scholarly journals Discussion: “Compliant Foil Bearing Structural Stiffness Analysis: Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry” (Ku, C.-P. Roger, and Heshmat, H., 1992, ASME J. Tribol., 114, pp. 394–400)

1992 ◽  
Vol 114 (2) ◽  
pp. 400-400
Author(s):  
A. Gu
Keyword(s):  
Theoretical Model ◽  
Structural Stiffness ◽  
Stiffness Analysis ◽  
Foil Bearing

Compliant Foil Bearing Structural Stiffness Analysis: Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry

1992 ◽  
Vol 114 (2) ◽  
pp. 394-400 ◽  
Author(s):  
C.-P. Roger Ku ◽  
H. Heshmat
Keyword(s):  
Theoretical Model ◽  
Variable Load ◽  
Distribution Profile ◽  
Friction Forces ◽  
Stiffness Analysis ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Load Distributions ◽  
Fixed End

This paper presents a theoretical model of corrugated foil strip (bump foil) deformation in compliant foil bearings and dampers. The friction forces between bump foils and the housing or the top foil, local interaction forces, variable load distributions, and bump geometries are taken into consideration. Following the trend of earlier published experimental data, the bumps near the fixed end have a much higher predicted stiffness (lower deflection) than those near the free end. Higher friction coefficients tend to increase stiffness and may pin down bumps near the fixed end. An increase in the friction coefficient between the top foil and the bump is a more effective method of achieving both Coulomb damping and higher stiffness. In addition to bump geometry, the load distribution profile greatly influences bump stiffness. A follow-up paper will present the experimental verification and discuss the comparison between theoretical and experimental results.

Design guidelines for bump-type compliant conical foil bearing

2021 ◽  
pp. 095440622110127
Author(s):  
Hongyang Hu ◽  
Ming Feng
Keyword(s):  
Load Capacity ◽  
Design Guidelines ◽  
Foil Thickness ◽  
Axial Stiffness ◽  
Structural Stiffness ◽  
Foil Bearing ◽  
Stiffness Model ◽  
Opposite Position ◽  
Stiffness Distribution ◽  
Half Length

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.

On the Integration of Hot Foil Bearings Into Gas Turbine Engines: Theoretical Treatment

2019 ◽  
Author(s):  
Hooshang Heshmat ◽  
James F. Walton
Keyword(s):  
High Temperature ◽  
System Dynamics ◽  
High Performance ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Structural Stiffness ◽  
Foil Bearings ◽  
Foil Bearing ◽  
High Temperature Operation ◽  
Bearing System

Abstract To achieve high power density Gas Turbine Engines (GTEs), R&D efforts have strived to develop machines that spin faster and run hotter. One method to achieve that goal is to use high temperature capable foil bearings. In order to successfully integrate these advanced foil bearings into GTE systems, a theoretical understanding of both bearing and rotor system integration is essential. Without a fundamental understanding and sound theoretical modeling of the foil bearing coupled with the rotating system such an approach would prove application efforts fruitless. It is hoped that the information provided in this paper will open up opportunistic doors to designs presently thought to be impossible. In this paper an attempt is made to describe how an advanced foil bearing is modeled for extreme high temperature operation in high performance turbomachinery including GTEs, Supercritical CO2 turbine generators and others. The authors present the advances in foil bearing capabilities that were crucial to achieving high temperature operation. Achieving high performance in a compliant foil bearing under the wide extremes of operating temperatures, pressures and speeds, requires a bearing system design approach that accounts for the highly interrelated compliant surface foil bearing elements such as: the structural stiffness and frictional characteristics of the underlying compliant support structure across the operating temperature and pressure spectrum; and the coupled interaction of the structural elements with the hydrodynamic pressure generation. This coupled elasto-hydrodynamic-Finite Element highly non-linear iterative methodology will be used by the authors to present a series of foil bearing design evaluations analyzing and modeling the foil bearing under extreme conditions. The complexity of the problem of achieving foil bearing system operation beyond 870°C (1600°F) requires as a prerequisite the attention to the tribological details of the foil bearing. For example, it is necessary to establish how both the frictional and viscous damping coefficient elements as well as the structural and hydrodynamic stiffness are to be combined. By combining these characteristics the influence of frictional coefficients of the elastic and an-elastic materials on bearing structural stiffness and hence the bearing effective coupled elasto-hydrodynamic stiffness coefficients will be shown. Given that the bearing dynamic parameters — stiffness and damping coefficients — play a major role in the control of system dynamics, the design approach to successfully integrate compliant foil bearings into complex rotating machinery systems operating in extreme environments is explored by investigating the effects of these types of conditions on rotor-bearing system dynamics. The proposed rotor/bearing model is presented to describe how system dynamics and bearing structural properties and operating characteristics are inextricably linked together in a manner that results in a series separate but intertwined iterative solutions. Finally, the advanced foil bearing modeling and formulation in connection with resulting rotor dynamics of the system will be carried out for an experimental GTE simulator test rig. The analytical results will be compared with the experiments as presented previously to demonstrate the effectiveness of the developed method in a real world application [1].

