Top Foil Research Articles

Thermal Characterization of a Gas Foil Bearing-A Novel Method of Experimental Identification of the Temperature Field Based on Integrated Thermocouples Measurements.

Maintenance of adequate thermal properties is critical for correct operation of a gas foil bearing. In this work, the authors present the results of the experimentally conducted thermal characterization of a prototype installation of the bearing. A novel method of temperature identification, based on integrated thermocouples readings, has been employed to determine the thermal properties of the specialized sensing top foil mounted in the tested bearing. Two measurement campaigns have been subsequently completed, applying freely-suspended and two-node support configurations, to gather complementary knowledge regarding the bearing’s operation. Apart from the rotational speed and temperature field measurements, the authors have also studied the friction torque and the shaft’s journal trajectories based on its radial displacements. The temporal courses for the above-mentioned quantities have enabled inference on the effects present during run-up, run-out and stable state operation at a constant speed. As confirmed, the applied distribution of the integrated sensors allows for temperature readings on the entire outer surface of the foil, and therefore, provides useful data for the bearing characterization. The work is concluded with presentation of the recommended directions regarding future improvements of the proposed measurement technique and more comprehensive study of the bearing’s characteristics.

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.

Experimental Study of Various Low-Friction Coatings for High-Temperature Gas Foil Bearings Under Cold-Start Conditions

Abstract This article presents the experimental research carried out on five different materials with which the top foils have been coated. A foil bearing with these foils was tested under different load conditions. The key operating parameters were determined, such as the moment of friction during the run-up and run-down tests as well as the temperature of the top foil. The AS20 coating, like the TiAlN coating, was intact (with the exception of several places where it was worn and where the Inconel sheet was visible) and was suitable for further use. The WC/C coating was damaged in many places, which shows that this type of coating cannot be used in combination with a journal coated with chromium oxide. The foil coated with MoS2/C had many areas where the coating was worn and also many areas where it was erased completely, so this type of coating was not durable. The use of a combination of TiAlN and MoS2/C coatings resulted in minor wear of the outer coating (made of MoS2/C) and the appearance of the inner coating, which is more resistant to abrasion. The tested materials will be used in the future to build a foil bearing resistant to operation at elevated temperatures in a gas microturbine.

Performance of the Compliant Foil Gas Seal with Surface Micro-Textured Top Foil

In various fields, micro-textures have been successfully applied to the surface of friction pairs to effectively improve flow field and friction performance. This paper aims to investigate how different textures affect the sealing performance of compliant foil gas film seals. In theoretical simulations, a facile method for characterizing the shape of micro-textures is proposed, and the equilibrium relationship between the gas film pressure, gas film thickness, and foil deformation is established. The transient Reynolds equation considering the eccentric convergence problem and abrupt Rayleigh step changes is solved to analyze the static and dynamic characteristics. The results show that (i) compared with the directionality of the texture, the gas volume accommodated by the texture has a greater impact on the sealing performance, and a convergent texture can effectively control the leakage rate; (ii) when the texture depth exceeds 9 μm, the sealing system may be unstable; (iii) the compliant foil seal is well suited to higher-speed service conditions, and the inverted triangular texture shows the best comprehensive sealing performance.

Performance studies of self-acting oil-lubricated bump journal bearing under lightly loaded conditions employing pocketed top foils

This paper explores the performance of oil-lubricated bump journal bearings employing micro-pockets on top foil surfaces for lightly loaded applications such as vertical rotor-bearing systems of centrifugal oil filters, vertical pumps, vertical shaft sinking machines and helicopter rotors. The influence of the number of pockets and their attributes on the performance behaviours of the bearing has been presented and explored herein. The six pocketed top foil yields the best performance, followed by four, eight and ten pocketed cases. With micro-pocketed top foil, the coefficient of friction is reduced by 7–18% compared to plain foil. Furthermore, pocketed foil provided improved stability of the rotor.

