Hydrodynamic Rolling Research Articles

The maximum dynamic eccentricity ratio of hydrodynamic rolling hybrid bearings

Hydrodynamic Rolling Hybrid Bearing (HRHB) is dual bearings combination where a hydrodynamic bearing and a rolling bearing with a clearance are assembled coaxially and side by side. The clearance of rolling bearing is a significant parameter for HRHBs. This paper aims to investigate the vibration characteristics of rotor supported by HRHBs to determine the permissible value of clearance of rolling bearing. The maximum dynamic eccentricity ratio is proposed based on the noninterference conditions of rolling bearing and rotor. Then an evaluation method of the maximum dynamic eccentricity ratio is developed. This paper also investigates the effects of the operation parameters such as rotational speed, perturbed force and structure parameters such as bearing span, diameter of rotor, and overhanging length on the maximum dynamic eccentricity ratio. The maximum dynamic eccentricity ratio on the front rolling bearing section is obviously larger than that on the back rolling bearing section. Moreover, the maximum dynamic eccentricity ratio reduces with the increase of the rotational speed and diameter of rotor, but increases with the augmentation of the perturbed force, bearing span, and overhanging length. When the maximum dynamic eccentricity does not go beyond the bound of the radius of the rolling bearing’s clearance circle, the rolling bearing does not interfere with the rotor. The paper provides theoretical basis for design of the minimum value of the rolling bearing’s clearance in HRHBs.

The Maximum Allowable Misalignment in Hydrodynamic Rolling Hybrid Bearings

A hydrodynamic rolling hybrid bearing (HRHB) assembled coaxially by a rolling bearing and hydrodynamic bearing is developed to achieve two functions at low and high speeds. At low speeds, the rolling bearing of the HRHB can be utilized to avoid wear in the hydrodynamic bearing. While at high speeds, the rotor is entirely supported by the hydrodynamic bearing, keeping away the interference of the rolling bearing. However, because the HRHB is mounted coaxially by two bearings, a misalignment cannot be avoided. This can lead two unexpected consequences: either the malfunction of the rolling bearing at low speeds or the interference of rolling bearing applied on the rotor. In this paper, a computational method to calculate the maximum allowable misalignment based on the noninterference conditions of the locus of the shaft center and rolling bearing at high speeds is proposed, and the influence of the rotating speed, the spindle, and bearing structural parameters on the maximum allowable misalignment is also analyzed. The results show that the locus of the maximum allowable misalignment forms a circle along the circumferential direction. The noninterference conditions are satisfied when the maximum allowable misalignment is inside the circle.

Effects of Rolling Bearing Type and Size on the Maximum Eccentricity Ratio of Hydrodynamic Rolling Hybrid Bearings

A hydrodynamic rolling hybrid bearing (HRHB) composed of a rolling bearing with a fixed clearance and a hydrodynamic bearing is developed to solve the wear problem in hydrodynamic bearings. In this study, the maximum eccentricity ratio is developed to assess the protection of the rolling bearing offers to the hydrodynamic bearing. An analytic model for the maximum eccentricity ratio is presented. The effects of the size of the ball bearing and cylindrical roller bearing on the maximum eccentricity ratio are investigated. The results show that the maximum eccentricity ratio is affected by the clearance constraint and contact deformation of the rolling bearing. The maximum eccentricity ratio presents itself at zero speed, at which the rolling bearing reaction is equal to the external load. The results also show that the type of rolling bearing has significant effects on the maximum eccentricity ratio. The increment of the maximum eccentricity ratio due to elastic deformation of ball bearings is about 8.6 times the increment due to elastic deformation of cylindrical roller bearings. In comparison, the size of the rolling bearing of the same type has a slight influence on the maximum eccentricity ratio. The maximum eccentricity ratio is a key parameter related to antiwear. When the maximum eccentricity ratio is smaller than the allowable value of the hydrodynamic bearing, direct contact between the hydrodynamic bearing and rotor can be avoided and the wear in the hydrodynamic bearing can thus be prevented by the rolling bearing.

The influence of the lubricant viscosity on the rolling friction torque

Authors propose a theoretical model and an experimental methodology for defining the friction torque in a modified thrust ball bearing, operating in mixed and full film lubrication conditions.The friction torque was measured at low loads and large Λ parameter range using a spin-down method.A comprehensive analytical bearing torque model is described using elastic rolling resistance, curvature effects, inertia forces, disc-air resistance and ball-races hydrodynamic rolling forces, the latter explaining 98% of the final bearing torque. Several sets of hydrodynamic rolling force relationships respecting the transition from IVR to EHL lubrication regime were tested. Final numerical results are shown to be very close to the experimental ones in both full film and mixed lubrication conditions.

