Bearing Clearance Research Articles

정압베어링에서 입구압력 및 틈새간격 변화에 따른 누설량의 상관관계에 관한 연구

정압베어링에서 입구압력 및 틈새간격 변화에 따른 누설량의 상관관계에 관한 연구

Nonlinear dynamic characteristic of the spindle-cutter system

A nonlinear dynamic model of spindle-cutter coupling system under cutting force, which takes into account the cutter stiffness and the nonlinearity of bearing clearance, is established. Analysis of the cross-section of a two-flute end mill is conducted to determine cutter stiffness. Then, the calculated cutter stiffness is introduced into the nonlinear dynamic model of coupling system. In the modeling of cutting force, the cutting width takes into account the cutter tip displacement. Moreover, nonlinear dynamic characteristics of spindle-cutter coupling system are studied and the effects of bearing clearance on the response of cutter tip are discussed as well, considering unbalanced force. The numerical results show that the bearing clearance strongly affects the equilibrium position. With different values of bearing clearance and rotation speed, the responses of cutter tip exhibit periodic, quasi-periodic and chaotic characteristics. Dynamic characteristics of spindle-cutter system depends on the bearing clearance and rotation speed. The proper bearing clearance and rotation speed should be chosen to ensure a stable cutting and high cutting rate according to the bifurcation diagram. The response of the cutter tip is a quasi-periodic motion when the cutting force is considered. The time-domain response of cutter tip predicted by nonlinear dynamic analysis can provide the basis for machining error prediction.

Scaling Laws for Radial Clearance and Support Structure Stiffness of Radial Foil Bearings

Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation, and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), support structure deflections (structural compliance), and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile, etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and support structure stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and support structure deflection equation. Power law relationships are established between the (1) radial clearance and bearing radius and (2) support structure stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.

Sensitivity of Computational Rotor Dynamics Towards the Empirically Estimated Lubrication Gap Clearance of Foil Air Journal Bearings

AbstractThis contribution is concerned with the computational analysis of a rigid rotor supported by means of two self‐acting foil air journal bearings. Even though the overall equation system is thereby typically written in a nondimensional form, prior knowledge about realistic value ranges of occurring dimensionless numbers is required in order to parameterize and interpret such simulations correctly. Unlike all other quantities, the nominal lubrication gap clearance between the rotating journal and the undeformed foil structure is reported to be only poorly known. Thus, even in the light of an advanced understanding of the bearing rotor system's fundamental behavior, the quantitative reproduction and prediction of experimental results by means of computational analysis need to be viewed critically. In this study, the sensitivity of numerical results towards the assumed nominal lubrication gap clearance will be investigated. To this end, the stability of the system is considered and the characteristics of occasionally observed equilibrium points and limit cycles are addressed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Slip and turbulence phenomena in journal bearings with application to implantable rotary blood pumps

This paper describes an investigation into journal bearings with geometries and working fluid similar to centrifugal blood pumps. The aim is to describe the phenomena that cause these journal bearings to deviate from classical predictions. Experimental, analytical and numerical methods are used to investigate the behaviour of a range of bearings with geometries and working fluid similar to blood pumps. It was found that the clearance had a significant effect on the force-eccentricity characteristic of the bearing, with smallest and largest clearances deviating from classical predictions. Experimentally measured pressure distributions show that slip occurs when the clearance is small and that turbulence occurs with the largest clearances. The effects of these phenomena on lubricant pressure and blood compatibility are discussed.

A method for contact analysis of revolute joints with noncircular clearance in a planar multibody system

Journal bearings are generally used to comprise a revolute joint in mechanical systems. Noncircularity and clearance in journal bearing are obvious due to a long time of nonuniform wear. In this regard, a method of analyzing the contact in revolute joints with noncircular clearances in a multibody system is proposed. The revolute joint with noncircular clearance is assumed to be constituted by an elliptic bore and a pin. The method described is not representative of an elliptic bore journal bearing in a detailed manner. This method involves discretizing the geometric profile of the bushing of the revolute joint. By analyzing the relative separations between the discrete points and the geometric center of the pin, the contact area between the bushing and the pin can be judged and the maximum contact depth obtained. Compared with traditional methods, the proposed method has the advantage that it can be used to analyze noncircular contact problems in revolute joints with a clearance. A slider–crank mechanism is used as an example to compare the effects of the geometrical properties of circular and noncircular (elliptical) revolute joints with clearance on the dynamic response of the mechanisms. The results show that clearance joints with noncircular geometry predominantly affect the dynamic stability of a high-speed mechanism. Moreover, the efficiency of the contact analysis and model solving precision are strongly dependent on the number of discrete points in the geometric profile of the joint elements. The size of the joint clearance has a small effect on the solving efficiency of the model.

