Elrod Cavitation Algorithm Research Articles

An Algorithm for Starved Lubricated Journal Bearings With Optionally Locked Lube Oil Feed Grooves

Abstract Starved lubrication occurs intentionally or unconsciously in many journal bearing applications. However, the determination of its concrete distribution in a journal bearing is rather complex as the different lube oil feed grooves interact with each other due to their connection by the lubricant flow along the pad surfaces and the periodic geometric property of the entire bearing. A robust numerical procedure to determine the lube oil distribution between the different feed grooves in a starved lubricated fixed-pad journal bearing is presented as an extension to Elrod's cavitation algorithm. The enhanced algorithm partly integrates flow rate boundary conditions into the linear system of equations for the solution of Reynolds equation and the transport equation. A strategy to couple these flow rate boundary conditions with the iterative procedure to determine the binary cavitation index is proposed. In particular, the algorithm enables an appropriate modeling of lube oil grooves with locked oil supply including the consideration of groove-specific dissipation or design features like bleed notches. The novel algorithm is implemented as a submodule of a thermo-elasto-hydrodynamic bearing code and validated with test data for a high-speed two-lobe bearing with embedded arc. Furthermore, a comprehensive parametric study provides an insight on the robustness of the implemented numeric procedure. Results, current limitations, and possible extensions to the algorithm are discussed.

Issues related to the numerical simulation of herringbone grooved journal bearing including cavitation condition

This study aims to address the complexities involved in determining the numerical solution of herringbone grooved journal bearing considering cavitation. A modification is made to the Reynolds’ equation to include the effect of cavitation as given by Elrod's cavitation algorithm. Grid transformation is performed to consider the effect of the inclined grooves. The partial differential equation is discretised using finite-difference method. Then, the solution of the resulting set of equations is determined by the alternating-direction implicit method and the pressure, load capacity and attitude angle are obtained. Time step (Δ t) and Bulk modulus have a significant impact on the convergence of the numerical solution incorporating Elrod's cavitation algorithm. Use of alternating-direction implicit method over point by point method like Gauss–Seidel is essential to obtain convergence. Load capacity of the herringbone grooved journal bearing rises with the rise in eccentricity ratio. As compared to the Reynolds boundary conditions, Elrod's model results into lower attitude angle for herringbone grooved journal bearing. Cavitation distribution for herringbone grooved journal bearing is much lower than that of plain journal bearing. The effect of variation of groove angle on the herringbone grooved journal bearing's load capacity, side leakage and friction parameter is also determined. A detailed discussion on the various complexities such as treatment at groove ridge boundaries; numerical oscillations; choice of time step and bulk modulus; and influence of compressibility in the Couette term in full film region in the numerical analysis of herringbone grooved journal bearing specifically considering cavitation is given in this work. Multiple methods to deal with the aforementioned complexities are examined and appropriate solutions are obtained.

Reynolds Model versus JFO Theory in Steadily Loaded Journal Bearings

Cavitation has a potential effect on the performance of full circle journal bearings. This paper studied the effects of cavitation on steadily loaded journal bearings, with the purpose of analyzing the necessity of adopting a mass-conserving model for ordinary journal bearings. The Christopherson’s method and Elrod cavitation algorithm were implemented to represent the non-mass-conserving Reynolds model and the mass-conserving Jakobsson-Floberg-Olsson (JFO) theory, respectively. The difference in the oil film reformation boundaries predicted by the two methods was focused on. The typical performance parameters including oil film pressure, load-carrying capacity, attitude angle, friction force, and leakage were comprehensively compared. The results show that the load-carrying capacity is improved by the decrease in cavitation pressure, and the effect is significant in lightly loaded cavitated bearings. In non-cavitated cases and the cavitated cases with intermediate and heavy loads, the difference between the Reynolds model and the JFO theory can be effectively ignored, but the accuracy of the leakage predicted using the Reynolds model should be carefully evaluated.

