Thermal Elastohydrodynamic Analysis Using a Generalized Non-Newtonian Formulation With Application to Bair-Winer Constitutive Equation

1994 ◽  
Vol 116 (1) ◽  
pp. 37-46 ◽  
Author(s):  
M. M. Khonsari ◽  
D. Y. Hua
Keyword(s):  
Shear Stress ◽  
Constitutive Equation ◽  
Fluid Model ◽  
Quantitative Agreement ◽  
Operating Conditions ◽  
Original Form ◽  
Shear Strain Rate ◽  
Limiting Shear Stress ◽  
Traction Coefficient ◽  
Local Shear

The governing equations together with a solution methodology are given which enables one to effectively handle an EHL line contact problem with simple non-Newtonian fluids including thermal effects. A computational algorithm is proposed that determines the equivalent viscosity as a function of shear strain rate for a specified constitutive equation. It is shown that the method effectively handles Bair-Winer’s rheological equation in its original form and without the need for an approximate perturbation analysis. Among the performance parameters presented are the local behavior of the shear stress as predicted by the Bair-Winer’s model and its comparison to that of the Ree-Eyrings constitutive equation. It is shown that these rheological equations predict a qualitatively similar trend for the traction coefficient. Nevertheless, depending on the operating conditions, the local shear stress as predicted by the Ree-Eyring equation may exceed the material limiting shear stress. A comparison study of the traction coefficient as predicted by the Bair-Winer’s fluid model and actual experimental measurements is also presented. The results are found to be in good quantitative agreement.

Lubricant Limiting Shear Stress Effect on EHD Film Thickness

1980 ◽  
Vol 102 (2) ◽  
pp. 213-220 ◽  
Author(s):  
B. Gecim ◽  
W. O. Winer
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Fluid Model ◽  
Operating Conditions ◽  
Stress Effect ◽  
Limiting Shear Stress ◽  
Viscous Fluid Model ◽  
Low Shear Stress ◽  
New Variables ◽  
Low Shear

A Grubin-like EHD inlet analysis utilizing a non-linear viscous fluid model with a limiting shear stress is reported. The shear rheological equation requires only a low shear stress viscosity and the limiting shear stress both functions of pressure. Values employed for these properties are taken from measurements on typical lubricants. Reductions of EHD film thickness are found to be up to 40 percent compared with the standard Grubin prediction for typical operating conditions. Slide-roll ratio, limiting shear stress dependence on pressure, and atmospheric pressure value of limiting shear stress are new variables required to determine film thickness with the first two being more important than the last. The EHD film thickness is reduced by increasing slide-roll ratio and/or decreasing the pressure dependence of the limiting shear stress.

Traction in EHL Line Contacts Using Free-Volume Pressure-Viscosity Relationship With Thermal and Shear-Thinning Effects

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Punit Kumar ◽  
M. M. Khonsari
Keyword(s):  
Free Volume ◽  
Elastohydrodynamic Lubrication ◽  
Approximate Equation ◽  
Shear Thinning ◽  
Operating Conditions ◽  
Limiting Shear Stress ◽  
Line Contacts ◽  
Traction Coefficient ◽  
Simulation Results ◽  
Volume Equation

This paper investigates the traction behavior in heavily loaded thermo-elastohydrodynamic lubrication (EHL) line contacts using the Doolittle free-volume equation, which closely represents the experimental viscosity-pressure-temperature relationship and has recently gained attention in the field of EHL, along with Tait’s equation of state for compressibility. The well-established Carreau viscosity model has been used to describe the simple shear-thinning encountered in EHL. The simulation results have been used to develop an approximate equation for traction coefficient as a function of operating conditions and material properties. This equation successfully captures the decreasing trend with increasing slide to roll ratio caused by the thermal effect. The traction-slip characteristics are expected to be influenced by the limiting shear stress and pressure dependence of lubricant thermal conductivity, which need to be incorporated in the future.

