Bump-type Foil Bearings Research Articles

Rotordynamics of a rotor radially and axially supported by active bump-type foil bearings and bump-type thrust foil bearings

The rotordynamics of a rotor supported by gas foil bearings (GFBs) has been studied, focusing mainly on the relation between radial loads and lateral vibration. Nevertheless, the various axial loads occurring during operation must be compensated by thrust GFBs. Their effect on lateral and axial vibrations of the rotor must be addressed. This research studied the effect of axial load on the rotordynamics of a rotor supported by active bump-type foil bearings (ABFBs). Two ABFBs and a pair of bump-type thrust foil bearings (BTFBs) supported a rigid rotor along the radial and axial directions, respectively. The 5 degree of freedom nonlinear dynamic model for the rigid rotor is shown in this paper and was validated through experimental measurements. The study considered the coupling of the time-variant nonlinear bearing forces of ABFBs and BTFBs. The rotordynamic behaviors of a rotor under various axial loads, rotor unbalances, and voltages are predicted. Moreover, the effects of various disk misalignments on the minimum gas film thickness of the BTFBs are discussed.

Analysis of misalignment characteristics for textured foil journal bearing based on multigrid method

Surface texturing is an excellent solution to the load capacity deficiency of foil journal bearings. However, it will also introduce significant discretization efforts. This paper explored the possibility of searching the static balance locus of textured foil journal bearing using the multigrid method to ensure design efficiency. The modified Reynolds equation characterized the ultra-thin gas film behavior inside bump-type foil bearing, and two foil models were adopted simultaneously to obtain the foil’s structural deflection. The predicted load capacity agreed well with the experimental data. The results indicate that multigrid can accelerate the solution process of the compressible pressure governing equation, and the speed can be increased up to 70% when the nonlinear discretization scheme is adopted. It is recommended that textures are located in the pressure-rising region along the shaft’s rotating direction and that the axial direction is fully textured to improve load capacity. Moreover, the above texture distribution scheme can increase the tolerable maximum misalignment angle by 11.8% and enhance the stability of rotors operated in light-load and high-speed cases.

Study on the static and dynamic performance of active bump-metal mesh foil bearings

The gas foil bearing (GFB) is an important component of high-speed, oil-free micro turbomachinery. However, the instability of GFBs under certain conditions hinders their widespread application. The traditional solution is to decrease the continuity of the gas film and increases the structural damping of GFBs through ‘passive’ structural improvements. Thus, the performances of improved bearings cannot be actively adjusted. This paper proposes an active bump-metal mesh foil bearing (AB-MFB) in which three metal mesh blocks (MMBs) are inserted into the active bump-type foil bearing (ABFB) to control radial preloads through piezoelectric actuators (PZTs) and increase the structural damping. A model coupling of the active-metal mesh substructures, bump foil, and top foil is presented to analyse the mechanical properties of the compliant structure of AB-MFB. Dynamic excitation tests are conducted to validate the model. This study then predicts the static and dynamic performance of the AB-MFB by combining the model and compressible gas Reynolds equation. Finally, the effects of different parameters on the dynamic performance of the AB-MFB are discussed.

A Simplified Model for Numerical Investigation of Bump-Type Foil Bearings Based on Contact Nonlinearity

Abstract The paper introduces a simplified structural model for the numerical investigation of bump-type foil bearings. This analytical model is based on an efficient nonlinear contact procedure with consideration of friction, small deformations, and elasticity. The bump foil is modeled with a truss structure, while the top foil uses two-dimensional (2D) beam elements. In this present model, the normal and tangential contact forces between the bump foil and the bearing sleeve and between the foils are dealt with the penalty method. Even for a simple loading, the contact state might change between separation, stick, and slip. To avoid convergence problems caused by discontinuity, the regularized smooth friction model is used instead of the Coulomb friction model. In addition, due to contact problems that depend on time are accompanied by nonlinear evolution, the solution of the system equation using the incremental iterative method and the Newton–Raphson method is presented. The deflection of the top foil is added to the film controlled by the Reynolds equation (RE) to obtain the air pressure distribution. The theoretical predictions of the rotor push-pull tests agree well with results from the literature, which verifies the validity of the model. Using this present model, the quasi-static behaviors of the foil structure are mainly discussed, and parametric studies concerning environmental pressure and radial clearance are also conducted.

