Turbulent Journal Bearings Research Articles

Stability analysis of fluid film bearings under laminar and turbulent regimes

Stability of short journal bearings is investigated in bith the linear and nonlinear regimes under laminar and turbulent operating conditions with consideration of drag force effects. Exerted forces on fluid film bearings comprises of two different components. (1) Pressure force components in radial and tangential directions, and (2) Drag force (shear/friction force) components in radial and tangential directions. In most existing literature, related to rotor bearing system supported on journal bearing stability analysis, the effect of fluid film drag force has been neglected. Utilizing Ng-Pan-Elrod model and the modified Reynold’s equation, detailed calculation of the turbulent pressure distribution is carried out. Local stability of periodic solutions was studied using Hopf bifurcation theory. The shaft stiffness and inclusion of drag force and turbulent effects were found to play an important role in stability regions and bifurcation profiles of a flexible rotor bearing system.It was found that for shafts supported on short journal bearings, consideration of drag force effect could lead to expansion of un-stable region at high Sommerfeld numbers (low shaft static loads). Dynamic coefficients of short length journal bearing were analytically calculated under laminar and turbulent regimes based on Ng–Pan–Elrod model. 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 discrepancy between laminar and turbulent models, when shaft stiffness is great than 10, for the entire range of Sommerfeld number by increasing the Reynolds number in turbulent models.

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.

Chaotic Response and Bifurcation Analysis of Rotor-Bearing System with Nonlinear Suspension and Roughness Effect under Turbulent Flow

This research aims to study a numerical analysis to investigate the dynamic orbits of a rotor supported by two turbulent journal bearings considering longitudinal and transverse roughness effect under nonlinear suspension. The dynamic response of the rotor center and bearing center are studied. The dynamic trajectories of the rotor center and bearing center, Poincare maps, bifurcation diagrams and the maximum Lyapunov exponent method are employed to analyze dynamic responses in this study. The results show that either the longitudinal and transverse or the values of roughness parameters c1 would not affect strongly nonlinear rotor-bearing system very much but the difference of dynamic response between considering with roughness effect and without roughness effect are very obvious. The modeling results provide some theoretical references for further researching of rotor-bearing system for rotating machinery that operate in highly rotational speed, especially it considers roughness effect, turbulent flow and nonlinear suspension of bearing system.

Analytical fluid film force calculation in the case of short bearing with a fully developed turbulent flow

The main purpose of this paper is to define a methodology to determine the analytical approximate closed-form expression of non-steady fluid film force and of the oil film coefficients for the liquid-lubricated journal bearings in the case of a fully developed turbulent flow regime. The considered model is a symmetrical rigid rotor supported on two lubricated journal bearings; this paper considers the cases of the short bearing approximation, introducing the turbulence correction flow factors in the classical Reynolds equation. The proposed methodology gives the opportunity to solve in approximate way the equation governing the distribution of pressure in the bearing oil gap and then to obtain the closed-form expressions for the non-steady fluid forces. This approach shows the benefit of minimising the calculation time required for the non-linear dynamic analysis of rotors on turbulent journal bearings without any significant loss of accuracy giving a better readability of the parameter involved on the system behaviour.

Approximate solution of oil film load-carrying capacity of turbulent journal bearing with couple stress flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.

Dynamic Analysis of a Flexible Rotor Supported on Two Turbulent Model Journal Bearings with Micropolar Fluid Lubrication

This paper presents the complex dynamic analysis of a flexible rotor–bearing system supported by two turbulent micropolar fluid film journal bearings under nonlinear suspension. The Modified Reynolds equation based on the assumptions of turbulent flow and the micropolar parameters has been considered. The system considers Short bearing approximation to simplify the numerical computations. The pressure distribution thus obtained is used to find out the resulting forces about the journal center in the radial and tangential directions. The Non-dimensional dynamic equations are derived considering appropriate non dimensional parameters and solved using MATLAB for a wide range of non-dimensional speed ratios. Plots of the journal center trajectories and rotor center trajectories are obtained. The results show that the system undergoes undesirable nonsynchronous vibrations due to bearing center displacement. Micropolar fluid is found to stabilize the system even when the flow of the system becomes turbulent. The study presented enhances the understanding of the nonlinear dynamics of turbulent journal bearings with respect to dimensionless parameters.

Chaotic Response and Bifurcation Analysis of Rotor-Bearing System with Nonlinear Suspension and Roughness Effect under Turbulent Flow

This research aims to study a numerical analysis to investigate the dynamic orbits of a rotor supported by two turbulent journal bearings considering longitudinal and transverse roughness effect under nonlinear suspension. The dynamic response of the rotor center and bearing center are studied. The dynamic trajectories of the rotor center and bearing center, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent method are employed to analyze dynamic responses in this study. The results show that either the longitudinal and transverse or the values of roughness parameters c1 would not affect strongly nonlinear rotor-bearing system very much but the difference of dynamic response between considering with roughness effect and without roughness effect are very obvious. The modeling results provide some theoretical references for further researching of rotor-bearing system for rotating machinery that operate in highly rotational speed, especially it considers roughness effect, turbulent flow and nonlinear suspension of bearing system.