A Theoretical Model for Self-Excited Vibrations in Hydraulic Gates, Valves and Seals

1980 ◽  
Vol 102 (2) ◽  
pp. 146-151 ◽  
Author(s):  
D. S. Weaver ◽  
S. Ziada
Keyword(s):  
Theoretical Model ◽  
Discharge Coefficient ◽  
Nonlinear Differential Equations ◽  
Check Valve ◽  
Structural Stiffness ◽  
Fluid Inertia ◽  
Vibration Displacement ◽  
Runge Kutta Method ◽  
Flow Control Devices ◽  
Control Devices

A general theoretical model is presented for the jet flow mechanism of self-excited vibrations of flow control devices operating at small openings. The coupled nonlinear differential equations are solved numerically using the Runge-Kutta method. The vibration displacement and discharge characteristics are given for a variety of parameters such as structural stiffness, fluid inertia and discharge coefficient. The predictions are shown to agree reasonably well with the experimental observations of swing check valve vibrations.

Structural Stiffness and Damping Coefficients of a Multileaf Foil Bearing With Bump Foils Underneath

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Ye Tian ◽  
Yanhua Sun ◽  
Lie Yu
Keyword(s):  
Excitation Frequency ◽  
Magnetic Bearing ◽  
Damping Capacity ◽  
Structural Stiffness ◽  
Test Rig ◽  
Domain Identification ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Applied Forces ◽  
Stiffness And Damping

This paper presents a multileaf foil bearing (MLFB), which consists of four resilient top foils and four stiff bump foils underneath; thus, a high supporting capacity and a high damping capacity can be achieved. A specially designed test rig is used to identify the structural stiffness and damping coefficients of the MLFB. The rotor of the test rig is supported by two journal MLFBs and a thrust active magnetic bearing (AMB) and the static and dynamic loads are applied by two radial AMBs. The tests on MLFBs were conducted under conditions of no shaft rotation at different angular positions and journal displacements with different excitation frequency. A frequency domain identification method is presented to determine the stiffness and damping coefficients. Static measurements show nonlinear deflections with applied forces, which varies with the orientation of the load angular position. The dynamic measurements show that the stiffness and equivalent viscous damping change with the excitation frequency. Furthermore, the stiffness and damping coefficients are related to the operating position where dynamic load tests were conducted. The investigation provides extensive measurements of the static and dynamic characteristics of the MLFB. These results can serve as a benchmark for the calibration of analytical tools under development.

Experiments and predictions on the performance of double-bump foil bearings: Effects of bearing loads and height difference between bumps

2017 ◽  
Vol 231 (11) ◽  
pp. 1474-1485 ◽  
Author(s):  
Kai Feng ◽  
Tao Zhang ◽  
Xueyuan Zhao
Keyword(s):  
Load Capacity ◽  
Load Test ◽  
Underlying Structure ◽  
Viscous Damping ◽  
Structural Stiffness ◽  
Static Load Test ◽  
Height Difference ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Foil Bearing

The concept of multilayer bump foils was introduced in the design of bump foil bearings to produce a double-bump foil bearing, which can provide increased load capacity and damping by adding another bump foil in the underlying structure. The height difference between the upper and lower bumps is a crucial parameter in the design and application of such structure. In this study, two double-bump foil bearings with various height differences between bumps are designed and fabricated to compare with an ordinary bump foil bearing. Three bearings are examined via static and dynamic load tests to estimate the structural stiffness and equivalent viscous damping. Test results indicate that lower bumps can enhance both the structural stiffness and equivalent viscous damping. A theoretical link-spring model, which exhibits good agreement with the data obtained from the static load test, is adopted to analyze the effect of height difference between bumps on gas film thickness and gas pressure of double-bump foil bearings. Results show that lower bumps of the double-bump foil bearing with a smaller height difference become active more easily and are more likely to form a stable double-bump supporting structure.

