Non-circular Bearings Research Articles

Investigating the steady state characteristics of noncircular journal bearings lubricated with ferrofluid under concentric finite wire magnetic field

The aim of the present work is to investigate the steady state performance of noncircular hydrodynamic two, three and four lobe journal bearings, lubricated with ferrofluid under concentric finite wire magnetic field. Applying momentum and continuity equation, for ferrofluid under the applied magnetic field, modified Reynolds equation is obtained. Assuming linear behaviour for the magnetic material of the ferrofluid, the Reynolds equation is solved, using finite element technique to obtain pressure distribution then applied to study the effect of magnetic lubricant on various bearing performance characteristics such as load capacity, attitude angle, friction coefficient, friction force and side leakage flow. The results indicate with increasing magnetic force coefficient, side leakage in noncircular bearings and friction coefficient is significantly reduced and improvement in load bearing capacity can be seen at the most values of eccentricity ratio, especially in two lobe noncircular bearing. The results also show that the eccentricity ratio has an effective influence on bearing performance characteristics, if the magnetic field and geometric configuration are selected properly.

Computational Model for Radial Plain Bearing with Non-Circular Bearing Surface Profile and Fusible Coating on Shaft Surface

The paper presents a study based upon: a Newtonian fluid flow equation (“thin layer”), a continuity equation, and an equation of the molten-profile radius for a shaft coated with a fusible metal alloy; considering a mechanical energy dissipation rate formula, the authors produced an asymptotic and accurate automodel solution for the zero approximation (melting ignored) and first approximation (adjusted for melting) of a radial plain bearing featuring a fusible metal coating and a bearing profile adapted to the specific friction parameters. The paper further presents analytical dependencies describing the molten surface radius, velocity and pressure fields for zero and first approximation. Besides, it determines the key operating parameters of the frictional couple, the bearing capacity, and the friction. It also shows how the parameters arising from the melting of the surface affect the bearing capacity and friction where the bearing surface profile is adapted to the specific conditions of friction.

Mathematical formulation of the film thickness in a multi-pad externally adjustable hydrodynamic bearing using the transformation technique

Instability problem of a hydrodynamic plain journal bearing at higher speeds is conventionally resolved by using the non-circular bearings. High speed precision rotating shafts demands accurate positioning of the journal centres. A multi-pad adjustable bearing is a non-circular bearing, provides a fine-tuning option of the journal centre by continuously changing the bearing profile. In the present study, the bearing has a configuration of four bearing pads that are adjustable both in the radial and tilt directions. The fluid film thickness profile is conventionally obtained using the trigonometric relations, which has computational limitations, especially in multi-pad adjustable bearings. In this investigation, the film thickness profile of a multi-pad adjustable bearing is mathematically formulated using the transformation technique. The results obtained are compared with those available in the literature for a similar bearing. The observation shows that transformation technique eliminates the projection approximation error present in the conventional technique.

Control of self-excited rotor disturbances in three-lobe journal bearing space using a couple stress lubricant

In this study, the dynamic behavior of three-lobe noncircular hydrodynamic journal bearings lubricated with couple stress fluid is presented. Currently, application of journal bearings with different geometries such as lobed bearings and using non-Newtonian lubricants, including various additives, are the common suggested solutions by tribology researchers to improve the performance of rotor-journal bearing systems. Due to the incompatibility of new lubricant behaviors including polymer chains or other types of suspended particles with considerable size from the classic Navier–Stokes equations, different models such as couple stress fluid theory have been proposed to evaluate their performance. To investigate the self-excited rotor disturbances caused by various factors, like operating in critical speeds, simultaneous solution of governing Reynolds equation of oil lubricant and the rotor motion equations has been done. The result of dynamic analyses using linear and nonlinear approaches indicates the possibility of enhancing the stiffness and damping ability of the three-lobe bearings by strengthening the couple stress properties of lubricant. It is seen from the results that by increasing the couple stress parameter of oil, the type of rotor perturbations in the bearing clearance space changes from divergent oscillations, as a leading cause of collision between the rotor surface and the bearing shell, to limit cycle motion around the rotor stable position or convergent fluctuations to the static equilibrium point. This improvement in the stability range of three-lobe journal bearings using a couple stress lubricant appears in the results of a linear analysis model in terms of increasing the critical mass parameter and decreasing the whirl frequency ratio. In addition, bifurcation diagram results show that using noncircular three-lobe bearings instead of circular types and replacing the Newtonian lubricant with the couple stress fluid improve the dynamic stability of rotor- bearing supports.

