The equal theoretical surface roughness grinding method for gear generating grinding

A new approach is developed in this paper to predict the three-dimensional gear surface topography in the process of gear generating grinding, and a parametric equation is derived to describe the trajectory on the tooth surface of gear left by each ideal sphere grain. To determine the final three-dimensional gear surface topography generated by thousands of single abrasive grain with randomly distributed locations and protrusion heights, an algorithm for geometrical analysis is developed to systematically process the gear surface profile. There are two steps for this method: the first step is to map the cutting path to the tooth profile in each generating stroke, and the second stage is to combine these generated surface topographies together and trim them in an appropriate manner to create a whole tooth surface. The simulation results show that the surface roughness is increasing monotonously along the tooth profile direction, which is confirmed by the experiment. In order to get uniform surface roughness, a non-uniform generation method is introduced by dividing the entire arc length into isometric n segments. With the use of this method, the surface roughness in each part is essentially equal. Besides, the surface roughness improves about 16.3 % when the machining time is the same, and the reduction of machining time is 42.8 % when the surface roughness of addendum is equal.