Numerical study on foil journal bearings with protuberant foil structure

A numerical model coupling the hydrodynamic pressure of lubricant film with the deformation of foil structure was developed for a type of foil journal bearing with protuberant foil structure. An isothermal and isoviscous lubricant was used in the fluid model, and a perturbation method was applied to linearize the Reynolds equation. The top foil was modeled as a strip of rectangular thin plate supported at a rigid point. The distributions of film pressure, film thickness, and foil deformation were solved by the finite element method (FEM). The effects of eccentricity ratio, bearing number, and number of protuberances on the characteristics of bearings were analyzed.     

Measurement of friction force and effects of oil fortifier in engine journal bearings under dynamic loading conditions

Commercial base oil and oil fortifier added to this oil are used to investigate the frictional behavior of the engine journal bearings using the theoretical Reynolds equation and experimental test rig. In the theoretical part of the study, the Reynolds equation that states the pressure distribution and friction force with finite width was solved by using the finite difference method. In the experimental part of the study, a new design test rig was conducted to measure the friction force, the lubricant film thickness of the engine journal bearing using base oil under dynamical loaded conditions. The effect of oil fortifier was detected measuring the friction force every three minutes in each 360 crank angle during 15 minutes of experiment. As the theoretical friction results showed similar variation with the experimental measurements of engine bearings, adding oil fortifier to the base oil presented a substantial reduction of friction force during the testing period.     

MHD steady and dynamic characteristics of wide tapered-land slider bearings

Based on the magneto-hydrodynamic (MHD) thin-film lubrication theory, steady load capacity and dynamic characteristics of wide tapered-land slider bearings lubricated with an electrically conducting fluid by the application of an external magnetic field are presented. Compared with the non-conducting lubricant (NLC) tapered-land bearing by Lin et al. (2006), the MHD bearing provides higher values of load capacity and dynamic coefficients. Compared with the MHD inclined-plane bearing by Lin et al. (2009), the MHD tapered-land bearing how an increase in load capacity and dynamic coefficients as well as a reduction in the steady friction parameter.     

基于成对双联角接触球轴承的摩擦力矩特性分析

对影响成对双联角接触球轴承精度和平稳度的摩擦力矩特性进行了分析研究.依据研究目的要求主要采用了试验验证和计算验证结合的试验方法.首先建立了特种轴承试验台系统.然后对成对双联角接触球轴承做了工况模拟和运转状态检测.从而得出了成对双联角接触球轴承变转速,变转向,变轴向载荷,变预紧力下的摩擦力矩曲线的大小和轴承曲线波纹度.进...     

Analysis of gas foil bearings integrating FE top foil models

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs, and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high-level vibrations. The performance of GFBs depends largely on the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as equivalent stiffnesses uniformly distributed around the bearing circumference. More complex finite element (FE) models couple the elastic deformations of the 2D shell or 1D beam-like top foil to the bump deflections as well as to the gas film hydrodynamics. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. For the GFB studied, 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data, reproducing closely the experimental circumferential wavy-like film thickness profile. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.     

Experimental investigations of porous bearings under vertical sinusoidally fluctuating loads

There are many papers on the experimental investigations of porous bearings under static loads but there is no paper on the experimental investigations under dynamic loads. In the present paper, the results of experimental investigation of porous bearings under vertical sinusoidally fluctuating loads are presented. The friction force was measured under various conditions of fluctuating load/steady load ratio, journal frequency and load frequency. The investigations were carried out in the hydrodynamic lubrication regime in a specially designed and fabricated test rig. It was found that at any given rpm, as the fluctuating specific load/steady specific load ratio, P_f/P_s, increases, the mean coefficient of friction μ_m increases. It was also found that the mean coefficient of friction is not affected by the load frequency even when the load frequency is half of the journal frequency.     

On the dynamics of the friction coefficient

The paper deals with the principal wear mechanism in brake systems and introduces a new dynamical model of the friction coefficient, where necessarily both friction and wear are taken into account. This model explains many open questions on the principal functionality of brake systems.In brake systems, characteristic structures are formed in the contact area by the flow of wear particles. Modulated by the friction power the wear particles are used by the system to build up hard contact patches on the brake pad. Nearly all energetic dissipation of the system is concentrated on these patches. By wear, these contact patches are destroyed after some time.So the friction coefficient is given by the equilibrium of flow of birth and death of contact patches. The resulting dynamical model describes the dynamical behaviour of the friction coefficient and the dependence of the temperature in the friction layer.This theory explains the fading effect of brake systems as well as complex hysteretic effects in the diagram of the friction coefficient versus the velocity, known from instationary measurement procedures.The structure of this theory seems to be quite general to describe other frictional systems too.     

Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances

The behaviour of rolling element bearings is of major importance to the vast majority of rotating machines. Due to the varying assembly compliance and the internal clearance existing in the bearing in most cases, a highly non-linear behaviour of the rotor bearing system appears. Thus, a dynamic model of a horizontal rotor supported on ball bearings with radial internal clearance is considered, taking into account contact forces between the balls and the races, as well as the effect of varying compliance and of the internal radial clearance. However, since rotational speed fluctuations of various levels practically appear in all rotating equipment, their effect is now additionally considered. Their effect is examined in two characteristic rotor bearing cases. The analysis includes all the characteristic states of the dynamic behaviour of the rotor, such as periodic, unstable periodic and chaotic responses, using methods like frequency spectra, phase spaces, higher-order Poincare maps and Lyapunov exponents. All results presented show a dominant stabilization effect of the speed fluctuations with respect to the system behaviour. From the analysis performed, it is concluded that even a minimum fluctuation of the rotor speed may result in major changes of the system dynamics, indicating that speed fluctuations of the rotor are a governing parameter for the dynamic behaviour of the system.     

The effect solid particle lubricant contamination on the dynamic behavior of compliant journal bearings

The proposed work concerns a theoretical and numerical investigation of the effect of solid particle contamination of lubricant oils on the static and dynamic characteristics of a finite length compliant journal bearing operating under isothermal conditions with laminar flow. In the present investigation, we use simple models based on the Einstein's mixture theory, which is characterized by the presence of suspended rigid particles in a fluid. Using the classical assumptions of lubrication, a Reynolds equation is derived and solved numerically by the finite difference method. The displacement field at the fluid film bearing liner interface due to pressure forces is determined using the elastic thin layer model. The results obtained show that the presence of suspended rigid particles in the lubricating oil (solid contamination) has significant effects on the hydrodynamic performance characteristics such as the pressure field, friction force, flow rate, elastic surface deformation as well as stability maps of the rotor‐bearing system (critical mass and whirl frequency) especially at high volumetric concentration.     

Determination of the dynamic coefficients of the coupled journal and thrust bearings by the perturbation method

This paper proposes a method to calculate the stiffness and the damping coefficients of the coupled journal and thrust bearings. Reynolds equations and their perturbation equations of journal and thrust bearings are transformed to the finite element equations by considering the continuity of pressure and flow at the interface between the journal and the thrust bearings. It also includes the Reynolds boundary condition in the numerical analysis to simulate the cavitation phenomenon. The stiffness and damping coefficients of the proposed mathematical method are compared with those of the numerical differentiation of the bearing force with respect to finite displacements and finite velocities of bearing center. It shows that the proposed method can calculate the dynamic coefficients of a coupled journal and thrust bearing more numerically stable and computationally efficient than the differentiation method. It also investigates the coupling effect of the coupled journal and thrust bearing and it shows that the proposed method makes it possible to calculate the cross-coupled dynamic coefficients in the radial–axial direction of the coupled journal and thrust bearing.     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

A study of friction in worn misaligned journal bearings under severe hydrodynamic lubrication

Friction occurs in all mechanical systems such as transmissions, valves, piston rings, bearings, machines, etc. It is well known that in journal bearings, friction occurs in all lubrication regimes. However, shaft misalignment in rotating systems is one of the most common causes of wear. In this work, the bearing is assumed to operate in the hydrodynamic region, at high eccentricities, wear depths, and angular misalignment. As a result, the minimum film thickness is 5–10 times the surface finish, i.e., near the lower limit of the hydrodynamic lubrication when taking into account that in the latest technology CNC machines the bearing surface finish could be less than 1–2 μm.An analytical model is developed in order to find the relationship among the friction force, the misalignment angles, and wear depth. The Reynolds equation is solved numerically; the friction force is calculated in the equilibrium position. The friction coefficient is presented versus the misalignment angles and wear depths for different Sommerfeld numbers, thus creating friction functions dependent on misalignment and wear of the bearing. The variation in power loss of the rotor bearing system is also investigated and presented as a function of wear depth and misalignment angles.     

The effect of Coulomb friction on the static performance of foil journal bearings

In foil bearings, the friction between bumps and their mating surfaces is the major factor which exerts great influence on the bearing performance. From this point of view, many efforts have been made to improve the understanding of the influence of the friction on the foil bearing performance by developing a number of analytical models. However, most of them did not consider the hysteretic behavior of the foil structure resulting from the friction. The present work developed the static structural model in which hysteretic behavior of the friction was considered. The foil structure was modeled using finite element method and the algorithm which determines the conditions of the contact nodes and the directions of the friction forces was used to take into account the friction. The developed model was integrated into the foil bearing prediction code to investigate the effects of the friction on the static performance of the bearing. The results of analysis show that multiple static equilibrium positions are presented for the one static load due to the friction, inferring its great effects on the dynamic performance. However, the effect of friction on the minimum film thickness which determines the load capacity of the bearing is negligible.     

On the performance of dynamically loaded journal bearings lubricated with couple stress fluids

A numerical study of the performance for a dynamically loaded journal bearing lubricated with couple stress fluids is undertaken. First of all, on the basis of micro-continuum theory, the generalized Reynolds equation for dynamic loads is derived. Then it is simultaneously solved with the force balance equation of the journal, thus obtaining the transient oil film pressure, the transient position and velocity of the journal center. Results from this analysis are presented for a typical engine crankshaft bearing. It is shown, compared with Newtonian lubricants, that under a dynamic loading lubricants with couple stress yield an obvious increase in oil film pressure and oil film thickness, but a decrease in the side leakage flow. Moreover, the effects of couple stress on friction force and friction coefficient vary considerably with time.     

