OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology In models (15) and (16), the components of the cutting force are expressed not through the parameters of machine modes of cutting by the wheel as a whole (depth feed, axial, longitudinal), but through the parameters of microcutting in the shear zone of the metal and friction of the blunting area of a single grain. The first term in models (15) and (16) determines the cutting force, when the metal is cut with an absolutely sharp grain necessary for plastic deformation of the metal in the shear zone. The addend determines the cutting force needed to overcome the indentation and friction of the blunting area. In flat grinding, metal is simultaneously removed by several grains (a group of single grains) in the contact zone between the wheel and the workpiece, so let us transform the microcutting parameters of many grains into the operating parameters of the wheel as a whole, based on the condition for ensuring the equality of energy expended to remove the same volume of metal by the grains and the wheel as a whole. In other words, let us assume that the volume of metal Wall (allowance) removed during one pass of the table from the workpiece by a set of single abrasive grains is equal to the same volume of metal Wall removed by the grinding wheel as a whole (fig. 3). To perform such a transformation, let us make the following assumptions: 1) the volume of metal Wall being removed from the workpiece is equal to the sum of all volumes Wzone of the metal in the shear zone, i.e. Wall = Wzone (fig. 3). 2) since the volume of the chips being cut consists of many metal shear layers in the cutting zone, the total volume of metal chips is Wchips= Wzone and is also equal to Wall = Wchips = Wzone (fig. 3). * Umax (Ymax) is the maximum possible number of chips (shear zones) Fig. 3. The equality of volumes of metal being removed in shear zones, in the chips, and in the workpiece: 1 – the total volume of metal in the shear zones; 2 – the volume of metal in the shear zone; 3 – the total volume of chips being removed; 4 – the volume of chips cut by a single grain; 5 – the total amount of metal being removed during one pass of the table 3) the metal volume Wall is determined by the length of the workpiece L (mm), the width of the wheel working surface B (mm), and the depth feed Sz,i (mm/pass), i.e. (fig. 3) = = = , . all z i chips zone W S LB W W (17) 4) the sum of cutting forces from all cutting grains that are in contact with the workpiece is equal to the cutting force for the wheel as a whole, i.e.: Σ Σ = = = + = + ∑ ∑ 1 1 , J J Z ZP ZT ZPj ZTj j j P P P P P (18) Σ Σ = = = + = + ∑ ∑ 1 1 , J J Y YP YT YPj YTj j j P P P P P (19)
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