Journal Bearing Of Finite Length Research Articles

Finite element analyses of rotor/bearing system using second-order journal bearings stiffness and damping coefficients

The rotor-bearing system is a crucial component of rotating machinery, such as turbines, pumps, compressors, and turbogenerators, which are widely used in various advanced engineering fields. This work presented a methodology for studying the behavior of an elastic Jeffcott rotor supported by two similar fluid film journal bearings. A finite element model using consistent matrix formulation was employed to simulate the shaft, including the external load, with four degrees of freedom per node. The small perturbation method was used to evaluate the second-order bearing coefficients of a journal bearing of finite length. These coefficients were further integrated with the finite element model to evaluate the dynamic response of the flexible rotors. Moreover, the system equations of motion were presented in dimensional form. The results of the second-order bearing coefficients analysis agreed with nonlinear analysis when the speed was less than the threshold speed, while there was a pronounced difference in second-order analysis when the speed was above the threshold speed. The behavior of the rotor-bearing system was studied using dynamic response and orbit diagrams, revealing that changes in rotational speed significantly affected the rotor’s stability.

Approximating fluid bearing characteristics using polynomials for the nonlinear dynamics of rotating machines

Modeling the nonlinear dynamics of rotors supported by finite length journal bearings is of great importance in various engineering applications. In this study, four-dimensional polynomial functions are evaluated to represent the nonlinear hydrodynamic force based on a previously evaluated database. These functions are then used to model the dynamics of flexible rotor/bearing systems. The quasi statics and dynamics of rotor-bearing systems are investigated, and the results are compared with the numerical solution obtained by solving the Reynolds equation at each timestep. The findings indicate that the current analysis yields favorable agreement with the direct solution of Reynolds equation in both perturbation analysis from the equilibrium position and dynamic analysis. Moreover, the analysis reveals that the computational time required to solve the dynamics of rotor-bearing systems is significantly lower than that of solving Reynolds equation at each timestep to acquire the bearing forces.

Effect of Chamfer Form and Parameters on the Characteristics of Finite Length Journal Bearing under Impact Load

Journal bearings in typical applications are subjected to misalignment due to several causes, such as shaft deformation under load and errors related to the installation and manufacturing processes. Misalignment has well-known severe negative consequences on the performance of the bearings. This paper deals with the bearing chamfer to reduce these consequences of misalignment, and two forms of bearing edge modification are considered in the analysis. These forms are linear and curved chamfering of the bearing edges, where the height of the chamfer in the circumferential direction and the length of the modification in the longitudinal direction are considered as geometrical design parameters. The investigation includes a numerical solution of the hydrodynamic lubrication problem of finite length journal bearing, considering 3D misalignment cases using the finite difference method. This includes the assessment of the chamfer forms and their effects on the bearing performance in terms of the main bearing design parameters. Furthermore, the stability of the chamfered bearings is also investigated under impact load. Results showed that both chamfer forms are beneficial for a certain limit of the design parameters in reducing the maximum pressure and coefficient of friction and in elevating the film thickness levels, extending the range of misalignment in which the journal bearing can operate safely. In addition, the chamfered bearings in both forms showed more stability range in terms of the critical speed and shaft center trajectories under impact load. The bearings with the curved chamfer, where the slope is continuous at the start of modification, showed more uniform film thickness levels, and their shaft center trajectories were closer to the perfectly aligned bearing in the stable operating range of the system.

Analysis of the Performance of Chamfered Finite-Length Journal Bearings under Dynamic Loads

Misalignment is one of the most common challenges that the normal operation of journal bearings faces. This type of problem may be the result of a wide range of reasons, such as bearing wear, shaft deformation, and errors related to the manufacturing and installation process. The main undesirable consequences of the misalignment, such as pressure rise and lubricant film reduction, are concentrated on the bearing edges. Therefore, chamfering the bearing edges reduces such misalignment-related drawbacks. This work presents a novel numerical solution to the problem of finite-length journal bearing considering edge chamfering. This solution involves the determination of the levels of lubricant layer thickness and pressure distribution in addition to the journal trajectory under impact load with the related stability limits. The finite difference method is used in this solution, and the equations of motion are also solved numerically using the Runge–Kutta method. The Results of this novel analysis show that chamfering the bearing edges increases the film thickness and reduces pressure spikes associated with the system operation under the case of 3D misalignment. Furthermore, the chamfered bearing shows a wide stability range under impact loads, where the normal bearing is unstable as the critical speed increases by 26.98%, which has positive consequences on the journal’s trajectory.