Lubrication of hydroelectric turbine thrust bearings with a diester-based synthetic lubricant

A diester-based lubricant was found to reduce friction substantially in the thrust bearings of a hydroelectric turbine, compared with a conventional petroleum oil. Bearing temperatures were immediately reduced by 10–11 °C and bearing failures were eliminated. Revenue savings estimated at $10,000,000 per year have been made due to an increase in power production, and the elimination of repair work and downtime costs.¹     

Experimental and analytical studies of dynamic friction at the head/disk interface

Friction is an important parameter that critically impacts the tribological performance of a head/disk interface. The head/disk interface with laser zone texture affords a model system for the study of dynamic friction by virtue of its precisely-controlled contact geometry. By using two types of head sliders, i.e. the conventional slider and the padded slider, and a matrix of hard disks with a wide range of laser zone texture parameters, head/disk contacts involving a small number as well as a large number of bumps are realized. A rich variety of dynamic friction behaviors are observed with respect to bump height and bump density variations. To shed new light on the nature of HDI dynamic friction, an analytical model that treats both the deformational and the adhesive friction components on equal footings is formulated. It is shown that, based on the model analysis, the friction is deformation-dominated for HDIs involving a small number of contacting bumps and adhesion-dominated for HDIs involving a large number of contacting bumps. In the former case the friction decreases with bump density, whereas in the latter the friction increases with bump density.     

Derivation of dynamic couple-stress Reynold’s equation of sliding-squeezing surfaces and numerical solution of plane inclined slider bearings

Deriving a general dynamic Reynold’s equation of sliding-squeezing surfaces with non-Newtonian fluids is necessary for the assessment of dynamic characteristics of a lubricating system. Taking into account the transient squeezing-action effect and considering the effects of couple stresses resulting from the lubricant blended with various additives, the non-Newtonian dynamic Reynold’s equation applicable to the general film shape is derived by using the Stokes micro-continuum theory. As an application, the numerical analysis of a two-dimensional plane inclined slider bearing is illustrated. Based upon the small perturbation technique, two Reynold’s-type equations responsible for both the steady performance and the perturbed characteristics are obtained. The steady and perturbed pressures are then numerically calculated by using the conjugate gradient method. From the results obtained, the effects of couple stresses provide an improvment on both the steady-state performance and the dynamic stiffness and damping characteristics especially for the bearing with a higher value of aspect ratio.     

Study on dynamic friction characteristics in reciprocating friction drive system

The dynamic friction characteristics of a reciprocating friction drive system are investigated under conditions of dry contact using 0·45% carbon steel pair. Three friction modes are found during the operation, i.e. stick-slip, sticking and a transition region. The critical operating conditions in classifying these three modes are examined under various driver speeds, normal loads and spring constants. The critical values of driver speed and normal load increase with increasing spring constant. Generally, in the friction drive system the disappearance of the stick-slip results in smooth rolling. It is also found that the slope at the first period of slip on the traction force–relative slip velocity curve would have a transition from negative to positive value when the friction mode of stick-slip changes into sticking. Moreover, results show that the sticking mode gives the best positioning accuracy with the least wear on the contact surfaces. In addition, a transition from severe wear to mild wear is found when the friction mode is transferred from stick-slip to sticking only.     

Effects of eccentricity defect on the nonlinear dynamic behavior of the mechanism clutch-helical two stage gear

This paper investigates the nonlinear dynamic behavior of an automotive clutch coupled with a helical two stage gear system. The nonlinear dynamic model is simulated by twenty seven degrees of freedom and including three types of nonlinearity: dry friction path, double stage stiffness and spline clearance. The utility of the proposed nonlinear model is illustrated by the industrial need to clearly identify the dynamic behavior of mechanical elements (shafts, bearings, gears, flywheel, pressure plate, hub of the clutch…) and reduce vibration. The governing nonlinear time varying motion equation formulated is resolved by the analytic Runge Kutta method.Then the modeling of the eccentricity defect located on the gear and the flywheel of the clutch is done. The effect of this defect on the nonlinear dynamic behavior of the system is investigated.     

Stability characteristics of rough submerged oil elliptical bearings under dynamic load

This paper discusses the effect of surface roughness on the stability of submerged oil elliptical journal bearings under unidirectional constant and unidirectional periodic load. The non-linear transient simulation, taking the oil film history into account, has been used to predict the threshold of instability. The average flow model of Patir and Cheng (An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. Trans. ASME, Journal of Lubrication Technology, 1979, 100, 12–17) has been used to describe the surface roughness effects. The effect of ellipticity ratio and that of various surface roughness parameters, viz., composite surface roughness, roughness orientation pattern and variance ratio on the stability has been studied.