Static thermal performance evaluation of elliptical journal bearings with nanolubricants

Journal bearings of different configurations have been extensively used in turbomachinery and power generating equipments. Although circular bearings have simplest configuration and commonly used journal bearings, non-circular bearings such as multi-lobe and elliptical bearings have an added advantage of lower lubrication film temperature alongwith stable operation. In this study, static thermal performance of pure elliptical bearing lubricated with nanoparticles based mineral oils has been studied at different eccentricity ratios and bearing speeds. Two types of nanoparticles, namely, CuO and TiO2 with 0.5, 1.0 and 2.0 wt.% concentrations have been separately added in three different viscosity grades of oils. The effect of nanoparticles on thermo-physical properties of oil was considered to compute bearing performance parameters (pressure distribution, load capacity, oil temperature and power losses). Bearing model was generated by taking into account the modified Krieger Dougherty method to determine viscosity at different combinations of oils and nanoparticles. The findings indicate the increase in maximum pressure and load capacity with addition of nanoparticles and this increase was more pronounced at higher concentrations of nanoparticles and at higher viscosity grade oils. Load capacity was found to be increased by 14.24% and 9.21% with 2 wt% concentration of TiO2 and CuO nanoparticles respectively in base oil (AW68) at eccentricity ratio of 0.7. An increase in load capacity with nanolubricants was achieved without an appreciable increase in oil temperature.

Thermal studies of steadily loaded surface‐textured noncircular journal bearing profiles to investigate the performance characteristics

AbstractThe present research study is carried out to study the performance characteristics of two noncircular journal bearing profiles. Experiments are conducted on a phosphorous bronze hydrodynamic journal bearing test rig to measure the circumferential oil film pressure as well as on the temperature profile at different radial loads and constant rotational speeds to measure bearing performance characteristics, such as oil flow rate, maximum temperature, and pressure. Results reported that noncircular bearings can withstand higher load and minimum power losses than circular bearings. Also, with an increase in the radial load, the oil film pressure and temperature also increased. However, a reduction in negative pressure gradient is reported along the circumference of the lobe resulting in lesser thermal degradation in comparison with the cylindrical bearing.

Influence of thermal pressure and temperature profile approximations in thermohydrodynamic analysis of surface‐textured noncircular journal bearing

AbstractThe present study aims to study the thermohydrodynamic performance of noncircular journal bearings lubricated with multigrade oil. Experimental investigations are carried out on phosphorous bronze hydrodynamic journal bearing with a surface textured at different loading conditions with multigrade oil (MAK 2T oil) as lubricant at different constant rotational speeds (i.e., 1000–4000 rpm) for studying the dynamic characteristics. The journal‐bearing's thermodynamic behavior is analyzed by simplifying modified Reynolds and energy equations to obtain surface‐textured bearing performance characteristics, such as load‐carrying capacity, mass flow rate, and power loss. The noncircular bearings suggest several design parameters, such as a tilt angle for designers. By considering thermal effects for MAK 2T oil lubricant, the requirements of a specific application can be fulfilled.

Dynamic stability of micropolar lubricated hydrodynamic offset-halves journal bearings

The plain circular journal bearings are not found to be stable by researchers when used in high speed rotating machineries. Hence, extensive research in the study of stability characteristics of non-circular bearings or lobed bearings assumed importance, of late. Present article deals with the stability analysis of non-circular offset bearing by taking selected set of input and output parameters. Modified Reynolds equation for micropolar lubricated rigid journal bearing system is solved using finite element method. Two kinds of input parameters namely, offset factors (0.2, 0.4) and aspect ratios (1.6, 2.0) have been selected for the study. The important output characteristics such as load, critical mass, whirl frequency ratio, and threshold speed are computed and plotted for various set of values of input parameters. The results obtained indicate that micropolar lubricated circular offset bearing is highly stable for higher offset factor and higher aspect ratio.

