Journal Center Trajectories Research Articles

Experimental and numerical study on the dynamic and lubrication characteristics of the rotor-bearing-frame system in a variable-speed scroll compressor

The variable-speed scroll compressors can adapt to the various demands of heating and cooling capacity, and the rotational speeds significantly influence the rotor dynamic and bearings lubrication, which might cause performance and reliability issues. In this paper, numerical models for the rotor-bearing-frame system are developed by coupling the Reynolds equation, rotor dynamic equation, and the flexibility equation of the frame. The experimental apparatus is also established to directly measure the journal displacement response in the hermetic high-pressure shell of the compressor. The predicted journal center trajectories are compared with the experimental results and they show good agreement. Results show that the whirl radius decreases with the increase of rotational speed at the measuring point, while the opposite tendency can be observed at the bottom of the main bearing. Transient dynamic analysis of the rotor shows that the tilting and deformation of the rotor vary with respect to different rotational speeds. The displacement of the crank part could lead to the separating tendency between orbiting and fixed scrolls through the coupled orbiting bearing, especially at the lower rotational speed, due to the pull of main balance weight. The numerical results also reveal that the distribution of oil film pressure is dominated by the squeeze effect due to the relatively stable magnitude but the variable direction of loads on the shaft. The influence of the deformation of the cantilevered bearing frame on the oil film thickness is significant but the maximum deformation moves downward at the higher rotational speed.

Nonlinear transient analysis of rigid rotor mounted on externally pressurized double-layered porous gas journal bearings accounting velocity slip

The present work aims at estimating the journal center trajectories of a rigid rotor mounted on a hybrid, finite gas lubricated journal bearings with double-layered porous bushing using nonlinear transient analysis. To consider velocity slip in the film at the interface between film and porous region, Reynolds equation is modified using the Beavers–Joseph boundary condition. The governing equations of flow at clearance, porous regions are discretized using finite volume method. The variable values at cell-face centers are obtained using interpolation scheme of third order. Those discretized equations coupled with equations of rigid rotor motion are solved by third-order total variation diminishing Runge–Kutta scheme. Influence of velocity slip and design parameters on critical mass parameter values were explored. The observations are presented in the form of graphs that serves as a reference during the design of such bearings.

Crosshead bearing analysis for low-speed marine diesel engines based on a multi-body tribo-dynamic model

An optimized lubrication condition of the crosshead bearing in low-speed marine diesel engines is pivotal to its prolonged service life, because the bearing oscillates at a low speed and the direction of the high load is always downward. Theoretical studies on the tribology of the crosshead bearing are very limited, with existing studies ignoring the effects of connecting rod inertia. Herein, a new multi-body tribo-dynamic model for the engine is presented by coupling the dynamics models of the connecting rod, piston assembly, and crosshead assembly with the mixed lubrication models of the multiple lubricated joints including the crosshead bearing. Based on this new multi-body tribo-dynamic model, the bearing load, journal center trajectories, friction torque, and minimum oil film thickness were calculated and compared with those based on the simplified method used in the previous literatures. The results show that due to the connecting rod inertia, the bearing load in the transverse direction calculated by the simplified algorithm is different from that calculated by the tribo-dynamic model proposed in this study. Compared with the results based on the previous simplified method, the inertia of the connecting rod reduces the friction torque of the bearing, especially at the end of the upward stroke.

Non-linear stability analysis of two-layered porous journal bearings with velocity slip and percolation effect of additives of coupled-stress lubricant

In this paper a non-linear stability analysis of the two-layered porous journal bearing under coupled-stress lubricant has been presented with velocity slip phenomenon and additive’s percolation effect. In this non-linear transient analysis, system stability is determined by tracing the locus of the journal center and various trajectories of journal center locus have been represented in graphical form for different operating conditions. Furthermore, stability characteristics in respect of critical mass parameter and whirl ratio have been studied under various parametric conditions and a comparison between the linear and non-linear stability analysis have been demonstrated. To acquire the non-dimensional pressure values, non-dimensional transient Reynolds equation has been solved and with these pressure values, bearing load carrying capacity are derived. Fourth order Runge-Kutta method is used to solve the second order equations of motion for journal bearing system to obtain the stability characteristics. Results of this analysis may be helpful for designing such bearings.