Spherical contact mechanical analysis of roller cone drill bits journal bearing

Abstract Fang contact model is introduced to analyze stress of the spherical fixed ring journal bearing. Developed calculation programs in the MATLAB software which are utilized to calculate the contact characteristics of roller cone drill bits spherical fixed ring journal bearing. In addition, effects of external load, radius clearance values, and material parameter on the mechanics performance were investigated. The results show that the value of external load has a direct pronounced effect on the contact characteristics of journal bearing. There is a significant positive correlation between contact pressure and external load, radius clearance value, and the Young's modulus of material. However, there is an evident negative correlation between contact radius of journal bearing and radius clearance value, and the Young's modulus of material. The smaller radius clearance value of journal bearing is, the more centralized contact region will be, so the corresponding contact pressure will be higher. From the perspective of reducing friction and wear, we need select the materials which have high strength and good toughness. Not only might this can improve the wear resistance, it also effectively decreases the contact pressure. In this case, we can prolong the service life of roller cone drill bits journal bearing.

Load carrying capacity of misaligned hydrodynamic water-lubricated plain journal bearings with rigid bush materials

This paper analyzes the ultimate hydrodynamic load carrying capacity of water-lubricated plain journal bearings with rigid bush materials under misalignment effect, aiming to help designers find appropriate design parameters. The relationships between the ultimate load carrying capacity and the misalignment angle for bearings with different relative clearances, different length-to-diameter ratios are gained. Bearings with different diameters and different rotational speeds are also studied to determine how the ultimate hydrodynamic load carrying capacity changes with diameter and rotational speed. Finally, a method is provided for determining the appropriate radial clearance and length of misaligned water-lubricated rigid plain journal bearings.

Model-Based Analysis of Friction-Induced Subsynchronous Whirl for a Rotor Contacting With Clearance Bearings Under Axial Load

For rotors supported by active magnetic bearings (AMBs), clearance bearings are commonly used to provide backup support under loss of AMB functionality. Test data from real machines shows that vibration during touchdown on backup bearings may involve steady forward whirling of the rotor with a subsynchronous frequency. This excitation is believed to be due to friction forces transmitted between the rotor and a bearing end-face under axial load. This paper proposes a new analytical approach to model and predict such friction-driven forward whirl behaviors. A set of constraint equations are derived that relate a circular whirl motion of arbitrary orbital speed to the frequency response functions for the rotor-housing structure. This model is coupled with an evaluation of Coulomb friction associated with slip between the rotor and the supporting end-face of a thrust bearing. The resulting equations can be used to compute a set of possible whirl motions via a root-finding procedure. A case study is undertaken for a 140 kW energy storage flywheel. Model-based predictions are compared with measured data from spin-down tests and show a good level of agreement. The study confirms the role of friction-related forces in driving forward-whirl response behaviors. It also highlights the key role of housing and machine support characteristics in response behavior. This influence is shown to be complex and not open to simple physical interpretation. Therefore, the proposed analytical method is seen as a useful tool to investigate this influence while avoiding the need for time consuming numerical simulations.

Analysis of the Influence of the Mechanical Imbalance and the Bearing Clearance on the Operating Stability of Hydro-power Unit

Analysis of the Influence of the Mechanical Imbalance and the Bearing Clearance on the Operating Stability of Hydro-power Unit

Analysis of grease contamination influence on the internal radial clearance of ball bearings by thermographic inspection

One of the most important factors influencing ball bearings service life is its internal radial clearance. However, this parameter is also very complex because it depends on applied radial load and ball bearings dimensions, surface finish and manufacturing materials. Thermal condition of ball bearings also significantly affects internal radial clearance. Despite many researches performed in order to find out relevant facts about different aspects of ball bearings thermal behaviour, only few of them are dealing with the real working conditions, where high concentration of solid contaminant particles is present. That?s why the main goal of research presented in this paper was to establish statistically significant correlation between ball bearings temperatures, their working time and concentration of contaminant particles in their grease. Because of especially difficult working conditions, the typical conveyor idlers bearings were selected as representative test samples and appropriate solid particles from open pit coal mines were used as artificial contaminants. Applied experimental methodology included thermographic inspection, as well as usage of custom designed test rig for ball bearings service life testing. Finally, by obtained experimental data processing in advanced software, statistically significant mathematical correlation between mentioned bearings characteristics was determined and applied in commonly used internal radial clearance equation. That is the most important contribution of performed research - the new equation and methodology for ball bearings internal clearance determination which could be used for eventual improvement of existing bearings service life equations.