Cage Speed of Hydrodynamic Rolling Hybrid Bearings

Hydrodynamic bearings are subjected to wear during starts and stops due to the absence of sufficient film pressure to effect complete separation of the sliding surfaces. In an earlier publication, our group reported the development of a new hydrodynamic rolling hybrid bearing (HRHB) to overcome the wear problem in hydrodynamic bearings. In the configuration, the transition of operation modes between the rolling bearing supporting state and the hydrodynamic bearing supporting state was realized by the clearance of the rolling bearing. Here we report on the development of a method to identify the operation modes for HRHBs based on monitoring the cage speed of the rolling bearing. The variation of cage speed with the shaft speed is measured. The effects of external load and starting time on the cage speed are also investigated experimentally. The results show that variation in the cage speed reflects changes in the load on the rolling bearing, as well as the operation modes of the HRHBs. With increases in the shaft speed, the variation in the cage speed presents three stages: the increasing stage, the decreasing stage, and the stationary stage. In the first two stages, the HRHB works at the rolling bearing supporting state while in stationary stage, the HRHB works at the hydrodynamic bearing supporting state. In additions to its property of no wear sufferance during starts and stops, compared to hydrodynamic bearings there is little risk of catastrophic failure with HRHBs during any interruption to the lubricant supply and compared to rolling bearings there is no fatigue failure. Therefore this hybrid design is useful at very high speeds.

Static characteristics of a new hydrodynamic–rolling hybrid bearing

An analytic model is developed to predict static characteristics of a new hydrodynamic–rolling hybrid bearing (HRHB). Experiments are carried out to measure the equilibrium positions, the load sharing, and the rotational speeds of the rolling bearing cage. The results show that the working states of HRHB are divided into two distinct phases by a transition speed at which the hydrodynamics and contact models are decoupled. The cage speeds can be used to determine transition speed. The theoretical results agree with the experimental results, and it can be employed to design the bearing parameters according to the expected performance.

Influence of the GZ calculation method on parametric roll prediction

Parametrically excited roll response in a container ship sailing in irregular head sea has been studied. Short-term predictions for roll have been made for a ship at a constant forward speed based on different hydrodynamic roll descriptions. The first order reliability method (FORM) has been used to obtain the probability that the roll motion will exceed a given limiting angle. The results have been compared to the results by a Monte Carlo simulation. Using FORM the computational time is greatly reduced as compared to direct simulations, still retaining the probability of failure of the correct order of magnitude. Calculations have been made for different sea states and operational conditions leading to parametric roll resonance and for relevant maximum pre-defined roll angles. The outcome of this comparative study could be useful for the decisions in an early design phase or for application to on-board decision support systems, where a computationally efficient method is needed in order to have an operationally feasible time frame.

CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations. Part III: Experimental Validation

Models used in CAGEDYN and described in Parts I and II have been validated by comparing calculated and measured values of the impact force of a ball falling on a beam, the hydrodynamic rolling force (due to the Poiseuille flow or pressure gradient in the inlet of an elastohydrodynamic lubrication [EHL] contact and responsible for the so-called hydrodynamic race torque, even when operating under pure rolling conditions), the sliding traction force in an EHL contact, bearing cage impact forces, and bearing cage slip. A description of the bearing test rig used for measuring cage impact force and cage slip is presented. The correlation obtained is satisfactory, especially when looking at the trends. The impact force increases when increasing the roller–cage pocket clearance, increasing the bearing end play (or bearing axial clearance, which causes a reduction of the load zone), and increasing the shaft speed. At very light radial load, the impact force increases with increasing radial load to a maximum value and then decreases as the radial load continues to increase. Cage slip increases as the radial load decreases and the shaft speed increases. Past cage failures and cage solutions to recent cage problems in real field applications have been explained using CAGEDYN and comparing the maximum calculated cage stress to the cage material fatigue limit.

Power Loss Predictions in High-Speed Rolling Element Bearings Using Thermal Networks

In high-speed rolling element bearings (REB), the lubricant is used to separate the mating surfaces but also to cool down the parts while the system is in operation. In the context of optimizing oil circuits, a clear understanding of the lubricant cooling mechanisms is therefore required in order to reach a compromise between a good cooling capacity and the constraints on mass, size, and power. In this article, a model is presented that makes it possible to predict temperature distributions in high-speed thrust ball bearings. It is found that the prediction or measurement of global power loss cannot discriminate between several combinations of traction and drag forces. On the other hand, the predicted temperature distributions appear as very sensitive to the relative importance given to hydrodynamic rolling tractions or drag losses. Based on these findings, a methodology is suggested in order to define the most realistic power loss models to be used in high-speed REB simulations.