A Technical Review on the Study of Stability Analysis of Non-Circular Bearings Lubricated with Newtonian/Non-Newtonian Fluids

In recent years, applications of non-Newtonian fluids as lubricants have received great interest since the use of these non-Newtonian lubricants showed an increase in load carrying capacity and reduction in frictional force with the escalation in additives concentration. The demands of the present day industry rotating machinery includes high speed, compactness, light weight engines, high operating loads, high power transmission, high efficiency, and high performance of the engine. As a result of high speed machines, bearings are inclined to have excessive power loss and increase in oil temperature. The former reduces the efficiency of the engine and the latter causes the undesired changes in the lubricating oil. The plain journal bearings at high rotation speeds are subjected to instability like oil whirl and whip ruining the bearing and also the machine. Therefore, this poses a need to change in the bearing design. In the present paper, an attempt is made to briefly introduce the various non-linear models used and the different approaches that have been carried out by the researches in the past few years to improve and achieve the stability of journal bearing along with enhanced performances and characteristics.

Thermo-hydrodynamic performance of tilted non-circular micropolar lubricated journal bearings

PurposeThe purpose of this study is to examine the thermo-hydrodynamic performance of tilted non-circular journal bearings lubricated with a micropolar fluid. The investigated bearing types are two- and three-lobe journal bearings with finite length.Design/methodology/approachFor this purpose, modified Reynolds, energy and three-dimensional Laplace equations are solved numerically by using generalized differential quadrature method. The effects of micropolarity characteristics of lubricants, such as characteristic length and coupling number, as well as tilt angle as a design parameter, on the performance of non-circular two- and three-lobe journal bearings are studied.FindingsThe results show that the tilt angle can affect the temperature and pressure profiles causing variation in the performance of non-circular bearings. Increasing coupling number and decreasing characteristic length cause the load-carrying capacity to decrease because of the increase in maximum oil temperature of the fluid film of lubricant and decrease in the minimum oil base viscosity. So, it is possible to select suitable values of tilt angle for achieving optimum performance of these bearings.Originality/valueThe non-circular bearings suggest several design parameters such as tilt angle for designers. By considering thermal effects for micropolar lubricant, the requirements of a specific application can be fulfilled.

Tilt angle effects on the performance of micropolar lubricated noncircular journal bearings

PurposeThe purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular, two, three and four lobe journal bearings.Design/methodology/approachReynolds equation in dynamic state is modified considering the micropolarity characteristics of lubricant, and it is solved using generalized differential quadrature method. The perturbed components of the dynamic pressure are extracted based on the linear dynamic model. To explain the transient state of the governing equation, through the linear dynamic approach, the whirling motion of rotor around the steady state position is assumed to be harmonic.FindingsIt is observed from the results that tilt angle has significant effects on the steady state and stability performance of lobed journal bearings. It may be selected suitably to improve the performance of rotor-bearing system, while all other lubricant properties and noncircular bearing design parameters are kept fixed. Results show that among the three types of bearings considered, the dynamic performance of two lobe bearings are more affected by the variation of tilt angle.Originality/valueThe present study is mainly concerned with the effects of tilt angle as a design parameter on the stability performance of a hydrodynamic noncircular journal bearing lubricated with micropolar fluid.

