Stiffness and damping characteristics of finite width journal bearings with a non-newtonian film and their application to instability prediction

Starting from the most general fluid flow equation of the power law type expressing rate of shear in terms of powers of shear stress for non-Newtonian lubricants a modified form of Reynolds'equation is derived for dynamically loaded finite width journal bearings. The finite difference technique with successive over relaxation is used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution. From the equations of fluid film forces, the values of stiffness and damping coefficients are obtained for a linearised case. The shear thinning effect of non-Newtonian lubricants at higher shear rates is shown to decrease the stiffness and damping values. Finally, the stability limit for such a bearing is obtained for different values of the nonlinear factor.     

Steady state and stability characteristics of a hydrodynamic journal bearing with a non-Newtonian lubricant

The effect of the non-Newtonian behaviour of lubricants, resulting from the addition of polymers, on the performance of hydrodynamic journal bearings was investigated. An empirical fluid flow equation which adequately represents the flow behaviour of lubricant was used to obtain a modified form of Reynolds' equation. Finite difference numerical solutions were obtained for steady state conditions at various width-to-diameter ratios. The results show a strong influence of the width-to-diameter ratio on the load capacity of journal bearings. Linearised stiffness and damping coefficients were evaluated from the fluid film force equations for the unsteady motion of the journal centre and were used to predict the stability limits of a simple rigid rotor-bearing system which showed a reduction in threshold speeds. The steady state load capacity and stability limits were verified experimentally for finite width bearings.     

Effect of Lubricant Non-Newtonian Behavior and Elastic Deformation on the Dynamic Performance of Finite Journal Plastic Bearings

This paper presents a numerical study of the performance of a dynamically loaded finite journal plastic bearing lubricated with a non-Newtonian fluid, taking into account the elastic deformation of the bearing. The non-Newtonian characteristics are adopted in this paper through an equivalent power-law. An expression for a modified Reynolds equation is derived in order to obtain the pressure gradient. Elastic deformation of the bearing surface was estimated in a direction normal to the bearing surface using Boussinesq equations. The film shape was modified accordingly and then iterated with the hydrodynamic pressure distribution in the bearing until a convergent solution was obtained. The Reynolds equation was solved numerically, considering three values of the flow-behavior index (n = 0.6, 1, and 1.2) and a wide range of journal speeds, materials, and clearance ratios. Consequently, the finite perturbation technique was used to determine the eight values of oil film stiffness and damping coefficients. By using the dynamic coefficients, the stability characteristics of the rotor-bearing system and the critical speed were calculated. The results show that increasing the flow-behavior index enhances the rotor-bearing system stability. A considerable destabilizing effect is obtained upon decreasing the elastic deformation coefficient.     

Influence of lubricants on the performance of journal bearings – a review

ABSTRACT

The lubricant properties have a significant influence on the static and dynamic performance characteristics of journal bearing such as load-carrying capability, minimum fluid film thickness, maximum pressure, lubricant flow rate, damping coefficients, stiffness coefficients, etc. The present document reviews the behaviour of various lubricants such as power-law lubricants, couple stress lubricants, micropolar lubricants, ionic liquid lubricants and space lubricants. The influence of these lubricants on the performance of hydrostatic, hydrodynamic and hybrid journal bearings is discussed. An effort is made to develop the understanding to choose the suitable lubricant for journal bearings for different journal bearing configurations. Journal bearings operated with non-Newtonian lubricants have shown better performance compared to Newtonian lubricants. Ionic liquid lubricants have shown high potential in vacuum applications and extreme temperature environment such as in bearings of spacecraft moving mechanical assemblies.     

The load capacity of a partial journal bearing with a non-Newtonian film

Lubricating oils with viscosity index improver additives exhibit non-Newtonian behaviour. Starting from the most general type of fluid flow equation, connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation has been derived and solved for the steady state load capacity for finite width full cylindrical journal bearings. The method has been extended to partial journal bearings both for the centrally loaded film and for the film with minimum thickness at the trailing edge. Numerical results are given for bearing arcs of 180° and 120° and length-to-diameter ratios of 1 and $\text{1}\text{2}$.     

Influence of the Wetting Properties of Liquids on the Tribological Behavior of Selected Sliding Materials in Mechanical Seals

Theoretical investigations are carried out for a plain journal bearing considering the influence of thermal effects on non-Newtonian lubrication. With reasonable assumptions, the steady state and dynamic characteristics are presented using a thermohydrodynamic analysis of a bearing lubricated by a nonlinear, i.e., cubic, fluid model.