Influence of contact friction on static characteristics of multileaf bump foil bearing

In order to reveal the influence mechanism of foil contact friction on the multi-leaf bump foil bearing performance, a deformation simulation model is established under the contact constraint of multi top foils and bump foils, and the analysis of the fluid-structure interaction is realized by combining with the Reynolds equation of compressible gas. The influence of the nonlinear variation of foil stiffness caused by contact friction on the static characteristics of the bearing under different bearing numbers is numerically analyzed. The results show: the foil stiffness increases nonlinearly with the foil deformation and presents the characteristic of circumferential non-uniformity. With the increase of the deformation of foil, the influence of friction coefficient on the foil stiffness is more significant. Within the parameters studied in this paper, the friction coefficient increases from 0 to 0.5, the bearing capacity increases first and then decreases when the bearing numbers is small; the bearing capacity increases monotonically when the bearing numbers is large, the higher the bearing numbers, the more significant the growth rate. The attitude angle increases with the increase of friction coefficient, and the bearing becomes more and more unstable. When the bearing numbers is large, we should pay more attention to the influence of friction on bearing performance. The computed model emphasizing nonlinear stiffness in this paper is close to the realities, and the results can provide guidance in the design of multi-leaf bump foil bearing.

A comparison of modal analyses of foil-air bearing rotor systems using two alternative linearisation methods

When applied to the free vibration (modal) analysis of foil-air bearing rotor systems, the classical linear force coefficients method (LFCM) can be regarded as an indirect form of linearisation that eliminates the air film and foil state variables. Research into its accuracy has been limited to its predictive ability for the instability onset speed compared against the low amplitude response of the nonlinear system. Two recent studies highlighted issues that artificially inflated the method discrepancies reported previously. This paper verifies the LFCM on a series of cases and identifies indisputable ones where it gives misleading results. A novel robust procedure is devised for the LFCM computation of Campbell diagrams and modal stability plots. A first-ever study of the accuracy of the LFCM’s modal analysis capability is carried out using as benchmark the recently developed direct linearisation method. In contradiction to a recent study, the LFCM results did not exhibit a systematic error as the foil compliance increases, though it is not excluded that such an error may occur in other situations. The two cases identified where the LFCM gave misleading predictions relate to pad flutter with top foil detachment and half engine order whirl modes attributed to the air film.

Performance of textured foil journal bearing considering the influence of relative texture depth

Both foil structure and surface texturing have been widely used to improve bearing performance. However, there is little research on their combination, namely, textured gas foil bearing. This paper adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearing to study the influence of textures located on the top foil. The Newton-Raphson iterative method and the perturbation method are employed to obtain static and dynamic characteristics, respectively. Thereafter, based on three texture distribution types, further analysis about the effect of the relative texture depth and the textured portion is carried out. The results indicate that an appropriate arrangement of textures could improve the performance of gas foil bearing. For #1 texture distribution, the maximum increment of load capacity could exceed 10% when ω = 1.4 × 105 r/min, ε = 0.2.

Experimental Evaluation of Bearing Characteristics of Bump Mesh Foil Bearing

Foil bearings are a type of gas bearing consisting of a thin metal top foil supported from behind by an elastic body. Therefore, the bearing characteristics of a foil bearing are highly dependent on the support structure, and there is a need to improve the damping and lifting performance. In this study, a new support structure, bump mesh foil, was proposed to achieve both damping and lifting performance, and its elastic properties at rest and lifting properties during shaft rotation were experimentally evaluated. The experimental results showed that the damping performance of bump mesh foil bearing was improved while having enough the same lifting performance as bump foil bearing.

Experimental Study on the Effect of Top Foil Sagging on the Performance of Thrust Foil Bearing

Experimental Study on the Effect of Top Foil Sagging on the Performance of Thrust Foil Bearing

Foil stiffness optimization of a gas lubricated thrust foil bearing in enhancing load carrying capability

Air Foil Thrust Bearings (AFTB) are self-acting hydrodynamic members that support axial loads of high-speed rotating turbo-machineries. The load bearing capacity of such bearings mainly depends on the foil structure. The proposed Foil Thrust Bearing of 60 mm in diameter, designed and fabricated for performance evaluation, consists of a single top foil with an inner edge height equal to that of outer edge. This paper focuses on optimizing the foil stiffness in terms of foil thickness for steel and copper foil material with 60° and 90° sector angles. Various configurations of Gas Foil Thrust Bearings (GFTB) are tested for structural stiffness and thrust loads at higher operating speeds with an instrumented test rig dedicated for the purpose. Both geometric and operating parameters are varied to determine the best possible foil stiffness that enhances the load carrying capability of the Air Foil Thrust Bearing operating under hydrodynamic condition. CFD Simulation is also carried out to indicate the pressure distribution on the foil surface for the said bearing at actual boundary conditions.

