Anton M. Krivtsov

Frictional chatter in orthogonal metal cutting

A comprehensive study of the frictional chatter occurring during metal–cutting process is given. A general mathematical model of the machine–tool–cutting process is established, and then a high–accuracy numerical algorithm is developed. Next, a two–degree–of–freedom model of orthogonal metal cutting is examined. Then stochastic properties of the material being cut are introduced to reflect variations in the workpiece properties, in particular, in the cutting resistance. Nonlinear dynamics techniques, such as constructing bifurcation diagrams and Poincare maps, are employed to ascertain dynamics responses for both the deterministic and the stochastic model. Untypical routes to chaos and unusual topology of Poincare cross–sections are observed. The conducted analysis has provided some practical design recommendations. Finally, occurrence of chatter was investigated analytically.

Dry Friction Model of Percussive Drilling

It is postulated that the main mechanism of the enhancement of material removal rate (MRR) in percussive drilling is associated with generating impact forces, which act on the workpiece and help to develop micro-cracking in the cutting zone. The inherent non-linearity of the discontinuous impact process is modelled as a frictional pair, to generate the pattern of the impact forces. A novel formula for calculating the MRR is proposed, which explains the experimentally observed fall in MRR at higher static forces.

Anomalies in mechanical characteristics of nanometer-size objects

In recent years, rapid development of nanotechnologies led to the necessity of constructing adequate physical models that make it possible to describe physicomechanical properties of objects with a nanometersize (nanosize) scale. The majority of existing models of such a kind adopt that basic mechanical characteristics of nanosize objects correspond to those obtained in macroscopic experiments. However, when dealing with structures containing only several atomic layers, the discrepancy arises between the evident discreteness of an object under study and a continual method of its description. The inconsistency of values of elastic moduli, which were obtained in microscale and macroscale experiments, was noted by many researchers. In particular, one of the methods of determining elastic characteristics of nanosize objects is investigating the microrelief arising in the course of tension of a specimen having an ultrathin coating [1–3]. The solution to an equivalent continual problem allows the Poisson’s ratio and Young modulus for the coating to be determined from such experiments [2, 4, 5]. However, the values of elastic characteristics measured by this method exhibit a substantial inconsistency by their macroscopic values for the same material.

Penetration rate prediction for percussive drilling via dry friction model

Abstract A dynamic model of percussive drilling assuming a dry friction mechanism to explain the experimentally observed drop in penetration rate is presented. The inherent nonlinearity of the discontinuous impact process is modelled as a frictional pair, and this can generate the pattern of the impact forces close to reality. Despite quite radical simplifying assumptions, the model is able do describe the fall of material removal rate for a higher static loading with a good agreement to experimental investigations.

Bending stiffness of a graphene sheet

The paper proposes a discrete mechanical model of monolayer graphene. A relation between parameters of the model and elastic characteristics of its equivalent continuum is derived by comparing the energy of small strains on micro- and macroscales. The relation allows one to determine the microscale interaction parameters from experimental data and, knowing the microscale parameters, to determine the mechanical properties of graphene. The main aim of the work is to estimate the bending stiffness of a graphene sheet. The proposed discrete model provides an analytical dependence of the graphene sheet bending stiffness on the microscale interaction parameters.

Energy Oscillations in a OneDimensional Crystal

Oscillations of the kinetic and potential energies in a onedimensional crystal (the chain of particles) are considered. An analytical solution for the linear inter� action of particles, random initial velocities, and zero initial displacements is derived. It is shown that the time dependence of energies is expressed by the Bessel function, and the period and the damping rate of oscil� lations are determined. Analytical conclusions are confirmed by computer modeling. According to the results found, in order to describe highspeed transient processes, apart from the consideration of velocities dispersion (which determines the temperature in the equilibrium statistical mechanics), the correlations of velocities of different particles should be considered. In particular, the damping of energy oscillations is associated with the fact that correlations associating the motion of remote particles are excited.

Heat transfer in infinite harmonic one-dimensional crystals

A closed system of differential-difference equations describing thermal processes in one-dimensional harmonic crystals is obtained in the paper. An equation connecting the heat flow and the kinetic temperature is obtained as a solution of the system. The obtained law of heat conduction is different from Fourier’s law and results in an equation that combines properties of the standard heat equation and the wave equation. The resulting equation is an analytic consequence from the dynamical equations for the particles in the crystal. Unlike equations of hyperbolic heat conduction, this equation is time-reversible and has only one independent parameter. A general analytical solution of this differential equations is obtained, and the analytical results are confirmed by computer simulations.

Inclusion of the Moment Interaction in the Calculation of the Flexural Rigidity of Nanostructures

In recent years, in addition to the investigation of the electronic and optical properties of nanostructures [1], the study of their mechanical properties has become particularly important. Many works have been devoted to the production of nanotubes and investigation of their properties [2–8]. According to the data obtained in [4], nanotubes can retain their elastic properties under significant strains. The stress–strain state of nanotubes is usually calculated in the theory of elastic shells [9]. In this case, the elastic moduli are determined in discrete models, where only the force interaction between atoms forming a nanotube is taken into account. However, the existence of monolayer nanotubes [5–8] makes it necessary to consider also the moment interaction between atoms. Otherwise, the atomic layer forming the nanotube would have zero flexural rigidity, so that such a nanotube would be unstable.

From nonlinear oscillations to equation of state in simple discrete systems

Abstract Nonlinear oscillations of a single particle in the potential well and for one-dimensional chain of interacting particles are considered. The law of interaction is of Lennard-Jones type, mimicking interaction in atomic systems. Similarities in average behaviour of the systems with one and many degrees of freedom are shown. Time averaging for the random oscillations is used to obtain thermodynamic characteristics such as pressure, specific volume, and thermal energy. Second order equation of state is obtained, which is valid in the conditions of strong extension, where fails the widely used Mie–Gruneisen equation of state.

Lattice with vacancies: elastic fields and effective properties in frameworks of discrete and continuum models

Linear elastic deformation of the two-dimensional triangular lattice with multiple vacancies is considered. Closed-form analytical expressions for displacement field in the lattice with doubly periodic system of vacancies are derived. Effective elastic moduli are calculated. The results are compared with the ones obtained by molecular dynamics simulations of a lattice with random distribution of vacancies. At low vacancy concentrations, less than 4%, random and periodic distributions of vacancies produce the same effect on elastic moduli. One of the main goals is to examine the possibilities and limitations of modelling of the lattice with vacancies by an elastic continuum with holes. It is found that the effective elastic properties are modelled adequately, provided the shape of the holes is chosen appropriately. On the contrary, the strain field, in particular, strain concentration differs significantly.