Integrated Numerical Model for Thermohydrodynamic Analysis of Bump-Type Foil Bearings

2011 ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko ◽  
Haruo Houjoh
Keyword(s):  
Experimental Data ◽  
Thermal Expansion ◽  
Ambient Temperature ◽  
Heat Convection ◽  
Foil Bearings ◽  
Thermal Expansion Coefficients ◽  
Thermal Growth ◽  
Bearing Load ◽  
Basic Equations ◽  
Air Film

This investigation presents a thermohydrodynamic (THD) analysis for bump-type foil bearings. Two basic equations, the generalized Reynolds equation and the energy equation, are simultaneously solved for the air pressure and generated heat due to the viscous shearing action in the air film. The compliant foil strip is described as a link-spring structure. The calculated foil deflection is coupled into the solution of the two basic equations to account for its effect on the film thickness. This model accounts for heat convection in the air film region and the material property variations of the lubricant air due to the temperature rise, heat convection with the cooling air, heat conduction between the solid components, heat transfer at the surface of the solid components, and thermal expansion of the bearing components as well as change in the bump foil elasticity. The airflow within the air film is a distinctive characteristic of bump-type foil bearings (BTFBs) compared to normal oil bearings because the top foil detaches at sub-ambient regions. The unique airflow is also taken into consideration in this model to modify the thermal boundary condition of the air film. Data from a published experimental investigation is used to validate the mathematical model. The predicted bearing temperatures, as well as the bearing load, agree well with the experimental data. The effects of ambient temperature on BTFB performance are discussed with the THD model. With increased ambient temperature, the influence of the bearing clearance changes, because the thermal growth of the bearing components is more significant than the decrease of the foil elasticity. Therefore, the thermal expansion coefficients of the bearing components should be considered during bearing design. The temperature profile within the foil bearing is predicted and compared with published tested temperature values. The calculated temperature correlates well with the experimental data at most of the positions. The deviation between the two values at the bearing-load position is demonstrated to be less than 10.3%.

A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Load Capacity ◽  
Computational Effort ◽  
Radial Clearance ◽  
Foil Bearings ◽  
Mesh Model ◽  
Thermal Growth ◽  
Bearing Load ◽  
Cooling Air ◽  
Air Film ◽  
Generalized Reynolds Equation

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.

Thermal expansion coefficients and Gruneisen parameters of quartz at high temperature by X-ray method

1994 ◽  
Vol 9 (2) ◽  
pp. 148-150
Author(s):  
Nabil N. Rammo ◽  
Saad B. Farid
Keyword(s):  
Thermal Expansion ◽  
High Temperature ◽  
Ambient Temperature ◽  
Least Squares ◽  
Temperature Variation ◽  
Ray Method ◽  
X Ray ◽  
Least Squares Fitting ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

The temperature variation of the interplanar spacings (101), (112), and (211) of 325 mesh quartz was determined in the range 300–966 °K using X-ray powder diffractometry. The measured lattice parameters have been found to increase nonlinearly with temperature, and the dependence has been expressed by a polynomial of second degree from the least-squares fitting of the data, the results of which are presented herein. Values are given for the thermal expansion coefficients and Gruneisen parameter in the range 300 to 768 °K. In the range 768–966 °K, the expansion is zero. The derivatives dαa/dT, dαc/dT, and dαv/dT at ambient temperature are also given.

Stresses in Polyimide Films during Cure and Thermal Cycling

1992 ◽  
Vol 264 ◽  
Author(s):  
David J. Monk ◽  
Yongxiang He ◽  
David S. Soane
Keyword(s):  
Experimental Data ◽  
Thermal Expansion ◽  
Thermal Cycling ◽  
High Stress ◽  
Maxwell Model ◽  
Solvent Evaporation ◽  
Thermal Expansion Mismatch ◽  
Polyimide Films ◽  
Thermal Expansion Coefficients ◽  
Linear Viscoelastic Theory

AbstractSeveral electronics packaging schemes involve polymer/inorganic interfaces, including: dual-in-line packages, tape automated bonding and multilayer interconnects. Typically, the thermal expansion coefficients are disparate, so these interfaces often cause high stress. Therefore, a phenomenological model describing transient stresses in spin-coated polyimide films was developed. The model is based on linear viscoelastic theory, and it accounts for shrinkage caused by solvent evaporation and imidization, viscoelastic relaxation, and thermal expansion mismatch. Strains have been defined from three mechanisms: thermal expansion mismatch, chemical curing, and solvent evaporation. Stress is, then, calculated by using the Classical Maxwell Model with one element. The concept of free volume is used throughout the model to estimate viscosity, modulus, and other quantities related to calculating strains. Model predictions for stress as a function of temperature during film cure and thermal cycling are fit with experimental data obtained from a bending beam apparatus.Stress has been estimated by using the thin film approximation of the Timoshenko bilayer stress equation. Experimental data agree well with wafer bowing stress measurements. Although the technique does not yet take into account changing polyimide thickness during curing, the results still show qualitative curing dynamics. This preliminary study revealed good agreement between predicted and observed effects of material properties on stresses developed during cure and thermal cycling. Specificially, an unexpected high in-cure stress was observed for a standard low CTE polyimide. High stresses during curing can be as detrimental to an electronics device as high stress during device operation, so this technique may be useful when screening polyimides and/or prescribing curing schedules. Future work will improve the predictive capability of the model.

