Hydrodynamic Analysis of Compliant Foil Bearings With Modified Top Foil Model

2011 ◽  
Author(s):  
Fangcheng Xu ◽  
Zhansheng Liu ◽  
Guanghui Zhang ◽  
Liang Xie
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Structural Model ◽  
Thickness Distribution ◽  
Hydrodynamic Analysis ◽  
Foil Bearings ◽  
Stiffness Model ◽  
The One ◽  
The Mathematical Model ◽  
Gas Bearing

The mathematical model of film thickness is developed with considering the compressibility of the gas and the deformation of the foil in this paper. By employing the Newton-Raphson method and the finite difference method, the compressible gas lubricated Reynolds equation and the film thickness equation are solved coupling together. The static characteristics such as pressure distribution and film thickness distribution for equivalent bump foil stiffness model are obtained to verify the validation of the proposed method. The gas film thickness model is modified by modeling the top foil as the one dimension curved beam, to meet the case of the real physical model. The numerical results of this modified structural model are compared with the other finite element top foil models. It indicates that the pressure distribution for bump foil gas bearing is in good agreement with the test data.

scholarly journals Numerical and experimental study on air thrust foil bearing performance with improved structural model based on real-time taper inlet height

2020 ◽  
Author(s):  
Fangcheng Xu ◽  
Liukai Hou ◽  
Bin Wu ◽  
Zeda Dong ◽  
Yongliang Wang
Keyword(s):  
Film Thickness ◽  
Real Time ◽  
Test Data ◽  
Gas Turbines ◽  
Structural Model ◽  
Load Capacity ◽  
Thickness Distribution ◽  
New Model ◽  
Bearing Load ◽  
Simulation Results

Abstract Air thrust foil bearings are key bearings of micro turbo-machinery (such as micro gas turbines, turbo blowers, and air compressors). The bearing load capacity is affected by many factors, and the taper inlet height of bearing structure is closely related to the load capacity. In many previous literature the taper inlet height, as a constant value, was used to calculate film thickness distribution. However, the reality is that the foil will be squeezed by the pressure generated between runner disk and top foil, which makes taper inlet height change during iteration. Therefore, the actual bearing taper inlet height should be chosen properly instead of the constant taper inlet height when iterating. In this paper, an improved computational model of film thickness for adjusting the taper inlet height in real-time is proposed. The relationship between the maximum bearing load capacity and taper inlet height at different rotor speeds of two models is obtained through numerical simulation. It is found that the optimal taper inlet height of the new model is larger than that of the old model. Three types of bearings with different taper inlet height (20μm, 70μm, 114μm) had been tested and the maximum load capacity at different rotor speeds had been obtained. Finally, test data and the simulation results of the two models are compared. It is found that the simulation results of the two models are quite different when the taper inlet height is near the optimal taper inlet height, and the new model is more agree well with the test data.

Inverse Hydrodynamic Methods Applied to Mr. Beauchamp Tower’s Experiments of 1885

1980 ◽  
Vol 102 (2) ◽  
pp. 172-179 ◽  
Author(s):  
C. M. McC. Ettles ◽  
M. Akkok ◽  
A. Cameron
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Hydrodynamic Lubrication ◽  
Pressure Profile ◽  
Hydrodynamic Theory ◽  
Two Dimensional ◽  
Hydrodynamic Analysis ◽  
Cubic Equation ◽  
Hydrodynamic Lubrication Theory ◽  
Measured Pressure

The experiments of Mr. Beauchamp Tower and their subsequent interpretation by Professor Osborne Reynolds form the basis of all hydrodynamic lubrication theory. In the experiments described in his second report, Tower made nine pressure tappings in a 157 deg partial arc bearing. Reynolds assumed that the film shape corresponded to a circular bearing and analyzed the results on this assumption. Inverse hydrodynamic theory allows the calculation of the actual film shape from this measured pressure distribution. It is found that the film was a slightly convergent wedge which does not correspond to a fitted bearing as assumed by Tower and certainly not to the clearance bearing assumed by Reynolds. Existing methods of inverse hydrodynamic analysis require the second differential of the pressure profile (or its equivalent in the two-dimensional case) to become zero at some point in the film. The film thickness can be found directly at this point and then elsewhere by the solution of a cubic equation. Two separate and more general methods are developed in this paper in which this requirement for the second differential is unnecessary.

scholarly journals Controlling Film Thickness Distribution by Magnetron Sputtering with Rotation and Revolution

Coatings ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 599
Author(s):  
Handan Huang ◽  
Li Jiang ◽  
Yiyun Yao ◽  
Zhong Zhang ◽  
Zhanshan Wang ◽  
...  
Keyword(s):  
Magnetron Sputtering ◽  
Film Thickness ◽  
Multilayer Film ◽  
Thickness Distribution ◽  
Parabolic Cylinder ◽  
Particle Model ◽  
Planetary Motion ◽  
X Rays ◽  
X Ray ◽  
Sputtering System

The laterally graded multilayer collimator is a vital part of a high-precision diffractometer. It is applied as condensing reflectors to convert divergent X-rays from laboratory X-ray sources into a parallel beam. The thickness of the multilayer film varies with the angle of incidence to guarantee every position on the mirror satisfies the Bragg reflection. In principle, the accuracy of the parameters of the sputtering conditions is essential for achieving a reliable result. In this paper, we proposed a precise method for the fabrication of the laterally graded multilayer based on a planetary motion magnetron sputtering system for film thickness control. This method uses the fast and slow particle model to obtain the particle transport process, and then combines it with the planetary motion magnetron sputtering system to establish the film thickness distribution model. Moreover, the parameters of the sputtering conditions in the model are derived from experimental inversion to improve accuracy. The revolution and rotation of the substrate holder during the final deposition process are achieved by the speed curve calculated according to the model. Measurement results from the X-ray reflection test (XRR) show that the thickness error of the laterally graded multilayer film, coated on a parabolic cylinder Si substrate, is less than 1%, demonstrating the effectiveness of the optimized method for obtaining accurate film thickness distribution.

