Full Film Region Research Articles

Study on the mixed lubrication of rough planar extrusion considering surface texture

Surface texture plays a crucial role in fluid dynamic lubrication. The non-Newtonian thermal elastohydrodynamic lubrication problem involving rough surfaces with texture has not been investigated to date. In this paper, a model for non-Newtonian thermal elastohydrodynamic lubrication incorporating rough surfaces and texture morphology is developed, focusing on the problem of mixed lubrication in planar extrusion with texture. The model builds upon the Reynolds equation with flow factor introduced. It considers the effects of rough surface texture, thermal effects, and non-Newtonian effects. The Reynolds equation is numerically solved using the Semi-System method to calculate the oil film pressure in full film region and contact pressure in dry contact area. The DC-FFT algorithm is employed to calculate surface elastic deformation. Comparing the calculated friction coefficient of the present model with the measured values in literature experiments, the average error is only 6.94%. Furthermore, the study investigates the effects of texture, temperature, and non-Newtonian on interfacial lubrication performance under mixed lubrication conditions. It’s found that compared to untextured surface, the average film thickness of textured surface increased by a maximum of 10.8%, and the friction coefficient decreased by a maximum of 67.4%; Compared to Newtonian fluids, shear thinning fluids reduce temperature by 0.18%, and shear thickening fluids are more conducive to improving mixed lubrication performance. A stepped pit texture is designed based on the dynamic pressure mechanism of the texture, indicating that the circular stepped pit texture has the best load-bearing capacity improvement.

A Modified Discrete Scheme in the Ausas Cavitation Algorithm

Abstract In order to reduce the dependence of accuracy on the number of grids in the Ausas cavitation algorithm, a modified Ausas algorithm was presented. By modifying the mass-conservative Reynolds equation with the concept of linear complementarity problems (LCPs), the coupling of film thickness h and density ratio θ disappeared. The modified equation achieved a new discrete scheme that ensured a complete second-order-accurate central difference scheme for the full film region, avoiding a hybrid-order-accurate discrete scheme. A journal-bearing case was studied to show the degree of accuracy improvement and the calculation time compared to a standard LCP solver. The results showed that the modified Ausas algorithm made the asymptotic and convergent behavior with the increase of nodes disappear and allowed for the use of coarse meshes to obtain sufficient accuracy. The calculation time of the modified Ausas algorithm is shorter than that of the LCP solver (Lemke’s pivoting algorithm) for middle- and large-scale problems.

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.

An Efficient Cavitation Model for Compressible Fluid Film Bearings

This article presents an efficient cavitation model for fluid film bearings, considering both gaseous and vaporous cavitation. This work presents a modification of Elrod’s cavitation algorithm, where the bulk fluid is similarly considered to be a mixture of liquid and bubbles, without the need for a switch function. By solving for properties of the bulk fluid in the film, the distribution of the gaseous, vapor, and liquid states is captured without detailed tracking of bubble dynamics, as well as the variable compressibility of the bulk fluid in both ruptured and full film regions. The model developed is implemented in a numerical algorithm to solve the compressible Reynolds equation. Finally, the approach developed is applied to test cases to demonstrate its potential, as well as for comparison with Elrod’s algorithm.

Performance of hydrodynamic journal bearing under the combined influence of textured surface and journal misalignment: A numerical survey

A wisely chosen geometry of micro textures with the favorable relative motion of lubricated surfaces in contacts can enhance tribological characteristics. In this paper, a computational investigation related to the combined influence of bearing surface texturing and journal misalignment on the performances of hydrodynamic journal bearings is reported. To this end, a numerical analysis is performed to test three texture shapes: square “SQ”, cylindrical “CY”, and triangular “TR”, and shaft misalignment variation in angle and degree. The Reynolds equation of a thin viscous film is solved using a finite differences scheme and a mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. Preliminary results are compared with benchmark data and are consistent with a positive enhancement in misaligned bearing performances (load carrying capacity and friction). The results suggest that the micro-step bearing mechanism is a key parameter, where the micro-pressure recovery action present in dimples located at the second angular part of the bearing (from 180° to 360°) can compensate for the loss on performances caused by shaft misalignment, while the micro-pressure drop effect at the full film region causes poor performances. Considering the right arrangement of textures on the contact surface, their contours geometries can have a significant impact on the performance of misaligned journal bearings, particularly at high eccentricity ratios, high misalignment degrees and when the misalignment angle α approaches to 0° or 180°.

