Progressive Mesh Densification Method for Numerical Solution of Mixed Elastohydrodynamic Lubrication

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Wei Pu ◽  
Jiaxu Wang ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Solution Process ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Machined Surface ◽  
Progressive Mesh ◽  
Wide Range

Numerical solution of mixed elastohydrodynamic lubrication (EHL) is of great importance for the study of lubrication formation and breakdown, as well as surface failures of mechanical components. However, converged and accurate numerical solutions become more difficult, and solution process with a fixed single discretization mesh for the solution domain appears to be quite slow, especially when the lubricant films and surface contacts coexist with real-machined roughness involved. Also, the effect of computational mesh density is found to be more significant if the average film thickness is small. In the present study, a set of sample cases with and without machined surface roughness are analyzed through the progressive mesh densification (PMD) method, and the obtained results are compared with those from the direct iteration method with a single fixed mesh. Besides, more numerical analyses with and without surface roughness in a wide range of operating conditions are conducted to investigate the influence of different compound modes in order to optimize the PMD procedure. In addition, different initial conditions are used to study the effect of initial value on the behaviors of this transient solution. It is observed that, no matter with or without surface roughness considered, the PMD method is stable for transient mixed EHL problems and capable of significantly accelerating the EHL solution process while ensuring numerical accuracy.

A Starved Mixed Elastohydrodynamic Lubrication Model for the Prediction of Lubrication Performance, Friction and Flash Temperature With Arbitrary Entrainment Angle

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Wei Pu ◽  
Dong Zhu ◽  
Jiaxu Wang
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Industrial Applications ◽  
Operating Conditions ◽  
Flash Temperature ◽  
Machined Surface ◽  
Lubrication Performance ◽  
Wide Range ◽  
Starved Lubrication

In this study, a modified mixed lubrication model is developed with consideration of machined surface roughness, arbitrary entraining velocity angle, starvation, and cavitation. Model validation is executed by means of comparison between the obtained numerical results and the available starved elastohydrodynamic lubrication (EHL) data found from some previous studies. A comprehensive analysis for the effect of inlet oil supply condition on starvation and cavitation, mixed EHL characteristics, friction and flash temperature in elliptical contacts is conducted in a wide range of operating conditions. In addition, the influence of roughness orientation on film thickness and friction is discussed under different starved lubrication conditions. Obtained results reveal that inlet starvation leads to an obvious reduction of average film thickness and an increase in interasperity cavitation area due to surface roughness, which results in significant increment of asperity contacts, friction, and flash temperature. Besides, the effect of entrainment angle on film thickness will be weakened if the two surfaces operate under starved lubrication condition. Furthermore, the results show that the transverse roughness may yield thicker EHL films and lower friction than the isotropic and longitudinal if starvation is taken into account. Therefore, the starved mixed EHL model can be considered as a useful engineering tool for industrial applications.

scholarly journals A Robust Numerical Solution of the Stochastic Collection–Breakup Equation for Warm Rain

2007 ◽  
Vol 46 (9) ◽  
pp. 1480-1497 ◽  
Author(s):  
Olivier P. Prat ◽  
Ana P. Barros
Keyword(s):  
Numerical Solution ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Discrete Equations ◽  
Warm Rain ◽  
Wide Range ◽  
Short Time ◽  
Rain Rates ◽  
The Impact

Abstract The focus of this paper is on the numerical solution of the stochastic collection equation–stochastic breakup equation (SCE–SBE) describing the evolution of raindrop spectra in warm rain. The drop size distribution (DSD) is discretized using the fixed-pivot scheme proposed by Kumar and Ramkrishna, and new discrete equations for solving collision breakup are presented. The model is evaluated using established coalescence and breakup parameterizations (kernels) available in the literature, and in that regard this paper provides a substantial review of the relevant science. The challenges posed by the need to achieve stable and accurate numerical solutions of the SCE–SBE are examined in detail. In particular, this paper focuses on the impact of varying the shape of the initial DSD on the equilibrium solution of the SCE–SBE for a wide range of rain rates and breakup kernels. The results show that, although there is no dependence of the equilibrium DSD on initial conditions for the same rain rate and breakup kernel, there is large variation in the time that it takes to reach steady state. This result suggests that, in coupled simulations of in-cloud motions and microphysics and for short time scales (<30 min) for which transient conditions prevail, the equilibrium DSD may not be attainable except for very heavy rainfall. Furthermore, simulations for the same initial conditions show a strong dependence of the dynamic evolution of the DSD on the breakup parameterization. The implication of this result is that, before the debate on the uniqueness of the shape of the equilibrium DSD can be settled, there is critical need for fundamental research including laboratory experiments to improve understanding of collisional mechanisms in DSD evolution.

