scholarly journals Influence of Centrifugal Forces on Oil Flow in Journal Bearing of Planetary Gear

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mikhail Temis ◽  
Alexander Lazarev
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Centrifugal Forces ◽  
Element Discretization ◽  
Oil Flow ◽  
Wheel Bearing

Mathematical model of oil flow in fluid film bearing in field of centrifugal forces is developed. Centrifugal forces for planet wheel bearing sliding surfaces and oil gap are formulated. This model is based on modification of two-dimensional Reynolds equation taking into account inertia centrifugal forces for oil film. Required modification of Reynolds equation is received from Navier–Stokes and continuity equations taking into account centrifugal forces acting on planet wheel bearing. Modified two-dimensional Reynolds equation is solved numerically using finite element discretization. Developed mathematical model, based on modified Reynolds equation, is verificated at comparison with solution of full Navier–Stokes equations system obtained in commercial software package. Results for pressure distribution in bearing with fixed axis and in planet wheel bearing are received and compared. The sufficient influence of centrifugal inertia forces in oil layer of planet wheel bearing on pressure distribution, bearing carrying force, and attitude angle is shown for specific shaft journal eccentricity ratio, eccentricity direction, and rotation velocity.

Determination of Dynamic Coefficients in a Hydrodynamic Journal Bearing Based on the 3-D Navier-Stokes Equations and Considering Cavitation Effects

2012 ◽  
Author(s):  
Changhu Xing ◽  
Minel J. Braun
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Maximum Magnitude ◽  
Navier Stokes Equations ◽  
Dynamic Coefficients ◽  
Finite Perturbation ◽  
Hydrodynamic Journal Bearing

Dynamic coefficients are very important for the stability of a hydrodynamic journal bearing and therefore for its design. In order to determine the stiffness, damping and added mass coefficients of the hydrodynamic bearing, the finite perturbation method around its stabilization position was employed. Based on the Reynolds equation with Gumbel cavitation algorithm, the maximum magnitude of the perturbation was judged by comparing results from finite perturbation (numerical way) to those from infinitesimal perturbation (additional analytical equations need to be derived based on order analysis), as well as theoretical analysis. Using the determined perturbation amplitude, the full three-dimensional Navier-Stokes equations in CFD-ACE+ were used to evaluate coefficients from an actual lubricant and compare to those obtained with Reynolds equation. Finally, a homogeneous gaseous cavitation algorithm is coupled with the Navier-Stokes equation to establish the pressure distribution in the bearing. When gas concentration was varied, the pressure distribution as well as the dynamic coefficients changed significantly.

Gas Lubrication Analysis Method of Step-Dimpled Face Mechanical Seals

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Shaoxian Bai ◽  
Xudong Peng ◽  
Yefeng Li ◽  
Songen Sheng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shear Flow ◽  
Pressure Distribution ◽  
Difference Method ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Leakage Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations

In solving Reynolds equation with the conventional finite difference method, keeping the flow continuity has ofen been ignored, which will lead to an analysis error in the pressure distribution and leakage rate, especially for discontinuous clearance caused by step structures such as laser surface texturing sealing surfaces. In this paper, a finite difference method is introduced to satisfy the flow continuity to solve the Reynolds equation. Then, the pressure distribution for a typical rectangular step structure is obtained via two different methods: a numerical solution of the exact full Navier-Stokes equations, and a solution of the Reynolds equation solved by the previously mentioned method. A comparison between the two solution methods illustrates that, for both pressure flow and shear flow, the pressure distribution from the new difference method is in good agreement with that from the Navier-Stokes equations, and the new difference method can reflect the characteristic of the pressure sudden-change of the shear flow at the steps. Finally, the pressure distribution and leakage rate of a step-dimpled seal face are acquired with the presented method. The results show that the presented method allows gas-lubricating analysis of mechanical face seals with discontinuous clearance, and can keep the leakage rate continuous in the radial direction.

Numerical analysis of textured piston compression ring conjunction using two-dimensional-computational fluid dynamics and Reynolds methods

2018 ◽  
Vol 232 (11) ◽  
pp. 1467-1485 ◽  
Author(s):  
Chengwei Wen ◽  
Xianghui Meng ◽  
Wenxiang Li
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Compression Ring ◽  
Dynamics Method

The Reynolds equation, in which some items have been omitted, is a simplified form of the Navier–Stokes equations. When surface texturing exists, it may unreasonably reveal the tribological effects in some cases. In this paper, both the two-dimensional computational fluid dynamics method, which is based on the Navier–Stokes equations, and the corresponding one-dimensional Reynolds method are adopted to analyze the performance of the textured piston compression ring conjunction. To conduct a comparison between these two methods, the modified Elrod algorithm for Jakobsson–Floberg–Olsson cavitation model is chosen to solve the Reynolds equation. The results show that the Reynolds method is somewhat different from the computational fluid dynamics method in the minimum oil film thickness, pressure distribution, and cavitation at given operating conditions. Moreover, for a low ratio of texture depth to length, the Reynolds equation is still suitable to predict the overall effects of the designed groove textures. The simulation results also reveal that it is not always beneficial for the tribological performance and sometimes may increase the total friction force when the ring is textured.

Influences of Recess Geometry and Restrictor Dimension on Flow Patterns and Pressure Distribution of Hydrostatic Bearings

2007 ◽  
Author(s):  
Cheng-Hsien Chen ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
De-Xing Peng ◽  
Ding-Wen Yang
Keyword(s):  
Pressure Distribution ◽  
Stokes Equations ◽  
Flow Patterns ◽  
Lubricant Film ◽  
Navier Stokes ◽  
Width Ratio ◽  
Navier Stokes Equations ◽  
Hydrostatic Bearing ◽  
Lubricant Flow ◽  
Land Width

This paper studies the influences of recess geometry and restrictor dimensions on the flow patterns and pressure distribution of lubricant film, which are coupled effects of hybrid characteristics of a hydrostatic bearing. The lubricant flow is described by using the Navier-Stokes equations. The Galerkin weighted residual finite element method is applied to determine the lubricant velocities and pressure in the bearing clearance. The numerical simulations will evaluate the effects of the land-width ratio and restriction parameter as well as the influence of modified Reynolds number and the jet-strength coefficient on the flow patterns in the recess and pressure distribution in lubricant film. On the basis of the simulation drawn from this study, the simulated results are expected to help engineers make better use of the design of hydrostatic bearing and its restrictors.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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