Perturbation Approach to Hydrodynamic Lubrication Theory

1994 ◽  
Vol 116 (1) ◽  
pp. 110-118 ◽  
Author(s):  
C. M. Myllerup ◽  
B. J. Hamrock
Keyword(s):  
Journal Bearing ◽  
Iterative Scheme ◽  
Hydrodynamic Lubrication ◽  
Perturbation Approach ◽  
Perturbation Scheme ◽  
Regular Perturbation ◽  
Corner Flow ◽  
Higher Order Terms ◽  
Hydrodynamic Lubrication Theory ◽  
Coordinate Perturbation

Three perturbation approaches that apply for regular hydrodynamic lubrication problems are discussed: a cross-film coordinate perturbation, an iterative scheme, and a regular perturbation in terms of the film aspect ratio. The methods are used to derive higher order terms for a driven corner flow with a Newtonian lubricant of constant properties. Reasons for preferring the regular perturbation scheme are presented, and this method is used to obtain the correct curvature correction in an infinitely long journal bearing. Criteria for identifying singular geometries in hydrodynamic lubrication are set fourth.

Modeling and Analysis of High-Speed Journal Bearing Based on Thermal Hydrodynamic Lubrication Theory

2013 ◽  
Vol 380-384 ◽  
pp. 82-86 ◽  
Author(s):  
Song Sheng Li ◽  
Yu Xin Lu ◽  
Ma Li Dong ◽  
Juan Shao ◽  
Feng Yu
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Lubrication Theory ◽  
Engineering Practice ◽  
Isothermal Model ◽  
Modeling And Analysis ◽  
Oil Film ◽  
Rotating Speed ◽  
Hydrodynamic Lubrication Theory

Journal bearing in high-speed working conditions will generate a lot of heat, which affects its working performance. Based on hydrodynamic lubrication theory, a model of the thermal hydrodynamic lubrication was built, and the distributions of temperatures and pressures of the oil film were obtained from the simultaneous solution of generalized Reynolds, energy and viscosity-temperature equations. The results show that the temperature will increase and the pressure decrease of the lubrication oil film with the rising of the rotating speed, which will make the the bearing capacity decrease. Compared with the traditional isothermal model, the thermal hydrodynamic lubrication model is more consistent with the engineering practice.

A Theoretical Analysis Considering Cavitation Occurrence in Oil-Lubricated Spiral-Grooved Journal Bearings With Experimental Verification

2004 ◽  
Vol 126 (3) ◽  
pp. 490-498 ◽  
Author(s):  
Tomoko Hirayama ◽  
Takeo Sakurai ◽  
Hiroshi Yabe
Keyword(s):  
Reynolds Equation ◽  
Flow Model ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Theoretical Studies ◽  
Bearing Stiffness ◽  
Hydrodynamic Lubrication Theory ◽  
The Difference ◽  
Theoretical Results

Performances of an oil-lubricated spiral-grooved journal bearing are investigated in this paper with special attention paid to cavitation occurrence. The “equivalent flow model,” which is a theoretical scheme for taking the cavitation occurrence into hydrodynamic lubrication theory, is applied to the analyses by a finite difference treatment of the Reynolds equation that deals with the geometry of a finite number of grooves. The calculated results are compared with experimental results under eccentric states, and verified in terms of cavitation map and pressure distribution. The cavitated area ratio, load capacity and bearing stiffness are also theoretically calculated. The difference between the theoretical results with and without consideration of the cavitation occurrence is considerable, and thus the influence of cavitation occurrence should not be ignored in theoretical studies on bearing characteristics.

The Optimum Design of Hydrodynamic Lubrication Bearing for Minimization of the Total Life Cost

2007 ◽  
Author(s):  
Takuzo Iwatsubo ◽  
Jun Yamabayashi
Keyword(s):  
Optimum Design ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Design Method ◽  
Inequality Constraints ◽  
Evaluation Functions ◽  
Initial Cost ◽  
Hydrodynamic Lubrication Theory ◽  
Running Cost ◽  
Total Life

This paper proposes an optimum design method of journal bearing for minimizing the total life cost which includes not only the initial cost but also the running cost. Journal bearing is one of the typical friction part and physically severe part in machine elements. Therefore, maintenance is required to prevent failure and to keep performance. For this object, the running cost by the maintenance is user’s burden. Thus, the optimum design method of the bearing for minimization of the total life cost is required. In this research, the evaluation functions of the total life cost which contains the initial cost and the running cost of the bearing are discussed and the optimum design is proposed under the physical constrain, that is Thermo Hydrodynamic Lubrication theory (THL theory), and inequality constraints. Then design valuables of the optimum journal bearing are obtained.

A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW

1994 ◽  
Vol 04 (05) ◽  
pp. 1319-1328 ◽  
Author(s):  
WILLIAM B. ZIMMERMAN
Keyword(s):  
Linear Theory ◽  
Landau Equation ◽  
Separation Of Variables ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Porous Media Flow ◽  
Perturbation Scheme ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Displacement Front

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.

Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

Sign in / Sign up

Export Citation Format

Share Document