About the Method for Solving the Navier-Stokes Equations: Mathematical Modeling of the Hydrodynamic Bearings

DOI

10.2991/978-94-6239-668-5_52How to use a DOI?

Keywords

Hydromechanics; Navier-Stokes equations; hydrodynamic bearing; friction moment; load-bearing capacity

Abstract

A methodology is provided for solving the Navier-Stokes equations with certain assumptions applied to the flow of lubricant between the bearing liner of a sliding bearing and the shaft journal. A plane problem of velocity distribution of oil particles filling the space between the shaft journal of a rotating crankshaft and the bearing liner is solved based on the hydrodynamic lubrication theory. Based on this solution, dependencies for determining the friction moment arising in the main bearing of a piston machine are derived. A methodology for determining the friction moment and load-bearing capacity of a hydrodynamic bearing with finite length under constant load is developed. The problem of determining the friction moment and load-bearing capacity of sliding bearings under the action of variable loads based on hydrodynamic lubrication theory arises when designing and calculating main bearings of piston compressor machines. As is well known, in these machines, liquid friction predominantly occurs, governed by the laws of hydrodynamic lubrication theory. However, these bearings operate under variable loads, caused by periodic pressure forces of gases in the cylinder and inertia forces of moving parts in piston compressor machines. The purpose of this work is to develop a methodology for solving the Navier-Stokes equations and determining the friction moment in the sliding bearing under constant load. The object of the study is the sliding bearings of piston compressors used in the oil and gas industries, operating under liquid friction conditions.

Copyright

© 2026 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Valeh Bakhshali
PY  - 2026
DA  - 2026/05/14
TI  - About the Method for Solving the Navier-Stokes Equations: Mathematical Modeling of the Hydrodynamic Bearings
BT  - Proceedings of the International Conference on Current Problems in Engineering and Applied Sciences (ICCPEAS 2025)
PB  - Atlantis Press
SP  - 502
EP  - 508
SN  - 2352-5401
UR  - https://doi.org/10.2991/978-94-6239-668-5_52
DO  - 10.2991/978-94-6239-668-5_52
ID  - Bakhshali2026
ER  -