Minimizing Misalignment Effects in Finite Length Journal Bearings

This paper focuses on a method to reduce the detrimental effects that occur due to the misalignment in journal bearings by approaching it with the more complete model of a finite length bearing. Such a drawback is quite common in industrial applications, and it is generally accepted that misalignment causes a significant thinning in the film thickness in the area that is close to the bearing edges. Therefore, removing a certain volume of material from the inner surface of the bearing (bushing) over a distance that is at the bearing edges provides an additional clearance to compensate for the clearance reduction that is due to misalignment. A numerical solution that is used in this work is based on the finite difference method where the Reynolds boundary conditions are considered in the solution scheme, thereby, using an iterative procedure to identify the cavitation zone. A three-dimensional misalignment model is incorporated in the solution in order to provide a more realistic presentation of the deviations and errors that there are in comparison with the ideal aligned case. It has been found in the present work that the edge modification increases the thickness of the lubricant layer considerably and reduces the pressure spikes that are associated with the presence of misalignment. The suggested design also reduces the coefficient of friction in comparison with that of the misaligned case. Furthermore, this method helps in reducing the asymmetry of the hydrodynamic pressure field that results from the misalignment. This method enables the operation of journal bearings over a wider range of misalignment levels without sacrificing the load-carrying capacity of the bearing by maintaining a relatively thicker layer of lubricant at the critical positions that are not so due to the effects of misalignment.

CFD ANALYSIS OF THERMOHYDRODYNAMIC BEHAVIOR OF NANOLUBRICATED JOURNAL BEARINGS CONSIDERING CAVITATION EFFECT

The present work displays an extensive numerical analysis for the thermo-hydrodynamic (THD) behavior in finite length journal bearings lubricated with different types of nano-lubricants considering cavitation effect. The effects of nanoparticle concentrations, cavitation and temperature rise on the performance parameters of such bearings have been explored. The bearing is simulated using Computational Fluid Dynamic (CFD) approach. The effect of using different types of nano-lubricants with different volume fractions of TiO2 and Al2O3 nanoparticles dispersed in Veedol Avalon ISO Viscosity grade 46 oil has been demonstrated. Modified Krieger-Dougherty equation has been implemented with the thermal viscosity model to to evaluate the oil effective viscosity. The obtained results show that concerning the TiO2 nanoparticles results in a higher oil film pressure and load carrying capacity in comparison with Al2O3. The bearing equilibrium position was obtained by using Response Surface analysis (RSA) with optimal space-filling design technique. The numerical model was validated by comparing the results obtained in the present work with that obtained by Feron et al. The results were found to be in a good confirmation. The attained results show that the maximum pressure grows by 21% when the bearing is lubricated with nano-lubricant.

Effects of linear modification on the performance of finite length journal bearings

Journal bearings are widely used in industry due to their favourable characteristics such as relatively low cost of manufacturing and maintenance, high load carrying capacity, and useful dynamic characteristics for rotor systems. Journal bearing misalignment, however, may have negative consequences for the general performance of this type of bearing. Misalignment commonly occurs due to errors in manufacturing tolerances, installation errors, wear, shaft deflection, and asymmetrical loading of systems. This paper presents a solution for hydrodynamic problems in journal bearings of finite length based on a 3D misalignment model and linear modification of the bearing profile to reduce the effect of misalignment on the characteristics of the journal bearing. The results showed that linear modification of misaligned journal bearings reduces the maximum pressure and improves the level of film thickness; additionally, the dynamic characteristics of the journal bearing are also improved by such linear profile modification.