Traction in Thermal Elastohydrodynamic Lubrication of Rough Surfaces

1992 ◽  
Vol 114 (1) ◽  
pp. 186-191 ◽  
Author(s):  
L. Chang
Keyword(s):  
Numerical Solutions ◽  
Rough Surfaces ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Wide Range ◽  
Line Contacts ◽  
Simulation Results

This paper studies the traction behavior of elastohydrodynamically lubricated line contacts between two rough surfaces. The study uses a thermal micro-elastohydrodynamic-lubrication (micro-EHL) model and obtains traction coefficients for a wide range of operating conditions and for film parameters as small as 1.50. The simulation results suggest that the traction is generally insensitive to the roughness structure and magnitude as long as the contact maintains a full EHL film. The results also indicate clearly that the lubricant squeeze induced by the motion and interaction of rough surfaces significantly affects the numerical solutions to thermal micro-elastohydrodynamic lubrication.

Numerical Solution of Mixed Thermal Elastohydrodynamic Lubrication in Point Contacts With Three-Dimensional Surface Roughness

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Xiaopeng Wang ◽  
Yuchuan Liu ◽  
Dong Zhu
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Three Dimensional ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Operating Conditions ◽  
Thickness Variation ◽  
Wide Range ◽  
Film Lubrication

Elastohydrodynamic lubrication (EHL) is a common mode of fluid-film lubrication in which many machine elements operate. Its thermal behavior is an important concern especially for components working under extreme conditions such as high speeds, heavy loads, and surfaces with significant roughness. Previous thermal EHL (TEHL) studies focused only on the cases with smooth surfaces under the full-film lubrication condition. The present study intends to develop a more realistic unified TEHL model for point contact problems that is capable of simulating the entire transition of lubrication status from the full-film and mixed lubrication all the way down to boundary lubrication with real machined roughness. The model consists of the generalized Reynolds equation, elasticity equation, film thickness equation, and those for lubricant rheology in combination with the energy equation for the lubricant film and the surface temperature equations. The solution algorithms based on the improved semi-system approach have demonstrated a good ability to achieve stable solutions with fast convergence under severe operating conditions. Lubricant film thickness variation and temperature rises in the lubricant film and on the surfaces during the entire transition have been investigated. It appears that this model can be used to predict mixed TEHL characteristics in a wide range of operating conditions with or without three-dimensional (3D) surface roughness involved. Therefore, it can be employed as a useful tool in engineering analyses.

On the Behavior of Friction in Lubricated Point Contact With Provision for Surface Roughness

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
H. Sojoudi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Friction Coefficient ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Type Curve ◽  
Lift Off

This paper presents a simple approach to predict the behavior of friction coefficient in the sliding lubricated point contact. Based on the load-sharing concept, the total applied load is supported by the combination of hydrodynamic film and asperity contact. The asperity contact load is determined in terms of maximum Hertzian pressure in the point contact while the fluid hydrodynamic pressure is calculated through adapting the available numerical solutions of elastohydrodynamic lubrication (EHL) film thickness formula for smooth surfaces. The simulations presented cover the entire lubrication regime including full-film EHL, mixed-lubrication, and boundary-lubrication. The results of friction, when plotted as a function of the sum velocity, result in the familiar Stribeck-type curve. The simulations are verified by comparing the results with published experimental data. A parametric study is conducted to investigate the influence of operating condition on the behavior of friction coefficient. A series of simulations is performed under various operating conditions to explore the behavior of lift-off speed. An equation is proposed to predict the lift-off speed in sliding lubricated point contact, which takes into account the surface roughness.

On the Stribeck Curves for Lubricated Counterformal Contacts of Rough Surfaces

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Dong Zhu ◽  
Jiaxu Wang ◽  
Q. Jane Wang
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Rough Surfaces ◽  
Elastohydrodynamic Lubrication ◽  
Real Data ◽  
Operating Conditions ◽  
Stribeck Curve ◽  
Flash Temperature ◽  
Wide Range ◽  
Stribeck Curves

The “Stribeck curve” is a well-known concept, describing the frictional behavior of a lubricated interface during the transition from boundary and mixed lubrication up to full-film hydrodynamic/elastohydrodynamic lubrication. It can be found in nearly every tribology textbook/handbook and many articles and technical papers. However, the majority of the published Stribeck curves are only conceptual without real data from either experiments or numerical solutions. The limited number of published ones with real data is often incomplete, covering only a portion of the entire transition. This is because generating a complete Stribeck curve requires experimental or numerical results in an extremely wide range of operating conditions, which has been a great challenge. Also, numerically calculating a Stribeck curve requires a unified model with robust algorithms that is capable of handling the entire spectrum of lubrication status. In the present study, numerical solutions in counterformal contacts of rough surfaces are obtained by using the unified deterministic mixed elastohydrodynamic lubrication (EHL) model recently developed. Stribeck curves are plotted in a wide range of speed and lubricant film thickness based on the simulation results with various types of contact geometry using machined rough surfaces of different orientations. Surface flash temperature is also analyzed during the friction calculation considering the mutual dependence between friction and interfacial temperature. Obtained results show that in lubricated concentrated contacts, friction continuously decreases as speed and film thickness increase even in the full-film regime until extremely high speeds are reached. This is mainly due to the reduction of lubricant limiting shear stress caused by flash temperature rise. The results also reveal that contact ellipticity and roughness orientation have limited influence on frictional behaviors, especially in the full-film and boundary lubrication regimes.

