An analytical study of wheel regeneration in surface grinding

Machining vibrations have been a topic of active research since the beginning of the 20th century, because of their harmful potential to deteriorate the surface finish of the workpiece, reduce the lifetime of the machine tool and limit the overall productivity of manufacturing operations. Grinding, often being a finishing operation responsible for the final quality of the workpiece, can be especially affected by unwanted process vibrations. Machining vibrations can arise from a number of sources, but they are usually classified as forced and self-excited vibrations. Forced vibrations, such as those resulting from runout or unbalance, are generally easier to avoid. However, self-excited vibrations, also known as chatter, originate in the machining process itself and are typically more difficult to predict and suppress. When it comes to grinding operations, chatter can occur as a result of uneven surface regeneration on both the wheel and the workpiece. In this paper we perform an analytical study of grinding chatter, to explore the intricate nature of wheel regeneration (i.e. chatter arising from uneven wear on the wheel) in surface grinding. Whilst there has been a great deal of previous research into grinding chatter, the present study explores a contrarian approach whereby a circumferential variation of the specific grinding energy occurs during the onset of instability. The specific energy is a fundamental quantity in grinding that relates the necessary grinding power to the prescribed material removal rate. It is also related to wheel wear and thus to grinding forces, since a worn wheel requires more grinding power and produces greater grinding forces to sustain the same material removal rate than a sharp one. Therefore, by characterising the specific energy variation around the circumference of the grinding wheel as a function of wheel vibration, we derive a stability model and discuss its practical potential.