Dynamic and stability performance improvement of the hydrodynamic bearing by using triangular-shaped textures

In the present study, the effect of triangular shape textured on the bearing dynamic and stability performance has been investigated. The triangular-shaped texture having variation in their depth size, number of textures, and location has been used in the study to find the stiffness, damping, and stability parameters and compared with un-textured bearing. The pressure and fluid-film thickness in the lubricant flow domain having characteristics of Newtonian and isothermal and which is governed with Reynold's equation have been computed by discretizing the domain into four-nodded quadrilateral isoparametric by using finite element method. Four different cases of texture distribution on the bearing surface have been studied. The study has been carried out considering the bearing operation only under average eccentricity ratios of 0.6. From obtained results, it is found that the value of direct stiffness coefficient and threshold speed is found maximum at lower texture depth and the direct damping coefficient is found maximum at higher value of texture depth corresponding to different texture distribution on the bearing surface. The optimum triangular-shaped textured parameters have been also finalized to get maximum dynamic performance and stability, which may be expected to be valuable for bearing designers. For the purpose of a better insight into the stability aspect of the optimal textured journal bearing, the journal center trajectories are also drawn and compared with un-textured bearing.

Numerical study on lubrication performance of engine main bearing with rough surface considering axial movement of crankshaft

In actual operation of an engine, the crankshaft will move along the axis direction of engine main bearings under the combined influence of various influencing factors. Considering the axial movement and crankshaft deformation, a new lubrication model of engine main bearings with rough surface was built based on the average Reynolds equation. The influence of axial movement of deformed crankshaft on performance of main bearing with rough surface was studied. In this study, the axial movement law of deformed crankshaft is measured through experiment, and the finite element method was applied to solve the tilting of crankshaft in the bearing bore resulted from the crankshaft deformation. The results show that the axial movement of deformed crankshaft has a significant impact on performance of main bearing with rough surface. No matter whether or not the surface roughness is considered, the journal center trajectories of main bearings are unclosed three-dimensional space curve due to the axial movement of deformed crankshaft. The influence level of the axial movement of deformed crankshaft on lubrication characteristics of main bearings is directly related to the surface roughness. The influence trend and level of the surface roughness on lubrication characteristics of main bearings are obviously changed when considering the axial movement of crankshaft.

Analysis of multi lobe journal bearings with surface roughness using finite difference method

Multi lobe journal bearings are used for high operating speeds and high loads in machines. In this paper symmetrical multi lobe journal bearings are analyzed to find out the effect of surface roughnessduring non linear loading. Using the fourth order RungeKutta method, time transient analysis was performed to calculate and plot the journal centre trajectories. Flow factor method is used to evaluate the roughness and the finite difference method (FDM) is used to predict the pressure distribution over the bearing surface. The Transient analysis is done on the multi lobe journal bearings for threedifferent surface roughness orientations. Longitudinal surface roughness is more effective when compared with isotopic and traverse surface roughness.

Non Linear Analysis on Multi Lobe Journal Bearings

Multi lobe journal bearings are used in machines which operate at high speeds and high loads. In this paper the multi lobe bearing are analyzed to determine the effect of surface roughness during non linear loading. A non-linear time transient analysis is performed using the fourth order Runge Kutta method. The finite difference method is used to predict the pressure distribution over the bearing surface. The effect of eccentric ratio is studied and the variation of attitude angle is discussed. The journal center trajectories were calculated and plotted.