scholarly journals Influence of Chatter of VMC Arising During End Milling Operation and Cutting Conditions on Quality of Machined Surface

1970 ◽  
Vol 2 (1) ◽  
Author(s):  
A.K.M.N. Amin, M.A. Rizal, and M. Razman
Keyword(s):  
Surface Roughness ◽  
Metal Cutting ◽  
Metal Removal ◽  
End Milling ◽  
Cutting Speed ◽  
Cutting Conditions ◽  
End Mill ◽  
Machined Surface ◽  
Operating Cycle ◽  
Wide Range

Machine tool chatter is a dynamic instability of the cutting process. Chatter results in poor part surface finish, damaged cutting tool, and an irritating and unacceptable noise. Exten¬sive research has been undertaken to study the mechanisms of chatter formation. Efforts have been also made to prevent the occurrence of chatter vibration. Even though some progress have been made, fundamental studies on the mechanics of metal cutting are necessary to achieve chatter free operation of CNC machine tools to maintain their smooth operating cycle. The same is also true for Vertical Machining Centres (VMC), which operate at high cutting speeds and are capable of offering high metal removal rates. The present work deals with the effect of work materials, cutting conditions and diameter of end mill cutters on the frequency-amplitude characteristics of chatter and on machined surface roughness. Vibration data were recorded using an experimental rig consisting of KISTLER 3-component dynamometer model 9257B, amplifier, scope meters and a PC.  Three different types of vibrations were observed. The first type was a low frequency vibration, associated with the interrupted nature of end mill operation. The second type of vibration was associated with the instability of the chip formation process and the third type was due to chatter. The frequency of the last type remained practically unchanged over a wide range of cutting speed.  It was further observed that chip-tool contact processes had considerable effect on the roughness of the machined surface.Key Words: Chatter, Cutting Conditions, Stable Cutting, Surface Roughness.

New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory

2010 ◽  
Vol 65 (8-9) ◽  
pp. 633-640 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun ◽  
Jonu Lee
Keyword(s):  
Evolution Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Diffusion Processes ◽  
Initial Conditions ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Wide Range ◽  
Finite Memory

The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results show that the extended tanh and exp-function methods are very effective in finding exact solutions of the considered problem and HPM is very powerful in finding numerical solutions with good accuracy for nonlinear partial differential equations without any need of transformation or perturbation

A Natural Convection Fin with a Solution-Determined Nonmonotonically Varying Heat Transfer Coefficient

1981 ◽  
Vol 103 (2) ◽  
pp. 218-225 ◽  
Author(s):  
E. M. Sparrow ◽  
S. Acharya
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Transfer Coefficient ◽  
First Principles ◽  
Numerical Solutions ◽  
Flow Direction ◽  
Operating Conditions ◽  
Fluid Temperature ◽  
Wide Range

A conjugate conduction-convection analysis has been made for a vertical plate fin which exchanges heat with its fluid environment by natural convection. The analysis is based on a first-principles approach whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, and energy in the fluid boundary layer adjacent to the fin. The natural convection heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. For a wide range of operating conditions, the local heat transfer coefficients were found not to decrease monotonically in the flow direction, as is usual. Rather, the coefficient decreased at first, attained a minimum, and then increased with increasing downstream distance. This behavior was attributed to an enhanced buoyancy resulting from an increase in the wall-to-fluid temperature difference along the streamwise direction. To supplement the first-principles analysis, results were also obtained from a simple adaptation of the conventional fin model.

Size Effect on the Behavior of Thermal Elastohydrodynamic Lubrication of Roller Pairs

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Xiaoling Liu ◽  
Jinlei Cui ◽  
Peiran Yang
Keyword(s):  
Size Effect ◽  
Newtonian Fluid ◽  
Effective Viscosity ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Load Parameter ◽  
Performance Results ◽  
Thermal Ehl ◽  
Strong Size Effect

In order to investigate the size effect on elastohydrodynamic lubrication (EHL) of roller pairs, complete numerical solutions for both the Newtonian fluid and the Eyring fluid thermal EHL problems of roller pairs under steady state conditions have been achieved. It can be seen that there is no size effect on the isothermal EHL performance; however, there is a very strong size effect on the thermal EHL performance. Results show that the term of shearing heat is the most important factor for the film temperature when the size of a contact changes. Comparison between the Newtonian solution and the Eyring solution has been made under some operating conditions. It is interesting to see that the effective viscosity of the Eyring fluid is nearly the same as that of the Newtonian fluid when the size of a contact is large enough. The non-Newtonian effect, therefore, can be ignored when the size of a contact is very large. It is equally interesting to see that the thermal effect can be ignored when the size of a contact is very small. In addition, the influence of the velocity parameter, the load parameter, and the slide-roll ratio on the lubricating performance for various sizes of contacts has been investigated.

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