Design guidelines for bump-type compliant conical foil bearing

The integral bump foil strip cannot optimize the performance for the compliant conical foil bearing (CFB) as the uneven distribution of structural stiffness. To maximize the bearing characteristics, this paper proposed different bump foil schemes. Firstly, the anisotropy of CFB was studied based on the nonlinear bump stiffness model, and the circumferentially separated foil structure was proposed. Moreover, an axially separated bump foil structure with the variable bump length was introduced to make the axial stiffness distribution more compliant with the gas pressure. In addition, the effect of foil thickness was also discussed. The results show that CFB with integral bump foil exhibits obvious anisotropy, and the suggested installation angle for largest load capacity and best dynamic stability are in the opposite position. Fortunately, a circumferential separated bump foil can improve this defect. The characteristics of CFB with axial separated foil structure can be improved significantly, especially for that with more strips and the variable bump half-length design. The suitable bump and top foil thickness should be set considering the improved supporting performance and proper flexibility. The results can give some guidelines for the design of CFB.

Research status and developing trends of gas bearing in recent years

As one kind of support elements for rotational machines, gas bearings that use air or gas as lubricant, have many attractive advantages such as low power loss, wide work temperature range, high rotating speed and low maintenance cost. However, gas bearings also have some disadvantages including low carrying load at low speed, wear at start-stop procedure, not easy to predict bearing performance due to the complex bearing structure and so on.The purpose of this paper is to explore the research status of gas bearing based on the Web of Science datasets and related tools, meanwhile, the developing trends emerged in gas bearing are further studied. The results shows that: 1) the top ten productive countries published 85% papers in the studies of gas bearing; 2) there are eight research clusters emerged in the topics analysis visualization and the top three largest clusters are #1 metal mesh foil bearing, #1 bump-type foil bearing and #2 aerostatic thrust bearing respectively; 3) Comparing to other research topics, foil bearings (metal mesh type and bump type)and aerostatic thrust bearing may be further explored in the future. This study presents intuitive state of research of gas bearings and proposes a fresh perspective for relevant researchers to perform research in the future.

Real-Time Control of Rotor Vibrations With Active Bump-Type Foil Bearings

The rotor supported by gas foil bearings (GFBs) suffers severe vibrations at extremely high rotating speed, which weakens the stability of the rotor-GFBs system. Although current solutions including increasing structural damping and mechanical preloads of GFBs suppress the rotor vibrations, they lead into larger wear during the lift-off process and higher friction torque during operation. In this article, active bump-type foil bearings with advantages of actively controlled mechanical preloads are utilized to rotor-GFBs system aiming at suppressing the rotor vibrations in real time. Open-loop control is utilized to obtain the proper U at different rotating speeds. The bifurcation diagrams of the rotordynamic responses under different voltages and rotating speeds are predicted to explain the relationship between U and real-time control of rotor vibrations theoretically. Proportional-integral-differential control method is utilized to control the vibrations of rigid rotor within relatively tight bounds under the conditions of constant rotating speed, coast-down process, and speed up and down process.

Nonlinear dynamic responses of a rigid rotor supported by active bump-type foil bearings

Active bump-type foil bearings (ABFBs) enhance the rotordynamic characteristics of rotor–bearing systems with the advantage of controllable mechanical preloads. However, the coupling of controllable mechanical preloads, compressible gas film, and foil structures induce strong nonlinear characteristics and affect the dynamic responses of rotor. In this study, a nonlinear theoretical model that considers the gyroscopic effect of rotor, nonlinear Reynolds equation, complicated foil structures, and dynamic motions of active substructures is presented. This model is verified by a corresponding rotordynamic test. The nonlinear dynamic responses of a rotor–ABFB system are discussed on the basis of waterfall plots, orbit simulations, and Poincare maps of rotor center, fast Fourier transform, minimum film thickness, and power loss during one cycle of journal orbit. The effects of voltage on piezoelectric actuators, nominal clearance, width of flexure hinge, and static load on the nonlinear rotordynamic responses of rotor are analyzed to provide guidelines on selecting the design and control parameters of rotor–ABFB systems.

