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Lubricants and Lubrication
Published in Ahmed Abdelbary, Extreme Tribology, 2020
In general, the Reynolds equation has to be solved using numerical methods such as finite difference, or finite element. Depending on the boundary conditions and the considered geometry, however, analytical solutions can be obtained under certain assumptions. Corresponding MATLAB code can also be applied upon solving of 1-D Reynolds equation using Finite Difference Method. A Matlab code for calculation of a semi-analytical solution of Reynolds equation using Grubin’s approximation (Stachowiak, 1993; Morales, 2007). At first, the Reynolds equation is integrated analytically using Grubin’s assumptions with respect to spatial coordinate and further numerically integrated with respect to temporal coordinate. The solution is then compared to the analytical Grubin’s solution for the central film thickness.
Almdst Unidirectional Flows
Published in Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou, ViscousFluid Flow, 2021
Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou
Reynolds equation, which is the main equation in hydrodynamic lubrication. In mixed lubrication the friction force is calculated using the load on the slider multiplied by a friction coefficient which is taken to be a function of the oil film thickness and surface roughness. The actual piston ring arrangement is sketched in Fig. 9.8.
Fundamentals of Hydrodynamic Lubrication
Published in Q. Jane Wang, Dong Zhu, Interfacial Mechanics, 2019
The Reynolds equation is, in principle, an elliptic partial differential equation for which boundary conditions are required when solving it for pressure distribution. The boundary conditions are briefly discussed in the next section.
Simulation analysis of dynamic coefficients for high-speed water-lubricated bearing-rotor system of satellite
Published in Waves in Random and Complex Media, 2023
Ying Zhou, Qinglei Zhang, Hongxiu Zhu, Jiyun Qin, Tao Xu, Jimin Zhang
The conditions for the establishment of the Reynolds equation are(1) incompressible flow and (2) laminar flow. However, these nonlinear factors such as temperature rise, cavitation, turbulence effect and other phenomena have not been considered. Based on the above conditions, the Reynolds equation for incompressible laminar flow in hydrostatics of cylindrical journal bearing can be written: where , , , , and , e is the eccentric distance of journal, c is the radial clearance of bearing, H is the dimensionless form of film thickness, h is the thickness of lubricant medium, is the dimensionless form of a length of bearing, is the eccentricity, is the angular direction from largest thickness, is the rotating angular speed of journal, L is the length of bearing, D is the diameter of bearing, P is the dimensionless form of pressure, p is the pressure of fluid film, and is dynamic viscosity.
Tribological Properties of Rock Bit Journal Bearings for Journal with Nanosecond Laser Surface Texture
Published in Tribology Transactions, 2020
Lin Zhong, Gang Wei, Guorong Wang, Xia He, Guihong Feng, Zongzheng Dong
The Reynolds equation is a special case of the Navier-Stokes equation, which is a differential equation of motion that describes the lubricating oil flow of the oil film bearing clearance. Therefore, if the Reynolds equation that describes the lubricating oil flow of oil film bearing clearance is the same, then the initial and boundary conditions should be the same. The two oil film bearings are similar in mechanics. The similarity criterion of dynamic bearing mechanics is expressed as follows (38): where Ps is the reference pressure, which can be any value. Ps is defined as Pa, which equals W/DL. W is the oil film load and D and L are the diameter and width of the hydrodynamic bearing, respectively.
Study on the characteristics of oil film load capacity for axial piston pump
Published in Australian Journal of Mechanical Engineering, 2020
Zhaoqiang Wang, Shan Hu, Hong Ji, Zhen Wang, Wei Liang
It can be seen from the simplified 2D polar coordinates Reynolds equation. The pressure according to Reynolds equation is related to the speed of the cylinder block, the viscosity and the oil film thickness. The oil film thickness is in turn related to the initial oil film thickness and the tilt angle of the cylinder block. Reynolds equation is derived from the Navier-Stokes equations, which is the basis of hydrodynamic lubrication and reflects the load-carrying capacity.