Simulation of plastic deformation and destruction in the process of chip formation

Abstract

Metal cutting is a complex process in which several mechanisms are at work simultaneously. The mathematical modelling allows carrying out research into the optimization of machining conditions. This work examines the simulation of chip formation during the process of cutting. The studies demonstrated that the chip formation process, taking into account the plastic deformation and destruction of metal in the local zone, is most appropriately represented by a rheological model in the form of a series connection of elasticductile- plastic relaxing medium of Ishlinskiy (reflecting the process of primary deformation of metal from the cut off layer) and the medium of Voigt with two elastic-dissipative elements (representing the process of deformation and frictions from the convergent shaving). The attained complex rheological model served as the basis for constructing a representative dynamic model for the chip formation process. The key factors that govern the chip formation have been taken into account, such as tool vibration frequency and amplitude, depth of cut, feed rate.

Comparison between finite element analysis and rheological models for chip formation

“…This leads to the shaping of local segments of shift in the primary deformation zone of the cut off layer. At this stage, permanent, irreversible deformation begins [20]. The Voigt model, which consists of the spring H 3 and the dash-pot N 3 in parallel, describes movement of the shift of material foreword in the direction of tool movement and prolonged viscoelastic deformation.…”

“…The differential constitutive relations between stress σ and strain ε for the model describing the process of chip formation can be presented in the form of the following rheological equation [11,20]:…”

“…, 6) depend on stiffness coefficients and coefficients of linear resistance, σ y is a yield stress. The solutions and analysis of this rheological equation were studied in [20]. We write the equation (2.1) in the short-hand notation using integral formulation and the Laplace transform.…”