Extension of the Friction Mastercurve to Limiting Shear Stress Models

2003 ◽  
Vol 125 (4) ◽  
pp. 739-746 ◽  
Author(s):  
B. Jacod ◽  
C. H. Venner ◽  
P. M. Lugt
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Numerical Simulations ◽  
Coefficient Of Friction ◽  
Rheological Model ◽  
Operating Conditions ◽  
Limiting Shear Stress ◽  
Wide Range ◽  
Two Parameters ◽  
Stress Models

A previous study of the behavior of friction in EHL contacts for the case of Eyring lubricant behavior resulted in a friction mastercurve. In this paper the same approach is applied to the case of limiting shear stress behavior. By means of numerical simulations the friction coefficient has been computed for a wide range of operating conditions and contact geometries. It is shown that the same two parameters that were found in the Eyring study, a characteristic shear stress, and a reduced coefficient of friction, also govern the behavior of the friction for the case of limiting shear stress models. When the calculated traction data is plotted as a function of these two parameters all results for different cases lie close to a single curve. Experimentally measured traction data is used to validate the observed behavior. Finally, the equations of the mastercurves for both types of rheological model are compared resulting in a relation between the Eyring stress τ0 and the limiting shear stress τL.

Traction of Synthetic Traction Fluids and Its Related Rheological Properties

2006 ◽  
Author(s):  
Masayoshi Muraki ◽  
Ryuta Kawabata
Keyword(s):  
Shear Stress ◽  
Contact Pressure ◽  
Transverse Direction ◽  
Rolling Direction ◽  
Quadratic Equation ◽  
Limiting Shear Stress ◽  
Traction Coefficient ◽  
Thermal Solution ◽  
Traction Fluids ◽  
Peak Value

The traction μsp in the transverse direction due to spin was experimentally determined for commercially available traction oils. An increase in contact pressure increased μsp because of an increase in elastic strain, while a decrease in the radius of the roller in the transverse direction increased μsp owing to an increase in the effective shear modulus. Then, the effect of contact pressure on the maximum traction coefficient μmax in the rolling direction was studied. Under a constant temperature, μmax increased with increasing contact pressure, and then it decreased after reaching a peak value. The calculated results by the thermal solution based on an elastic-plastic model, using the limiting shear stress as a quadratic equation of pressure, agreed well with the experimental traction curves. This suggested that a peak value of μmax was brought about by less than a proportional increase in the limiting shear stress with pressure.

Elastohydrodynamic Lubrication Model With Limiting Shear Stress Behavior Considering Realistic Shear-Thinning and Piezo-Viscous Response

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Punit Kumar ◽  
Parinam Anuradha
Keyword(s):  
Shear Stress ◽  
Contact Zone ◽  
Present Model ◽  
Glassy State ◽  
Elastohydrodynamic Lubrication ◽  
Viscosity Coefficient ◽  
Shear Thinning ◽  
Limiting Shear Stress ◽  
Stress Behavior ◽  
Traction Coefficient

This paper addresses a largely ignored aspect pertaining to the elastohydrodynamic lubrication (EHL) traction behavior of fragile lubricants which undergo transition to glassy state at typical EHL contact zone pressures. For such lubricants, a conventional EHL model predicts extremely high and unrealistic values of traction coefficient, especially under near pure rolling conditions where thermal effect is negligible. Therefore, an EHL model incorporating the effect of limiting shear stress and the associated wall slip phenomenon is presented herein. Unlike the other such investigations involving limiting shear stress behavior, the present model employs Carreau-type power-law based models to describe the rheology of lubricants below the limiting shear stress along with realistic pressure-viscosity relationships (WLF and Doolittle-Tait). The use of Carreau-type shear-thinning model in this analysis allows the simultaneous prediction of minimum film thickness and traction coefficient for lubricants which shear-thin in the inlet zone and exhibit limiting shear stress behavior in the contact zone, a feature absent in the existing EHL models utilizing ideal visco-plastic or some other unrealistic rheological model. Using published experimental data pertaining to the shear-thinning and pressure-viscosity response of two fragile lubricants (L100 and LVI260), it has been demonstrated that the present model can explain the appearance of plateau in the experimental traction curve. Also, the influence of shear-thinning parameters and the pressure-viscosity coefficient on the predicted limiting shear stress zone has been studied.

