Synergetic approach to improve the efficiency of machining process control on metal-cutting machines

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS allowance variation, then force stabilization by feed variation can fully compensate the effect of allowance variation on diameter accuracy. In all cases, it is necessary not to stabilize cutting forces, but to ensure the constancy of elastic deformations on the basis of its coordination with the law of cutting properties change and a priori specified disturbances. 2. The possibilities of controlling the accuracy of parts by varying the feed rate are limited. It follows from (4) that variations in the feed rate ( ) P S t , which affects the cutting forces, depend both on the time window T in which the feed rate is integrated and on the velocities of ,2 ( ) X v t . Usually, the natural frequencies of oscillatory loops, which are formed in the subsystems on the tool and workpiece side, are at least an order of magnitude greater than the rotation frequency of the workpiece. Then, when considering deformation displacements, we can limit ourselves to elastic reactions, and with this in mind, analyze the transformation of the feed rate into its value in the frequency domain. It is not difficult to obtain the amplitude-phase frequency response of 2 ( ) V t the transformation in ( ) P S t view of (10). First, let us give an expression for the transfer function [ ] [ ] , 2 1 exp( ) ( ) 1 exp( ) ( ) 1 , ( ) 1 1 exp( ) − −   − − = = −  + − −   P V S A pT S p pT W p V p p A pT (12) where (0) 0 0 r = P t A c is the dimensionless parameter of the influence of the cutting system on the transformation 2 → P V S ; 0 ñ = 2 X ∆ ∆ ; 2 1,1 1 0 2 1 3,1 1 0 2 1,2 2 0 2 2 3,2 2 0 2 1,3 3 0 2 3 3,3 3 0 2 1 0 2 1 4,4 2 1 0 2 0 ( ) + χ r χ χ r     + χ r χ χ r   ∆ =   + χ r χ χ r   χ r χ + χ r     X c V T c V T c V T c V T c V T c V T V T c L V T . Or after the obvious transformations we have { } { } , sin( ) 1 cos( ) ( ) ( ) ( ) , ω − ω ω = − ω + ω ω ω V S T T W j j R jI (13) where [ ] [ ] [ ] 2 2 2 [1 2 ] 1 cos( ) 1 cos( ) ( ) 1 1 2 (1 )(1 cos( ) 1 cos( ) sin ( ) + − ω + − ω ω = − = + + − ω + − ω + ω A A T A A T R A A T A A T A T ; [ ] [ ] 2 2 2 sin( ) sin( ) ( ) 1 2 (1 )(1 cos( ) 1 cos( ) sin ( ) ω ω ω = = + + − ω + − ω + ω A T A T I A A T A A T A T . Examples of changes , ( ) ω V S W j in the dimensionless frequency function W = ω T are given at Fig. 4. The analysis of (13), as well as Fig. 4. allow to draw the following important conclusions. First, at varia- tions in velocity 2 ( ) V t with the frequency of rotation of the workpiece, the deformation displacements of the tool relative to the workpiece are uncontrollable. Second, in the low-frequency region (up to a frequen- cy of 0,1 W ), the feed variations ( ) P S t differ from the velocity 2 ( ) V t by a constant “ T ” factor. Then, there is rapid phase rotation and periodic, with monotonic decay of the maximum amplitude, variation of ( ) P S t . The phase rotates between “0-π”, which affects the dynamic properties, including stability. Third, the dy- namic properties of the conversion 2 ( ) V t to forces depend not only on the properties of the drives, but also on the stiffness parameters of the tool and workpiece subsystems, as well as on the parameters of the dy-