Dynamic analysis of a 2-lobe geometrically imperfect journal bearing system

The present study is concerned with the linear and nonlinear transient motion analysis of a 2-lobe geometrically imperfect hybrid journal bearing system compensated with constant flow valve restrictor. The trajectories of journal center motion for a geometrically imperfect rotating journal (barrel, bellmouth and undulation type journal) have been numerically simulated by solving the linear and nonlinear equations of motion of journal center using a fourth order Runga–Kutta method. The numerically computed results for the journal center trajectories indicate that the 2-lobe bearing [Formula: see text] is more stable with geometrically imperfect journal as compared to the circular bearing with imperfect journal.

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.

Effects of turbulence on dynamic performance of accelerated/decelerated hydrodynamic journal bearing system

The hydrodynamic journal bearing system has found the wide spread application in high speed rotating machines such as compressors, gas turbines, steam turbines, etc. The rotors generally operate at high speed; therefore the lubricant flow in the clearance space of journal bearing does not remain laminar for accelerated/decelerated journals. Then, study of the dynamic response of the hydrodynamic journal bearing system considering superlaminar flow is needed. In this paper, the analysis is done for the fluid-low-field in the clearance space of hydrodynamic journal bearing system using short bearing assumption under laminar, transition and turbulent flow conditions. The positive pressure zone is established after deleting sub-ambient pressure around clearance space. Linear and non-linear motion trajectories at constant speed are obtained using the fourth order Runge-Kutta method. The non-linear motion trajectories during acceleration and deceleration are also obtained. Journal centre trajectories at constant speed and laminar flow, show the expected trend, i.e., system is stable below threshold speed curve, unstable above it, whereas for superlaminar flow, stable behaviour is found at some distance away from the stability curve. The behaviour during stopping/starting of journal centre trajectories is also obtained by non-linear equations of motion. The results also show the expected trend.

Nonlinear dynamics of flexible rotor supported on the gas foil journal bearings

Investigation on nonlinear dynamics of a flexible rotor supported on the gas foil journal bearings is attempted. A time domain orbit simulation is carried out that couples the equations of rotor motion, unsteady Reynolds equation and foil deformation. The unsteady Reynolds equation is solved using control volume formulation with power law hybrid scheme and Gauss–Seidel method. The nonlinear dynamic response is analyzed using disc center and journal center trajectories, Poincaré maps, Fast Fourier transforms and bifurcation plots. The analysis is carried out for different system parameters, namely, rotating speed, unbalance eccentricity, compliance and loss factor of gas foil bearing. The analysis reveals highly nonlinear behavior with periodic, multi-periodic and quasiperiodic motion of the disc and the journal center. The present analysis can be useful in designing and selection of suitable operating parameters of rotor bearing system.

Stabilization Method for Small-Bore Journal Bearings Utilizing Starved Lubrication

This paper describes the stabilization method for small-bore circular journal bearings using starved lubrication. First, we describe the experimental examination to confirm the effect of supply oil conditions on stability of circular journal bearing by using a high-speed test rig. Then, the theoretical model considering the effect of amount of supply oil is discussed. Journal center trajectories are calculated by nonlinear motion analysis under various conditions. The theoretical results agree well with the experimental ones for three types of supply oil conditions and the mechanism of the stabilization by using the starved lubrication for small-bore journal bearings is clarified. Moreover, we suggest a supply oil control mechanism to stabilize the journal bearing using starved lubrication. Finally, the effectiveness of the proposed control mechanism on stability for high-speed small-bore journal bearings is verified experimentally.

The effect of misalignment on performance characteristics of engine main crankshaft bearings

The effect of static misalignment on the dynamic behaviour of a main crankshaft bearing is examined in this paper. The mobility method of Booker is used to predict the performance parameters of the bearing such as the minimum oil-film thickness and the journal centre cyclic path under dynamic load conditions. The theoretical results are compared with those of an aligned bearing. The Ruston–Hornsby 6 Veb-X Mk III engine big-end bearing is selected as an example to validate the computer program incorporating the present analysis. It is shown that the misalignment has significant effects on the minimum film thickness and the journal centre trajectories even for the low values of misalignment parameters. It is also found that the presence of circumferential feed grooves can cause metal-to-metal contact in such bearings.