Characterization of Foil Bearing Structure for Increasing Shaft Temperatures: Part I—Static Load Performance

2008 ◽  
Author(s):  
Tae Ho Kim ◽  
Anthony W. Breedlove ◽  
Luis San Andre´s
Keyword(s):  
Material Properties ◽  
Static Load ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Radial Clearance ◽  
Structural Stiffness ◽  
Test Configuration ◽  
Hollow Shaft ◽  
Foil Bearing ◽  
Simple Physical Model

Oil-free turbomachinery relies on gas bearing supports for reduced power losses and enhanced rotordynamic stability. Gas foil bearings (GFBs) with bump-strip compliant layers can sustain large loads, static and dynamic, and provide damping to reduce shaft vibrations. The ultimate load capacity of GFBs depends on the material properties and configuration of the underlying bump strips structure. In high temperature applications thermal effects changing operating clearances and material properties can affect considerably the performance of the FB structure. The paper presents experiments conducted to estimate the nonlinear structural stiffness of a test FB for increasing shaft temperatures. A 38.17 mm inner diameter FB is mounted on a non-rotating hollow shaft affixed to a rigid structure. A cartridge heater inserted into the shaft provides a controllable heat source and thermocouples record temperatures on the shaft and FB housing. For increasing shaft temperatures (up to 188°C) a static load (ranging from 0 N to 133 N) is applied to the bearing and the deflection recorded. Load versus deflection tests render the FB static structural stiffness coefficient. In the test configuration, thermal expansion of the FB housing, larger than that of the shaft, nets a significant increase in bearing radial clearance which produces a significant reduction in the foil bearing structural stiffness. A simple physical model assembling individual bump stiffnesses predicts well the measured FB structural stiffness when accounting for variations with temperature of the bump elastic modulus and the actual radial clearance affected by the thermal growth of the shaft and bearing cartridge. Further tests identifying the FB structure dynamic stiffness and its equivalent viscous damping follow in a companion paper (Part II) for a similar range of shaft temperatures.

Experimental Structural Stiffness Analysis of a Surgical Haptic Master Device Manipulator

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
İbrahimcan Görgülü ◽  
Mehmet İsmet Can Dede ◽  
Giuseppe Carbone
Keyword(s):  
Model Fitting ◽  
Experimental Results ◽  
Fine Tuning ◽  
Structural Stiffness ◽  
Stiffness Analysis ◽  
Stiffness Model ◽  
Stiffness Evaluation ◽  
Institute Of Technology ◽  
Master Device

Abstract This paper deals with haptic devices for master–slave telesurgical applications. Namely, a stiffness model fitting methodology and its fine-tuning are proposed based on experimental results. In particular, the proposed procedure is based on virtual joint structural stiffness modeling to be applied in time-efficient compliance compensation strategies. A specific case study is discussed by referring to the HISS haptic device that has been developed and built at Izmir Institute of Technology. Two different experimental setups are designed for stiffness evaluation tests. Experimental results are discussed to demonstrate their implementation in the proposed methodology for the fine-tuning of stiffness model.

Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism

Robotica ◽  
2004 ◽  
Vol 22 (4) ◽  
pp. 463-475 ◽  
Author(s):  
Woo-Keun Yoon ◽  
Takashi Suehiro ◽  
Yuichi Tsumaki ◽  
Masaru Uchiyama
Keyword(s):  
Parallel Mechanism ◽  
Rotation Axis ◽  
Haptic Interface ◽  
Structural Stiffness ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Elastic Deformations ◽  
Stiffness Analysis ◽  
Analysis And Design ◽  
Parallel Link

In our previous work, we developed a compact 6-DOF haptic interface as a master device which achieved an effective manual teleoperation. The haptic interface contains a modified Delta parallel-link positioning mechanism. Parallel mechanisms are usually characterized by a high stiffness, which, however, is reduced by elastic deformations of both parts and bearings. Therefore, to design such a parallel mechanism, we should analyze its structural stiffness, including elastic deformations of both parts and bearings. Then we propose a simple method to analyze structural stiffness in a parallel mechanism using bearings. Our method is based on standard concepts such as static elastic deformations. However, the important aspect of our method is the manner in which we combine these concepts and how we obtain the value of the elasticity coefficient of a rotation axis in a bearing. Finally, we design a modified Delta mechanism, with a well-balanced stiffness, based on our method of stiffness analysis.

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