A Numerical Model to Predict Dynamic Performance of Layered Gears at Starved Lubrication

2019 ◽  
Author(s):  
Qingbing Dong ◽  
Jing Wei ◽  
Yan Li ◽  
Lixin Xu
Keyword(s):  
Reynolds Equation ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Material System ◽  
Stress Concentrations ◽  
Damage Resistance ◽  
Influence Coefficients ◽  
Load Carrying ◽  
Potential Energy Method

Abstract Gears of modern industry are required to have a good fatigue performance to transmit power and motion through the contact interfaces. Composite layered surfaces can effectively improve the damage resistance of gears and decrease the friction coefficients. However, improper surface modification may induce intensive stress concentrations at the joint interfaces of the strengthening layers and cause unexpected damages to the flanks. Furthermore, the amount of lubricant at the inlet may probably be insufficient to establish fully flooded condition, which may result in starvation and accelerate damages to the gear sets. In this study, a starved elastohydrodynamic lubrication (EHL) model in three-dimensional (3D) line contact for layered gears is developed. The potential energy method is employed to determine the load distribution along the action line. The loading force is assumed to be balanced by the lubrication pressure, which is derived by discretizing the dimensional Reynolds equation into a solvable matrix with the consideration of the enforced boundary conditions due to the inlet oil supply. The transient evolution of lubrication is investigated to evaluate the load-carrying capability of the lubricant film at various starvation conditions. The influence coefficients related to the displacements and stresses of the layered material system are determined with the assistance of the fast Fourier transform (FFT) algorithm, and the effects of the layer properties and the fabrication methods are evaluated. Such analysis may provide insightful information for the optimization of material systems with fabricated layers and engineering design of gears.

Calculation of Gear Meshing Stiffness Considering Lubrication

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Gong Cheng ◽  
Ke Xiao ◽  
Jiaxu Wang ◽  
Wei Pu ◽  
Yanfeng Han
Keyword(s):  
Rough Surface ◽  
Calculation Method ◽  
Contact Stiffness ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Meshing Stiffness ◽  
Roughness Amplitude ◽  
Meshing Process

Abstract Gear meshing stiffness is the key parameter to study the gear dynamic performance. However, the study on the calculation of gear meshing stiffness considering lubrication, especially mixed lubrication, is still insufficient. Based on the three-dimensional linear contact mixed elastohydrodynamic lubrication model and the contact stiffness calculation method of rough surface, a method for calculating the gear meshing stiffness under mixed lubrication is proposed in this paper. According to the proposed calculation method, the effects of speed, external load, and roughness amplitude on gear meshing stiffness are further explored. The method can take into account the real rough surface topography and lubrication in the meshing process, so it may be more advantageous than the conventional method to some extent.

Three-Dimensional Plasto-Elastohydrodynamic Lubrication (PEHL) for Surfaces with Irregularities

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Ning Ren ◽  
Dong Zhu ◽  
Q. Jane Wang
Keyword(s):  
Plastic Deformation ◽  
Work Hardening ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Continuous Variable ◽  
External Loading ◽  
Surface Irregularity ◽  
Asperity Contact ◽  
Stress Concentrations ◽  
Subsurface Stress

Elastohydrodynamic lubrication (EHL) is one of the most common types of lubrication, which widely exists in many machine elements such as gears, rolling bearings, cams and followers, metal rolling tools, and continuous variable transmissions. These components often transmit substantial power under heavy loading conditions that may possibly induce plastic deformation of contacting surfaces. Moreover, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the average EHL film thickness. Consequently, most components operate in mixed lubrication with considerable asperity contacts, which may result in localized pressure peaks much higher than the Hertzian pressure, causing subsurface stress concentrations possibly exceeding the material yield limit. Plastic deformation, therefore, often takes place, which not only permanently changes the surface profiles and contact geometry, but alters material properties through work-hardening as well. Available mixed EHL models, however, do not consider plastic deformation, often yielding unrealistically high pressure spikes and subsurface stresses around asperity contact locations. Recently, a three-dimensional (3D) plasto-elastohydrodynamic lubrication (PEHL) model has been developed for investigating the effects of plastic deformation and material work-hardening on the EHL characteristics and subsurface stress/strain fields. The present paper is a continuation of the previous work done by Ren et al. (2010, “PEHL in point contacts,” ASME J. Tribol., 132(3), pp. 031501) that focused on model development and validation, as well as investigation of fundamental PEHL mechanisms in smooth surface contacts. This part of the study is mainly on the PEHL behavior involving simple surface irregularities, such as a single asperity or dent, which can be considered as basic elements of more complicated surface roughness. It is found that considerable plastic deformation may occur due to the pressure peaks caused by the surface irregularity, even though sometimes external loading is not heavy and the irregularity is concave. The plastic deformation may significantly affect contact and lubrication characteristics, resulting in considerable reductions in peak pressure and maximum subsurface stresses.

