3 - Kinematic models of abrasive contacts

Abstract

A kinematic analysis defines relationships between removal rate and penetration of the abrasive grains into the workpiece for the various abrasive machining processes. A kinematic study is an essential precondition for the design of an abrasive machining system. The kinematic process design governs the stresses imposed on the individual grains of the abrasive, which must be neither too small nor too large. Commencing with the speeds and motions of the tool and workpiece, a kinematic analysis proceeds to the physical consequences of the distribution of the cutting edges. This chapter provides measures for the size, duration of contact, and scale of the minute interactions, which take place in the abrasive process. Penetration depth, the length of contact between an abrasive grain and a workpiece, the implications of grain size, grain speed and grain trajectory for grain forces, grain wear, and workpiece roughness are considered. Study of the scale of the grain–workpiece interactions underpins all aspects of abrasive machine process behavior and the tribology of the process. Cutting edge density is analyzed including implications of the stochastic nature of abrasive processes and effects of dressing. A key feature of kinematic analysis is to relate the thickness, width and length of typical grain penetrations to depth of cut and machine variables, such as workspeed and abrasive speed. References are provided to previous work.