THERMAL EXPANSION OF SINGLE CRYSTALS OF ZINC AT LOW TEMPERATURES

1965 ◽  
Vol 43 (7) ◽  
pp. 1328-1333 ◽  
Author(s):  
D. A. Channing ◽  
S. Weintroub
Keyword(s):  
Experimental Data ◽  
Thermal Expansion ◽  
Single Crystals ◽  
Low Temperatures ◽  
Linear Thermal Expansion ◽  
Optical Interference ◽  
Temperature Range ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients ◽  
Good Agreement

The linear thermal expansion coefficients αψ of two single crystals of Zn of orientations ψ = 10.8° and 63.9 ° with the hexad axis were measured over the temperature range of about 20–270 °K using an absolute Fizeau optical interference technique. The two principal coefficients, [Formula: see text] and [Formula: see text], corresponding to ψ = 0° and 90 ° respectively, were calculated from the Voigt relation, and their values are compared with previously reported experimental data. Above 60 °K there is good agreement with previous work, and below 60 °K the results confirm, in general, the data obtained by McCammon and White. The Grüneisen parameter γ is essentially constant at about 2.1 in the range 100–270 °K, but below 100 °K γ rises appreciably with decreasing temperature and reaches the value of about 3.5 at 20 °K.

Thermohydrodynamic Analyses of Bump Air Foil Bearings With Detailed Thermal Model of Foil Structures and Rotor

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Donghyun Lee ◽  
Daejong Kim
Keyword(s):  
Thermal Model ◽  
Analysis Model ◽  
Transfer Resistance ◽  
Cooling Channels ◽  
Foil Bearings ◽  
Thermal Growth ◽  
Bearing Sleeve ◽  
Energy And Momentum ◽  
Energy Equations ◽  
Air Film

A new thermohydrodynamic analysis model for bump air foil bearings with a detailed thermal model of bump foil structures and rotor is presented. In the developed model, temperatures of lubricating air film, top foil, bump foils, bearing sleeve, and rotor are calculated simultaneously through an iterative process. Reynolds equation and 3D energy equation were applied to the air film, and energy equations were applied to all the other structures around the bearing. Energy and momentum equations were applied to cooling channels to predict spatial temperature distribution along the cooling channels. The thermal growth of the rotor, foil structure, bearing sleeve, and centrifugal growth of the rotor are also considered. For the accuracy of the model, effective heat transfer resistance between the top foil and bearing sleeve was measured for various conditions and implemented into the thermal analysis around the cooling channels. The model was also bench marked with published experimental results for verifications. Using a developed model, parametric studies were performed with different bearing nominal clearances, applied loads, rotating speeds, and cooling conditions through channels.

Influence of Cr deficiency on sintering, thermal expansion and electrical properties of La0.75Sr0.25Cr1−xO3−δ as a SOFC interconnect material

2016 ◽  
Vol 30 (11) ◽  
pp. 1650127 ◽  
Author(s):  
Yi Ren ◽  
Wen Ma ◽  
Xiaoying Li ◽  
Jun Wang ◽  
Yu Bai ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Electrical Properties ◽  
Perovskite Phase ◽  
Ignition Process ◽  
Thermal Expansion Coefficients ◽  
Auto Ignition ◽  
Pure Perovskite Phase ◽  
Maximum Conductivity ◽  
Expansion Coefficients ◽  
Interconnect Material

The SOFC interconnect materials La[Formula: see text]Sr[Formula: see text]Cr[Formula: see text]O[Formula: see text] [Formula: see text]–[Formula: see text] were prepared using an auto-ignition process. The influences of Cr deficiency on their sintering, thermal expansion and electrical properties were investigated. All the samples were pure perovskite phase after sintering at 1400[Formula: see text]C for 4 h. The cell volume of La[Formula: see text]Sr[Formula: see text]Cr[Formula: see text]O[Formula: see text] decreased with increasing Cr deficient content. The relative density of the sintered bulk samples increased from 93.2% [Formula: see text] to a maximum value of 94.7% [Formula: see text] and then decreased to 87.7% [Formula: see text]. The thermal expansion coefficients of the sintered bulk samples were in the range of [Formula: see text]–[Formula: see text] (30–1000[Formula: see text]C), which are compatible with that of YSZ. Among the investigated samples, the sample with 0.02 Cr deficiency had a maximum conductivity of 40.4 Scm[Formula: see text] and the lowest Seebeck coefficient of 154.8 [Formula: see text]VK[Formula: see text] at 850[Formula: see text]C in pure He. The experimental results indicate that La[Formula: see text]Sr[Formula: see text]Cr[Formula: see text]O[Formula: see text] has the best properties and is much suitable for SOFC interconnect material application.

Novel Silicon-Elastomers for Advanced Soft Lithography

2006 ◽  
Vol 947 ◽  
Author(s):  
Kyung Choi
Keyword(s):  
Thermal Expansion ◽  
High Resolution ◽  
Soft Lithography ◽  
Materials Properties ◽  
Nano Scale ◽  
Thermal Expansion Coefficients ◽  
High Thermal Expansion ◽  
Expansion Coefficients

ABSTRACTHigh resolution pattern transfers in the nano-scale regime have been considerable challenges in ‘soft lithography’ to achieve nanodevices with enhanced performances. In this technology, the resolution of pattern integrations is significantly rely on the materials' properties of polydimethylsiloxane (PDMS) stamps. Since commercial PDMS stamps have shown limitations in nano-scale resolution soft lithography due to their low physical toughness and high thermal expansion coefficients, we developed stiffer, photocured PDMS silicon elastomers designed, specifically for nano-sized soft lithography and photopatternable nanofabrications.

Thermal expansion coefficients of NH4ReO4and NH4IO4down to 58 K

1985 ◽  
Vol 82 (3) ◽  
pp. 1611-1612 ◽  
Author(s):  
Stanley L. Segel ◽  
H. Karlsson ◽  
T. Gustavson ◽  
K. Edstrom
Keyword(s):  
Thermal Expansion ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients
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