The Effect of Non-Circular Bearing Shapes in Hydrodynamic Journal Bearings on the Vibration Behavior of Turbocharger Structures

Increasing quality demands of combustion engines require, amongst others, improvements of the engine’s acoustics and all (sub)components mounted to the latter. A significant impact to the audible tonal noise spectrum results from the vibratory motions of fast-rotating turbocharger rotor systems in multiple hydrodynamic bearings such as floating bearing rings. Particularly, the study of self-excited non-linear vibrations of the rotor-bearing systems is crucial for the understanding, prevention or reduction of the noise and, consequently, for a sustainable engine acoustics development. This work presents an efficient modeling approach for the investigation, optimization, and design improvement of complex turbocharger rotors in hydrodynamic journal bearings, including floating bearing rings with circular and non-circular bearing geometries. The capability of tonal non-synchronous vibration prevention using non-circular bearing shapes is demonstrated with dynamic run-up simulations of the presented model. These findings and the performance of our model are compared and validated with results of a classical Laval/Jeffcott rotor-bearing model and a specific turbocharger model found in the literature. It is shown that the presented simulation method yields fast and accurate results and furthermore, that non-circular bearing shapes are an effective measure to reduce or even prevent self-excited tonal noise.

A comparative study of the preload effects on the stability performance of noncircular journal bearings using linear and nonlinear dynamic approaches

In this work, the effects of preload factor on the stability performance of noncircular two and three lobe journal bearings with incompressible micropolar lubricant are presented based on the linear and nonlinear dynamic models. Assuming that the rotor is rigid, the governing Reynolds equation for the hydrodynamic lubrication of finite length lobed journal bearings has been modified using micropolar theory. Then, the linear and nonlinear dynamic models which include a certain harmonic disturbance and a time dependent trajectory of rotor center are applied to analyze the stability performance of the considered bearings. The generalized differential quadrature method and fourth-order Runge–Kutta technique have been used to solve the governing Reynolds equation and time-dependent dynamic equations of rotor motion, respectively. Finally, the numerical results for the critical mass parameter and the whirl frequency ratio of the rotor as the stability characteristics of the lobed bearings are obtained for different values of preload factor and are compared together. Results show that the dynamic stability of the noncircular bearings is enhanced by decreasing the preload factor i.e. increasing the amount of bearing noncircularity. These enhancements are in terms of increase of the critical mass parameter and decrease for the whirl frequency ratio. Also, by comparing the two dynamic analysis methods, it is seen that the results of linear model are more conservative in different investigated cases. The results of nonlinear analysis reveal that by changing the preload factor the dynamic responses of the lobed bearings appear in different manners. From the responses, it is observed that the type of dynamic trajectory of rotor center varies from stable fixed point to limit cycle periodic motions and also contact between rotor and bearing’s shell.

A study on the stability performance of noncircular lobed journal bearings with micropolar lubricant

In this paper, steady-state and stability performance characteristics of circular and noncircular two-, three-, and four-lobe journal bearings with micropolar fluids are presented. For this purpose, lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation in dynamical state is obtained using the micropolar lubrication theory, and it is solved by finite element method. The bearing performance characteristics in terms of load carrying capacity, whirl frequency ratio, and critical mass parameter of journal are determined for different values of design parameters such as eccentricity and aspect ratio, preload factor, and micropolarity characteristics of lubricant in terms of material characteristic length and coupling number. Results show that in the case of noncircular bearings, the critical mass to load carrying capacity ratio decreases with increasing of preload factor, so for a constant vertical external load, the stability performance of rotating system can be improved by replacing the circular journal bearing with similar noncircular types. The results compared with Newtonian fluids indicate that micropolar lubricant exhibits better steady-state and dynamic performance. Also, results reveal that upgrading the micropolarity characteristics of lubricant causes increase in critical mass, load carrying capacity but decrease in whirl frequency ratio. It is also observed that the effect of micropolar fluids is more pronounced at high coupling numbers.

Preload effects on the static performance of multi-lobe fixed profile journal bearings with micropolar fluids

The performance of non-circular bearings, such as multi-lobe bearings is influenced by many bearing parameters such as the number of lobes, the preload factor, and the tilt angle. In this study, the effects of bearing preload factor on the static performance characteristics of micropolar lubricated two-, three-, and four-lobe bearings are investigated. For this purpose, modified Reynolds equation for micropolar fluids is solved by FEM, to find the fluid film pressure.Then, in turn, bearing performance characteristics, namely, load-carrying capacity, attitude angle, frictional force, friction coefficient, and side leakage flow are calculated. Results show that, in general, micropolarity of the lubricant improves the performance of the bearings; however, non-circularity parameter of the lobe of the bearings, preload, has a favourable effect on certain performance characteristics of the bearings, such as the attitude angle which decreases as non-circularity of the bearing increases. The results further show that the rate of influence of preload factor on the performance characteristics of different lobed bearings is not the same.

