Geometric parameters of surfaces in internal grinding

Abstract

For internal grinding by a wheel, with longitudinal supply, as in other grinding methods, cutting is mainly due to grains on the frontal section of the wheel’s working surface and depends on the longitudinal supply. The machined section again encounters the wheel’s working surface on subsequent rotations of the part, which reduces its surface roughness. On each rotation, some of the grains will be aligned with the grooves already formed, so that the load will not be uniform over the wheel’s working surface. This leads to nonuniform abrasion of the machined surface over the contact area. In addition, in the zones where the grinding wheel is in contact with the surface and then moves away, the contact changes, as indicated by the longitudinal and transverse shape errors. In machining continuous holes, to eliminate nonlinearity of the machined surface, overrunning of the grinding-wheel paths over (1/3)‐(1/2) of the wheel’s height was recommended in [1]. However, no physical or analytical basis for this recommendation was provided. This may be attributed to the lack of definitive qualitative and quantitative estimates of the grindingwheel overrun and the lack of a relation between the overrun and the specific operating conditions. Note here that constant contact of a certain part of the wheel’s working surface with the machined surface is facilitated to some extent by reducing the difference in the cutting force at the sections where the wheel makes and breaks contact. Hence, there is a pressing need for more precise physical determination of the nonuniform abrasion over the contact area between the wheel and the machined surface and analytical description of such abrasion as a function of the input and output parameters of internal grinding. This may facilitate optimization of the internal-grinding parameters in each specific operation. To explain the processes in the zones of wheel introduction and extraction, the working surface of the wheel prior to initial contact is divided into initial bands, as a function of the degree of abrasion at the machined surface. The number of bands is determined by the ratio H / S d of the wheel height H to the longitudinal supply S d . Note that, each time that the wheel encounters the already machined surface, some of the abrasive grains in the cutting zone will be ineffective, because they will be aligned with already cut sections of the surface. The influence of this effect on the number of cutting grains is taken into account by correction factor q . Note that, in the zones of wheel entry and withdrawal, each band of width equal to the longitudinal supply in the rotation of the part (in their sequence over the cutting zone) will repeatedly encounter the machined surface. The first band in the direction of longitudinal supply (the frontal band) performs a cutting function, while the subsequent bands smooth the cut surface. The width of the last band is determined by the initial contact area. The smoothing effect of the bands increases with increase in the number of encounters with the already machined surface.