As can be seen from Fig. 1a) and Fig. 1d), a more uniform temperature field model is obtained when the medium and high frequency frequency ratio is 2.25 along the outer path L1-L2 of the tooth profile. The maximum temperature value appears at the tooth top, which is determined by the bevel gear structure. The mutation of the bevel gear tooth top structure is large. Because of the sharp angle effect, the induction heating efficiency of the tooth top is significantly higher than that of the tooth root. Moreover, compared with the tooth root, the volume of the tooth top is smaller than that of the tooth root. The tooth root is in direct contact with the bevel gear matrix, and the heat conduction strength is stronger than that of the tooth top. It can also be seen from figures 1a) and 1d) that when the current density increases from 2.25 to 2.5, the temperature difference of the outer surface profile increases sharply. Therefore, it is of obvious significance to reasonably select the current density ratio to reduce the temperature difference of the tooth profile.
As can be seen from figure 1c), the temperature difference between path L1-L2 and path L3-L4 is not large, and the maximum temperature difference is about 40 º C, which occurs at the tooth root. This is mainly because the tooth root is close to the bevel gear matrix, and the heat conduction rate is directly proportional to the temperature difference, while the bevel gear matrix temperature is low, resulting in a large tooth root temperature difference; However, as the current density ratio increases, the temperature difference decreases slightly, because the higher frequency is higher than the heating efficiency.
Because the bevel gear has a special structure, with large end and small end, along the width direction, from the large end to the small end, the tooth shape gradually becomes smaller, and the bevel gear is generally longer in width, so it is of great significance to analyze the temperature distribution along the tooth width direction of the bevel gear. Next, three paths are selected from the tooth top, tooth root and the middle of tooth height for analysis to analyze the uniformity of temperature distribution along the tooth width direction. The specific position of path curve is shown in Figure 2.
As can be seen from Figure 3, along the direction of tooth width, the distribution law of temperature at the top, root and middle of tooth surface is obviously different.
It can be seen from 3a) that in the tooth top part, the temperature distribution along the tooth width direction is relatively uniform, and the temperature at the small end of the bevel gear is slightly higher than that at the large end, which is related to the small tooth shape and narrow tooth groove of the small end of the bevel gear. The higher the current density ratio is, the higher the tooth top temperature is. 45 steel will lose magnetism at about 760 º C, but the tooth top temperature is above the Curie point temperature. It can be seen that the loss of magnetism will not prevent the rise of temperature.
It can be seen from Fig. 3b) that the temperature at both ends of the tooth at the middle position of the tooth height is significantly higher than that in the middle part, which is related to the characteristics of induction heating, because there is also sharp angle effect, or end effect, at the end of the tooth. It is also related to the small volume of the corner part at the end of the bevel gear relative to the middle width part, which requires reasonable control of the current size and the medium and high frequency current density ratio during induction heating to avoid overheating at the end.
As can be seen from Fig. 3c), for the bevel gear tooth root, the temperature in the middle of the tooth root is high, because compared with the middle, the magnetic fields on both sides are divergent, and the induction heating efficiency of the middle part is high. With the increase of medium and high frequency current density ratio, when the current density ratio increases by 0.25, the temperature of the tooth root increases more and more along the direction of the tooth width, and the effect is more obvious in the middle of the tooth width. Although the induction heating efficiency increases, the temperature difference with the end of the tooth also increases.
As can be seen from Fig. 3d), when the medium and high frequency current density ratio is 2.25, the maximum temperature difference of the three paths in the bevel gear tooth width direction is the smallest. Therefore, during dual frequency induction heating, the temperature difference in the tooth width direction can be reduced by adjusting the medium and high frequency current density ratio.