Shaft Sensor Based on Modeling Diagnostic Signs of Power Unit Defects

A perfection concept is proposed for automated control diagnostics systems used at power plants with application of shaft sensors. It is proposed a systematic approach to solve a number of practical problems related with safety and performance of power generating turbosets. Diagnostics of multi-rotor turboset technical condition are significantly improved due to “complete” set of shaft motion sensors, applied at both sides of each journal bearing. There have been given diagnostics signs of defects measured with shaft sensors and suggested some extra criteria of reliability of the shafting and supports.To illustrate the method let us compute correcting alignments of fragment of shafting.Using simplified 2-rotor 4-support turboset, it is shown that: corrective alignments of supports, recommended by manufacturers of turboset and generator, may be not sufficient to compensate misalignments of supports, caused by thermal deformations of turboset support system. Those corrective misalignments should be computed individually for each turboset, using real thermal deformations and real clearances of journal bearings.

動圧軸受を用いた小型遠心血液ポンプ羽根車の運動特性

An implantable Left Ventricular Assist Device (LVAD) is used as a Right Ventricular Assist Device (RVAD) because there is no implantable blood pump specialized for a right ventricular assist. As a demanded pump head of the implantable RVAD is different from that of LVAD, LVAD used as RVAD is operated at off-design points. In the operation of blood pumps at off-design points, hemolysis (destruction of blood cells) and thrombosis (formation of blood clots) can occur. As a realization of the implantable RVAD specialized for a right ventricular assist has been expected due to these backgrounds, the implantable RVAD has been developed by our research group. In the present study, motions of the impeller in a developed RVAD were investigated to clarify a floating mechanism of the impeller supported by dynamic pressure bearings. In experiments, performance tests of RVAD were carried out and motions of the impeller were measured by using two laser displacement sensors. As a result, it was confirmed that a main motion of the impeller was a whirling motion and its frequency was a rotational frequency of the impeller. The amplitude of the whirling motion was about 0.2 times as large as a mean radial clearance of bearings.

Studies on thermal contraction of crankshaft bearings under extreme low temperatures

This paper presents how the contractions of the main components of a V6 motor with low engine displacement are determined for the cold-start phase under extreme low temperature. Internal combustion engine components have complex geometries and to obtain the thermal contractions, in the research, used the method of finite element analysis. The phenomena of thermal contractions are studied for the cold-start situations at extreme low temperature, knowing that the cold-start phase of an internal combustion engine is the main factor that determines moving rotational and translational parts wear life. Checking the proper choice of clearance is particularly important, as the use of inappropriate values of it leads to rapid operation destruction of the engine group components. The results obtained for the thermal clearances of crankshaft bearings are mathematically modeled and the relations can be used for calculating the clearances. The mathematical models are also useful for implementing in different software tools.

An Investigation into the Thermal Effects on a Hydrodynamic Bearing's Clearance

The scope of this article is to examine the effects of thermal expansion (up to seizure) on the clearance of a hydrodynamic bearing under prescribed operating conditions. This parametric study uses angular speed, eccentricity, and the journal/bushing material pairings as varying parameters. The study focuses on how the size of the clearance varies with temperature and pressure (elastic deformation) and whether it is possible for a complete thermal lockup (seizure) to occur when certain material pairings are used. The effects of the thermal expansion on the load-carrying capacity, torque, and total deformation of the clearance are presented. Thermal versus mechanical effects domination are also analyzed in order to establish the conditions under which one, or the other become dominant. The present model uses the three-dimensional Navier-Stokes equations and a fully termed energy equation for the fluid coupled in a two-way feedback mode with the 3D energy and the elasticity equations for the bushing and journal. The effects of the viscosity variation with temperature and that of cavitation are also incorporated in the presented results.