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.

The current hysteresis effect of tower-like MoS2 nanocrystalline film for field emission and memristor applications

In this work, we investigate the hysteresis effect of the current-voltage characteristic for the magnetron sputtered molybdenum disulfide (MoS2) nanocrystalline films. The field emission hysteresis of MoS2 cold cathode is studied by sweeping mode with voltage upward/downward, the vacuum pressure has a remarkable effect on the hysteresis of the emission current and overall the hysteresis becomes more prominent as pressure rises. Besides, we also demonstrate the current-voltage behaviors of MoS2 film using thermal evaporated Al dot as top electrode and copper foil substrate as bottom electrode. The Al/MoS2/Cu configuration device presents an obvious current hysteretic effect and the current increases with the increase of the voltage sweeping times. The possible mechanism of the hysteresis has been proposed herein and also investigations provide a great promise for the development of magnetron sputtered MoS2 nanocrystalline films in applications such as field emitters and memristor devices.

Warpage modeling and characterization of intelligent power modules (IPMs)

Abstract Intelligent power modules (IPMs) are widely used in the electric vehicle (and hybrid electric vehicle industry nowadays due to their high power density and ability to integrate multiple components within a single package. However, the reliability of IPMs is severely degraded by the substrate warpage effect produced during the packaging process. This study therefore develops a computational model to analyze the warpage of the IPM assembly at various stages of the packaging process. The validity of the simulation model is confirmed by comparing the numerical results for the warpage of the direct plated copper substrate with the experimental observations. Taguchi experiments are then performed to examine the effects of eight control factors on the IPM package warpage following the post-mold cure (PMC) process, namely (1) the dam bar layout, (2) the epoxy molding compound (EMC) thickness, (3) the lead frame thickness, (4) the ceramic thickness, (5) the bottom layer Cu foil thickness, (6) the top layer Cu foil thickness, (7) the ceramic material type and (8) the EMC material type. Finally, the Taguchi analysis results are used to determine the optimal packaging design that minimizes the warpage of the post-PMC package.

A novel method for calculating the dynamic force coefficients of Gas Foil Bearings and its application in the rotordynamic analysis

Bearing force coefficients are a fundamental and convenient concept in the dynamic analysis of a bearing–rotor system. However, for a rotor system supported by gas foil bearings (GFBs), recent studies have shown that the onset speed of instability (OSI) predicted using the force coefficients model is inconsistent with that obtained using nonlinear time-domain analysis. To solve this problem, this study proposed a novel method for calculating the dynamic force coefficients of GFBs. The correctness and effectiveness of the proposed method were confirmed by examining the calculation of the bearing force coefficients, the stability prediction and the calculation of unbalance responses. For a classical symmetric GFB–rotor system, application of the proposed calculation method demonstrated that the OSI predicted by the force coefficients model can be in complete agreement with the OSI predicted by the fully coupled model for all compliance levels. This indicates that the force coefficient method has the potential to make accurate prediction for the stability characteristics of GFB–rotor systems. Furthermore, the proposed method is derived based on the general dynamic equation for linear structures; hence it is able to adopt a complex foil structure model. The one-dimensional finite element foil model that considers detachments of the top foil from the bump foil was used to show the ability of the proposed method to use a complex foil structure model.