Preload effect on nonlinear dynamic behavior of a rigid rotor supported by noncircular gas-lubricated journal bearing systems

This paper presents the effect of preload, as one of the design parameters, on nonlinear dynamic behavior of a rigid rotor supported by gas-lubricated noncircular journal bearings. A finite element method has been employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using the Runge–Kutta method. To analyze the behavior of the rotor center in horizontal and vertical directions under different operating conditions, dynamic trajectory, power spectra, Poincare maps, and bifurcation diagrams are used. Results of this study reveal how the complex dynamic behavior of two types of noncircular bearing systems comprising periodic, KT-periodic, and quasi-periodic responses of the rotor center varies with changes in preload value.

Effect of bearing number on non-linear dynamic behaviour of aerodynamic non-circular journal bearing systems

The present article presents the effect of bearing number on non-linear dynamic behaviour of a rigid rotor supported by aerodynamic non-circular journal bearings. A finite-element method has been employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using the Runge-Kutta method. To analyse the behaviour of the rotor centre in the horizontal and vertical directions under different operating conditions, dynamic trajectory, power spectra, Poincare maps, and bifurcation diagrams are used. The results of this study reveal how the complex dynamic behaviour of these three types of non-circular bearing systems comprising periodic and KT-periodic responses of the rotor centre varies with changes in bearing number values.

Lubrication Analysis of a Connecting-Rod Bearing in a High-Speed Engine. Part II: Lubrication Performance Evaluation for Non-Circular Bearings

In this article a numerical investigation of a connecting rod bearing operating at 6,500 rpm is performed. This is a companion to an earlier article that took into account the effects of the inertial force and the variable bolt tension force, which are considered to be the principal factors that affect the connecting rod bearing lubrication characteristics of an engine running at high speed. It was found that a thinner minimum oil film and a larger peak hydrodynamic pressure are predicted in a deformed connecting rod bearing than in a rigid connecting rod bearing. Multi-peaked hydrodynamic pressure was found to appear as well because of two or more converging-diverging film regions.

Study on Improvement of Stability of Noncircular Journal Bearings(Stability Analysis for Various Bearing Orientation Angles)

Noncircular journal bearings, such as multi-lobe, offset, stepped bearings are used widely for supporting the high speed rotating machinery because of their advantages of relatively low manufacturing costs, stability, load carrying capacity and durability as compared with fullcircular bearings. The stability of noncircular journal bearings are influenced by many bearing parameters such as clearance, preload factor, length-to-diameter ratio, feed hole location etc. However, it is not clear the effects of bearing orientation angle, which is equivalent to the location of applied load line, on the stability of hearings. In this study, the effects of bearing orientation angle on the stability of rotating shaft supported symmetrically by the noncircular bearings are examined theoretically.

A comparative thermal analysis of the static performance of different fixed profile bore plain bearings

Profile bore bearings are important components in high-speed rotating machinery. In order to provide bearing designers with some useful information on the performances of different bearing profiles, this paper presents a theoretical evaluation of five commonly used types of bearing through a comparison of their steady state performance characteristics. The bearings investigated were two-lobe circular, elliptical (lemon-bore), offset-half, three-lobe and four-lobe types. Their operating characteristics, including the minimum film thickness, maximum temperature, power loss and flowrate, have been calculated using a computerized detailed thermohydrodynamic model developed by the authors. The influences of the shaft speed, specific load, bearing pre-load ratio and lubricant viscosity index on the performance of the bearings have been investigated. In addition, the effect of oil groove angle and load orientation on a four-lobe bearing is briefly examined. Results show that, in general, the performance of the non-circular bearings is inferior to that of the circular bearing; of the non-circular types, the offset-half and elliptical bearings have better overall performances. Also, it is shown that reasonably increasing the angular size of an oil groove has a favourable effect on the static performance of a multi-lobe bearing.