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

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS varying 4,4 ñ so that the natural frequency and damping coefficient of the workpiece subsystem remain constant. The trajectories of stiffness 4,4 2 ( ) ñ L , deformation displacements 2 ( ) Σ ∆ L , and velocity 2 2 ( ) V L providing 2 ( ) const Σ ∆ = L are given as example in Fig. 2. Depending on the parameters, the image point in Fig. 2 may intersect the figurative line. Then the trajectory 2 2 ( ) V L becomes unstable. The loss of stability also depends on 2 V changing along 2 L , that is tool wear. It is necessary to change the parameters of subsystems by design methods or to correct the cutting speed (0) 3 = P V V and the corresponding feed rate 2 V to ensure condition (10). Fig. 3 shows that with increasing speed, the stability Ta b l e 1 Parameters of the matrix of velocity coefficients and elasticity 1,1 h 2,2 h 3,3 h 1,2 2,1 = h h 1,3 3,1 = h h 2,3 3,2 = h h 4,4 h 0.25 0.15 0.15 0.1 0.08 0.08 0.18 1,1 ñ 2,2 ñ 3,3 ñ 1,2 2,1 ñ ñ = 1,3 3,1 ñ ñ = 2,3 3,2 ñ ñ = 4,4 ñ 1000 800 800 200 100 100 200...300 Ta b l e 2 Parameters of the dynamic link 2 , [kg/mm ] r , m/s ς 0 , ñ T µ 500 0.1 0.001...0.005 0.5 Fig. 2. Changing the properties of the system along the axis L 2 : a – trajectory of radial stiffness change 4,4 ñ ( 1 ) and rational feed rate trajectory V 2 ( 2 ); b – error caused by elastic deformations Σ ∆ at (1) – constant feed, at ( 2 ) – constant force, at ( 3 ) – feed rate control a b