A mixed lubrication model for studying tribological behaviors of surface texturing

An analytical numerical model is specifically developed to understand the tribological behavior of textured surface in mixed lubrication regime. The model employs the average flow Reynolds equation and an elasto-plastic contact model, established on the basis of finite element analysis, to calculate (i) the hydrodynamic pressure in full film region and (ii) the contact pressure in contact region, respectively. Fast Fourier transform (FFT) method is used to compute the elastic deformation of substrate. It is able to simulate Stribeck curve for the textured surface. Predictions demonstrate surface texturing reducing friction coefficient. Studies on the tribological influence of texture shape, depth, distance and diameter are also performed.

A mixed lubrication model with consideration of starvation and interasperity cavitations

This article presents a mixed lubrication model for point contacts with considering the inlet starvation and interasperity cavitations. The pressure distribution on the entire computational domain is obtained through solving a unified Reynolds equation system without identifying hydrodynamic or asperity contact regions. The Jacobsson–Floberg–Olsson mass-conservative boundary conditions are incorporated in the lubrication analysis based on Elrod’s algorithm. The inlet oil supply condition which may bring about starvation and local cavitation phenomenon is considered by defining the inlet lubricant thickness distribution. The fast Fourier transform based technique is employed to speed up the surface deformation calculation. A unique solution scheme is constructed to solve full film region, cavitation region, and contact region simultaneously. The model has been applied to the lubrication problems of textured surface under starved conditions. Numerical examples are analyzed and the results show that the present model can be used to investigate the lubrication performance under starved conditions, and that the solution methods are computationally efficient and robust.

Analysis of Single-Grooved Slider and Journal Bearing With Partial Slip Surface

In this paper, pressure and shear stress are derived under steady state using one-dimensional analysis of the single-grooved slider bearing and journal bearing with partial slip on the stationary surface. The Reynolds boundary conditions are used in the analysis of journal bearing to predict the extent of the full film region. In the cases of partial slip slider and journal bearing, the pressure distribution is higher compared with the conventional bearing with no slip. In the case of partial slip on both slider and journal bearing surfaces, the single-groove, immediately followed by the partial slip region, results in the increase in pressure distribution. The results also show that in comparison to the conventional bearing with no slip, in the cases of partial slip slider and journal bearing, the shear stress increases before the region of slip/no slip interface, while the shear stress decreases in the region of no slip. In the case of the partial slip region on bearing surfaces, the shear stress distribution is lower in the region immediately after the groove. Significant pressure distribution is obtained due to the influence of partial slip on the slider bearing with uniform film thickness and the concentric journal bearing. The maximum pressure occurs at the end of the region of groove, immediately followed by the region of the partial slip. It is found that the pressure distribution of the slider and journal bearing with partial slip surface are not influenced with the further increase in the nondimensional slip coefficient (A) from 10 to 100.

HISTORY MOVING OF CAVITATION FOR DYNAMICALLY LOADED JOURNAL BEARING

On the base of the Elrod algorithm, a generalized equation is derived to describe the lubrication in full film region and in cavitation region of dynamically loaded journal bearing, which is nominated as the incompressible mass-conserving cavitation algorithm. A numerical technique with this algorithm has been solved. By the definition of a switch function g and a variable ξ, which have different meaning in different zone, a generalized equation is derived to integrate the Reynolds equation in full film region with the lubrication equation in cavitation region. This algorithm can predict the moving oil boundary automatically and make the mass conserving boundary condition (JFO theory) more easily and precisely to be applied in actual analysis. It is found that the analysis results with the incompressible mass-conserving cavitation algorithm have good agreement with the existing experiment data. The incompressible cavitation algorithm can predict the history moving of cavitation well. And it is also shown that the pressure value in the cavitation has great effect on the analysis results.

Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects

A numerical study of the non-Newtonian behavior for a finite journal bearing lubricated with micropolar fluids is undertaken considering both thermal and cavitating effects. The modified Reynolds equation and energy equation are derived based on Eringen's micropolar fluid theory. The solution to the modified Reynolds equation is determined using the Elord's cavitation algorithm. The effects of the size of material characteristic length and the coupling number on the thermohydrodynamic performance of a journal bearing are investigated. It is shown, compared with Newtonian fluids, that micropolar fluids exhibit the increase in load capacity and temperature, but the decrease in coefficient of friction and side leakage flow. It is also indicated that, in the full film region, micropolar fluids increase the values of non-dimensional density, while in the cavitated region, both micropolar fluids and Newtonian fluids yield the same values of the fractional film content.

Stability Characteristics of Herringbone Grooved Journal Bearings Incorporating Cavitation Effects

Stability characteristics of the herringbone grooved journal bearings (HGJBs) are analyzed taking into account cavitation of the fluid flow. The perturbed values of pressure and film thickness from a given equilibrium position are substituted into the Elrod’s universal equation, which considers mass conservation in the complete bearing geometry. In order to analyze the herringbone groove configuration, the governing equations under steady and perturbed states are transformed to a rectangular domain using the grid transformation techniques. It is assumed that under perturbed conditions, the cavitation extent in the bearing remains unchanged and the pressure gradients are computed in the full film region. The linearized stiffness and damping coefficients are evaluated in the complete bearing geometry from the predicted values of pressure gradients. The threshold speed parameter and whirl frequency ratio are computed using the linearized stability analysis. Results are generated for various eccentricity ratios and groove angles. The results of this study validate the use of HGJBs at the very higher operating speeds (at concentric journal operation) in rotating machinery.

Linear Stability Analysis for a Hydrodynamic Journal Bearing Considering Cavitation Effects

The purpose of this paper is to present the two-dimensional linear stability analysis considering the fluid flow in both full film and cavitation regions for a plain cylindrical journal bearing. The Lund's infinitesimal perturbation procedure is applied to Elrod's universal equation for evaluation of unsteady pressure gradients. Based on JFO theory, the pressure distribution, film rupture, and reformation boundaries can be obtained using Elrod's universal equation, for a given operating position of the journal. In this work, it is assumed that for infinitesimal perturbation of a journal about the equilibrium position, the film rupture and film reformation boundaries are the same as those obtained for steady state. However, the unsteady pressure gradients in the full film region are evaluated taking into consideration the perturbed flow parameters in the cavitation region, i.e., at both rupture and reformation boundaries. The linearized stiffness and damping coefficients, whirl frequency ratio, and threshold speed for various values of eccentricity and L/D ratios are obtained for a plain cylindrical journal bearing with an axial groove along the load line. Measured data of dynamic coefficients for a 120° partial arc bearing are chosen for comparison with this work. Results show good agreement between the theoretical and experimental results. Presented at the 57th Annual Meeting in Houston, Texas May 19–23, 2002

A Study on Nonlinear Frequency Response Analysis of Hydrodynamic Journal Bearings With External Disturbances

The nonlinear vibration characteristics of hydrodynamic journal bearings with a circumferential groove are analyzed numerically in case that external sinusoidal disturbances are given to the rotor-bearing system. The cavitation algorithm implementing the Jakobsson-Floberg-Olsson boundary condition is adopted to predict cavitation regions in the fluid film. The comparison of the steady state journal orbits using linear dynamic coefficients with the transient motion calculated from nonlinear analysis is performed. The frequency response functions obtained by linear and nonlinear analysis are also presented. When an external sinusoidal disturbance is applied to the bearing, the range of the full film region varies periodically and it becomes smaller than that of static equilibrium state. The difference between linear and nonlinear analysis increases as the excitation amplitude or the frequency of the external disturbance increases. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in San Francisco, CA October 21–24, 2001

Analytical Solution of Piston Ring Lubrication Using Mass Conserving Cavitation Algorithm