Static Performance Characteristics of Finite-Width Turbulent Journal Bearings with THD Effect

Static performance characteristics were comprehensively investigated for adiabatic finite-width turbulent journal bearings. A numerical method developed using the Legendre collocation technique was used to simulate liquid lubricant flows in various geometric conditions over a wide range of the mean Reynolds number. Both isoviscous and thermohydrodynamics (THD) were investigated. The least-squares method was applied to groups of parameters, yielding formulas for load capacity, friction coefficient, attitude angle, and side leakage. With the formulas derived in this study, designers can quickly determine static parameters of turbulent full journal bearings without the burden of labor-intensive numerical computation for the governing differential equations.

Numerical Analysis of Nonlinear Behaviors of a Flexible Rotor Dynamic System with Turbulent Journal Bearings Support

For description of rotor-bearing system, a symmetrical flexible rotor supported by two turbulent journal bearings is modeled. The analysis of the rotor-bearing system is implemented under the assumptions of turbulent lubricant flow and a long bearing approximation. The bifurcation and chaos behaviors of the system are investigated for various rotational speeds. The motion equations are solved by the self-adaptive Runge-Kutta method. The numerical results show that the bifurcation of nonlinear responses of the system varies with the rotational speed of the rotor. It is found that the rich and complex dynamic behaviors of the system include period-1, period-doubling, quasi-periodic and chaotic motions etc.

THD Effects of Static Performance Characteristics of Infinitely Wide Turbulent Journal Bearings

Formulas for static parameters were found for infinitely wide turbulent full journal bearings that correlate either load capacity or friction coefficient for thermohydrodynamics (THD) effects in terms of a single THD parameter. The database was built by numerical simulation of turbulent liquid lubricant flows with various eccentricity ratios in a wide range of the Reynolds number for both isoviscous and THD cases. The least-squares method was applied to the groups of parameters yielding the formulas of load capacity, friction coefficient, and attitude angle. The isoviscous attitude angle was fitted as a function of the maximum-to-minimum film thickness ratio, and the variation of attitude angle due to THD is linearly dependent on the THD-to-isoviscous load capacity ratio. With the formulas provided in this study, designers can quickly determine static parameters of turbulent journal bearings without the burden of labor-intensive numerical computation of the governing differential equations.

Non-linear dynamic analysis of rub-impact rotor supported by turbulent journal bearings with non-linear suspension

This study presents a dynamic analysis of a rub-impact rotor supported by two turbulent model journal bearings with non-linear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor-bearing system is investigated under the assumptions of turbulent lubricant flow and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios and dimensionless unbalance parameter. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the non-dimensional unbalance parameters. The contribution of this study is to provide a further understanding of the characteristics and dynamic behaviors of the rotor-bearing system.

Nonlinear dynamics of a flexible rotor supported by turbulent journal bearings with couple stress fluid

This study presents a dynamic analysis of a rotor supported by two turbulent flow model journal bearings and lubricated with couple stress fluid under nonlinear suspension. The dynamics of the rotor center and bearing center is studied. The dynamic equations are solved using the Runge–Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The results show that the values of dimensionless parameters l ∗ strongly influence dynamic motions of bearing and rotor centre. It is found that couple stress fluid improve the stability of the system when l ∗ > 0.4 even if the flow of this system is turbulent. We also demonstrated that the dimensionless rotational speed ratios s and the dimensionless unbalance parameter β are also significant system parameters. The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.

Bifurcation and chaos of a flexible rotor supported by turbulent journal bearings with non-linear suspension

This study presents a dynamic analysis of a rotor supported by two turbulent model journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor-bearing system is investigated under the assumptions of turbulent lubricant flow and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The dynamic equations are solved using the fourth-order Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor centre and bearing centre, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the dynamic behaviours of the system include 3 T-periodic, jump phenomena, and chaotic motions. The modelling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behaviour of the rotor and bearing centre can be avoided.

An optimised short bearing theory for nonlinear dynamic analysis of turbulent journal bearings

An approximate method for nonlinear dynamic analysis of turbulent journal bearings supporting an unbalanced rigid shaft is proposed. The method is based on two assumptions: the separation of variables for pressure and a parabolic pressure distribution in the axial direction of the bearing. To take into account inertia effects, the well-known algebraic turbulent model based on the Prandtl mixing length hypothesis is used. Using the Constantinescu's approach, the pressure equation is modified by introducing two turbulent coefficients which are depending on the local Reynolds number. The nonlinear equations of motion for the rotor-bearing system are solved by means of the Euler's scheme, and the journal centre trajectories are examined for cases with and without unbalance forces. To illustrate the validity of the present study, three cases of journal bearings are analysed. The accuracy of the minimum film thickness, the dynamic transmissibility coefficient and the peak-to-peak displacement amplitudes obtained by the proposed methodology are comparable to the more elaborate and time consuming 2-D finite difference solution, while the turbulent journal centre orbits are comparable to those obtained experimentally. It is concluded that the optimised short bearing theory shows the advantage of minimising the computation time required for nonlinear dynamic analysis of laminar and turbulent journal bearings without any significant loss of accuracy.

