# Determination of tooth side clearance of straight bevel gear

The tooth clearance of straight bevel gear will affect the dynamic performance of straight bevel gear transmission and cause impact and vibration. The approximate polynomial of tooth side clearance is solved by MATLAB programming. Let f (x (T)) be the tooth side clearance function of tooth meshing and C be the tooth side clearance. The function expression is as follows:

Use matlab to solve the function curve, as shown in Figure 1, so that C = 5×10-5

m. Then use the curve fitting toolbox to fit with polynomial curve. The fitting results of polynomial of degree 1 to 9 are shown in Fig. 2 and Fig. 3.

It can be seen from Fig. 2 and Fig. 3 that the higher the degree of the fitting polynomial, the closer the fitting curve is to the original tooth side clearance function. However, when the fitting polynomial exceeds the 7th degree polynomial, the obtained polynomial fitting curve can no longer significantly improve the fitting accuracy. In addition, it can be seen that the 3rd degree polynomial curve is very close to the curve trend of the original tooth side clearance function, Therefore, in order to facilitate the solution of the dynamic equation of straight bevel gear, the original tooth side clearance function can be expressed by cubic polynomial, and the expression of tooth side clearance function can be obtained as follows:

a1 =0.344, a3 =1201000

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