# Grinding particle trajectory of spiral bevel gear

The spiral bevel gear is processed according to the principle of “imaginary production wheel”, that is, through the meshing between the imaginary production wheel and the cut gear, the grinding wheel representing the production wheel processes the required tooth profile on the cut gear workpiece. The envelope surface of the inner and outer conical surfaces of the straight cup grinding wheel is trimmed to completely coincide with the convex and concave surfaces of the spiral bevel gear. During grinding, the straight cup grinding wheel rotates at a high speed around the main shaft at the set grinding speed. At the same time, the spiral bevel gear workpiece moves relative to the straight cup grinding wheel at the set generation speed according to a specific track, and its convex and concave surfaces contact the inner and outer sides of the grinding wheel respectively, so as to grind the profile of the convex and concave surfaces of the spiral bevel gear. Therefore, in the simulation, it is assumed that the spiral bevel gear workpiece remains stationary, the inner and outer sides of the straight cup grinding wheel move on the convex and concave surfaces of the spiral bevel gear with the same trajectory, and rotate at high speed around its axis, as shown in the figure.

In order to improve the simulation accuracy, the curved surface of spiral bevel gear is measured by three-dimensional laser scanning microscope (keans vk-x100). The grinding groove parallel to the grinding direction is the relative motion track of the grinding wheel. Select a track line in the grinding direction, extract its spatial coordinates, and use polynomials to fit the track line. The fitting equation is as follows:

According to the formula, the helix fitting equation of convex surface and concave surface can be obtained, which is the motion trajectory of gear workpiece during spiral bevel gear grinding and the motion trajectory of straight cup grinding wheel during simulation. The trajectory fitting equation of the formula is used to obtain the motion trajectory of abrasive grain grinding spiral bevel gear through coordinate transformation. The conversion equation is shown in the following formula. After conversion, the grinding coordinates of the abrasive particles on the spiral bevel gear workpiece.

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