OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 = β = cos , j Sj k ZSj k N R V P V (7) where RSj, PZPj are the resultant and tangential components of the cutting force of the sharp grain, respectively, N; Vk is the wheel speed, m/s; β is the angle between RSj and vector Vk (fig. 2, b), degrees. Let us find the tangential component of the force of cutting with a single grain by equating formulas (6) and (7). = σe β 1 . sin s j ZPj k a mb P V (8) The radial component of the cutting force PYPj with a single grain can be found by the formula: = β = β sin tg , YPj Sj ZPj P R P (9) = σe β β 1 tg . sin s j YPj k a mb P V (10) During grinding, the abrasive grains of the wheel blunt, forming an area lj on the back edge. The blunting area prevents the penetration of abrasive grains into the metal during cutting. An additional radial force PYТj appears, which is necessary to deepen the blunt grain (fig. 2, b), without which metal shear is impossible. During cutting, friction occurs between the grain blunting area along the metal surface, which results in an additional tangential force PZТj. Therefore, it becomes necessary to take into account the influence of the blunting area on the total force, the radial cutting force PYj, and the tangential force PZj. Let us use the model of the cutting force acting on an abrasive grain with a blunting area as the basis (figs. 1 and 2, a). Fig. 2, a shows a kinematic diagram of flat grinding. Many of the elements in fig. 2 are shown conditionally and enlarged in size for clarity (guide marks, abrasive grains, etc.). Let us construct equations to find the components of the force of cutting by the wheel grains (fig. 2, b [1]): = + , Yj YPj YTj P P P (11) = + . Zj ZPj ZTj P P P (12) Let us take into account the influence of the blunting area of the abrasive grain on the components of the cutting forces resulting from the friction force [1]: σ = , 3 YTj j j P b l (13) σ = µ = µ , 3 ZTj Ytj j j P P b l (14) where µ is the coefficient of the abrasive grain friction along the material being machined; lj is the length of the grain blunting area, m. We substitute formulas (9), (10), (13), and (14) into equations (11)–(12) to obtain the following equations: σ = σe β + β 1 tg , sin 3 s j Yj j j k a mb P b l V (15) σ = σe + µ β 1 . sin 3 s j Zj j j k a mb P b l V (16) Formulas (15) and (16) are models for calculating the radial and tangential components of the cutting force during plastic deformation of the metal volume in the shear zone by a single blunt grain.
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