Hydrodynamic force and moment in pure rolling lubricated contacts. Part 1: Line contacts

Hydrodynamic rolling force and moments in line contact have been studied in detail using isoviscousrigid (IVR) and elastohydrodynamic (EHL) models. Using fully flooded assumptions, curve-fitted relationships are suggested for calculating the IVR and EHL hydrodynamic rolling force per unit length. At high speed and light load, EHL numerical results converge towards IVR results so that a single curve-fitted relationship has been derived for covering the full range of operating conditions with a rapid transition from IVR to EHL regime of lubrication. Results obtained are often close to published results (especially in the IVR regime). The EHL hydrodynamic rolling force per unit length is found to be load independent, while load exponents ranging from 0.01 to 0.37 can be found in the literature. A single relationship for both lubrication regimes (IVR and EHL) is given for deriving a starvation factor function of the ratio between the film thickness at the inlet meniscus and the fully flooded minimum film thickness. Finally, the calculation of the total power loss per unit length has also been conducted by integrating through the film and along the rolling direction the power loss per unit volume (defined as the product shear stress time shear rate). Results obtained are consistent with the calculation of the rolling force per unit length.

Hydrodynamic force and moment in pure rolling lubricated contacts. Part 2: Point contacts

Hydrodynamic rolling force and moments in point contact have been studied in detail using isoviscousrigid (IVR) and elastohydrodynamic (EHL) models. Using fully flooded assumptions, curve-fitted relationships are given for calculating the IVR and EHL hydrodynamic rolling forces. Both are proportional (or almost proportional in the IVR case) to 2 a, the Hertzian contact length being perpendicular to the rolling direction, and are also functions of the dimensionless speed parameter. A single curve-fitted relationship has been derived to cover the full range of operating conditions with a smooth transition from IVR to EHL regime of lubrication. The results obtained are slightly higher than those previously published (the ratio being of the order of 1.5 for usual operating conditions). Point contact and line contact (with a contact length £ being equal to the point contact length 2 a) hydrodynamic rolling forces have also been compared. The point contact forces are about 26 per cent larger than those obtained using line contact relationship (published in part 1) because of a larger domain of integration in the lateral direction. By limiting the width of the integration domain to £ (roller length or ball diameter), the effect of 2 a/£ on the hydrodynamic rolling force has been studied, leading to the derivation of a truncation factor C. As the load increases, 2 a increases and the truncation factor decreases until reaching a limit when ellipse truncation starts because 2 a/£ is equal to or larger than one. Using the truncation factor and limiting the 2 a/£ ratio to one, it was found that point contact and line contact hydrodynamic forces are the same within a few per cent. A single point contact relationship can therefore be suggested, covering the IVR to EHL operating conditions with a smooth transition between these lubrication regimes, and also a smooth transition from point contact to line contact as the load increases and contact ellipse truncation occurs. Finally, calculations of power losses due to the Poiseuille flow in the rolling direction x and in the perpendicular direction z show that the power loss in the z direction is usually very small for wide elliptical contacts and that most of the power is dissipated in the inlet and outlet, with a 26 per cent contribution of the integration domain defined out the range − a < z < a. This result is in line with the truncation factor defined previously.

CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations Part I: Basic Tribology Concepts

Basic relationships and physical concepts used for the development of a bearing dynamic tool (called CAGEDYN) are explained. Emphasis is put on some key physical concepts affecting the calculated cage impact forces: the appropriate roller-cage contact stiffness (derived herein using a novel equivalent stiffness), the tangential hydrodynamic rolling and pressure forces, the hydrodynamic effect on the roller normal load (for which a new relationship is given for calculating a load, even when there is no interference between the roller surface and counter race or cage bridge surface), and the appropriate traction force calculated using a nonlinear viscous model and contact temperature increases.

Estimation of the Roll Hydrodynamic Moment Model of a Ship by Using the System Identification Method and the Free Running Model Test

When a fast container ship or a naval vessel turns, accompanying roll motions occur. This roll effect must be considered in the horizontal equations of the motion of the ship to predict the maneuverability of the ship properly. In this paper, a new method for determining a model structure of the hydrodynamic roll moment acting on a ship and for estimating the hydrodynamic coefficients is proposed. The method utilizes a system identification technique with the data from sea trial tests or from free running model (FRM) tests. To obtain motion data that is applied to the proposed algorithm, an FRM of a large container ship was developed. Using this model ship, standard maneuvering tests were carried out on a small body of water out of doors. A hydrodynamic roll moment model was constructed utilizing the data from turning circle tests and a 20-20 zig-zag test. This was then confirmed through a 10-10 zig-zag test. It was concluded that a model structure of the hydrodynamic roll moment model could be established without difficulty through a system identification method and FRM tests.

