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

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.

Hysteresis curves and loops for harmonic and impulse perturbations in some non-equilibrium gases

Evolution of sound in a relaxing gas whose properties vary in the course of wave propagation, is studied. A relaxing medium may reveal normal acoustic properties or be acoustically active. In the first case, losses in acoustic energy lead to an increase in internal energy of a gas similarly as it happens in Newtonian fluids. In the second case, acoustic energy increases in the course of sound propagation, and the internal energy of a medium decreases. Variations in the internal energy of a gas are proportional to some generic parameter, the sign of which is responsible for acoustical activity, and depends on intensity and shape of the sound waveform. Hysteresis curves in the plane of thermodynamic states are plotted. Curves for harmonic and several aperiodic sound impulses are plotted, discussed and compared.

Time estimates for the Cauchy problem for a third-order hyperbolic equation

A classical solution is considered for the Cauchy problem:(utt−Δu)t+utt−αΔu=f(x,t),x∈ℝ3,t>0;u(x,0)=f0(x),ut(x,0)=f1(x), andutt(x)=f2(x),x∈ℝ3, whereα=const,0<α<1. The above equation governs the propagation of time-dependent acoustic waves in a relaxing medium. A classical solution of this problem is obtained in the form of convolutions of the right-hand side and the initial data with the fundamental solution of the equation. Sharp time estimates are deduced for the solution in question which show polynomial growth for small times and exponential decay for large time whenf=0. They also show the time evolution of the solution whenf≠0.