Elasto-Hydrodynamic Model of Hybrid Journal Bearings for Aero-Engine Gear Fuel Pump Applications

Abstract Gear pumps are largely employed in aero-engine fuel systems to provide the combustor with fuel at adequate pressure and flow rate. The radial load applied on the gears, as a consequence of the pump pressure rise, is entirely supported by the hybrid journal bearings. Lubrication of these is accomplished using low viscosity aviation fuel, which makes the design and analysis of journal bearings particularly challenging. A numerical model has been developed to support the analysis and future design of hybrid journal bearings for fuel pump applications. The primary objective of the tool is to characterise the equilibrium position of the journal during steady-state operation at part and full load, where the resultant elastic displacements are more significantly affecting the pressure distribution of the lubrication film. The developed method effectively combines Elrod's cavitation algorithm with the dimensionless pressure definition known as the Vogelpohl parameter, resulting in a simple and robust methodology to characterise the pressure distribution within the lubricant for different bearing designs and operating conditions. Six different multidimensional root-finding solvers have been implemented and their performance evaluated against robustness, accuracy and computational speed requirements. Newton-Raphson based methods have shown promising trade-offs for the problem at hand. Validation of the tool has been made comparing experimental film thickness measurements, performed on a fuel pump from a modern turbofan engine, with predicted data from the numerical model.

Investigating the effect of different slip zone locations on the lubrication performance of textured journal bearings

Purpose This study aims to purpose the suitable location of slip boundary condition and microscale surface textures to enhance the tribological performance of the hydrodynamic journal bearings. Design/methodology/approach Mass conserving Elrod cavitation algorithm with considering slip boundary condition has been used for predicting the static performance characteristics (load carrying capacity, coefficient of friction and volumetric inflow rate) of finite cylindrical shape textured journal bearings. Findings It has been observed that the full textured bearing with slip boundary condition in between 0°–180° circumferential region gives a significant reduction in the lubricant rupture zone. However, the introduction of textures up to the interface of slip and the no-slip region is increasing the load-carrying capacity and reduces the shear stress. This reduction in shear stress with combined slip and surface textures is effective in increasing the volumetric inflow rate of the lubricant. Practical implications The combined effect of slip boundary condition and surface texturing is increasing the scope of liquid lubricants in hydrodynamic journal bearings and further contributing toward the development of small-scale rotating machines. Originality/value The study related to the use of mass conserving Elrod cavitation algorithm for finding the optimum location of slip and surface texture zones has been found rare in the literature. Previous studies show that the mass conserving Elrod cavitation algorithm gives realistic results for textured bearings and its findings show good agreement with the experimental observations.

Two-scale homogenization of hydrodynamic lubrication in a mechanical seal with isotropic roughness based on the Elrod cavitation algorithm

A two-scale homogenization method for modelling the hydrodynamic lubrication of mechanical seals with isotropic roughness was developed and presented the influence of surface topography coupled into the lubricating domain. A linearization approach was derived to link the effects of surface topography across disparate scales. Solutions were calculated in a polar coordinate system derived based on the Elrod cavitation algorithm and were determined using homogenization of periodic simulations describing the lubrication of a series of surface topographical features. Solutions obtained for the hydrodynamic lubrication regime showed that the two-scale homogenization approach agreed well with lubrication theory in the case without topography. Varying topography amplitude demonstrated that the presence of surface topography improved tribological performance for a mechanical seal in terms of increasing load-carrying capacity and reducing friction coefficient in the radial direction. A Stribeck curve analysis was conducted, which indicated that including surface topography led to an increase in load-carrying capacity and a reduction in friction. A study of macro-scale surface waviness showed that the micro-scale variations observed were smaller in magnitude but cannot be obtained without the two-scale method and cause significant changes in the tribological performance.

Numerical optimization of surface texture for improved tribological performance of journal bearing at varying operating conditions

PurposeJournal bearings are used in numerous rotary machines. The load carrying capacity and friction of a bearing have been major concerns in design. Recent developments in surface texturing have showed potential outcomes to improve the tribological characteristics of mating surfaces. This study aims to investigate surface textures, which are transverse to the sliding direction, for frictional response of the journal bearing.Design/methodology/approachA hydrodynamic lubrication model is considered to evaluate the effect of surface texturing on the performance of a journal bearing at varying operating conditions. The two-dimensional generalized Reynolds equation, coupled with mass-conserving Elrod cavitation algorithm, is solved to evaluate texture-induced variations in tribological performance parameters.FindingsResults have showed remarkable improvements in frictional response. Moreover, micro-textures on the journal surface alter the cavitation response and film-reformation in the hydrodynamic conjunction of the plain bearing.Originality/valueOperating condition-based comprehensive exhaustive optimization of texture geometry is performed to generate widespread conclusion.