자유수면을 포함한 사각기둥의 횡동요 유체동역학 수치해석

Accurate prediction of ship dynamics, particularly roll motion, is very important in ship safety. In the past, empirical or vortex based methods were commonly used for the hydrodynamic roll damping predictions but they could not be applied to practical ship roll motion cause of limitations about geometries ad design conditions. Recently RANS-based techniques are developed for the practical ship motion analysis. In this study, RANS based roil analysis about a rectangular cylinder with WAVIS developed by MOERI/KORDI are performed and compared with the experimental data and other RANS results.

Deformation Inhomogeneity and Texture Development brought about in Steel Strip by Multi‐Step Cold Rolling

Predicting the microstructure obtained in cold‐rolled strips is of major importance with regard to optimizing the production of deep‐drawing steels with high and defined mechanical and technological properties. By using the hydrodynamic rolling theory of A. Kneschke, it has been possible to determine the effects of the most important rolling parameters and also of the rolling strategy on the velocity field and on the in‐homogeneous distribution of deformation over the strip thickness. Rolling on experimental laboratory facilities has provided the opportunity to observe the texture evolution. The tests were carried out on two deep‐drawing steel grades IF and ULC. The initial thickness of the strip samples was 3.0 mm. The textures were determined at 3 locations over the strip thickness by means of pole figure measurements according to the X‐ray diffraction method.

Anomalous rolling of spheres down an inclined plane

A sphere in air will roll down a plane that is tilted away from the vertical. The only couple acting about the point of contact between the sphere and the plane is due to the component of the weight of the sphere along the plane, provided that air friction is negligible. If on the other hand the sphere is immersed in a liquid, hydrodynamic forces will enter into the couples that turn the sphere, and the rotation of the sphere can be anomalous, i.e., as if rolling up the plane while it falls. In this paper we shall show that anomalous rolling is a characteristic phenomenon that can be observed in every viscoelastic liquid tested so far. Anomalous rolling is normal for hydrodynamically levitated spheres, both in Newtonian and viscoelastic liquids. Normal and anomalous rolling are different names for dry and hydrodynamic rolling. Spheres dropped at a vertical wall in Newtonian liquids are forced into anomalous rotation and are pushed away from the wall while in viscoelastic liquids, they are forced into anomalous rotation, but are pushed toward the wall. If the wall is inclined and the fluid is Newtonian, the spheres will rotate normally for dry rolling, but the same spheres rotate anomalously in viscoelastic liquids when the angle of inclination from the vertical is less than some critical value. The hydrodynamic mechanisms underway in the settling of circular particles in a Newtonian fluid at a vertical wall are revealed by an exact numerical simulation based on a finite-element solution of the Navier-Stokes equations and Newton's equations of motion for a rigid body.

Lubrication and Slippage in Roller Finger Follower Systems in Engine Valve Trains

To predict the performance of the energy-efficient finger follower system with a roller follower requires an adequate understanding of the kinematics and forces in the roller cam contact. This paper analyzes the kinematics, lubricant film thickness and normal/friction tractions in the finger follower and the roller itself The analysis includes the EHD tractions, hydrodynamic rolling friction and bearing torque to determine the cam-roller slippage and tractions for various positions of a cam cycle. For a roller finger follower and a sliding finger follower of similar design, a comparison is given for the calculated EHD film thickness and power losses in various parts of the tappet. Presented at the 45th Annual Meeting in Denver, Colorado May 7–10, 1990

Influence of adsorbed fluids on the rolling contact deformation of MgO single crystals

Basic phenomena associated with rolling contact deformation were studied using MgO as a model bearing material. A hardened steel ball was rolled on MgO single crystals in slow speed reciprocating motion and in high speed circular motion. The resulting deformation was studied by dislocation etch pit techniques. The presence of adsorbed fluids, such as silicone oil, white mineral oil and toluene, with slow speed sliding caused a dramatic change in slip mode and premature surface spalling compared with similar experiments in air or under water. In contrast dimethyl formamide inhibited these slip processes. The results are consistent with the dependence of dislocation mobility on adsorbed species. High speed hydrodynamic rolling with mineral oil lubrication produced a different slip phenomenon entirely than that produced by slow speed rolling. The slip bands resembled those produced in tensile tests and all slip apparently initiated at subsurface sites.

High-frequency shear instability in nematic liquid crystals

The behavior of MBBA nematic liquid cells under an applied shear is studied at high frequency. It is shown that hydrodynamic roll instabilities can be excited. The rolls develop in a direction perpendicular to the shear motion of the cell plates. Interference between two roll patterns can be obtained with nonparallel glass plates of the cell.