Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant:
01 Jun 2019-Vol. 233, Iss: 6, pp 884-898
TL;DR: In this article, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant, and the governing Reynolds equation for pressu...
Abstract: In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressu...
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TL;DR: In this paper, the authors studied the dynamic response of fluid film bearing of finite length which is subjected to rotor misalignment Vibration analysis of the rotor is used to obtain the limits of stability at different operating conditions The lubricant flow in the bearing is considered laminar, incompressible and isoviscous.
Abstract: The present work studies the dynamic response of fluid film bearing of finite length which is subjected to rotor misalignment Vibration analysis of the rotor is used to obtain the limits of stability at different operating conditions The lubricant flow in the bearing is considered laminar, incompressible and isoviscous For a given small excitation of the bearing shaft, a time dependent Reynolds equation is introduced to investigate the dynamic response of the fluid film bearing At a misalignment direction angle and misalignment degree, nonlinear perturbation dynamic equations are introduced and solved to determine the critical stability limit of motion for different values of eccentricity ratio Vibration data is collected to obtain the transition from stable to unstable operating conditions (stability map) It is concluded here that increasing the value of misalignment degree yields to an increase in the value of critical bearing stability limit for a given value of misalignment direction angle The critical stability number increases as the misalignment direction angle decreases and/or the steady state eccentricity ratio increases
13 citations
TL;DR: In this article, the authors present a review of various numerical and experimental studies conducted for enhancing the tribological performance of journal bearings with different lubricants, and provide a valuable guide for researchers to choose the correct lubricant(s), nanoparticles, and selection of numerical and analytical methods for further exploration in the field of nanolubricants for performance enhancement of journal bearing.
Abstract: The emergence of nanotechnology and existence of computational techniques for measuring the thermophysical properties of nanolubricants has culminated in a substantial number of experimental studies over past two decades Development of nanoparticles is a field that has more proximity to innovations taking place in the domain of physics and chemistry but their application aspects have attracted the researchers towards the performance analysis of equipments with nanolubricants in diverse engineering fields This paper presents a state-of-the-art review of various numerical and experimental studies conducted for enhancing the tribological performance of journal bearings with different lubricants A comprehensive review of previously published studies has been provided as a valuable guide for researchers to choose the correct lubricant(s), nanoparticle(s), and selection of numerical and analytical methods for further exploration in the field of nanolubricants for performance enhancement of journal bearings Several practical and technical issues with their potential solutions have also been explored in the field of nanolubricants Despite their exemplary tribological performance, there is a dire need to formulate computational methods for the evaluation of journal bearing performance by taking the effects of nanolubricants into consideration
7 citations
TL;DR: In this paper , a numerical solution to the problem of finite-length journal bearing considering edge chamfering is presented, which involves the determination of the levels of lubricant layer thickness and pressure distribution in addition to the journal trajectory under impact load with the related stability limits.
Abstract: Misalignment is one of the most common challenges that the normal operation of journal bearings faces. This type of problem may be the result of a wide range of reasons, such as bearing wear, shaft deformation, and errors related to the manufacturing and installation process. The main undesirable consequences of the misalignment, such as pressure rise and lubricant film reduction, are concentrated on the bearing edges. Therefore, chamfering the bearing edges reduces such misalignment-related drawbacks. This work presents a novel numerical solution to the problem of finite-length journal bearing considering edge chamfering. This solution involves the determination of the levels of lubricant layer thickness and pressure distribution in addition to the journal trajectory under impact load with the related stability limits. The finite difference method is used in this solution, and the equations of motion are also solved numerically using the Runge–Kutta method. The Results of this novel analysis show that chamfering the bearing edges increases the film thickness and reduces pressure spikes associated with the system operation under the case of 3D misalignment. Furthermore, the chamfered bearing shows a wide stability range under impact loads, where the normal bearing is unstable as the critical speed increases by 26.98%, which has positive consequences on the journal’s trajectory.
3 citations
TL;DR: In this article, the impact of misalignment and inherent uncertainties in bearings on the stability of a rotor-bearing system was investigated, where the unknown gPC coefficients were obtained by using the collocation method.