Experimental and theoretical investigation of rotordynamic characteristics of a rigid rotor supported by an active bump-type foil bearing

This study aims to investigate the rotordynamic characteristics of a rigid rotor supported by an active bump-type foil bearing (ABFB) with real-time controllable mechanical preload. ABFB is composed of a traditional bump-type foil bearing with controlling substructures that consist of flexure hinges, lever amplifiers and piezoelectric stack actuators (PZTs). The structure realises the adjustment of bearing's mechanical preloads by actively controlling the DC voltage on the PZTs (U). Experimental investigations based on rotordynamic test rig are performed to measure the effects of ABFB on rotordynamic responses of rotor-ABFB system. Combined with the dynamics of the active control structures and modified link-spring model, linear and nonlinear mechanical models of the rotor-ABFB system are established, and the rotordynamic responses of the rotor are predicted. Both the experimental and theoretical results verify the possibility of building active rotor-gas foil bearing systems. Moreover, the effects of rotor unbalance on the rotordynamic responses of the rotor-ABFB system are investigated.

A simplified structural model of bump-type foil bearings based on contact mechanics including gaps and friction

Abstract The paper introduces a structural model for bump-type foil bearings based on contact mechanics including gaps and friction. The starting point is a model introduced in [32] were the bump foil is approximated by a specific structure of interacting springs. Following this model, contacts between the top and bump foils and between the bump foil and the sleeve are always closed. Recent analyses [31] showed that this not always verified: contacts can become loose even for very simple loading situations. A new model is then developed for considering these situations. The new model takes into account the elasticity of the top foil and three kind of gaps: between the rotor and the top foil, between the top and the bump foils and between the bump foils and the sleeve. The former model of the bump foil was extended by considering an additional degree of freedom per bump. Friction was modeled with Coulomb law. An efficient numerical procedure borrowed from contact mechanics ([41], [42]) was implemented for solving the structural problem with friction and close/loose gaps. The procedure uses the augmented Lagrangian algorithm for the normal contact forces and the penalty method for the tangential friction force. The procedure is very robust in dealing with stick-slip situations and close/loose contacts. The model was validated by comparisons with results from the literature ([31], [32]). By considering gaps in the foil structure and close/loose contacts, the model is not only closer to reality but can also handle manufacturing errors of the foil structure. This is shown by considering bump foil height manufacturing errors.

Identification of Dynamic Characteristics of Hybrid Bump-Metal Mesh Foil Bearings

The stability of oil-free high-speed turbo-machinery can be effectively improved by increasing the damping characteristic of the gas foil bearing (GFB). Novel hybrid bump-metal mesh foil bearings (HB-MFBs) have been previously developed. Prior experimental results show that the parallel combination of bump structure and metal mesh not only can improve the structure stiffness but also provide better damping property compared with the bump-type foil structure. To investigate the dynamic behavior of floating HB-MFBs and promote its application, this study measured the dynamic force coefficients of HB-MFBs on a rotating test rig. The vibrations of HB-MFBs with different mesh densities (40%, 32.5%, and 25%) and a generation І bump-type foil bearing (BFB) with similar size are measured under static and impact loads to estimate the bearing characteristics. Static load test results show that the linear stiffness decreases when the air film is generated (from 0 rpm to 20 krpm) but increases gradually with speed (from 20 krpm to 30 krpm, and 40 krpm). Moreover, the dynamic force coefficients of HB-MFBs indicate the significant influence of metal mesh density on bearing dynamic characteristics. The growth in block density increases the dynamic stiffness and damping coefficients of bearing. The comparison of HB-MFB (32.5% and 40%) and BFB emphasizes the good damping characteristics of HB-MFB.

Active bump-type foil bearing with controllable mechanical preloads

Abstract This paper presents an active bump-type foil bearing (ABFB), in which mechanical preloads can be actively adjusted by controlling the driving voltages of piezoelectric actuators (PZTs) to create a variable multiple-lobe clearance and enhance bearing performance. A theoretical model that couples active and compliant foil structures is proposed, and static load–deformation tests and measurements of airborne drag torque on the basis of a prototype bearing are conducted at different driving voltages. Tests results show that the proposed active structure is feasible and effective in controlling mechanical preload. Moreover, the static and dynamic performances of ABFB are discussed. This work lays foundation for the further study of active control methods in gas foil bearings.

Analysis of novel hybrid bump-metal mesh foil bearings

Hybrid bump-metal mesh foil bearings (HB–MFBs) are novel gas foil bearings which comprise bump foil and metal mesh blocks in bearing substructure. HB–MFBs have the advantages of both bump-type foil bearings and metal mesh foil bearings in terms of assembly accuracy, stability and can work at high temperatures. This paper proposes a theoretical model by assembling the models of the bump foil and metal mesh blocks. A prototype bearing was manufactured to measure the lift-off speed, drag torque and temperature. The bearing performance with respect to mesh density, journal speed and applied load were predicted and analysed. The influence of Coulomb friction and mesh density on bearing stability with respect to friction coefficient and applied load was also discussed.