Nonlinear Dynamics Analysis of a Gear-Shaft-Bearing System with Breathing Crack and Tooth Wear Faults

Considering backlash, time-varying mesh stiffness and radial clearance of bearing, nonlinear dynamic model of gear bearing flexible shaft system is established taking into account breathing crack in shaft and tooth wear. Nonlinear dynamic equations are solved by Runge-Kutta method. Effect of backlash, crack in shaft and tooth wear faults on the nonlinear dynamic behavior of gear-shaft-bearing system is studied. The results show that gear-shaft-bearing system may change from periodic motion to non-periodic motion as backlash increases, and gear pair change from normal mesh to tooth separation, double-sided impact fault. If crack fault appears, quasi-periodic and chaos motion region increases, and gentle crack fault can result in instantaneous tooth separation and double-sided impact faults. Serious tooth wear fault will also induce tooth separation and double-sided impact faults. If both shaft crack and tooth wear faults exist, tooth wear fault will be intensified by double-sided impact fault from shaft crack, which will result in early failure of the gear system.

Optimization analysis on assembly interference of cylindrical roller bearings

Distribution of loads and contact stress has a great influence on fatigue life of bearings. In view of the fact that the nonload area is ubiquitous in cylindrical roller bearings, there is a method for prolonging the fatigue life design by adjusting the working clearance of cylindrical roller bearings. In this article, optimization model of fatigue life of cylindrical roller bearings is developed with a quasi-dynamic method and calculated method of bearing life based on micro-area contact, considering the effect of assembly interference, temperature rise, and high-speed centrifugation. Aiming to the different geometry parameters and operating parameters of bearings, the effects of assembly interference on bearing fatigue life are discussed. The results show that the optimum fatigue life of roller bearings is achieved at negative working clearance with the loads distributed evenly within half ring. The optimum working clearance of roller bearings is not influenced by radial load. But with the increase in pitch diameter or decrease in rolling elements, the optimum assembly interference increases, and accelerating revolution of roller bearings will increase the optimum assembly interference as well.

The Numerical Analysis of Influence of Crankshaft Main Spindles Regeneration in Marine Engine on Stiffness and Eigenfrequency of the Crankshaft

Engine operating conditions of the main propulsion, static in principle with steady-state rotation speed of the crankshaft and engine load, also work under dynamic load conditions. These conditions cause additional distortion of the crankshaft and changes in the operating conditions of the shaft bearings. However, the greatest impact on the long and trouble-free operation has proper engine maintenance. Variable operating conditions and engine operating errors, unfortunately, often cause damage to the main bearings of the crankshaft. Repair of the damaged main bearing spindles of the shaft involves performing the machining of the spindle surface then its re-hardening and selecting new bearing bushings with the appropriate bearing clearance. Trusting the engine manufacturer, there is no check of the influence of the machining of bearing spindles on the structural properties of the shaft. Therefore, the paper presents the model tests of the structure of medium-rev marine engine crankshaft aimed at determining the changes in the mechanical properties of the structure resulting from carrying out the regeneration of the main shaft spindles.

Bifurcations and hysteresis of varying compliance vibrations in the primary parametric resonance for a ball bearing

This paper investigates the bifurcation and resonant hysteresis of varying compliance (VC) vibrations in a rigid-rotor ball bearing system with Hertzian contact and radial internal bearing clearance. With the aid of arc-length continuation, the harmonic balance and alternating frequency time (HB-AFT) technique is employed to trace the branches of periodic responses, for which the stability is also investigated using Floquet theory. It is found that the soft resonant hysteresis resulted from the Hertzian contact resonance dominates the primary parametric resonance. In addition, this paper also demonstrates that the mechanism of the period doubling in the case of small bearing clearances is arisen from one to two parametrical internal resonance in the primary resonant area, which can lead nonlinear responses such as quasi-period and chaotic motions to the system, and the evolvements of these complex behaviors are also explored.

Monte Carlo simulation of the manufacturing tolerance in FDBs to identify the sensitive design variables affecting the performance of a disk-spindle system

This research proposes the Monte Carlo simulation for manufacturing tolerances in major design variables of fluid dynamic bearings (FDBs) to identify their sensitive design variables on the performance of FDBs and the dynamic performance of a disk-spindle system. Friction torque and critical mass were chosen as the performance indexes of FDBs and the disk-spindle system. The proposed method was applied to the FDBs of a 2.5? HDD, and the Monte Carlo simulation was performed for 16 major design variables of the FDBs. The clearance of the journal bearing was the most sensitive design variable of both the friction torque and critical mass. Additionally the groove to groove and ridge ratio and groove depth of the grooved journal bearing, which were manufactured by electrochemical machining, were also sensitive to determining the friction torque and critical mass of the FDBs, respectively. This research can be utilized to manage the manufacturing tolerance of FDBs to maintain consistent performance of FDBs and a disk-spindle system in an HDD.