Thermo-Mixed Hydrodynamics of Piston Compression Ring Conjunction

A new method, comprising Navier–Stokes equations, Rayleigh–Plesset volume fraction equation, an analytical control-volume thermal-mixed approach and asperity interactions, is reported. The method is employed for prediction of lubricant flow and assessment of friction in the compression ring–cylinder liner conjunction. The results are compared with Reynolds-based laminar flow with Elrod cavitation algorithm. Good conformance is observed for medium load intensity part of the engine cycle. At lighter loads and higher sliding velocity, the new method shows more complex fluid flow, possessing layered flow characteristics on the account of pressure and temperature gradient into the depth of the lubricant film, which leads to a cavitation region with vapour content at varied volume fractions. Predictions also conform well to experimental measurements reported by other authors.

A Modification of the Switch Function in the Elrod Cavitation Algorithm

The implementation of the mass-conservative cavitation algorithm, as derived by Elrod, requires an automatic setting of a binary switch function that delineates the full-film and cavitation zones. Abrupt changes associated with this function often causes convergence and instability issues. A method is that which improves numerical instability and overcomes the convergence issues caused by the conventional binary switch function. Two test cases are presented, which show that by using the new switching algorithm together with a successive over-relaxation solver, the Elrod cavitation algorithm converges up to 61% faster while it is less prone to numerical instabilities.

Surface Roughness and Pressure Effect on Viscosity in Elastohydrodynamic Lubrication Model of Engine Bearings (Friction)

In this study, Patir and Cheng's surface roughness model is introduced in a mass conserving elastohydrodynamic lubrication model of a dynamically loaded journal bearing and described consistent with the model of regular striations. The lubrication model is based on a modified Elrod's cavitation algorithm and pressure effect on viscosity is expressed by Barus's equation. The model was applied to a con-rod big-end bearing of an engine and the effect of surface texture, roughness and striations, on friction power loss was calculated. The friction power loss of the bearing with circumferential striations is the lowest and is as much as that of the bearing with a smooth surface. The friction power loss of the bearing with transversal striations is the highest. The friction power losses of the bearing with the surface roughness take the value between them according to directional ratio. The results also showed the pressure effect on viscosity plays an important role in the friction power loss.

A Legendre collocation method for thermohydrodynamic journal-bearing problems with Elrod's cavitation algorithm

A Legendre collocation method is proposed for journal-bearing problems. The model combines the Legendre collocation method, the bulk-flow model and Elrod's cavitation algorithm. The Legendre collocation method is used to solve the momentum equations and energy equation to determine the velocity and temperature distributions while the pressure is determined by solving the bulk-flow equations using the SIMPLER scheme. This model can analyze a wide range of problems from laminar to turbulent flow with or without thermohydrodynamic (THD) effects, and resolve the detailed flow structure such as the temperature distribution near the wall region in the turbulent THD case.

Mass Conserving Elastohydrodynamic Lubrication Model of Engine Bearings Having Regular Striations

Regular striations exist on bearing surfaces due to machining. In this study, a mass conserving elastohydrodynamic lubrication model of an engine journal bearing having regular striations on a surface has been developed for analyzing lubrication characteristics. The model is based on a modified Elrod's cavitation algorithm and a theory of surface roughness. The cross sectional shape of the regular striations is formed into by isosceles trapeziums. The model was applied to a con-rod big-end bearing and the effect of striations on friction power loss was calculated. Friction power loss of the bearing with circumferential striations is lower than that of the bearing with transversal striations and is as much as that of the bearing with a smooth surface. The calculated results of the model were compared with those of an elastohydrodynamic lubrication model without cavitation algorithm. Though the calculated values are slightly different, the same tendencies are obtained.

Lubrication regime transitions at the piston ring-cylinder liner interface

An experimental apparatus and an analytical model have been developed to investigate and determine the lubrication condition and frictional losses at the interface between a piston ring and cylinder liner. In order to obtain a solution for the lubrication condition between the piston ring and cylinder liner, the system of Reynolds and film thickness equations subject to boundary conditions were simultaneously solved. The effects of boundary and mixed lubrication conditions were implemented using the Greenwood-Tripp stochastic approach. The Elrod cavitation algorithm was used to investigate the effects of fluid rupture and reformation at the top and bottom dead centres. The experimental results indicate that the piston ring and liner experience all the different lubrication regimes (i.e. boundary, mixed, and hydro-dynamic lubrication) during a stroke. A comparison between experimental and analytical results indicated that they are in good agreement and the analytical model developed for this study can capture the different lubrication regimes that the piston ring and liner experience.

