OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 (0) (0) ( ) 2 X Y P P D iT t S (5) where (0) (0) 1,1 0 1 2,1 3,1 0 1 (0) (0) 1,2 0 2 2,2 3,2 0 2 (0) (0) 1,3 0 3 2,3 3,3 0 3 (0) (0) ( ) 0 1 0 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 ( ) P P P P P P Y P P c S iT c c S iT c S iT c c S iT iT c S iT c c S iT S iT c S iT ; (0) 1 2,1 3,1 0 1 (0) 2 2,2 3,2 0 2 (0) 3 2,3 3,3 0 3 (0) ( ) 1 0 1 ( ) ( ) ( ) ( ) 0 0 ( ) P P X P Y P c c S iT c c S iT iT c c S iT c S iT ; (0) 1,1 0 1 2,1 3,1 1 (0) 1,2 0 2 2,2 3,2 2 (0) 1,3 0 3 2,3 3,3 3 (0) 0 1 1 ( ) ( ) ( ) ( ) ( ) 0 0 P P Y P P c S iT c c c S iT c c iT c S iT c c S iT . An analysis of equation (5) shows that, depending on ΔD(iT), there is a branching of solutions SP (0) (iT). Moreover, there are areas in which there are no real solutions. It all depends on the ratio of stiffness of the workpiece subsystem c(Y), matrix elements c and allowable values ΔD(iT) for given values of the allowance tP (0). In the case if c → ∞ and ΔD(iT) = ΔD 0 = const., then (5) becomes an equation: (0) (0) 0 1 0 (0) ( ) 0 1 ( ) ( ) 2 ( ) ( ) ( ) P P P Y P P V S iT D t c iT V S iT , (6) from which the set of paths SP (0)(iT,V P) is determined, each of which depends on the cutting speed VP = const. Obviously: ( ) (0) 0 (0) 0 1 0 ( ) ( , ) ( ) [ ] Y P P P P D c iT S iT V V t D , (7) SP (0)(iT,V P) – path of the feed per revolution along the slide motion, at which ΔD0 = const. Analysis of the equations (5) and (6) makes it possible to draw some conclusions about the choice of tool parameters and cutting modes to reduce the infl uence of elastic deformations on the part diameter, also known from practice. 1. As the depth of cut decreases, the diameter variations due to changes in stiffness decrease. Therefore, machining a part, the stiffness of which changes along the tool path, is performed in several passes with a successive decrease in the allowance. 2. The value ΔD(iT) is infl uenced by the angular coeffi cient χ1. Angular coeffi cients depend on the tool geometry, fi rst of all, on the back rake angle and the rake angle [56].
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