal force received by each roller was f = F / 5. The load torque of each roller was M = f × D / 2, where the diameter of each roller in the transmission was D = 80 mm, and the calculated value was M = 26.14 N·m. This torque was directly transmitted to the bevel gears through the rollers, so this torque could be used as the load condition for the finite element simulation. The power of the motor was calculated as P = M × n / 9550, and with the rotational speed of the bevel gears being 20 r/min, the calculated value was P = 54.7 kW.
