Finite Element Simulation of Physical Phenomena in Real Conditions of a Single Grain Cutting Process

Abstract

The cutting process was presented as a real object as well as its physical and mathematical modelling. For the description of the non-linear phenomena, at the typical increment ratio, the updated Lagrange's description was used. Adequate deformation and stress increments measurements were used, e.g. Green-Lagrange's deformation tensor increment and the increment of the Piola-Kirchhoff's second symmetrical tensor. Nonlinearity of the material was described by means of the increment model taking into consideration the deformation and deformation rate records. The workpiece is treated as a body in which there may be elastic deformation (in the range of reversible deformation) and visco and plastic (in terms of irreversible deformation), with nonlinear hardening. For the construction of the material model Huber-Mises-Hencky's non-linear plasticity condition was used, associated principle of flow as well as mixed hardening (isotopic-kinematic). The condition of the material after pre-machining processes was also taken into account by means of implementation of initial conditions of: displacement, strain and stress. Yield stress of the body was described by a Cowper-Symonds' model allows for linear-isotropic, kinematic or mixed plastic strain hardening and the effect of the intensity of plastic strain velocity. The applications in ANSYS program and results of numerical calculations were presented. A method of generating a three-dimensional abrasive grain with a geometry close to actual were describes. The influence of the process parameters on the states of strains and stresses and on the quality of the product was presented. Numerical calculations of cutting process with single abrasive grain were made and investigated the deformation and stress occurring in the workpiece. The experimental test stand of single abrasive grain cutting process, the test plan and the verifications of results of numerical simulations were describes. The results were statistically developed and that’s give the models in the regression function form.