Hydrodynamic Plain Journal Bearing Research Articles

Multi-objective design optimization of hydrodynamic journal bearings using a hybrid approach

PurposeIn this work, the design problem of hydrodynamic plain journal bearings is formulated as a multi-objective optimization problem to improve bearing performance under different operating conditions.Design/methodology/approachThe problem is solved using a hybrid approach combining genetic algorithm and sequential quadratic programming. The selected state variables are oil leakage flow rate, power loss and minimum oil film thickness. The selected design variables are the radial clearance, length-to-diameter ratio, oil viscosity, oil supply pressure and oil supply groove angular position. A validated empirical model is adopted to provide relatively accurate estimation of the bearing state variables with reduced computations. Pareto optimal solution sets are obtained for different operating conditions, and secondary selection criteria are proposed to choose a final optimum design.FindingsThe adopted hybrid optimization approach is a random search algorithm that generates a different solution set for each run, thus a different bearing design. For a number of runs, it is found that the key design variables that significantly affect the optimum state variables are the bearing radial clearance, oil viscosity and oil supply pressure. Additionally, oil viscosity is found to represent the significant factor that distinguishes the optimum designs obtained using the implemented secondary selection criteria. Finally, the results of the proposed optimum design framework at different operating conditions are presented and compared.Originality/valueThe proposed multi-objective formulation of the bearing design problem can provide engineers with a systematic approach and an important degree of flexibility to choose the optimum design that best fits the application requirements.

Performance of nano-bio-lubricants, ISO VG46 oil and its blend with Jatropha oil in statically loaded hydrodynamic plain journal bearing

In this experimental study, three stable nano-bio-lubricants were prepared by dispersing CuO nanoparticles in three bio-lubricants and later investigations were carried out to determine pressure distribution and frictional performance of ISO VG46 oil, bio-lubricants and nano-bio-lubricants in hydrodynamic journal bearing under different loads and speeds. The experimental results revealed that pressure of oils inside bearing depends on viscosity of oils. Addition of nanoparticles in bio-lubricants did not help to enhance the maximum pressure of oil inside bearing. Frictional performance of ISO VG46 oil and bio-lubricants was according to their viscosity but coefficient of friction of nano-bio-lubricants was higher compared to ISO VG46 oil inspite of having approximately same viscosity compared to ISO VG46 oil. Among all the oils, ISO VG46 oil and bio-lubricant 9010 had similar performance and hence Bio-lubricant 9010 can be used in place of ISO VG46 oil in journal bearing.

Necessary parameter setting of the finite‐difference method for determining selected rotor‐dynamics characteristics

AbstractThe aim of the study is to analyse the adequacy of the finite difference‐method (FDM) for determining the stability boundary of a rigid rotor mounted on short hydrodynamic plain journal bearings through the solution of the Reynolds partial differential equation (PDE). The Reynolds equation, obtained by coupling the equation of motion with the continuity equation, governs the pressure distribution in a lubricant film. The quasi stationary form of this equation requires normalization prior to solving, for the numerical error of the FDM to be minimized. Except for numerical benefits, the dimensionless form of the PDE is universally applicable to a bride spectrum of tribological problems, including hydrodynamic plain journal bearings. The present study first examines the adequacy of solver settings, including the computational grid, through comparison of the corresponding numerical results with an analytical solution obtained by means of the Short Bearing Theory (SBT). Two characteristic tribological quantities are selected as the basis for comparison: the modified Sommerfeld number and the bearing attitude angle. Further, dimensionless stiffness and damping tensors, valid for any short hydrodynamic plain journal bearing, are determined from the numerically obtained distribution of the dimensionless hydrodynamic pressure. These two dimensionless tensors allow for the subsequent estimation of the stability boundary, which marks the dimensionless speed at which a given rigid rotor becomes dynamically unstable. The results of the current study demonstrate sensitivity of the FDM results to the numerical step size. The corresponding numerical error is verified using the SBT and presented as function of the dimensionless (relative) journal eccentricity together with rotor start‐up curves. As a major finding, a dimensionless range of the step size is identified for the error to remain below 5%.

