Undercutting and interference for thread form grinding with a tilt angle

In the form grinding that is widely used to produce precision threads, screws, and gears, the grinding wheel profile is usually calculated from a given tooth profile and the so-called equation of meshing. However, in the presence of undercutting or secondary enveloping, the grinding wheel calculated cannot be guaranteed to produce the desired thread profile. Therefore, this paper proposes a geometric approach to determining the grinding wheel profile and the conditions to avoid undercutting by means of the tilt grinding wheel axis. Specifically, we calculate the thread’s profile based on its relationship to each transverse plane of the grinding wheel in the form grinding process. The grinding wheel profile on each transverse plane is then determined using the shortest distance from all the thread profile points to the grinding wheel revolution axis. Obtaining these distances allows derivation of a formula to calculate the minimum tilt angle that avoids undercutting. This proposed geometric approach is numerically more stable than the conventional equations of meshing, and the derivation of the undercutting equation is straightforward and easy to understand.