Behaviour of hydrodynamic journal bearing under the combined influence of textured surface and Non-Newtonian Rabinowitsch fluid model

In the present study, the static characteristics of hydrodynamic circular journal bearings of finite length are highlighted, using the combined influences of textured surface and non-Newtonian lubricants behavior, obeying to the Rabinowitsch fluid model. The associated nonlinear Rabinowitsch-Reynolds equation has been discretized using finite differences scheme and solved by the mean of Elrod’s algorithm taking into account the presence of cylindrical textures on full/optimum bearing surface. Following to the absence of textures on the bearing surface or the non-Newtonian fluid behavior, the obtained results are in good agreement with the reference ones. The hydrodynamic lubrication static performances are computed for various parameters such as textures location; eccentricity ratio and the rheological coeffcient. The results suggest that texturing the bearing’s convergent zone enhances significantly the load carrying capacity and reduces the friction coeffcient, whereas texturing the full bearing surface may leads to bad performances. It is also noticed that the pseudoplastic lubricant coeffcient decreases the bearing performances (load capacity and pressure) compared to Newtonian fluid cases. Considering the optimal arrangement of textures on the contact surface, a significant improvement in terms of load capacity and friction can be achieved, especially at low pseudoplasticity effect.

Dynamics of on-board rotors on finite-length journal bearings subject to multi-axial and multi-frequency excitations: numerical and experimental investigations

On-board rotating machinery subject to multi-axial excitations is encountered in a wide variety of high-technology applications. Such excitations combined with mass unbalance forces play a considerable role in their integrity because they can cause parametric instability and rotor–stator interactions. Consequently, predicting the rotordynamics of such machines is crucial to avoid triggering undesirable phenomena or at least limiting their impacts. In this context, the present paper proposes an experimental validation of a numerical model of a rotor-shaft-hydrodynamic bearings system mounted on a moving base. The model is based on a finite element approach with Timoshenko beam elements having six degrees of freedom (DOF) per node to account for the bending, torsion and axial motions. Classical 2D rectangular finite elements are also employed to obtain the pressure field acting inside the hydrodynamic bearing. The finite element formulation is based on a variational inequality approach leading to the Reynolds boundary conditions. The experimental validation of the model is carried out with a rotor test rig, designed, built, instrumented and mounted on a 6-DOF hydraulic shaker. The rotor’s dynamic behavior in bending, torsion and axial motions is assessed with base motions consisting of mono- and multi-axial translations and rotations with harmonic, random and chirp sine profiles. The comparison of the predicted and measured results achieved in terms of shaft orbits, full spectrums, transient history responses and power spectral densities is very satisfactory, permitting the experimental validation of the model proposed.

Computational investigation on the performance of hydrodynamic micro-textured journal bearing lubricated with micropolar fluid using mass-conserving numerical approach

The tribological characteristic of journal bearing systems can be enhanced with the integrating of textures in the contact interfaces, or using the lubricating effect of non-Newtonian fluids. In this study, the combined effects of bearing surface texturing and non-Newtonian lubricants behavior, using micropolar fluid model, on static characteristics of hydrodynamic circular journal bearings of finite length are highlighted. The modified Reynolds equation of micropolar lubrication theory is solved using finite differences scheme and Elrod's mass conservation algorithm, taking into account the presence of the cylindrical texture shape on full and optimum bearing surfaces. The optimization textured area is carried out through particle swarm optimization algorithm, in order to increase the load lifting capacity. Preliminary results are in good agreement with the reference ones, and present an enhancement in the performances of micro-textured journal bearings (load carrying capacity and friction). The results suggest that texturing the bearing convergent zone significantly increases the load carrying capacity and reduce friction coefficient, while fully texturing causes bad performances. It is also shown that the micropolar fluids exhibit better performances for smooth journal bearings than a Newtonian fluid depending on the size of material characteristic length and the coupling number. The combined effects of fully surface textured with micropolar fluids reduce the performance of journal bearing, especially at lower eccentricity ratios. Considering the optimal arrangement of textures on the contact surface, a significant improvement in terms of load capacity and friction can be achieved, particularly at high eccentricity ratios, high material characteristic lengths and high values of the coupling numbers of micropolar fluids.