Experiments are conducted on a rig to study the steady state and dynamic performance of a full journal bearing with different types of non-Newtonian lubricants. Experiments include the measurements of eccentricity ratio, critical speed, and stability limit.

The theoretical investigation reveals that the interaction of the non-Newtonian effect and the thermohydrodynamic effect is strong for friction, and the interaction effect is negligible in the case of eccentricity ratio, attitude angle, and lubricant flow rate. Further, for relatively high values of non-Newtonian parameter, α_n , the effect due to the non-Newtonian parameter is not negligible.     

Effect of fluid inertia on stability of flexibly supported oil journal bearings: linear perturbation analysis

A theoretical analysis to study the effect of fluid inertia on the stability of oil film journal bearings mounted on flexible support using linear perturbation technique is presented. The Navier–Stokes equations have been solved using the parabolic velocity profile. The dynamic coefficients are calculated without neglecting the mass of the oil in the bearing for different length to diameter ratios and modified Reynolds numbers. These are then used to find stability margin for different support parameters to study the effect of fluid inertia.     

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

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.     

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.     

Controllable high speed journal bearings, lubricated with electro-rheological fluids. An analytical and experimental approach

The problem of journal bearings control is of great importance in mechanical engineering. A very recent method for doing this is the creation of ‘smart' journal bearings using electro-rheological (ER) fluids. If such a fluid is used to lubricate a journal bearing system, it is expected that the imposition of an electric field between the rotor and the stator will cause an alteration in the dynamic properties of the journal bearing. In this paper an experiment in a high speed journal bearing (16 000 to 35 000 s⁻¹), with small radial clearance is presented. The alternation of the attitude locus (eccentricity and attitude angle) and the stiffness coefficients in a loaded journal bearing lubricated with ER fluid is investigated and presented. The Reynolds equation is solved using the finite element method in order to get the dynamic characteristics of the ER bearings vs the electric field and to simulate its dynamic behavior. The Bingham plastic model of non-Newtonian fluid flow behavior is used to described the ER lubricant. The accuracy of the algorithm is obtained by comparing the results published by previous investigators and the experimental data described in this paper. It is concluded that ER fluids can be used to create ‘smart' journal bearings. and vibration controllers can be constructed to control the dynamics and stability of the ER fluid lubricated bearings.     

Stiffness and damping coefficients of an inclined journal bearingSteifigkeit und dämpfungskoeffiziente eines schrägen gleitlagers

In the determination of the dynamic behaviour of a rotating shaft, the fluid film stiffness and damping coefficients of the bearings play an important role. The general practice is to ignore the rotational stiffnesses and damping coefficients due to the tilt of the journal in the bearing. This paper presents the stiffness and damping coefficients of such journal bearings. Using the expression for film thickness, the modified Reynolds' Equation for the tilted finite journal bearing is set up. The solution of this equation for the film pressure is obtained by using Fedor's proportionality hypothesis. The results obtained are presented in the form of non-dimensional charts.     

Stiffness and damping coefficients for journal bearing using the 3D transient flow calculation

The dynamic coefficients of journal bearing are necessary components in the analysis of linear stability and response of rotating dynamic systems. We propose a new method for the numerical identification of bearing support force coefficients in flexible rotor-bearing systems based on the 3D transient flow calculation. The CFD commercial software FLUENT is mainly used in this simulation, which employs a finite volume method for the discretization of the Navier-Stokes equations. To determine the dynamic coefficients, a new mesh movement approach is presented to update the volume mesh when the journal moves during the 3D transient flow calculation of a journal bearing. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. Measurements and identification are performed on a test rotor supported on a pair of identical two-lobe fluid film bearings, and the results obtained from the CFD methods agree well with experimental results. The results indicate that the methods proposed in this paper can predict the dynamic coefficients of the journal bearing in a rotor-bearing system effectively, and provide a further tool for stability analysis.     

Bifurcation analysis of flexible rotor supported by couple-stress fluid film bearings with non-linear suspension systems

This study analyzes the dynamic behavior of a flexible rotor supported by two couple-stress fluid film journal bearings with non-linear suspension systems. The analysis employs a short journal bearing assumption and considers the respective effects on the dynamic response of the system of the lubricant type (i.e. Newtonian or non-Newtonian), the bearing housing suspension system (i.e. linear or non-linear), the rotor speed and the degree of rotor unbalance. The behavior of the system is analyzed by reference to bifurcation diagrams, dynamic trajectory diagrams and Poincaré maps, respectively. In general, the results show that the dynamics of the system are significantly dependent on the rotor speed and the degree of rotor unbalance. Furthermore, it is found that the use of a couple-stress fluid lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. Finally, the results show that the common assumption of a linear journal housing suspension system results in a significant underestimation of the vibrational amplitudes of both the rotor and the bearing and should therefore be replaced by a non-linear assumption.     