An Analysis of Grease and Oil Lubricated Spiral Grooved Bearings

1974 ◽  
Vol 96 (2) ◽  
pp. 275-283
Author(s):  
D. M. Dewar
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Three Dimensional ◽  
Thermal Conditions ◽  
Load Carrying Capacity ◽  
Thrust Bearings ◽  
Through Flow ◽  
Load Carrying ◽  
Running Torque ◽  
Spiral Groove Bearing

Mathematical models for grease and oils are put forward and used to solve a two-dimensional Reynolds’ equation with a quasi three-dimensional energy equation for any geometry of spiral groove bearing. Using numerical methods, results are presented for the temperature distributions in through-flow and block-centered thrust bearings; conical bearings and herringbone grooved journal bearings can also be dealt with. The overall bearing parameters, namely, load-carrying capacity, stiffness, and running torque at various eccentricity ratios are shown along with their dependence upon the prevailing thermal conditions.

Analysis of Static and Dynamic Performance Parameters of Two-Lobe Journal Bearing Operating With Non-Newtonian Lubricant

2019 ◽  
Author(s):  
Ashutosh Kumar ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Variable Viscosity ◽  
Dynamic Performance ◽  
Load Carrying Capacity ◽  
Performance Parameters ◽  
Noticeable Increase ◽  
Load Carrying ◽  
Nano Lubricant

Abstract Static and dynamic performance parameters of two-lobe journal bearing, working with non-Newtonian lubricant has been obtained. Krieger-Dougherty model is used to obtain the effective viscosity of nano-lubricant for a given concentration of solid-particle in base lubricant. Modified Reynolds equation is solved to obtain bearing performance parameters for couple stress model and variable viscosity model. Dynamic coefficients are also determined for various couple stress parameter. Results reveal a noticeable increase in flow co-efficient and load carrying capacity while there is a decrease in friction variable. It also reveals a significant betterment in dynamic co-efficient of bearing.

Steady-state performance of elliptical contact lubricated with micropolar fluids

2019 ◽  
Vol 234 (9) ◽  
pp. 1482-1499
Author(s):  
Dhanendra Dewangan ◽  
Mihir Sarangi
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Continuum Theory ◽  
Micropolar Fluids ◽  
Load Carrying ◽  
Molecular Length ◽  
Traction Coefficient ◽  
Modified Reynolds Equation ◽  
Steady State Performance

In this work, the numerical investigation is done for the steady-state performance of elliptical contacts lubricated with micropolar fluids. The Eringen’s micro-continuum theory is applied to deduce the modified Reynolds equation for micropolar fluids. The modified Reynolds equation is discretized by the finite difference technique and evaluated by a multigrid technique for finding the steady-state pressure distribution; simultaneously, the elasticity equation is solved with the multilevel multi-integration method. The numerical solution is achieved under isothermal conditions and considering the exponential variation of viscosity with pressure. The effect of micropolar parameters, i.e. nondimensional characteristics length defines the molecular length of the blended additives, and coupling number measures the coupling between the angular and linear momentum of molecules, and operating parameters are studied. Owing to the analysis, the pronounced effect of the micropolar parameters on the elastohydrodynamic lubrication of elliptical contacts is observed and which cannot be avoided. Lubricants added with solid additives and coupling between linear and angular momentum improved the overall film thickness and pressure and enhanced the load-carrying capacity. Also, a nominal rise in the traction coefficient is noticed, but this increase in the traction coefficient is quite less when compared to Newtonian fluids.

Model for Elastohydrodynamic Lubrication of Multilayered Materials

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Zhanjiang Wang ◽  
Chenjiao Yu ◽  
Qian Wang
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Functionally Graded ◽  
Material System ◽  
Multilayer Material ◽  
Influence Coefficients ◽  
Surface Displacements ◽  
Graded Material ◽  
Multilayered Materials ◽  
Novel Model

A novel model is constructed for solving elastohydrodynamic lubrication (EHL) of multilayered materials. Because the film thickness equation needs the term of the deformation caused by pressure, the key problem for the EHL of elastic multilayered materials is to develop a method for calculating their surface deformations, or displacements, caused by pressure. The elastic displacements and stresses can be calculated by employing the discrete-convolution and fast Fourier transform (DC-FFT) method with influence coefficients. For the contact of layered materials, the frequency response functions (FRFs), relating pressure to surface displacements and stress components, derived from the Papkovich–Neuber potentials are applied. The influence coefficients can be obtained by employing FRFs. The EHL of functionally graded material (FGM) can also be well solved using a multilayer material system. The effects of material layers and property gradient on EHL film thickness and pressure are further investigated.