Stability Analysis of a Rough Journal Bearing Considering Cavitation Effects

A modified governing equation is derived incorporating the effects of roughness and cavitation in a journal bearing. The available theories of Reynolds roughness and cavitation algorithm proposed by Elrod are utilized in this work to develop a numerical procedure for stability analysis of a liquid lubricated rough journal bearing. The Elrod generalized theory of Reynolds roughness provides a governing equation based on the surface configuration. The Elrod cavitation algorithm conserves mass throughout the bearing and automatically predicts the full film and cavitation regions using a switch function. The roughness is considered on either or both the bearing and journal surfaces. The instability threshold speed increases significantly for the roughness patterns on the grooved bearing surface only at higher eccentricity ratios. The threshold speed increases significantly with increase in the inclination of herringbone type striated roughness patterns on the journal surface from 110° to 150°.

Mass Conserving Elastohydrodynamic Lubrication for Con-Rod Bearings with an Oil Passage (3rd Report, Comparison with Measured Oil Flow Rate)

In the 1st report, the Elrod's cavitation algorithm was modified and applied to the mass conserving elastohydrodynamic lubrication, EHL, theory with a simple model of oil flow in an oil passage. In the 2nd report, the feature of the mass conserving EHL with oil passage was shown in comparison with the conventional EHL. In this report, the oil flow rate to a con-rod big-end bearing of an experimental engine was measured using a hot film anemometer under many operating conditions. The experimental results were compared with the theoretical calculations using the mass conserving EHL with oil passage. The theoretical cycle averaged oil flow rates to con-rod big-end bearing qualitatively agreed with the experimental ones.

The effects of surface irregularities on the performance characteristics of flexible finite journal bearings lubricated with couple stress fluids

AbstractA numerical solution for the elastohydrodynamic lubrication of finite journal bearings is presented. Couple stress effects resulting from blending the lubricant with various additives are considered. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearings, is implemented in the solution scheme. A simple elastic model is used to describe the elastic deformation of the bearing liner. Furthermore, the effects of surface waviness on the performance of the bearing are incorporated into the analysis. A comprehensive study illustrates the effects of couple stress, liner flexibility, and surface waviness on the steady‐state performance of finite‐width journal bearings. The results show that these effects should be considered at higher values of the eccentricity ratio.

A study of a journal bearing lubricated by couple stress fluids considering thermal and cavitation effects

A theoretical study of a finite grooved journal bearing lubricated with couple stress fluids is made considering both thermal and cavitation effects. On the basis of the Stokes couple stress fluid model, the modified Reynolds equation and the energy equation are derived and then numerically solved together with the heat conduction equation. The solution to the modified Reynolds equation is determined using the Elrod cavitation algorithm. The effects of couple stress on the performance of a journal bearing are investigated. It is observed that the lubricants with couple stress, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in coefficient of friction but also produce a slight increase in the temperature of lubricants and bush and a slight decrease in the side leakage flow.

Mass Conserving Elastohydrodynamic Lubrication for Con-Rod Bearings with an Oil Passage. 2nd Report, Comparison with Previous Methods.

In the 1st report, the Elrod's cavitation algorithm was modified and applied to the mass conserving elastohydrodynamic lubrication, EHL, of a con-rod bearing with a simple model of an oil passage. In this report, the modified Elrod's cavitation algorithm and the mass conserving EHL with oil passage were compared with the conventional method with the Murty's algorithm. The Elrod's cavitation algorithm modified in the 1st report was also compared with that of original one and that modified by Vijayaraghavan and Keith to clarify the effect of density in full film zone. The mass conserving EHLs with and without oil passage were applied to a con-rod bearing with practical clearance shape under full load operating conditions of an engine to clarify the effect of oil passage.

Performance of a Plain Journal Bearing with Flooded Ends

An analysis for an incompressible plain hydrodynamic journal bearing operating with flooded ends is presented. Examples of such applications include completely submerged bearings, bearings supplied by oil rings, and bearings with flooded lubricant supplies at their ends. A variation of El rod's cavitation algorithm developed by Vijayaraghavan and Keith is used to predict pressures and load capacities as a function of eccentricity ratio and the cavitation pressure in bearings with constant viscosity lubricants. A normalized cavitation parameter is introduced that incorporates the cavitation pressure of the lubricant, the geometry of the bearing, and the operating conditions. General results are presented in terms of normalized parameters that can be used to determine the performance of specific bearings.

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.