scholarly journals An Assessment of Quantitative Predictions of Deterministic Mixed Lubrication Solvers

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Yuechang Wang ◽  
Abdel Dorgham ◽  
Ying Liu ◽  
Chun Wang ◽  
Mark C. T. Wilson ◽  
...  
Keyword(s):  
Reynolds Equation ◽  
Thickness Distribution ◽  
Computation Time ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Mixed Lubrication ◽  
Contact Ratio ◽  
Lubricated Contacts ◽  
Discretization Schemes ◽  
Parametric Studies

Abstract The ability to simulate mixed lubrication problems has greatly improved, especially in concentrated lubricated contacts. A mixed lubrication simulation method was developed by utilizing the semi-system approach which has been proven to be highly useful for improving stability and robustness of mixed lubrication simulations. Then different variants of the model were developed by varying the discretization schemes used to treat the Couette flow terms in the Reynolds equation, varying the evaluation of density derivatives and varying the contribution of terms in the coefficient matrix. The resulting pressure distribution, film thickness distribution, lambda ratio, contact ratio, and the computation time were compared and found to be strongly influenced by the choice of solution scheme. This indicates that the output from mixed lubrication solvers can be readily used for qualitative and parametric studies, but care should be taken when making quantitative predictions.

The investigation of contact ratio in mixed lubrication

2006 ◽  
Vol 39 (5) ◽  
pp. 409-416 ◽  
Author(s):  
J.B. Luo ◽  
S. Liu
Keyword(s):  
Mixed Lubrication ◽  
Contact Ratio

Application of Jacobi - Conjugate Gradient Method in the Two-Dimensional Magnetotelluric Forward

2013 ◽  
Vol 416-417 ◽  
pp. 2123-2127
Author(s):  
Chong Li Zhu
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Linear Equations ◽  
Hessian Matrix ◽  
Simulation Method ◽  
Coefficient Matrix ◽  
Fine Grid ◽  
Solution Efficiency

Using the finite element method and all kinds of numerical simulation method, A large-scale system of linear equations is solved eventually,the solution method of the system of equations largely determines the solution efficiency and precision of numerical calculation. The Jacobi iteration preconditioning conjugate gradient method is adopted, Both overcome the coefficient matrix pathological characteristics and the characteristics of slow convergence speed ,and avoid the disadvantages such as Newton's method to store and Hessian matrix is calculated and inversed,improve forward modeling calculation speed and accuracy. Guarantee for solving numerical stability and efficiency ,of the thick grid combined with verification, the algorithm is feasible and it is verified by coarse grid combine with fine grid.

A Simulation Method of Establishing Fatigue Life Distribution

1976 ◽  
Vol 98 (1) ◽  
pp. 183-188 ◽  
Author(s):  
H. A. Elmaraghy ◽  
J. N. Siddall
Keyword(s):  
Fatigue Life ◽  
Material Properties ◽  
Digital Simulation ◽  
Simulation Method ◽  
Fatigue Tests ◽  
Design Tool ◽  
Statistical Characteristics ◽  
Life Distribution ◽  
Parametric Studies ◽  
Life Distributions

This paper presents a Monte Carlo simulation method for fatigue failure, by which the randomness of two material properties as well as that of the applied load can be incorporated into a stochastic model using an appropriate failure criterion to predict the statistical characteristics of fatigue life under constant and random amplitude cyclic loading conditions. In this technique, both the endurance limit Se and the fatigue strength coefficient Sf′ are treated as stochastic variables. The combined effect of the randomness of Se, Sf′, and the applied stress on the statistical characteristics of fatigue lives is predicted analytically using digital simulation of fatique tests. The life distributions and their statistical characteristics are found to be in good agreement with those obtained from analyzing the experimental results, indicating that the proposed technique and the underlying assumptions and hypotheses are adequate. The suggested method is believed to be an effective, fast, and easy-to-use design tool which is suitable for use on electronic computers. It is ideal for parametric studies compared with the costly and time-consuming laboratory fatigue tests. Minimum experimental data are needed as a basis for the analysis. New results are presented which show the effect of the randomness of the loads and material properties on the randomness of fatigue life distribution.

EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling

2005 ◽  
Vol 219 (4) ◽  
pp. 285-290 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Validity Of Results ◽  
Erroneous Conclusion ◽  
Low Speeds ◽  
Lubrication Models ◽  
Circular Contact

When numerical and experimental results are compared to validate elasto-hydrodynamic lubrication (EHL) models, it is of utmost importance that grid-converged results are used. In particular at low speeds and high loads, solutions obtained using grids that are not sufficiently dense will exhibit an artificial trend that does not represent the behaviour of the continuous modelling equations. As it coincides with a trend observed in experiments this may lead to the erroneous conclusion that the theoretical model on which the numerical simulations are based is accurate. This risk is illustrated in detail. It is further shown that EHL models based on the Reynolds equation in a steady state circular contact predicts a positive film thickness as long as the grid used in the calculations is sufficiently dense. This has significant implications for the validity of results obtained using mixed lubrication models based on a Reynolds model and a film thickness threshold.

scholarly journals An Alternative Simulation Method for Calculation of Microgas Flows under Flying Head Sliders

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Ching Shen
Keyword(s):  
Reynolds Equation ◽  
Simulation Method ◽  
Air Bearing ◽  
Bearing Surface ◽  
Rotating Disc ◽  
Information Preservation ◽  
Precise Knowledge ◽  
Micrometer Size ◽  
Methods Of Calculations ◽  
Generalized Reynolds Equation

The precise knowledge of the force and moment generated by the air squeezed under the read-write slider by the rotating disc is an engineering necessity in designing the air bearing surface slider. This paper reviews methods addressing the thin gas film bearings problem. It firstly reviews briefly the relatively well-known two methods of calculations of the microgas flows under flying head sliders, the generalized Reynolds equation, having given a number of useful results of slider design, and the DSMC method, which is precise and appropriate for the flow of complex configurations but is restricted to miniature (~micrometer) size sliders. The main purpose of the paper is to introduce to the reader an alternative method, the information preservation (IP) method, for use in simulation of the flows under air bearing surfaces. Some recent results of IP simulation of slider flows published on conference proceedings are introduced here.

scholarly journals About the Accuracy and the Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication

2018 ◽  
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact the complete energy equation has no analytic solution that could be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests and the energy equation is artificially decoupled from Reynolds. This approach enables to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitudes more efficient than the NDM in terms of computation time. The energy equation is then coupled with Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

scholarly journals Analysis of couple-stresses and piezo-viscous effects in a layered connecting-rod bearing

2018 ◽  
Vol 19 (6) ◽  
pp. 607
Author(s):  
Bouzid Laouadi ◽  
Mustapha Lahmar ◽  
Benyebka Bou-saïd ◽  
Hamid Boucherit ◽  
Ahcene Mouassa
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Thickness Distribution ◽  
Continuum Theory ◽  
Algebraic Equations ◽  
Connecting Rod ◽  
Viscous Effects ◽  
Time Step ◽  
Compression Ignition Engine ◽  
Couple Stresses

In this work, the combined effects of couple-stresses and piezo-viscosity on the dynamic behavior of a compression ignition engine big-end connecting-rod bearing with elastic layer are investigated using the V. K. Stokes micro-continuum theory. It is assumed that the journal (crankpin) is rigid and the big-end bearing consists of a thin compressible elastic liner fixed in an infinitely stiff housing. The governing Reynolds' equation and the viscous dissipation term appearing on the RHS of energy equation are modified using the V. K. Stokes micro-continuum theory. The non-Newtonian effect is introduced by a new material constant η, which is responsible for couple-stress property, and the piezo-viscosity effect by the pressure–viscosity coefficient α appearing in the well-known Barus' law. In the proposed model, the nonlinear transient modified Reynolds equation is discretized by the finite difference method, and the resulting system of algebraic equations is solved by means of the subrelaxed successive substitutions method to obtain the fluid-film pressure field as well as the film thickness distribution. The crankpin center trajectories for a given load diagram are determined iteratively by solving the nonlinear equilibrium equations of the journal bearing system with the improved and damped Newton–Raphson method for each time step or crankshaft rotation angle. According to the obtained results, the effects of couple-stresses and piezo-viscosity on the nonlinear dynamic behavior of dynamically loaded bearings with either stiff or compliant liners are significant and cannot be overlooked.

