The number of abrasive grains in the contact area and cutting thickness during a grinding process

Abstract

Purpose. This article is supposed to determine the formulas for calculation of the active depth of the relief of the cutting surface of the grinding wheel, relative bearing length of the cutting surface pattern of the workpiece, numberof cutting grains in the contact area between grinding wheel surface and workpiece, as well as the cutting thickness per single grain. Methodology. The study is based on the application of analytical and probabilistic methods for calculation of the active depth of abrasive relief of the cutting surface of the grinding wheel and relative bearing length of the contact cutting surface of the workpiece. The initial data include the parameters of the grinding pattern (speed, feed and depth) and relief of cutting surface of the grinding wheel after dressing: relative bearing length and distance between the grain patterns depending on their distribution through depth. The mathematical models of distribution through relative depth are presented by the exponential functions of the relative bearing length and distance between the grain profiles.The relative depth of profile from the zero level is the argument of specified functions. At the same time, a natural constraint was introduced for the values of the relative depth of profile, which should not exceed the value of 0.5. Findings. We obtained the formulas for determination of the instant thickness of the cross section being cut by the grinding wheel, active depth of the relief of the cutting surface of the grinding wheel, relative bearing length of the cutting surface pattern of the workpiece, number of cutting grains in the contact area between grinding wheel surface and workpiece, as well as the cutting thickness per single grain. Originality. We developed a functional relationship for the instant thickness of the cross section being cut by the grinding wheel, relative bearing length and distance between the grain patterns in the contact area between grinding wheel surface and workpiece. The abovementioned functional relationships were introduced instead of parameters of grinding process kinematics (speed, feed and depth) and characteristics of the abrasive tool (graininess, hardness and structure). The chief accomplishment is the proposed mathematical models of the number of abrasive grains in the contact area between grinding wheel surface and workpiece, as well as the cutting thickness per single grain. Practical implications. The findings of an investigation make it possible to elaborate the number of abrasive grains in the contact area and cutting thickness per single grain during a grinding process, which are necessary as initial data for analytical calculations constituting the cutting force grinding temperature, roughness of treated surface and optimum conditions of the overall grinding process.