On the modified Reynolds equation for journal bearings in a case of non-Newtonian Rabinowitsch fluid model

In this paper, a theoretical analysis of hydrodynamic plain journal bearings with finite length at taking into account the effect of non-Newtonian lubricants is presented. Based upon the Rabinowitsch fluid model (cubic stress constitutive equation) and by integrating the continuity equation across the film, the nonlinear modified 2D Reynolds type equation is derived in details so that to study the dilatant and pseudoplastic nature of the lubricant in comparison with Newtonian fluid. A dimensionless equation of hydrodynamic pressure distribution in a form appropriate for numerical modeling is also presented. Some particular cases of 1D applications can be recovered from the present derivation.

Theoretical study on a novel electromagnetically supported hydrodynamic bearing under static loads

Abstract A novel hydrodynamic plain journal bearing is presented, in which the thickness of the lubricant is simultaneously used as an airgap of the electromagnetic system. The bearing combines the advantages of hydrodynamic and magnetic bearings, and can be manufactured as one coherent unit. This paper develops a new governing equation system describing stationary loci of such an electromagnetically supported short hydrodynamic plain journal bearing under hydrodynamic, electromagnetic and gravity forces. The derived ordinary equation system describing an implicit equilibrium position of the bearing is solved semi-analytically for different hydrodynamic and electromagnetic loads to provide equilibrium loci. This solution is subsequently verified by means of the Finite Difference Method.

Determination of stiffness coefficients of hydrodynamic water-lubricated plain journal bearings

The purpose of this paper is to provide an efficient method for determining the stiffness coefficients of hydrodynamic plain journal bearings lubricated by water. In addition to the different physical properties of water and oil, the cavitation effect of water is taken into account. The relationships between the stiffness coefficients and the load for bearings with different relative clearances, different length-to-diameter ratios and different rotational speeds are obtained. Bearings with different diameters are also studied to determine how load carrying capacity and stiffness coefficients change with diameter. Finally, a method is provided for determining the stiffness coefficients of such bearings.

Fuzzy Logic based Model to Predict Maximum Oil-Film Pressure in Journal Bearing

Oil-film pressure response is one of the key parameters that describe the operating conditions in hydrodynamic lubrication regimes. In the present study, a fuzzy logic model is developed to predict the maximum oil-film pressure in hydrodynamic plain journal bearing. In the development of predictive model, journal bearing parameters of rotational speed, bearing load and oil-feed pressure are considered as model independent variables. For this purpose, a number of experiments, based Box-Behnken experiment Design technique (BBD), are performed to observe the maximum oil-film pressure values. The results revealed that the model is able to predict maximum oil-film pressure adequately.

Application of Fuzzy Logic Approach to Predict Maximum Oil-Film Pressure in Journal Bearing

In the present work, a fuzzy logic model is developed to predict the oil-film pressure in hydrodynamic plain journal bearing. In the development of predictive model, journal bearing parameters of speed, load and oil-feed pressure are considered as model independent variables. For this purpose, a number of experiments, based Box-Behnken experiment design technique, are performed to observe the oil-film pressure values. The results revealed that the model is able to predict the oil-film pressure adequately.

Application of Response Surface Methodology to Predict Oil-Film Friction in Journal Bearing

Oil-film friction response is one of the key parameters that describe the operating conditions in hydrodynamic lubrication regimes. In the present paper, response surface methodology (RSM) with Box-Behnken experiment Design technique (BBD) has been utilized to predict and evaluate the effects of the three-level-three-independent variables on the oil-film friction. The design independent variables including rotational speed, load and oil-feed pressure were used to develop an empirical model for the oil-film friction in hydrodynamic plain journal bearing. A salient feature of this study is to investigate the interaction between the main three factors and provide a profound understanding on the significance of each factor. The analysis of variance (ANOVA) of the regression model and comparison of predicted and observed response values have showed good correspondence, implying that empirical model derived from response surface approach can predict the response adequately.