Hydrodynamic self-lubricating journal bearings analysis using Rabinowitsch fluid lubricant

Abstract In this study, the effects of non-Newtonian pseudo-plastic lubricants behavior, using Rabinowitsch fluid model, on static characteristics of circular self-lubricating porous journal bearings of finite length with sealed ends are highlighted. The nonlinear Reynolds equation based on the Rabinowitsch fluid model has been developed specifically for porous journal bearing cases by considering the fluid flow in the porous matrix described by Darcy's law. The Governing equations are discretized using a centered finite difference scheme and solved numerically using an iterative method. Following to the absence of the porous matrix or the non-Newtonian fluid behavior, the obtained results showed a good agreement with those of the literature review. The static characteristics of hydrodynamic lubrication are calculated numerically for various parameters such as bearing dimensions; the porous bush permeability and the lubricant pseudo-plastic coefficient. It is shown that the dimensionless permeability has significant effects on the static characteristics of the bearings. The pseudo-plastic lubricant coefficient decreases the bearing characteristics (load capacity, pressure) compared to Newtonian lubricant cases. The use of the pseudo-plastic fluids reduces the performance of the bearings and this reduction grows with the porous bearing properties.

EFFECT OF LUBRICANT TEMPERATURE ON THE DYNAMIC AND STABILITY BEHAVIOR OF NANO-LUBRICATED JOURNAL BEARING

The effects of lubricant temperature on the dynamic behaviour of Nano-lubricated finite length journal bearings has been investigated in the present work. Modified time dependent Reynolds equation include the effect of oil film temperature was perturbed in order to calculate the eight dynamic coefficients (four stiffness, and four damping) required to evaluate the dynamic characteristics of the journal bearing, the oil film temperature was obtained by solving numerically the energy and heat conduction equations simultaneously with the Reynolds equation using appropriate boundary conditions. Suitable viscosity temperature model has been used to consider the effect of oil film temperature. The bearing lubricated with oil containing Titanium dioxide (TiO2 ) nanoparticles dispersed in to the base oil with various particle concentration. The effect of adding TiO2 Nano-particles with various particle concentrations (0.1%, 0.5%, 1%, 1.5% and 2%) in order to enhance its viscosity has been discussed. A validation to the mathematical model and the computer program written in Fortran90 prepared to solving the governing equation has been carried out by comparing the result for the dynamic coefficients (stiffness and damping) obtained in the present work with that obtained by Sheeja and Prabhu . The results seen to be in a good agreement with percentage of error less than 2%. The results obtained in the present study show that the bearing stiffness coefficients increases by 30% while the damping coefficients increased by 27% when the bearing lubricated with Nano lubricant that contains TiO2 Nano particles with particle concentration of (1.5%).

Dynamic coefficients of finite length journal bearing. Evaluation using a regular perturbation method

Fil: Merelli, Claudio Ernesto. Universidad Nacional de la Patagonia San Juan Bosco; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Bahia Blanca. Planta Piloto de Ingenieria Quimica. Universidad Nacional del Sur. Planta Piloto de Ingenieria Quimica; Argentina. Universidad Nacional del Sur. Departamento de Ingenieria Quimica; Argentina

Threshold stability curves for a nonlinear rotor-bearing system

Design parameters of fluid film bearings affect the stability of rotor-bearing systems, which can be characterized using so called threshold speed and a threshold curve (depending on a shaft speed and a chosen design parameter). The paper brings a detailed study of the shape of the threshold curve for a rigid rotor supported on a plain bearing. A novel comparison of stability threshold curves obtained employing various approaches to the hydrodynamic force modelling for all relevant bearing parameters is presented. Hydrodynamics forces are solved using four approaches: the infinitely short (IS) approximation, the infinitely short approximation extended by multiplicative correction polynomials for finite-length journal bearings (IScor), the finite differences method and the finite elements method. The influence of run-up time and acceleration is also investigated. All obtained threshold curves are compared to the analytical expressions for the threshold curves calculated for the IS approximation.