A Thermal Elastohydrodynamic Lubrication Model for Crowned Rollers and Its Application on Apex Seal–Housing Interfaces

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Zhong Liu ◽  
David Pickens III ◽  
Tao He ◽  
Xin Zhang ◽  
Yuchuan Liu ◽  
...  
Keyword(s):  
Temperature Rise ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Frictional Heating ◽  
Elastohydrodynamic Lubrication ◽  
Design Equation ◽  
Rotary Engine ◽  
Influence Coefficients ◽  
Heavy Loads ◽  
Thermal Ehl

This paper presents a thermal elastohydrodynamic lubrication (EHL) model for analyzing crowned roller lubrication performances under the influence of frictional heating. In this thermal EHL model, the Reynolds equation is solved to obtain the film thickness and pressure results while the energy equation and temperature integration equation are evaluated for the temperature rise in the lubricant and at the surfaces. The discrete convolution fast Fourier transform (DC-FFT) method is utilized to calculate the influence coefficients for both the elastic deformation and the temperature integration equations. The influences of the slide-to-roll ratio (SRR), load, crowning radius, and roller length on the roller lubrication and temperature rise are investigated. The results indicate that the thermal effect becomes significant for the cases with high SRRs or heavy loads. The proposed thermal EHL model is used to study the thermal-tribology behavior of an apex seal–housing interface in a rotary engine, and to assist the design of the apex seal crown geometry. A simplified crown design equation is obtained from the analysis results, validated through comparison with the optimal results calculated using the current crowned-roller thermo-EHL (TEHL) model.

Elastohydrodynamic analysis of one-layered journal bearings

1998 ◽  
Vol 212 (3) ◽  
pp. 193-205 ◽  
Author(s):  
M Lahmar ◽  
A Haddad ◽  
D Nicolas
Keyword(s):  
Reynolds Equation ◽  
Mathematical Problem ◽  
Elastohydrodynamic Lubrication ◽  
Stability Margin ◽  
Journal Bearings ◽  
Perturbation Approach ◽  
Variable Approach ◽  
Load Carrying ◽  
Fast Solution ◽  
The Stability

Steady state and dynamic solutions to the problem of isothermal elastohydrodynamic lubrication of single-layered journal bearings are derived and presented. The mathematical problem comprises two parts: fluid and elasticity. The elasticity problem is governed by the elastostatic equations which are solved by application of a complex variable approach using the complex Kolosov-Muskhelishvili potentials. The fluid problem is described by the two-dimensional Reynolds equation which is discretized using a finite difference approach and solved by application of the Gauss-Seidel scheme with the Swift-Stieber boundary conditions. The fluid-structure coupling is achieved by an iterative procedure with an under-relaxation algorithm. The dynamic coefficients are obtained by use of a first-order perturbation approach. The results obtained show that the proposed elasticity model permits a fast solution of the problem, particularly under dynamic conditions. They also show that, under the effect of coating elastic deformation, the contact geometry is modified and the load-carrying capacity decreases while the stability margin of the journal bearing system increases.

A Study of Elastohydrodynamic Lubrication of a Centrally Loaded 120° Arc Partial Bearing in Different Flow Regimes

1983 ◽  
Vol 197 (2) ◽  
pp. 97-108 ◽  
Author(s):  
S C Jain ◽  
R Sinhasan ◽  
D V Singh
Keyword(s):  
Elastic Deformation ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Performance Characteristics ◽  
The Finite Element Method ◽  
Elasticity Equations ◽  
Laminar And Turbulent Flow ◽  
Deformation Coefficient ◽  
Three Dimensional Elasticity

The elastic deformation of the bearing liner is considered in determining the static and dynamic performance characteristics of the centrally loaded 120° arc bearing for eccentricity ratio up to 0.8 and mean Reynolds number up to 7500. Using the finite element method, the pressure distribution in the fluid film and the elastic deformation in the bearing shell are obtained by solving the Reynolds equation and the three-dimensional elasticity equations iteratively. The performance characteristics of the bearing are computed for different values of the deformation coefficient which is a measure of the flexibility of the bearing shell. In addition, some results are also reported for laminar and turbulent flow conditions treating viscosity as a function of pressure.

A Transient Model for Micro-Elastohydrodynamic Lubrication With Three-Dimensional Irregularities

1993 ◽  
Vol 115 (1) ◽  
pp. 102-110 ◽  
Author(s):  
Xiaolan Ai ◽  
Herbert S. Cheng ◽  
Linqing Zheng
Keyword(s):  
Reynolds Equation ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Asperity Height ◽  
Transient Model ◽  
Implicit Finite Difference Scheme ◽  
Line Contacts ◽  
Pressure Bump ◽  
Implicit Finite Difference ◽  
Newtonian Behavior

A transient model for micro-elastohydrodynamic lubrication with three-dimensional asperities in line contacts is presented in this paper. To take into account the effect of non-Newtonian behavior of lubricant, the Ree-Eyring viscous constitutive equation is employed in deriving Reynolds equation. The numerical solution of this model is based on an implicit finite difference scheme with under relaxation. Numerical simulation results show that the pressure bump caused by an asperity or asperities depends not only on asperity height and orientation but also on asperity dimension. The increase in asperity dimension decreases the pressure bump. The decrease in load and increase in sliding speed increases pressure bump.

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