After the surface modeling and Simulation of straight cup grinding wheel is completed, the tooth surface needs to be discretized in order to realize the grinding surface morphology simulation of spiral bevel gear. The tooth surface is represented by the topological matrix GMN. Each element g (m, n) in the matrix represents the z-coordinate value corresponding to each grid point (m, n) in the XY plane of the tooth surface in the global coordinate system oxyz, that is, the residual height of the tooth surface after grinding. The grinding wheel surface is discretized and represented by topological matrix hij, where H (I, J) represents the abrasive particle height in the circumferential and axial (I, J) positions of the grinding wheel. The process of grinding tooth surface with grinding wheel can be regarded as the process of scoring the surface successively by I abrasive particles on J xoz sections. Calculate and store the operation track of the first to I abrasive particles on the first to j sections. At each point G (m, n) on the workpiece plane GMN of spiral bevel gear, there are corresponding values Zi (m, n) of several trajectory lines at this point. Since grinding is a material removal process, the abrasive particles with the smallest track Z coordinate value at a specific coordinate position will determine the state of the spiral bevel gear workpiece and finally determine the tooth surface at this point, then the final surface morphology of the spiral bevel gear workpiece after grinding can be expressed as the set of the lowest value of the track line remaining on the surface of the spiral bevel gear workpiece, that is:

The simulation process of grinding surface morphology of spiral bevel gear is as follows.

(1) The grinding parameters and grinding wheel geometric parameters are set, and the mesh size of spiral bevel gear workpiece is defined, which is expressed by topological matrix GMN. Each point Gij (I = 1,2,…, m; J = 1,2,…, n) on the workpiece plane of spiral bevel gear represents the z-direction height value corresponding to each grid point on the workpiece surface of spiral bevel gear.

(2) The discrete points of abrasive particles are corresponding to the matrix elements. According to the corresponding relationship between (x, y) and the subscript (I, J) of spiral bevel gear workpiece height matrix Gij, judge the corresponding relationship between wear particle discrete point G and spiral bevel gear workpiece grid point. When the coordinates (x, y) of the abrasive particle discrete point G just fall on the spiral bevel gear workpiece grid point (I, J), it means that the point just corresponds to the matrix element Gij. Otherwise, find the closest spiral bevel gear workpiece grid point (I, J) of (x, y), and use the matrix element Gij where the grid point is located to correspond to this point.

(3) Cutting judgment. Compare the height direction coordinate value Z of the discrete point G on the abrasive particles selected at the current time in the spiral bevel gear workpiece coordinate system with the stored value of the corresponding matrix element Gij. If Z is small, it means that the abrasive particles have cut into the spiral bevel gear workpiece. At this time, use Z to update the stored value of Gij. Otherwise, no treatment will be made.

(4) According to the deposit data in the matrix Gij, the three-dimensional surface topography is drawn. Simulation flow chart of grinding surface morphology of spiral bevel gear.