Dynamic Analysis of Tilting-Pad Journal Bearing—Influence of Pad Deformations

1994 ◽  
Vol 116 (3) ◽  
pp. 621-627 ◽  
Author(s):  
H. Desbordes ◽  
M. Fillon ◽  
C. Chan Hew Wai ◽  
J. Frene
Keyword(s):  
Film Thickness ◽  
Pressure Field ◽  
Journal Bearing ◽  
Maximum Pressure ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Dimensional Finite Element ◽  
The One ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

A theoretical nonlinear analysis of tilting-pad journal bearings is presented for small and large unbalance loads under isothermal conditions. The radial displacements of internal pad surface due to pressure field are determined by a two-dimensional finite element method in order to define the actual film thickness. The influence of pad deformations on the journal orbit, on the minimum film thickness and on the maximum pressure is studied. The effects of pad displacements are to decrease the minimum film thickness and to increase the maximum pressure. The orbit amplitude is also increased by 20 percent for the large unbalance load compared to the one obtained for rigid pad.

Foil Gas Bearing With Compression Springs: Analyses and Experiments

2007 ◽  
Vol 129 (3) ◽  
pp. 628-639 ◽  
Author(s):  
Ju-ho Song ◽  
Daejong Kim
Keyword(s):  
Loss Factor ◽  
Load Capacity ◽  
Underlying Structure ◽  
Equivalent Viscous Damping ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Different Types ◽  
Structural Loss ◽  
Compression Springs ◽  
Gas Bearing

A new foil gas bearing with spring bumps was constructed, analyzed, and tested. The new foil gas bearing uses a series of compression springs as compliant underlying structures instead of corrugated bump foils. Experiments on the stiffness of the spring bumps show an excellent agreement with an analytical model developed for the spring bumps. Load capacity, structural stiffness, and equivalent viscous damping (and structural loss factor) were measured to demonstrate the feasibility of the new foil bearing. Orbit and coast-down simulations using the calculated stiffness and measured structural loss factor indicate that the damping of underlying structure can suppress the maximum peak at the critical speed very effectively but not the onset of hydrodynamic rotor-bearing instability. However, the damping plays an important role in suppressing the subsynchronous vibrations under limit cycles. The observation is believed to be true with any air foil bearings with different types of elastic foundations.

Thermohydrodynamic Behavior of a Slider Pocket Bearing

2005 ◽  
Vol 128 (2) ◽  
pp. 312-318 ◽  
Author(s):  
Mihai B. Dobrica ◽  
Michel Fillon
Keyword(s):  
Pressure Distribution ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Convective Boundary ◽  
Inertia Effects ◽  
Good Convergence ◽  
Bearing Design ◽  
The One ◽  
Volume Method ◽  
Generalized Reynolds Equation

Pocket-pads or steps are often used in journal bearing design, allowing improvement of the latter’s dynamic behavior. Similar “discontinuous” geometries are used in designing thrust bearing pads. A literature review shows that, to date, only isoviscous and adiabatic studies of such geometries have been performed. The present paper addresses this gap, proposing a complete thermohydrodynamic (THD) steady model, adapted to three-dimensional (3D) discontinuous geometries. The model is applied to the well-known geometry of a slider pocket bearing, operating with an incompressible viscous lubricant. A model based on the generalized Reynolds equation, with concentrated inertia effects, is used to determine the 2D pressure distribution. On this basis, a 3D field of velocities is constructed which, in turn, allows the resolution of the 3D energy equation. Using a variable-size grid improves the accuracy in the discontinuity region, allowing an evaluation of the magnitude of error induced by Reynolds assumptions. The equations are solved using the finite volume method. This ensures good convergence even when a significant reverse flow is present. Heat evacuation through the pad is taken into account by solving the Laplace equation with convective boundary conditions that are realistic. The runner’s temperature, assumed constant, is determined by imposing a zero value for the global heat flux balance. The constructed model gives the pressure distribution and velocity fields in the fluid, as well as the temperature distribution across the fluid and solid pad. Results show important transversal temperature gradients in the fluid, especially in the areas of minimal film thickness. This further justifies the use of a complete THD model such as the one employed.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Effect of Freestream Radial Velocity Component on Hydrodynamic Analysis of Propellers

1983 ◽  
Vol 27 (02) ◽  
pp. 131-134
Author(s):  
Terry Brockett
Keyword(s):  
Mathematical Model ◽  
Radial Velocity ◽  
Performance Prediction ◽  
Velocity Component ◽  
Additional Term ◽  
Radial Component ◽  
Radial Velocity Component ◽  
Hydrodynamic Analysis ◽  
The Mathematical Model ◽  
Wake Fields

For wake fields with circumferential averages that include a small radial component, an additional termarises in the mathematical model used for design or performance prediction of propellers that has been previously overlooked. This term arises from the boundary condition that the blade is impenetrable and is a function of only geometry and the inflow radial velocity component. This simple additional term is shown to be important for the example considered, leading to a variable change in camber and a pitch reduction.

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