# The Application of Molecular Dynamics in Fullerene-Based Journal Bearing Simulation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}–10

^{6}particles during a 10

^{−6}–10

^{−9}s in this stage of computer technology development. These restrictions prevent us from studying the macroscopic objects in the usual time slots, but help to clarify many important physical laws.

## 2. Molecular Model of Fullerene-Like Lubricant and Journal Bearing

_{60}. At the vertices of the hexagon there are atoms that are similar in physical properties to carbon atoms. The central atom compensates stiffness and mass of the volumetric fullerene molecule C

_{60}in its 2nd model. Such a two-dimensional model was used in the study of the motion of a monolayer fullerene lubricant between the parallel walls [7].

_{i}

_{,j}—the distance between i-th and j-th atoms, m;

- ξ—characteristic energy that determines the depth of the potential well, J;
- σ—characteristic length that determines the distance with zero energy, m.

_{m}= 2

^{1/6}σ. This is evident from the Equation (1).

_{i}—the mass of the atom, kg;

- —speed of i-th atom, m/s;
- N—the quantity of interacting atoms.

## 3. Research of the Convergence of the Numerical Solutions

_{0}the distance between them is equilibrium r = r

_{m}, and the modules of their velocities are equal to some characteristic velocity V* = ωR. This value corresponds to the circumferential velocity of the molecules on the surface of the trunnion with radius R (Figure 1). It is required to determine the period of time enough to stop the atoms fully. Since the interaction of atoms is potential, the law of conservation of mechanical energy in dimensionless variables takes the form:

- —dimensionless criterion of the energy balance of atoms;
- —dimensionless distance between atoms.

_{0}to time of atoms stop is one time step Δt = h and during this period of time the value of acceleration is constant and the speed decreases linearly from the value V* to zero. The value of the time step can be found by a joint decision of the two equations:

**Figure 2.**The dependence of the time step h on the criteria S for different values of the properties ξ/m, (1) −ξ/m = 2.3, J/kg; (2) −ξ/m = 0.23, J/kg; (3) −ξ/m = 23, J/kg.

## 4. Fullerene-Based Journal Bearing Simulation

_{m}as usual) and summary force of intramolecular interaction on each acting atom.

_{i}= 1…N

_{g}and inner cycle of b

_{i}= 1…n

_{g}, where N

_{g}and n

_{g}—are predefined in “Block 1” number of molecules of fullerenes and number of atoms in each molecule respectively.

^{7}rad/s; the mass of the lubricant atom is m

_{a}= 12 Da; the mass of the lubricant molecule m

_{m}= 60m

_{a}; radius of the lubricant molecule r = 3.5 A; parameters of the potential Lennard Jones [9] ξ = 275/N

_{A}J, and σ = 3.47 A. In the process of calculation we controlled the motion of a single molecule of grease that is in contact with the bush and trunnion of bearing. At a certain point of time the value of the modulus of the molecule velocity was fixed for different values of time step. The results of a series of numerical experiments are presented in Figure 4. The vertical line in the figure indicates the value of the time step, calculated according to the Formula (4). The figure shows that the value of the step recommended by Equation (4) provides sufficient convergence of result (indicated by a vertical line on the chart). It should also be noted that an increase of recommended magnitude of step by one order leads to the “explosion” of molecules in motion, and a decrease by one to two orders of magnitude improves convergence of results.

_{ρφ}—shear stress in polar coordinates;

- μ—shear viscosity coefficient (or shear viscosity);
- ξ
_{ρφ}—shear strain rate; - V
_{φ}—tangential velocity; - ρ—radial coordinate.

Process time/(trunnion rotation angle), s/(radian) | Summary kinetic energy in fractions of its initial value, E_{k}^{0} ~ 10^{-20}, J | Average friction force on the trunnion, N | Shear viscosity on the trunnion, Pa·s | |
---|---|---|---|---|

Fullerene-based journal bearing | 10^{-7} /(1) | (1…1.25)E_{k}^{0} | 1.1×10^{-12} | 1.8×10^{-12} |

Fullerene-based journal bearing with damped walls | 10^{-7} /(1) | (0.95…1.05)E_{k}^{0} | 1.3×10^{-12} | 4×10^{-12} |

## 5. Conclusions

^{11}steps. Too small a number of steps leads to inadequate results, too large slows down the calculation. On the basis of similarity theory and dimensional analysis, the criterion of energy balance and the method of calculation of the indicative value of the time step were proposed. This technique allows us to determine in advance the computational complexity of numerical solutions of the problem and an approximate calculation of the value of computer time.

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Kornaev, A.; Savin, L.; Nozdrichkin, M.
The Application of Molecular Dynamics in Fullerene-Based Journal Bearing Simulation. *Lubricants* **2014**, *2*, 1-10.
https://doi.org/10.3390/lubricants2010001

**AMA Style**

Kornaev A, Savin L, Nozdrichkin M.
The Application of Molecular Dynamics in Fullerene-Based Journal Bearing Simulation. *Lubricants*. 2014; 2(1):1-10.
https://doi.org/10.3390/lubricants2010001

**Chicago/Turabian Style**

Kornaev, Alexey, Leonid Savin, and Mikhail Nozdrichkin.
2014. "The Application of Molecular Dynamics in Fullerene-Based Journal Bearing Simulation" *Lubricants* 2, no. 1: 1-10.
https://doi.org/10.3390/lubricants2010001