# Dynamic Induction Heating Temperature Field Analysis of Spiral Bevel Gears
## 3 Simulation Results and Discussion
### Effect of Coil Structure on Gear Tooth Surface Temperature Distribution  
Because of the complex shape of the spiral level gear tooth surface, to study the temperature distribution law of the spiral level gear tooth surface, five circumferential curves were selected in the axial position of the tooth surface, namely, A, B, C, D, and E. Each curve represents the outer surface profile in the gear tooth width direction. The plane where each curve was located was parallel to each other with a spacing of 11 mm, and 16 points on each curve were taken as the study object (Figure 10).  
Figure 9: Temperature rise process under two coil structures.  
The axial temperature distribution on the spiral bevel gear surface after induction heating using a TC is shown in Figure 10. When the gears were heated using TC, the circumferential temperature distribution of the tooth surfaces was not uniform. The five temperature curves in the figure show periodic changes as the temperature increases and decreases. For example, between 250\({}^{\circ}\) and 300\({}^{\circ}\), the temperature curves A, C, and E increase and then decrease, whereas curves B and E decrease and then increase. Between 250\({}^{\circ}\) and 300\({}^{\circ}\), the temperature curves A, C, and E increase and then decrease and then decrease, whereas curves B and E decrease and then increase. This is due to the difference in the shapes of the spiral bevel gears with different curves at the same angle. The teeth of the spiral bevel gears have a helix angle, so there are different tooth tops and roots at the same angle. There is a radial distance difference between the tooth root and top. When the tooth top was close to the heating coil, the electromagnetic heating power in this area was high, and the temperature was high. When the tooth root is far from the heating coil, the electromagnetic heat power in this area is low, and the corresponding temperature is low.  
According to the results of TC heating (Figure 11), curves A, B, C, D, and E have the lowest temperature at the coil opening from 135\({}^{\circ}\) to 225\({}^{\circ}\). In contrast, the temperature farther away from the coil opening was higher, and the distribution was more uniform. The temperature distribution in the gear axial direction was uneven. The B, D, and E curves correspond to higher temperatures because the gear area where these three curves are located is closer to the induction heating coil. Conversely, the gear area where the A and C curves are located is farther away from the induction heating coil, and their corresponding temperatures are lower.  
Figure 11: Temperature distribution of the gear tooth surface during TC heating.  
Figure 10: Selection of gear surface study curves.  
As illustrated in Figure 12, when using an LC to heat the spiral bevel gear, the temperature distribution around the gear's circumference was similar to the results of the TC heating, and the temperature curve varies periodically. The temperature was the lowest at the coil opening from 135\({}^{\circ}\) to 225\({}^{\circ}\), the highest tooth surface temperature was located near 90\({}^{\circ}\) and 270\({}^{\circ}\), the coil was roughly parallel to the tooth direction of the gear, and the efficiency of induction heating was the highest. In the axial direction, the LC was more uniformly heated than the TC, and the temperature difference between the five curves was smaller.