Fluid Dynamic Forces Acting on the Rotor of a Shaft-Less Miniature Pump

2011 ◽  
Author(s):  
Baotang Zhuang ◽  
Xianwu Luo ◽  
Xin Wang ◽  
Bin Ji ◽  
Hongyuan Xu
Keyword(s):  
Reynolds Equation ◽  
Static Pressure ◽  
Fluid Dynamic ◽  
Thickness Distribution ◽  
Static Pressure Distribution ◽  
Simulation Based ◽  
Social Fields ◽  
Dynamic Forces ◽  
Rotating Impeller ◽  
Fluid Dynamic Bearing

For a miniature pump used in many social fields, it is expected to be able to operate without any shaft and mechanical bearing. Recently, a double-suction shaft-less miniature pump has been developed at the Lab of Multiphase Flow and Biomechanics, Tsinghua University. Because the rotor of the miniature pump is rotating inside the pump casing, a fluid dynamic bearing is necessary to support the pump rotor. In this paper, a fluid dynamic bearing was designed to support the rotating impeller and motor rotor, and was manufactured combined with the miniature pump. In order to evaluate the bearing capability, the numerical simulation based on Reynolds equation was conducted for the fluid dynamic bearing. Both the performance experiment of the pump and the numerical results for the bearing indicate that the fluid dynamic bearing designed for the miniature pump in this study is usable and reliable. It is also noted that the performance including the liquid film thickness distribution, static pressure distribution, bearing capability, etc. of the bearing has been reasonably predicted using the present numerical methods. Further, the bearing capability increased remarkably with eccentric ratio between the bush and journal, and rotational speed of the pump for the fluid dynamic bearing.

An Efficient Simulation Method for Distributed Lumped Fluid Networks

1977 ◽  
Vol 99 (1) ◽  
pp. 34-40 ◽  
Author(s):  
R. S. Sidell ◽  
D. N. Wormley
Keyword(s):  
Finite Difference Methods ◽  
Computation Time ◽  
Simulation Method ◽  
Transmission Network ◽  
Efficient Simulation ◽  
Fluid Networks ◽  
Lumped Elements ◽  
Simulation Results ◽  
Core Storage ◽  
Nonlinear Resistance

A method is presented for the simulation of fluid networks consisting of uniform distributed elements and lumped dynamic, nonlinear elements. The uniform transmission elements may be lossy and dispersive. General relationships are derived for their terminations in junctions with other elements and/or with dynamic, nonlinear lumped elements. The basic computer simulation method is efficient in terms of computation time and core storage requirements in comparison to direct finite difference methods and may be implemented on a minicomputer. Simulation results are compared with experimental data for a pneumatic transmission line terminated with a nonlinear resistance and for a pneumatic transmission network consisting of three lines of incommensurate lengths.

Effects of Foil Bending Rigidity on Spacing Height Characteristics of Hydrostatic Porous Foil Bearings for Web Handling Processes

1997 ◽  
Vol 119 (3) ◽  
pp. 422-427 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Computation Time ◽  
Finite Width ◽  
Bending Rigidity ◽  
Weighted Residual Method ◽  
Web Handling ◽  
Foil Bearings ◽  
Wide Range ◽  
Foil Bending

In this paper, the effects of foil bending rigidity on the spacing height characteristics of hydrostatic foil bearings with a hollow porous shaft for web handling processes are analyzed by the finite width bearing theory. In the analysis, in order to save computation time and to improve the convergence of solutions, the two-dimensional modified Reynolds equation considering the added flow through porous shaft is reduced to an ordinary differential equation based on the weighted residual method. The reduced Reynolds equation and elastic equation for the foil are discretized by the finite difference method and solved numerically by the iterative technique. The numerical solutions for the pressure and film thickness distributions between foil and shaft are obtained for a wide range of bearing width-to-diameter ratio under various combinations of foil bending rigidity and foil wrap angle, and the spacing height characteristics of the foil bearings are examined theoretically.

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