OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology The sum of the metal removal rates by a group of grains in the contact zone is equal to the metal removal rate of the wheel Qw: = = ∑ 1 J w j j Q Q , (27) where Qw is the metal removal rate by the wheel, m3/s. Then formula (4) will be as follows: Σ σe = P w k L A Q V , (28) When metal is removed by the wheel, the metal removal rate Qw is equal to the ratio of the metal volume to the time during which the metal volume Wall is removed at the table speed Vtable. The metal volume Wall is a metal layer with a height equal to the infeed radial feed, a length equal to the length of the machined surface, and a width equal to the grinding width (fig. 3). The grinding width can be equal or less than the height of the grinding wheel. = = = , , z i all w z i table table table S BL W Q S BV t t , (29) or at = table table L t V , = , w z i table Q S BV , (30) where ttable is the table pass time per workpiece length L, s. By substituting expression (29) into equation (28), we obtain Σ σe = , P z i table k L A S BV V . (31) Then, the grinding energy АΣР expended by absolutely sharp grains of the wheel on plastic metal deformation in the cutting zone can be written as: Σ σe = = , P ZP z i table k L A P L S BV V . (32) Let us find the tangential component of the cutting force PZP for an absolutely sharp wheel: σe = , z i table ZP k S BV P V . (33) Let us establish the relationship between the energy expended by the friction forces of blunt grains separately for a single grain and for the wheel as a whole (in which the grains have a blunting area) σ µ = = 3 j j Tj ZTj b l A P L L. (34) After summing the energy of all grains, we obtain the formula for the friction force energy: Σ = = = = σµ σµ σe = = = = = ∑ ∑ ∑ ∑ 1 1 1 1 3 3 J J J J T Tj ZTj j j j fr k j j j j L A A P L L b l L f F V , (35) = = ∑ 1 J fr j j F f , (36) where fj is the blunting area of a single grain, m2; F fr is the sum of the blunting areas of single grains, m2.
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