Thermohydrodynamic Analysis of High-Speed Journal Bearings With Surface Roughness

This parer describes thermohydrodynamic analysis of turbulent journal bearings with isotropic, homogeneous surface roughness. Applying the modified Reynolds equation and energy equation considering the surface roughness effects, the film pressure and temperature distributions are obtained for various roughness heights

Stability of a rigid rotor in turbulent hydrodynamic worn journal bearings

In this paper, the effects of geometric change due to wear on stability of hydrodynamic turbulent journal bearings have been investigated numerically, following Constantinescu's turbulent lubrication theory. Stability curves have been drawn for various values of wear depth parameter considering turbulence. Wear causes the stability of the rotor to deteriorate in the case of lightly loaded bearings, and in the case of worn bearings a lower L D ratio gives better stability.

Thermohydrodynamic Lubrication Theory for Turbulent Journal Bearings with Surface Roughness. 2nd Report. Theoretical Analysis Considering the Heat Transfer to Both Journal and Bearing' Bush.

This second paper shows the full solution to the thermohydrodynamic turbulent lubrication problems including the surface roughness effect. The generalized modified lubrication equation and energy equation, which were newly established in the previous paper, are applied to the full circular journal bearings covered with homogeneous surface roughness. These two equations are solved numerically by combining with the equation for heat transfer to the bearing' bush, in which the shaft surface temperature is calculated by averaging the mean temperature of fluid film over the circumference of the journal. Numerical results for the various kinds of bearing characteristics such as pressure and temperature distributions, Sommerfeld number, attitude angle, friction coefficients and flow rate are presented in graphic form for the suitable combination of Reynolds number and relative roughness, and the temperature rise effects on the bearing characteristics are discussed in detail.

The Effects of “O-Type” Cavitation on the Performance Characteristics of Turbulent Journal Bearings

In this research work, the effects of “O-type” cavitation on the static and dynamic characteristics of turbulent journal bearings submerged in the low viscosity lubricant are investigated theoretically. Extending an idea of “general short bearing theory” proposed by Pan to submerged turbulent journal bearings, “O-type” cavitation pattern, load carrying capacity and altitude angle are determined for a wide range of eccentricity ratio in both laminar and turbulent flow cases. In addition, under the assumption of small displacement of the journal center, the dynamic characteristics such as linearized spring and damping coefficients and whirl onset speed of rotor-bearing systems are obtained. Sample numerical results are indicated in graphic form and the relation between the “O-type” cavitation and the static and dynamic characteristics of submerged turbulent journal bearings is discussed. Presented at the 44th Annual Meeting in Atlanta, Georgia May 1–4, 1989

Thermohydrodynamic Lubrication Theory for Turbulent Journal Bearings with Surface Roughness. 1st Report, Modified Energy Equation and Adiabatic Approximate Solution.

This paper describes the derivation of a new type of modified energy equation including turbulence and surface roughness effects and presents an adiabatic approximate solution for the static and dynamic characteristics of an 180°partial journal bearing with homogeneous surface roughness. Applying the modified turbulent lubrication equation and energy equation to the finite width partial journal bearings, the static and dynamic characteristics such as pressure and temperature distributions, load carrying capacity, friction coefficient, whirl onset velocity and so on are obtained numerically. In the numerical analysis of the modified energy equation, the adiabatic condition is assumed and then the heat transfer terms in the energy equation are omitted. The numerical results are indicated in graphic form for the various combinations of Reynolds number and relative roughness. Moreover, some numerical results of static characteristics are compared with the experimental results.

Dynamic Behavior of Unbalanced Rigid Shaft Supported on Turbulent Journal Bearings—Theory and Experiment

In this paper, the combined effects of turbulence and fluid film inertia on the dynamic behavior of an unbalanced rigid shaft supported horizontally on two identical aligned short journal bearings are investigated theoretically and experimentally. Utilizing analytical expressions for the dynamic fluid film force components considering the effects of turbulence and fluid film inertia, the nonlinear equations of motion for the rotor-bearing systems are solved by the improved Euler’s forward integration method. The journal center trajectories with unbalance eccentricity ratio of εμ = 0, 0.1 and 0.2 are examined theoretically for Reynolds number of Re = 2750, 4580, and 5500, and the theoretical results are compared with experimental results. From the theoretical and experimental results, it was found that the fluid film inertia improves the stability of unbalanced rigid shaft under certain operating conditions.