A Simple Approach to Evaluate Non-Newtonian Viscosity Effects in a Lubricating System

1987 ◽  
Vol 109 (1) ◽  
pp. 177-182 ◽  
Author(s):  
Patrick Bourgin ◽  
Joseph-Marc Francois
Keyword(s):  
Computer Code ◽  
Simple Approach ◽  
Rheological Parameters ◽  
Finite Width ◽  
Slider Bearing ◽  
Empirical Formulas ◽  
Newtonian Viscosity ◽  
Pocket Calculator ◽  
Viscosity Effects ◽  
Analytical Formulas

The working characteristics of a finite width slider bearing lubricated by a non-Newtonian fluid are computed. The analysis proposed here allows its performances to be evaluated by means of a pocket calculator. For that purpose, a computer code based on a finite element method is used. The program runs for different values of pertinent kinematical, geometrical and rheological parameters. The corresponding results are fitted by means of adequate analytical formulas, which are very easy to handle. The accuracy of these empirical formulas is investigated in several typical cases. The agreement with the numerical solution is proven to be satisfactory.

scholarly journals Cross sections of electron collisions with noble gases atoms

2021 ◽  
pp. 11-16
Author(s):  
Rusudan Golyatina ◽  
Sergei Maiorov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Noble Gas ◽  
Empirical Formulas ◽  
Electron Collisions ◽  
Wide Range ◽  
Analytical Formulas ◽  
The Cross ◽  
Approximation Coefficients ◽  
Ionization Cross Sections

Consideration is given to the analysis of data on the cross sections of elastic and inelastic col-lisions of electrons with noble gas atoms. The transport (diffusion) cross section, the excita-tion and ionization cross sections are studied. For the selected sets of experimental and theo-retical data, optimal analytical formulas are found and approximation coefficients are select-ed for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of collision energies from 0.001 to 10000 eV with an accuracy of sev-eral percent.

scholarly journals Influence of particle size and gradation on shear strength–dilation relation of granular materials

2019 ◽  
Vol 56 (2) ◽  
pp. 208-227 ◽  
Author(s):  
Samaneh Amirpour Harehdasht ◽  
Mahmoud N. Hussien ◽  
Mourad Karray ◽  
Varvara Roubtsova ◽  
Mohamed Chekired
Keyword(s):  
Particle Size ◽  
Grain Size ◽  
Shear Strength ◽  
Granular Materials ◽  
Plane Strain ◽  
Computer Code ◽  
Direct Shear ◽  
Shear Tests ◽  
Empirical Formulas ◽  
Direct Shear Tests

Upon close scrutiny of data reported in the literature, taking into account particle-scale characteristics to optimize the precision of the well-known empirical Bolton’s equations and imposing particle-size limits on them is recommended. The present paper examines the potential influence of particle size and grading on the shear strength–dilation relation of granular materials from the results of 276 symmetrical direct shear tests. The applicability of physical symmetrical direct shear tests to interpret the plane strain frictional shearing resistance of granular materials has been widely discussed using the discrete element method (DEM) computer code SiGran. Sixteen different grain-size distribution curves of three different materials were tested at different normal pressures and initial relative densities. It is demonstrated that while the contribution of dilatancy to shear strength is not influenced by the variation in the coefficient of uniformity, Cu, in the investigated range, it significantly decreases with increasing mean particle size, D50. The coefficients of Bolton’s equations have been, therefore, adjusted to account for D50. A comparison of the predictions by the proposed empirical formulas with plane strain friction angle, [Formula: see text], and dilation angle, ψ, data from the literature shows that accounting for the grain size yields more accurate results.

Thixotropy of Semisolid Metals

1999 ◽  
Vol 578 ◽  
Author(s):  
Andreas N. Alexandrou ◽  
Gilmer R. Burgos ◽  
Vladimir M. Entov
Keyword(s):  
Volume Fraction ◽  
Fluid Model ◽  
Flow Behavior ◽  
Solid Volume Fraction ◽  
Computer Code ◽  
Rheological Parameters ◽  
Structural Parameter ◽  
Order Kinetic ◽  
Thixotropic Behavior ◽  
Dependent Flow

AbstractUnderstanding the time-dependent flow behavior of metal alloys in semisolid state is essential for the further development of the process. In the present investigation, the thixotropic behavior of semisolid slurries is modeled using conservation equations and the Herschel-Bulkley fluid model. The rheological parameters are assumed to be functions of the solid volume fraction, and of a structural parameter that changes with processing history. The evolution of the structural parameter is described by a first order kinetic differential equation that relates the rate of build-up and break-down of the solid skeleton. The model is implemented into a computer code to predict die filling.

Thermal Effects in Slider Bearings

1968 ◽  
Vol 183 (1) ◽  
pp. 631-645 ◽  
Author(s):  
E. J. Hahn ◽  
C. F. Kettleborough
Keyword(s):  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Finite Width ◽  
Thermal Distortion ◽  
Slider Bearing ◽  
Lubricant Flow ◽  
Flow Heat ◽  
Mathematical Equations ◽  
Basic Equations

The authors have shown previously by solving numerically the relevant mathematical equations describing lubricant flow, heat transfer and thermal distortion of bearing components in a slider bearing of infinite width, that, for the particular operating and boundary conditions assumed, thermal distortion rather than variation of the lubricant properties is the cause of hydrodynamic lubrication of initially parallel, radially grooved, thrust bearings. In this paper, numerical solutions are presented to show the effect of relaxing these conditions. The beneficial effect of thermal distortion is proved to hold generally and the importance of proper mixing of the lubricant at the inlet is illustrated. Comparison of numerical solutions with existing experimental observations shows only a qualitative agreement. A realistic three-dimensional mathematical model of a slider bearing of finite width is derived from basic equations, and the solution of the resulting equation, allowing for variable lubricant properties and thermal distortion of the bearing components, is developed and discussed.

The Optimum Rayleigh Bearing in Terms of Load Capacity or Friction for Non-Newtonian Lubricants

1985 ◽  
Vol 107 (1) ◽  
pp. 59-67 ◽  
Author(s):  
P. Bourgin ◽  
B. Gay
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Slider Bearing ◽  
Generalized Newtonian Fluid ◽  
Newtonian Viscosity ◽  
One Dimensional ◽  
Minimum Film Thickness ◽  
The One ◽  
Numerical Program

Pontryagin’s Maximum Principle is used to show that the configuration of the one-dimensional slider bearing which carries the maximum load for a specified minimum film thickness, is a modified Rayleigh bearing. The lubricant may be any Generalized Newtonian Fluid. Having selected two optimization criteria (1: maximum load capacity for a given minimum film thickness—2: minimum friction force for a specified load), a numerical program allows one to determine the optimal step bearing associated with the lubricant non-Newtonian viscosity. Several examples are worked out, showing that significant gains are expected, in comparison with the results obtained for the classical (Newtonian) Rayleigh bearing.

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