Using the above method to calculate the NC machining coordinate of spiral tooth non, the gear pitch curve is shown in Fig. 1. The processing parameters are: RA = 46.6 mm, Rb = 34.6 mm, RC = 88.9 / 2 mm, number of teeth n = 12, helix angle β = 35 ° and tooth thickness B = 12 mm. The position coordinate series (xwi, ywi, zwi) of the milling cutter head, the axial rotation angle (the difference between pitch angle and root cone angle) and the rotation angle (α I, φ I) of the cutter head are calculated by MATLAB.
With the shaping cutter, each tooth’s left and right tooth surfaces are machined with one cutter, and the 12 teeth of the pinion need to be machined with 24 cutters. Table 1 shows the values of milling cutter head position coordinates (xwi, ywi, zwi) and machining angle values (δ I, φ I) of the cutting wheel blank during the processing of the left side of the first tooth of the pinion. Fig. 2 shows the corresponding coordinate value curve, and Fig. 3 shows the setting marks (xwi, ywi, zwi) of the milling cutter head and the machining angle (α I, φ I) of the 12 teeth of the pinion Each group of curves represents the machining coordinates of the left or right tooth surface of an arc tooth. As can be seen from Figure 3, the machining coordinates of each tooth are different.
According to the above method, a pair of meshing non bevel gear samples are respectively machined by five axis CNC machine tool. The main parameters are as follows: the outer spherical diameter of the gear is 46.6 mm, the number of teeth of the big gear is 24, the number of teeth of the small gear is 12, the modulus of the milling cutter of the forming disc is 3.5, the radius of the cutter head is 44.3 mm, and the spiral angle of the spiral tooth is 35 °. Figure 4 shows a pair of non-circular bevel gears with spiral teeth machined by this method, which is consistent with the gear parameters designed. And the two gears can mesh correctly, which shows that the machining method in this paper is correct and effective.