Linear Stability Analysis of Hydrodynamic Journal Bearings with a Flexible Liner and Micropolar Lubrication

A linear stability analysis of hydrodynamic journal bearings is presented, including the effects of elastic distortion of the liner and micropolar lubrication. Hydrodynamic equations of the lubricant and equations of motion of the journal are solved simultaneously with the deformation equations for the bearing surface to predict the fluid film pressure distributions theoretically. The components of stiffness and damping coefficients, critical mass parameter, and whirl ratio, which reflect the dynamic characteristic of the journal bearing, are calculated for varying eccentricity ratio taking into account the flexibility of the liner and the micropolar properties of the lubricant. The results presented show that stability decreases with an increase in the value of the elasticity parameter of the bearing liner and micropolar fluids exhibit better stability in comparison to Newtonian fluids.     

Analysis of hydrodynamic journal bearings lubricated with non-Newtonian fluids

A procedure for solving the Navier-Stokes equations for the steady, three-dimensional flow of a non-Newtonian fluid within a finite-breadth hydrodynamic journal bearing is described. The method uses a finite-difference approach, together with a technique known as SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) which has now become established in the field of computational fluid dynamics. The concept of ‘effective viscosity’ to describe the non-linear dependence of shear stress on shear rate is used to predict the performance of bearings having a single full-width axial inlet groove situated at the position of maximum film thickness. To illustrate the capabilities of the procedure, results are obtained for a range of non-linearity factors, and lead to the conclusion that the pressure distribution, attitude angle, end-leakage rate, shear force and load capacity can all be predicted for a variety of non-Newtonian lubricants using the SIMPLE numerical integration technique.     

Thermo-hydrodynamic analysis of herringbone grooved journal bearings

Steady-state and stability characteristics of herringbone grooved journal bearings (HGJBs) are found considering thermal effect. The temperature of the fluid film rises significantly due to the frictional heat, thereby the viscosity of the fluid and the load carrying capacity decrease. A thermodynamic analysis requires the simultaneous solution of Reynolds equation along with energy equation of the fluid and heat conduction equations in the bush and the shaft. The linearized first-order perturbation technique is employed for the prediction of stiffness and damping coefficients of the oil film. Thereafter mass parameter and whirl ratio are found from the stability analysis. It is difficult to obtain the solution due to the numerical instability when the bearing is operated at high eccentricity ratios.     

Severity Estimation of Cracked Shaft Vibrations within Fluid Film Bearings

The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings.

Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts.     

直齿轮传动非牛顿流体瞬态弹流润滑研究

综合考虑润滑流体的非牛顿特性以及齿轮传动的瞬态效应，采用Bair-Winer粘塑模型推导了非牛顿流体雷诺方程，建立了非牛顿流体瞬态弹流润滑模型；进行直齿轮传动非牛顿流体弹流润滑数值分析，获得了齿轮传动沿啮合线的油膜压力、油膜形状以及摩擦因数的分布。结果表明：在非牛顿流体工况下，油膜厚度、油膜压力以及轮齿表面摩擦因数均有所降低,因此在齿轮弹流润滑研究中应考虑流体的非牛顿特性的影响。     

Nonlinear stability boundary of journal bearing systems operating with non-Newtonian couple stress fluids

The non-Newtonian effects on the nonlinear stability boundary of short journal bearings are investigated through the transient nonlinear analysis. Two coupled nonlinear equations are solved by using the fourth-order Runge-Kutta method. According to the results, there exists a nonlinear stability boundary within the clearance circle. Any initial positions of the shaft center outside of this boundary would yield an unstable trajectory, even though the bearing should be stable in accordance with the linear stability theory. The non-Newtonian effects provide a larger stability boundary within the clearance circle as compared to the bearing lubricated with a Newtonian fluid.     

Identification of nonlinear dynamic coefficients in plain journal bearings

This work proposes a framework to the numerical identification of nonlinear fluid film bearing parameters from large journal orbital motion (20–60% of the bearing clearance). Nonlinear coefficients are defined by a third order Taylor expansion of bearing reaction forces and are evaluated through a least mean square in time domain technique. The journal response is obtained from a computational fluid dynamic (CFD) model of a plain journal bearing on high dynamic loading conditions. The model considers fluid–structure interaction between the fluid flow and the journal. The case in study considers a laboratory test rig. Results indicate that nonlinear coefficients have an important effect on stiffness and damping. It was found a change on nonlinear behavior occurred when the Oil Whirl phenomenon starts, which it is not seen in classical linear models.