Abstract: Stability is a well-known challenge for rotating systems supported by hydrodynamic bearings (HDBs), particularly for the condition where the misalignment effect and the parametric uncertainty are considered. This study investigates the impact of misalignment and inherent uncertainties in bearings on the stability of a rotor-bearing system. The misalignment effect is approximately described by introducing two misaligned angles. The characteristics of an HDB, such as pressure distribution and dynamic coefficients, are calculated by the finite difference method (FDM). The stability threshold is evaluated as the intersection of run-up curve and borderline. Viscosity and clearance are considered as uncertain parameters. The generalized polynomial chaos (gPC) expansion is adopted to quantify the uncertainty in parameters by evaluating unknown coefficients. The unknown gPC coefficients are obtained by using the collocation method. The results obtained by the gPC expansion are compared with those of the Monte Carlo (MC) simulation. The results show that the characteristics of the HDB and the stability threshold are affected by misalignment and parameter uncertainties. As the uncertainty analysis using the gPC expansion is performed on a relatively small number of predefined collocation points compared with the large number of MC samples, the method is very efficient in terms of computation time.
3 citations
TL;DR: In this paper , a numerical solution of the hydrodynamic lubrication problem of a finite length journal bearing, considering 3D misalignment cases using the finite difference method is presented.
Abstract: Journal bearings in typical applications are subjected to misalignment due to several causes, such as shaft deformation under load and errors related to the installation and manufacturing processes. Misalignment has well-known severe negative consequences on the performance of the bearings. This paper deals with the bearing chamfer to reduce these consequences of misalignment, and two forms of bearing edge modification are considered in the analysis. These forms are linear and curved chamfering of the bearing edges, where the height of the chamfer in the circumferential direction and the length of the modification in the longitudinal direction are considered as geometrical design parameters. The investigation includes a numerical solution of the hydrodynamic lubrication problem of finite length journal bearing, considering 3D misalignment cases using the finite difference method. This includes the assessment of the chamfer forms and their effects on the bearing performance in terms of the main bearing design parameters. Furthermore, the stability of the chamfered bearings is also investigated under impact load. Results showed that both chamfer forms are beneficial for a certain limit of the design parameters in reducing the maximum pressure and coefficient of friction and in elevating the film thickness levels, extending the range of misalignment in which the journal bearing can operate safely. In addition, the chamfered bearings in both forms showed more stability range in terms of the critical speed and shaft center trajectories under impact load. The bearings with the curved chamfer, where the slope is continuous at the start of modification, showed more uniform film thickness levels, and their shaft center trajectories were closer to the perfectly aligned bearing in the stable operating range of the system.
1 citations
References
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TL;DR: In this paper, a generalized form of the Reynolds equation is developed which permits variation of relevant quantities across, as well as along, the lubricant film, and it can be reduced to any of the forms currently employed in the analysis of fluid-film bearings.
484 citations
TL;DR: In this article, the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined, and a suitable symmetry was given to the rotor, to the supporting system, to acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl.
Abstract: In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined. A suitable symmetry was given to the rotor, to the supporting system, to the acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected conveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be carried out by means of numerical investigation, the procedure here adopted by the authors consists of numerical integration of the rotor's equations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half non-dimensional mass of the rotor, σ, the modified Sommerfeld number relating to the lubricated bearings, and ρ, the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces due to the lubricating film are written under the assumption of isothermal and laminar flow in short bearings. The number of numerical trials needed to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when the value of the dimensionless static eccentricity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabew7aLnaaBaaaleaacaWGZbaabeaaaaa!4046!\[\varepsilon _s \] is greater than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (ρ=0.05), whereas higher values (ρ>0.4) make the rotor motion periodic and synchronous with the driving rotation. The present investigation has also identified the route that leads an assigned rotor to chaos when its angular speed is varied with prefixed values of the dimensionless unbalance ρ. The theoretical results obtained have then been compared with experimental data. Both the theoretical and the experimental data have pointed out that in the circumstances investigated chaotic motions deserve more attention, from a technical point of view, than is normally ascribed to behaviours of this sort. This is mainly because such behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The present analysis has shown that when the rotor exhibits chaotic motions, the centres of the journals describe orbits that alternate between small and large in an unpredictable and disordered manner. In these conditions the thickness of the lubricating film can assume values that are extremely low and such as to compromise the efficiency of the bearings, whereas the rotor is affected by inertia forces that are so high as to determine severe vibrations of the supports.
224 citations
TL;DR: In this article, the effects of the size of material characteristic length and the coupling number on the static performance of noncircular bearing configurations were investigated, and the results showed that micropolar lubricants can produce significant enhancement in the dynamic performance characteristics.
86 citations
TL;DR: In this paper, the impact oscillators with one-sided elastic and rigid constraints were investigated by a path-following (continuation) method and the grazing bifurcations were computed and classified for both oscillators.
81 citations