液体水素ターボポンプ用静圧軸受の動的挙動の数値シミュレーション

In the present paper, the dynamic behavior of a rotor supported by externally pressurized liquid hydrogen bearing is theoretically investigated. The bearing treated in this study has 20 recesses arranged in two rows in a staggered manner and will be used in the liquid hydrogen turbopump of rocket engines for space transport systems. The equations of motion for a rotor are numerically solved using predictor-corrector scheme. The dynamic bearing reaction forces are calculated from the numerical solution of unsteady turbulent Reynolds lubrication equation. The transient responses of hydrostatic bearing under several operating conditions are presented. Furthermore, the journal center trajectories with imbalanced moment are examined theoretically.

A Methodology for Dynamic Coefficients and Nonlinear Response of Multi-Lobe Journal Bearings

A methodology for prediction of dynamic coefficients and nonlinear simulation of multi lobe bearings is developed. This simple formulation that is an extension of Reason and Narang (1982) approach. An easy to implement finite perturbation method is used to evaluate stiffness and damping coefficients. In order to obtain the fluid film forces, the oil film pressure generated in the bearing is solved using a semi analytical pressure model. Four multi lobe journal bearings, namely: two-axial groove, elliptical, three-lobe and offset bearings are studied in terms of non dimensional stiffness and damping coefficients. The parameters are: L/D ratios of 0.5 and 1.0, pre-load factor of 0.5 and offset factor of 0.5; except for the offset bearing, for which the offset factor is 1.0. The results are provided in graphical form and compared with existing numerical techniques. All the coefficients show the influence of Sommerfeld (long) bearing solution at high eccentricity ratios. Results also indicate the applicable range of reciprocal relationship combining the Ocvirk (short) and Sommerfeld bearing solutions for all multi lobe bearing configurations. The journal center trajectories obtained are compared with numerical results and the effect of stability on rotor bearing system is studied for both balanced and unbalanced rotor. It is concluded that the approximate bearing solutions which are predominantly applied to cylindrical bearing configuration, can also be successfully implemented for noncircular profiles.

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.

Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings

The journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed. The formulas are for externally pressurized bearings, but results are shown only for self-acting bearings. For certain cases, the validity of the theoretical results is verified by comparison with the experimental data available from the literature. Through intensive use of the program, journal center trajectories are obtained and effects of fluid inertia are investigated. New stability parameters are presented and stability diagrams are established for bearings with L/D = 0.25, 0.5, 1, 1.5, and 2. The rotor unbalance effects on bearing stability limits are illustrated for several cases.

Stability of Rough Journal Bearings Using Nonlinear Transient Method

The stability of rigid rotors supported on finite oil rough journal bearings has been investigated using nonlinear transient method. The effect of various surface roughness parameters, viz., composite surface roughness, roughness orientation pattern, variance ratio on the stability is presented in the form of journal center trajectories. Although the stability is affected marginally with the increase in composite roughness, the variation is quite significant when the shear flow factor comes into the picture.

The Effect of Journal Surface Shear Stress on the Stability of Turbulent Bearings. 2nd Report. Theoretical Analysis by Finite Bearing Theory.

In this second report, the effects of journal surface shear stress on the stability of rigid rotor supported by hydrodynamic journal bearings operated in the turbulent flow regime are examined theoretically for a wide range of bearing length-to-diameter ratios. Based on the finite width turbulent lubrication theory considering the fluid shear stress acting on the journal surface, the numerical solutions for the whirl onset velocities and journal center trajectories are obtained. It is clarified from the numerical results that the rate of decrease of whirl onset velocities due to the effects of journal surface shear stress under the constant Sommerfeld number decreases with an increase of bearing length-to-diameter ratio.