Dynamic coefficients and stability analysis of finite-length journal bearings considering approximate analytical solutions of the Reynolds equation

The paper presents linearized coefficients for finite-length journal bearings based on the HD forces with multiplicative correction polynomials applied to the infinitely short and the infinitely long solutions under the assumption of π-film boundary condition. Based on the linear theory, stability thresholds and their dependence on the length-to-diameter ratio are investigated. Moreover, using the numerical continuation method the change of the generalized Hopf bifurcation which separates regions with subcritical and supercritical Hopf is documented. All results are compared with those of the solution obtained using the finite differences method.

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part II: Numerical Bearing Model

The nonlinear stability of a flexible rotor-bearing system supported on finite length journal bearings is addressed. A perturbation method of the Reynolds lubrication equation is presented to calculate the bearing nonlinear dynamic coefficients, a treatment that is suitable to any bearing geometry. A mathematical model, nonlinear coefficient-based model, is proposed for the flexible rotor-bearing system for which the journal forces are represented through linear and nonlinear dynamic coefficients. The proposed model is then used for nonlinear stability analysis in the system. A shooting method is implemented to find the periodic solutions due to Hopf bifurcations. Monodromy matrix associated to the periodic solution is found at any operating point as a by-product of the shooting method. The eigenvalue analysis of the Monodromy matrix is then carried out to assess the bifurcation types and directions due to Hopf bifurcation in the system for speeds beyond the threshold speed of instability. Results show that models with finite coefficients have remarkably better agreement with experiments in identifying the boundary between bifurcation regions. Unbalance trajectories of the nonlinear system are shown to be capable of capturing sub- and super-harmonics which are absent in the linear model trajectories.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position.

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

Linear stability analysis of finite length journal bearings in laminar and turbulent regimes

Dynamic coefficients of a finite length journal bearing are numerically calculated under laminar and turbulent regimes based on Ng–Pan–Elrod and Constantinescu models. Linear stability charts of a flexible rotor supported on laminar and turbulent journal bearings are found by calculating the threshold speed of instability associated to the start of instable oil whirl phenomenon. Local journal trajectories of the rotor-bearing system were found at different operating conditions solely based on the calculated dynamic coefficients in laminar and turbulent flow. Results show no difference between laminar and turbulent models at low loading while significant change of the size of the stable region was observed by increasing the Reynolds number in turbulent models. Stable margins based on the laminar flow at relatively low Sommerfeld numbers [Formula: see text] were shown to fall inside the unstable region and hence rendering the laminar stability curves obsolete at high Reynolds numbers. Ng-Pan turbulent model was found to be generally more conservative and hence is recommended for rotor-bearing design.

Effects of fluid inertia and bearing flexibility on the performance of finite length journal bearing

The paper describes the theoretical study concerning the effect of lubricant inertia forces and deformability of the bearing elastic layer on the performance of a plane journal bearing. The problem is investigated for a Newtonian lubricant under isothermal and isoviscous conditions. The analysis considers the generalized Reynolds equation governing the flow of lubricant in the clearance space and the linear elasticity equation governing the displacement field in the bearing shell. An iterative numerical procedure with successive over relaxation is used to pressure distribution within the lubricated conjunction. Bearing performance characteristics have been presented for typically selected values of generalized Reynolds number Re* and elasticity parameters of the elastic liner. It has been observed that the combined effect of fluid inertia forces and bearing flexibility affects the performance characteristics of dynamically loaded journal bearing.

Approximate Modeling of Finite Length Journal Bearing for Bifurcation Analysis

Approximate Modeling of Finite Length Journal Bearing for Bifurcation Analysis