Morton Effect Induced Synchronous Instability in Mid-Span Rotor–Bearing Systems, Part 2: Models and Simulations

The mechanism of the Morton Effect induced synchronous instability has been discussed in Part 1, using an assumption of isotropic linear bearings. The second part of the current study will now focus on the more realistic systems, mid-span rotors supported by the hydrodynamic journal bearings. First, the models to calculate the thermal bending of the shaft and the temperature distribution across the journal surface are established. This can be used to calculate the equivalent thermal imbalance. The calculations of the temperature difference and its equivalent thermal imbalance using hydrodynamic plain journal bearing models are conducted and discussed with the comparison to the analytical results obtained in Part 1. It shows that the thermal imbalance induced by the Morton Effect may increase to the level of the mechanical imbalance and then its influence on the system stability should be included. The suggested thermal bending model also partially explains that the mid-span rotors are less liable to be influenced by the Morton Effect induced instability than are the overhung configurations, because of the restraining effect between two supports. Finally, a symmetric mid-span rotor - hydrodynamic journal bearing system is calculated to show its stability performance. The results show the inclusion of the Morton Effect may lead to an unstable operation of the system. Considering the existence of the oil film self-induced vibration due to the dynamic characteristics of fluid film bearings, the Morton Effect may make a further negative impact on the stability of the system. The simulation results of the unbalance response show that the Morton Effect changes the shapes of the whirling orbits and makes them no longer the standard elliptical orbits around the static equilibriums.

Experimental measurement of the friction torque on hydrodynamic plain journal bearings during start-up

Due to the increasing interest in energy savings, the start-up friction coefficient is a very useful parameter for engineers, who design hydrodynamic bearings. It is most often based on an approximation. Several studies can be found in the literature on this topic, but most of them are concerned with air bearings or are just numerical models. Some studies are more general and deal with the transient thermal behavior in both journal bearings and thrust bearings. Other studies deal with the friction coefficient during running, given a constant rotational speed. In order to understand the mechanisms occurring during the transition between mixed lubrication and hydrodynamic lubrication, several studies [1–4] have been conducted over the past three years. The aim of this paper is to provide an overview of the results of these studies and also to draw several general conclusions on the behavior of a plain journal bearing during start-up. The first part of the results focuses on the measurement of bearing torque during start-up with varying specific pressure (load divided by the projected area). Thus, the friction coefficient at start-up (deduced from measurements) is obtained for four different bearings, varying feeding conditions, radial clearance and length. The second part of the results consists of observations relating to the stick–slip phenomenon which occurs during this transient period. Finally, a study dealing with bearing characteristics influencing the friction coefficient (surface roughness and bearing materials) is presented. The main focus of this work is then to provide useful experimental data for bearing users and designers.

Stability analysis of a disk-spindle supported by a plain journal bearing and pivot bearing

A hydrodynamic bearing is widely used for hard disk drives, and it is better than a ball bearing in terms of vibration suppression, noise reduction and shock resistance. However, its cost to performance ratio should be further improved. In this study we analyzed the stability of a disk-spindle assembly supported by a hydrodynamic plain journal bearing and a pivot bearing at the bottom of the shaft. As a result, we found that a half-frequency whirl of a vertical spindle caused by the plain journal bearing becomes stable if the gyro factor of the rotor is larger than 0.5. We examined the effects of the bearing design parameters on the stability of the disk-spindle assembly, including the flexibility of the shaft. We also compared the stability of a disk-spindle assembly supported by two plain journal bearings and found that the vertical spindle is always unstable. Thus, the bottom end of the shaft should be supported as a fulcrum.

The effects of journal lobing on the performance of a hydrodynamic plain journal bearing

Accurately ground journals nominally of 44.25 mm diameter and 63.5 mm wide were produced. One was cylindrical and the others had three, four, five, six, nine or twelve equispaced lobes, 0.025 mm high, on their peripheries. Each journal was fitted into a cylindrical lead-bronze bearing liner with a radial working clearance of 0.05 mm and operated at speeds of up to 1000 rev min −1 and at bearing loads of up to 10 kN whilst the oil pressure was maintained at or just above atmospheric pressure. The test results indicated that when a comparison is made between the lobed journals and the cylindrical journal (1) there are no significant differences in the load-carrying capacity of the bearing and (2) in the higher portion of the loading range the boundary lubrication conditions are improved when using three- or four-lobed journals whilst the presence of lobes on the other journals produces only a slightly adverse effect, It was concluded that the effect of lobing, which often occurs accidentally during the manufacture of plain cylindrical journals, is not detrimental to the performance of the bearing when operated within the range of speeds and loads used.