The grinding process of spiral bevel gear is a very complex material removal process. In order to simplify the complexity of analysis, the following assumptions are made: ① the envelope surface of grinding wheel is trimmed to an ideal shape; ② The influence of grinding wheel vibration on the surface morphology of spiral bevel gear is not considered; ③ When the grinding wheel is fed, the spiral bevel gear material in contact with the abrasive cutting edge is completely removed; ④ Phenomena such as flow measurement and chip tumor are not considered.
In the grinding process, due to the uneven height distribution of abrasive particles along the radial direction of the grinding wheel, the cutting trajectories of different abrasive particles are distributed on concentric circles with different diameters. A single abrasive particle leaves uneven cutting marks on the gear surface along the grinding path, and the cutting marks of several abrasive particles on the gear surface are superimposed with each other to form the final grinding surface morphology of the gear surface. The cutting model of each abrasive particle is studied, and its motion trajectory on the tooth surface is obtained by derivation and transformation.
In the process of ordinary surface grinding, the geometric model of single abrasive particle motion is shown in Figure 1, and the grinding wheel coordinate system o ′ x ′ y ′ Z ‘and spiral bevel gear coordinate system oxyz are established. In Figure 1, oxyz is fixed on the machined surface of spiral bevel gear and coincides with the abrasive particle position at the lowest position around the grinding wheel. The trajectory AOB of abrasive particles is composed of the rotation of grinding wheel and the translation of spiral bevel gear. According to the geometric position relationship between abrasive particles and spiral bevel gear in Figure 1, the motion trajectory equation of abrasive particles G is shown in the formula.
Where, Xi and Zi are the instantaneous coordinates of abrasive particle g, θ Is the relative rotation angle of the abrasive particle, I is the number of discrete points of the workpiece along the X direction, RI is the distance from the vertex of the abrasive cutting edge to the center of the grinding wheel, NS is the speed of the grinding wheel, and VW is the speed of the workpiece. The grinding mode is reverse grinding. If the grinding mode is forward grinding, the feed speed direction of the worktable is reversed.
