# Influence of hypoid gear cutter and cutter head parameters on tooth surface

The influence of five parameters of cutter and cutter head on the tooth surface is analyzed, including tooth profile angle, rake angle, offset angle, radius of cutter head and initial installation angle. The results are shown in Fig. 1-4 (each curve corresponds to one grid point, and each color corresponds to the same row of grid points)

It can be clearly seen from figure 1-4 that not all parameters have linear influence on tooth surface error, and some parameters show obvious nonlinear relationship. In addition, the sensitivity of different grid points on the tooth surface to the same machining parameters is not the same among the selected cutter and cutter head parameters.

In order to show the rule more clearly, the results of 9 points (the top and root of the tooth and the starting and ending points and the middle point of the middle line of the tooth surface) at different positions of the tooth surface are selected, as shown in Fig. 5-8.

It can be seen from figure 5-8 that:

The sensitivity of tooth surface to cutter profile angle, initial installation angle and cutter head radius to large and small gears is high, while the sensitivity of rake angle and offset angle to tooth surface is low; the tooth height direction is more sensitive to the cutter profile angle, rake angle, offset angle and initial installation angle, while the tooth direction is more sensitive to the deviation of cutter head radius which mainly affects the tooth direction.

For further analysis, the tooth surface error caused by the above parameters is fitted as quadratic polynomial, as shown in the following formula:

According to the binomial coefficient, the sensitivity of tooth surface to each parameter can be judged (here, the binomial coefficient less than 10-3 can be approximately regarded as linear). Only the fitting coefficients of 1 ~ 18 serial numbers in the direction of offset angle tooth height are listed. The influence of the offset angle on the tooth surface is nonlinear and presents a negative correlation to a positive correlation along the tooth height direction.

Accordingly, combined with the fitting coefficient table and figure 1-8, it can be concluded that in the tooth height direction, the sign of the binomial coefficient of the cutter profile angle, rake angle and offset angle is opposite from the tooth root to the tooth top, and the influence on the tooth surface is nonlinear. The influence of rake angle on tooth surface is small and can be ignored. However, the binomial coefficient is very small, which can be approximately regarded as linear. The influence of the initial installation angle on the tooth surface is positive correlation, and the influence is great, but the binomial coefficient is very small negative number, which can be approximately regarded as linear. The positive and negative correlation of the influence of offset angle and rake angle on big and small gears is opposite in the direction of tooth height.

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