Investigation of Parameters Affecting the Limiting Shear Stress-Pressure Coefficient: A New Model Incorporating Temperature

1994 ◽  
Vol 116 (3) ◽  
pp. 612-620 ◽  
Author(s):  
Victoria Wikstro¨m ◽  
Erik Ho¨glund
Keyword(s):  
Shear Stress ◽  
Film Thickness ◽  
Contact Pressure ◽  
Pressure Coefficient ◽  
Oil Viscosity ◽  
New Model ◽  
Lubricated Contacts ◽  
Limiting Shear Stress ◽  
Essential Parameter ◽  
Maximum Contact

When calculating film thickness and friction in elastohydrodynamically lubricated contacts, assuming a non-Newtonian fluid, the lubricant limiting shear stress is an essential parameter. It influences minimum film thickness and determines traction in the contact. The limiting shear stress is pressure dependent according to the Johnson and Tevaarwerk equation: τL=τ0+γp The limiting shear stress-pressure coefficient γ has in a previous screening investigation been shown to depend on several parameters: oil type, oil viscosity at + 40°C, maximum contact pressure and temperature. In the present investigation, the preliminary data is used together with response surface methodology. With these results in mind, further experiments are made and an empirical model is built. This paper presents a new model for γ which is valid for two types of oil (a polyalphaolefine with diester and a naphthenic oil) with different viscosities at +40°C. The model incorporates the influence of maximum contact pressure and oil temperature on γ. The measurements on which the model is based were carried out at temperatures ranging from −20 to + 110°C. The pressure range was 5.8–7 GPa and the shear rate was about 106 s−1.

scholarly journals CFD simulation of gas-liquid floating particles mixing in an agitated vessel

2017 ◽  
Vol 23 (3) ◽  
pp. 377-389 ◽  
Author(s):  
Liangchao Li ◽  
Bin Xu
Keyword(s):  
Velocity Field ◽  
Cfd Simulation ◽  
Solid Phase ◽  
Fluid Model ◽  
Surface Region ◽  
Operating Conditions ◽  
Gas Dispersion ◽  
Agitated Vessel ◽  
Superficial Gas Velocity ◽  
Floating Particles

Gas dispersion and floating particles suspension in an agitated vessel were studied numerically by using computational fluid dynamics (CFD). The Eulerian multi-fluid model along with standard k-? turbulence model was used in the simulation. A multiple reference frame (MRF) approach was used to solve the impeller rotation. The velocity field, gas and floating particles holdup distributions in the vessel were first obtained, and then, the effects of operating conditions on gas dispersion and solid suspension were investigated. The simulation results show that velocity field of solid phase and gas phase are quite different in the agitated vessel. Floating particles are easy to accumulate in the center of the surface region and the increasing of superficial gas velocity is in favor of floating particles off-surface suspension. With increasing solids loading, the gas dispersion becomes worse, while relative solid holdup distribution changes little. The limitations of the present modeling are discussed and further research in the future is proposed.

scholarly journals Analysis of dynamics variation against thixotropic parameter’s preferential range

2018 ◽  
Vol 45 (2) ◽  
pp. 231-251
Author(s):  
Nazish Shahid
Keyword(s):  
Shear Stress ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Axial Velocity ◽  
Fluid Model ◽  
Current Model ◽  
Velocity Shear ◽  
Structural Parameter ◽  
Velocity Flow ◽  
Analysis Of Dynamics

Variation in the dynamics of a steady-state blood flow through a stenosed tapered artery has been investigated corresponding to changes in thixotropic parameter ? over the range [0,1]. To probe the role of parameter ? and differentiate the current model from other known non-Newtonian models, expressions of axial velocity, shear stress, wall shear stress and flow rate have been calculated depending upon this parameter and pressure gradient. Also, pressure gradient has been deduced uniquely with the help of the continuity equation. Our choice of calculating pressure gradient has led to obtaining shear stress such that its dependence on the structural parameter of our model, unlike most available results, motivates for further investigation. The simultaneous effects of varying yield stress and parameter ? on axial velocity, flow resistance and flow rate have been studied such that the differences between the Herschel?Bulkley fluid model and our current model can be pointed out. To validate the suitability of our model and some results in history, we have also obtained limiting results for particular values of ?.

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