# Dynamic Induction Heating Temperature Field Analysis of Spiral Bevel Gears
## 4 LC Heating Experimental Test
### Comparison of the Experimental and Simulation Results  
During the experiment, because the ambient temperature changed with time, the fluctuation of the ambient temperature affected the temperature of the tooth surface, and the infrared thermal imager had a measurement error of 1.5%. To improve the accuracy of the experimental results we conducted the same experiment three times, and the final experimental results are presented as the average of the three experiments. The main purpose of this section is to verify the correctness of the simulation through experiments. Therefore, to quantitatively analyze the error between the experiment and the simulation, the temperature changes of tooth apex point A and tooth root point B during the numerical simulation and experiment of induction heating were collected. The error between the experiment and simulation was compared, and temperature curves were plotted (Figure 19).  
Figure 18: Gear tooth surface temperature distribution: (**a**) heating for 3 s in the experiment; (**b**) heating for 3 s in the simulation; (**c**) heating for 18 s in the experiment; (**d**) heating for 18 s in the simulation; (**e**) heating for 30 s in the experiment, and (**f**) heating for 30 s in the simulation.  
From the temperature curve in Figure 19, the temperatures at points A and B on the tooth surface of the spiral bevel gear show an increasing trend during the heating process, and the curve trends of the simulated and experimental temperatures are the same. How-ever, the experimental temperature is higher than the simulated temperature, and the experimental temperature is more volatile than the simulated temperature. This is because the gear exchanged heat with the air during the experiment, and the temperature of the tooth surface was radiated to the induction coil, resulting in changes in the physical properties of the coil.  
As shown in Figure 19a, the average temperature changes during the induction heating of the spiral bevel gear were 5.23 \({}^{\circ}\)C/s and 6.1 \({}^{\circ}\)C/s. The maximum temperature difference between the simulated and experimental groups at the top of tooth A was 35.75 \({}^{\circ}\)C, and the average temperature difference was 20.20 \({}^{\circ}\)C, with a maximum relative error of 16.75%. It took 27 s to heat the tooth root point B to 170 \({}^{\circ}\)C in the experiment and 30 s to reach the corresponding temperature in the simulation, and the relative error of heating time was 10%. The average temperature change between the simulation and experiment for point B was 4.97 \({}^{\circ}\)C/s and 5.4 \({}^{\circ}\)C/s. The maximum temperature difference between the simulation and experiment was 20 \({}^{\circ}\)C, the average temperature difference was 10.30 \({}^{\circ}\)C, and the maximum relative error was 12.36%.  
The temperature difference between top A and root B of the spiral bevel gear is shown in Figure 20. The temperature difference between the root and the top of the tooth in the simulation was relatively stable, with an average temperature difference of approximately 9.5 \({}^{\circ}\)C, while the temperature difference between the top and the root of the tooth in the experiment fluctuated more, with a maximum temperature difference of 27.3 \({}^{\circ}\)C and an average temperature difference of 19.24 \({}^{\circ}\)C. This is because of the assumptions of the simulation conditions, which did not consider the influence of the surrounding air and the coil temperature change, the experimental process's external environment, and the measuring instrument's conditions. Overall, the experimental and simulated data for the heating phase are in good agreement.  
Figure 19: Comparison of the experimental and simulated temperatures: (**a**) tooth top point A; (**b**) tooth root point B.