A novel analytical approach for piston ring lubrication solution is presented by taking proper account of mass conservation in the cavitated region (JFO boundary conditions). A system of five nonlinear equations is employed to calculate such parameters as oil film thickness, frictional force, power loss, and oil flow rate. For an enclosed cavitation pattern in piston-ring assembly it was found, that JFO boundary conditions give much better accounting of the estimation of friction force, power loss and flow rate. To show the effectiveness of the undertaken approach, the widely accepted Jeng's approach (Jeng, 1992a) was selected, in which the pressure contribution from the cavitated and the second full film regions, as well as the trailing edge pressure, are ignored. Presented as a Society of Tribologiats and Lubrication Engineers Paper at the STLE/ASME Trlbology Conference in Orlando, Florida, October 11–13, 1999

Analytical Solution of Piston Ring Lubrication Using Mass Conserving Cavitation Algorithm

A novel analytical approach for piston ring lubrication solution is presented by taking proper account of mass conservation in the cavitated region (JFO boundary conditions). A system of five nonlinear equations is employed to calculate such parameters as oil film thickness, frictional force, power loss, and oil flow rate. For an enclosed cavitation pattern in piston-ring assembly it was found, that JFO boundary conditions give much better accounting of the estimation of friction force, power loss and flow rate. To show the effectiveness of the undertaken approach, the widely accepted Jeng's approach (Jeng, 1992a) was selected, in which the pressure contribution from the cavitated and the second full film regions, as well as the trailing edge pressure, are ignored. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

An Elastohydrodynamic Cavitation Algorithm for Piston Ring Lubrication

An elastohydrodynamic cavitation algorithm is developed for piston ring lubrication. This algorithm combines a compressible fluid model, a pressure-viscosity relation and elastic surface deformation with cavitation. Also, it conserves mass flow and automatically determines full film, cavitation and pressure reformation regions. Results for a typical automotive engine reveal that the pressure calculated by using the Reynolds boundary condition leads to a large error in pressure in the full-film region and, in turn, affects the film thickness prediction. Piston ring lubrication using the Reynolds boundary condition is considered to be valid only when the pressure acting on the trailing edge of a piston ring is negligible. Presented at the 49th Annual Meeting in Pittsburgh, Pennsylvania May 1–5, 1994

Dynamic Behavior of Oil Film between Piston Ring and Cylinder Liner : Visualization of Oil Film Rupture and Measurement of Oil Film Pressure Using Simulating Rig

In order to clarify the behavior of oil film between a piston ring and cylinder liner, pressure measurement and visualization of oil film are carried out simultaneously using a simulation rig. In this rig, the piston ring is simulated by a straight glass bar test piece and the cylinder by a reciprocating flat plate. The following observations were obtained. The oil film pressure of the full film region before oil film rupture is negative and the maximum magnitude of negative pressure, i.e., tension, reaches to 0. 35 MPa. Cavities are formed at 20°-30° crank angle from dead center in the full film region, and grow with the increase of the crank angle. Then a new series of cavities is formed at the rear edge of the test piece. The two series of cavities then coalesce and the flow becomes perturbed momentarily. Negative pressure is detected at a 20°-30° crank angle after dead center and is not released until this coalescence of cavities has occurred.

A Study on the Dynamic Behavior of Oil Film between Piston Ring and Cylinder Liner. 1st Report, The Visualization of Oil Film Rupture Using Simulating Rig.

In order to verify the prediction concerning the conditions of oil film rupture and the phenomenon of transition between the separation boundary condition and the Reynolds' condition, the region of oil film rupture and the process of development of cavitation were visually observed using a test rig with a glass test piece (straight bar) as the piston ring and reciprocating flat plate as the cylinder liner. As a result, we found that cavities are formed at 20°∼30° crank angle from dead center (DC) in the rear, full film region where the negative pressure is predicted, and grow as the crank angle is increased. Then, a new series of cavities is formed at 50°∼60° from DC at the rear edge of the test piece. These two series of cavities then coalesce and the flow becomes turbulent momentarily, indicating that the pressure in the cavities forms at 20°∼30° after DC is negative and is released when the coalescence occurs.