Dimensional analysis of plate heating

Abstract

The polishing of plates by free abrasive on a ZPD�320A machine tool does not maintain the shape of the plate in most cases. This may be attributed to plastic deformation at the plate surface as a result of inadequate heat transfer from the cutting zone. The small plate thickness (0.2–0.4 mm) also contributes to its shape instability. On that basis, we need to assess the rate of heat transfer. As a result of dimensional analysis of plate polish� ing by free abrasive, we may simplify the correspond� ing model and assess the time constants of heat trans� fer, in terms of the Biot number [1–3]. The contact region is in the XOY plane and corre� sponds to the boundary of a halfspace. The character� istic dimensions along the OX and OY axes are denoted by b, while the characteristic dimension along the OZ axis is the plate thickness δ. Then X = b Y = b Z = δ where are dimensionless quantities. We will use the following notation: θ0 is the charac� teristic temperature; U0 is the characteristic slipping speed; τm is the characteristic tangential stress. The dimensionless time may be selected from the condi� tion t0 = b/Ub [1]. Hence, = t/t0. Here Ub is a charac� teristic parameter that will be established later.