Dynamics, stability and bifurcation analysis of rotors in air ring bearings

Classical air foil bearings consist of a top foil, which is usually supported by a bump or beam foil structure. For this bearing type, the air gap is a function of the top foil deformation. Here, an alternative air bearing design – called air ring bearing – is investigated, which may be regarded as a straightforward and very obvious modification of the classical air bearing design. The basic idea is to insert a rigid ring between the shaft and the foil structure. The ring may therefore be considered to be elastically mounted in the housing by means of a bump or beam-type structure. Alternatively, a viscoelastic supporting structure (elastomer) may be used to connect the ring with the housing. Hence, the air film is separated by a rigid ring from the supporting structure. As a consequence, the bearing gap for the fluid film has rigid walls, which simplifies the numerical calculation significantly.In this manuscript, a detailed numerical analysis of rotor systems supported in air ring bearings is presented. The basic nonlinear dynamical effects occurring in such rotor systems are investigated with a particular focus on the stability and bifurcation behavior. Therefore, a detailed co-simulation model of the rotor/bearing system is used. Different possible bifurcation scenarios are described and explained with the help of run-up simulations.Rotor systems with air ring bearings exhibit a completely different vibration and stability behavior than rotors in classical air foil bearings. Diverse interesting nonlinear vibration phenomena, not known in connection with classical air foil bearings, are discussed in detail and physically explained in a clear manner.

Investigation of rotor–gas foil bearing system and its application for an ultra-high-speed permanent magnet synchronous motor

In this study, an ultra-high-speed rotor–gas foil-bearing system is designed and applied to a permanent magnet synchronous motor. Gas foil journal bearings and gas foil thrust bearings are used to provide journal and axial support to the rotor, respectively. The bearings are analyzed theoretically considering the nonlinear deflection of the top foil, and the static and dynamic characteristics are obtained with which the rotor dynamic performances of the tested rotor are calculated using the finite element method. During the experiment, the permanent magnet synchronous motor can operate stably at 94,000 r/min, which demonstrates a great dynamic performance of the gas foil bearings and the stability that it provides to the entire system. The sub-synchronous vibration also occurs when the rotating speed reaches 60,000 r/min and as the speed keeps rising, the amplitude of such vibration increases, which will contribute to the destabilization of the rotor–gas foil-bearing system. Finally, the axial force of the rotor is calculated theoretically as well as measured directly by four micro force sensors mounted in the thrust end cover of the permanent magnet synchronous motor. The experimental results presented in this article are expected to provide a useful guide to the design and analysis of the rotor–gas foil-bearing system and high-speed permanent magnet synchronous motor.

Study on the temperature and strain fields in gas foil bearings – measurement method and numerical simulations

Gas foil bearings belong to the group of slide bearings and are used in devices in which operation at high rotational speeds of the shafts are of key importance, e.g., in gas turbines. The air film developed on the surface of the bearing’s top foil allows this structural component to be separated from the shaft. This ensures a non-contact operation of the bearing. In the case of the mentioned type of bearings, their resultant operational properties are influenced by both thermal and mechanical phenomena. The current work presents a model of a gas foil bearing developed making use of the Finite Element Method. The model takes into account thermomechanical couplings which are necessary for the correct simulation of the operation of physical components of the modeled system. The paper reports the results of numerical analyzes conducted for the elaborated model as well as the relevant conclusions concerning thermomechanical couplings present in gas foil bearings. The method for the experimental identification of the temperature and strain fields in the bearing’s top foil proposed to validate the numerical model is also presented.

Performance improvement of foil air journal bearing employing micro-pocket and textures on top compliant surface

Investigations to reduce the friction and improve the dynamic performance of a self-acting air foil journal bearing have been performed and presented herein employing the texture, micro-groove and micro-pocket on the top foil. Significant improvements in the static and dynamic performances have been found in presence of micro-pocketed/grooved and textured top foils in comparison to conventional plain foil. The micro-pocketed top foil yields better performance as compared to textured and conventional cases. In the presence of micro-pocket on top compliant foil, the bearing yielded a significant reduction in friction coefficient varying in the range of 8%–11% as compared to conventional one. Moreover, better dynamic stability has also been found even at lightly loaded conditions in the presence of texture and micro-pocket.

バンプフォイル軸受の理論最大負荷容量に及ぼすトップフォイル変形解析モデルの影響（第2報） ―アイソパラメトリックシェル要素の適用―

バンプフォイル軸受の理論最大負荷容量に及ぼすトップフォイル変形解析モデルの影響（第2報） ―アイソパラメトリックシェル要素の適用―