Numerical and Compact Model of Metal Mesh Foil Bearings

ABSTRACTMetal mesh foil bearings (MMFBs) are novel gas foil bearings with lower manufacturing costs and higher inherent material energy dissipation ability than traditional bump-type foil bearings. To improve the design guidelines of MMFBs and predict bearing performance, a compact theoretical model is presented by considering the metal mesh substructure as assembled springs and dry friction joints. The proposed analytical model considers the effects of several factors such as relative density, wire diameter, geometrical size, and radial interference of the metal mesh substructure. The predicted stiffness coefficients, which take the dry friction effect into account, show strong nonlinear characteristics with the increasing displacement and have a significant difference between the loading and unloading process. A series of static load tests are conducted to verify the theoretical model of MMFBs. The hysteresis loops of static load versus bearing deflection with respect to the different relative densities predicted by this model are demonstrated by experimental data. The minimum film thickness, journal eccentricity, and attitude angle with respect to different relative densities, rotational speeds, and applied loads are presented and analyzed. The predicted results of the dynamic force coefficients show that the equivalent viscous damping coefficient and relative density have significant effects on bearing dynamic performance. Furthermore, the influence of radial thickness, wire diameter, and radial interference on bearing static and dynamic performance is discussed.

Experimental Evaluation of the Structure Characterization of a Novel Hybrid Bump-Metal Mesh Foil Bearing

Rotors supported by gas foil bearings (GFBs) experience stability problem caused by subsynchronous vibrations. To obtain a GFB with satisfactory damping characteristics, this study presented a novel hybrid bump-metal mesh foil bearing (HB-MMFB) that consists of a bump foil and metal mesh blocks in an underlying supporting structure, which takes advantage of both bump-type foil bearings (BFBs) and MMFBs. A test rig with a nonrotating shaft was designed to estimate structure characterization. Results from the static load tests show that the proposed HB-MFBs exhibit an excellent damping level compared with the BFBs with a similar size because of the countless microslips in the metal mesh blocks. In the dynamic load tests, the HB-MFB with a metal mesh density of 36% presents a viscous damping coefficient that is approximately twice that of the test BFB. The dynamics structural coefficients of HB-MFBs, including structural stiffness, equivalent viscous damping, and structural loss factor, are all dependent on excitation frequency and motion amplitude. Moreover, they exhibit an obvious decrease with the decline in metal mesh density.

Bump-Type Foil Bearings and Flexure Pivot Tilting Pad Bearings for Oil-Free Automotive Turbochargers: Highlights in Rotordynamic Performance

Oil-free turbochargers (TCs) require gas bearings in compact units of enhanced rotordynamic stability, mechanical efficiency, and improved reliability with reduced maintenance costs compared with oil-lubricated bearings. Implementation of gas bearings into automotive TCs requires careful thermal management with accurate measurements verifying model predictions. Gas foil bearings (GFBs) are customarily used in oil-free microturbomachinery because of their distinct advantages including tolerance to shaft misalignment and centrifugal/thermal growth, and large damping and load capacity compared with rigid surface gas bearings. Flexure pivot tilting pad bearings (FPTPBs) are widely used in high-performance turbomachinery since they offer little or no cross-coupled stiffnesses with enhanced rotordynamic stability. The paper details the rotordynamic performance and temperature characteristics of two prototype oil-free TCs; one supported on foil journal and thrust bearings and the other one is supported on FPTP journal bearings and foil thrust bearings of identical sizes (outer diameter (OD) and inner diameter (ID)) with the same aerodynamic components. The tests of the oil-free TCs, each consisting of a hollow rotor (∼0.4 kg and ∼23 mm in OD at the bearing locations), are performed for various imbalances in noise, vibration, and harshness (NVH; i.e., cold air driven rotordynamics rig) and gas stand test facilities up to 130 krpm. No forced cooling air flow streams are supplied to the test bearings and rotor. The measurements demonstrate the stable performance of the rotor–gas bearing systems in an ambient NVH test cell with cold forced air into the turbine inlet. Post-test inspection of the test FPTPGBs after the hot gas stand tests evidences seizure of the hottest bearing, thereby revealing a notable reduction in bearing clearance as the rotor temperature increases. The compliant FPTPGBs offer a sound solution for stable rotor support only at an ambient temperature condition while demonstrating less tolerance for shaft growth, centrifugal, and thermal, beyond its clearance. The current measurements give confidence in the present GFB technology for ready application into automotive TCs for passenger car and commercial vehicle applications with increased reliability.

Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: An Assessment of a Simple Engineering Practice

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large subsynchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is an absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study toward assessing the effect of shimming on a first generation BFB (L = 38.1 mm and D = 36.5 mm). Three metal shims, 120 deg apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. In static load tests, a bearing with shims shows a (nonlinear) structural stiffness larger than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency, thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor—average from test data collected at 300 Hz to 400 Hz—than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes subsynchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.

Effects of misalignment on the structure characteristics of bump-type foil bearings: a comparison between experimental and theoretical results

Purpose – The purpose of this paper is to investigate the effects of misalignment on the static and dynamics characteristics of bump-type foil bearings (BFBs). High-speed and high-temperature oil-free turbomachinery can be realized with the use of gas foil bearings (GFBs). GFBs have a flexible supporting structure; thus, they can tolerate a higher degree of misalignment compared with rolling element bearings. Design/methodology/approach – A test rig for GFBs has been developed to measure the effects of misalignment on the structure characteristics of bump-type foil bearings. The link-spring model, which is the foil structure model presented previously by the authors, is used as a basis in the present study to predict the static and dynamic performances of the foil structure. In general, predictions of the dynamic characteristics exhibit good agreement with the measurements acquired from the dynamic load tests. Findings – Results from the static tests show that GFBs develop high stiffness when the misalignment angle increases. Moreover, the dynamic characteristics of GFBs are identified by considering the test bearing supported by a non-rotating shaft as a one-degree-of-freedom system. The results indicate that the dynamic characteristics of GFBs strongly depend on excitation frequency and excitation amplitude because of the variation in the dynamic friction force within the foil structure. The structural stiffness and equivalent viscous damping increase with an increase in the misalignment angle. Originality/value – The present study focuses on the misalignment of GFBs and investigates experimentally the effects of misalignment on the structure characteristics of GFBs.

A New Structural Stiffness Model for Bump-Type Foil Bearings: Application to Generation II Gas Lubricated Foil Thrust Bearing

A new structural stiffness model for the compliant structure in foil gas bearings is introduced in the first part of this work. The model investigates the possibility that the flat segment between bumps, in bump foil strip, may deflect laterally and separate from the rigid bearing surface, and it also considers the interaction between bumps in the bump foil strip, the friction between the bump foil, and the surrounding structure. The validity of the analytical solution was verified through direct comparison with previous numerical and analytical models. In the second part of this work, the introduced bump foil model is used to investigate the static characteristics of generation II gas foil thrust bearing. The numerical simulations of the coupled fluid-structure interactions revealed that the foil thrust bearings share many features with their rigid bearing counterpart and the results showed clearly that the load carrying capacity of foil thrust bearings increases nonlinearly with the rotation speed and is expected to reach an asymptote as the rotation speed exceeds a certain value. The effects of ramp height and interface friction (i.e., friction at bump foil/rigid bearing interface and bump foil/top foil interface) on the static characteristics of generation II foil thrust bearings are investigated.

A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

A numerical model for 3D thermohydrodynamic analysis of bump-type foil bearings with a sparse mesh across the air film is described. The model accounts for heat convection into cooling air, thermal expansion of the bearing components, and material property variations due to temperature rise. Deflection of the compliant foil strip, described as a link-spring structure, is coupled to the solution of the generalized Reynolds equation and the energy equation to account for the effect of foil deformation on the film thickness. The variation in bump stiffness with the thermal growth of bumps is also considered in the model. The unique airflow in foil bearings created by the top foil detachment in the subambient region is analyzed for use in modifying the thermal boundary condition. The Lobatto point quadrature algorithm is used to represent the model on a sparse mesh and thereby reduce the computational effort. The calculated bearing temperatures are in remarkable agreement with both the published test data with the use of cooling air and that without the use of cooling air. The change of bearing radial clearance due to thermal growth of the bearing components was found to significantly affect the bearing load and to be a likely cause of the obvious drop in load capacity with a rise in ambient temperature.