Several advantages, including lower weight and smaller size, better performance at high rotational speeds and high temperatures, and higher reliability, can be gained with the usage of gas foil bearings as compared to conventional oil bearings. The achievements of gas foil bearings in recent 30 years enhance their applicants in high-speed turbo machinery, such as aircraft gas turbine engines, auxiliary power units, micro gas turbines, and hybrid fuel cell-turbine power systems. However, major technical hurdles impeding the application and widespread use of gas foil bearings are the lack of enough load carrying capacity and damping due to the low viscosity of air and the high temperature performance. Therefore, several designs of gas foil bearings have been proposed, which resulted in significant improvements in the performance of gas foil bearings. In order to reduce time and financial cost of design, this research introduces theoretical models for the performance prediction of gas foil bearings, based on two types of gas foil bearings, multiwound foil bearings (MWFBs) and bump-type foil bearings (BTFBs). With the developed models, the static and dynamic performances as well as the temperature dependent characteristics of gas foil bearings are predicted, and the calculated results from the models are compared with published experimental data to ensure the correctness.

Due to the incidence relation between the air film and the foils, the performance prediction models need couple the air pressure to the elastic deflection of the compliant foil structure. The pressure field within the air film is solved with the Reynolds' equation using the finite difference method and Newton-Raphson technique. However, the solution of the foil deflection is not so easy and it is still the main challenge for an accurate performance prediction of a gas foil bearing. In the model of MWFBs, the triply wound foil is separated into three layers, top foil, middle foil and bottom foil. A finite element plate model is presented to compute the deflections of the top foil and the middle foil. The bottom foil is assumed to have no deflection because of the supporting of the housing. The deflections of the top foil and the middle foil are both added to the air film thickness to take into consideration the effects of the foil local deflections. On the other hand, a link-spring model, replacing each bump with two rigid links and a horizontally spaced spring, is proposed to simulate the corrugated bump structure in the model of BTFBs. The equivalent vertical stiffness in each link-spring structure is calculated with the Castigliano' theorem. A finite element shell model is presented to describe the elasticity of the top foil. The obtained equivalent vertical stiffnesses of bumps are appended to the stiffness matrix of the top foil at appropriate positions. Finally, the deflection of the top foil is calculated with the direct matrix method and coupled to the air film thickness for iterative calculations. The advantage of this model is that the horizontal spring, which is parallel to the bump strip, makes it easy to account for the effects of the interaction forces and the friction forces within the foil structure. With this model, the bump elasticity, the interaction forces and the friction forces within the foil structure, and the local deflection of the top foil are all taken into consideration. Both the presented models of MWFBs and BTFBs are validated with published experimental data. Furthermore, based on the developed models of gas foil bearings, an approach with the perturbation of journal with respect to a small displacement about its equilibrium position is used for the prediction of the dynamic coefficients of gas foil bearings.

Predicted results from the model demonstrate that the load capacity and the torque of MWFBs will decrease if the effects of foil deflection are taken into account. However, since the deflections of foils create a space for the shaft eccentricity, which can increase up to a value much lager than the nominal clearance, MWFBs can also support a heavy load. According to the analysis of BTFBs, the elasticity of bumps is noted related not only to the geometry of bumps but also to the deflection of bumps and the friction forces within the foil structure. The predicted results demonstrate that the bearing radial clearance and the friction forces significantly affect the performance of BTFBs. An optimum clearance of BTFBs for the largest load carrying capacity is noted in the calculation of the load capacity, and the optimum value decreases as the journal speed increases.

Thermohydrodynamic models based on the two types of gas foil bearings are also presented. The simulations of the foil structures follow the ways in the above analysis. The thermal Reynolds' equation for the air film pressure and the energy equation for the temperature field of air film are simultaneously solved. The Lobbato point quadrature algorithm is utilized to reduce the effort of computation. An iteration procedure is conducted between the two equations and the calculation of foil deflections until the convergence is achieved. The THD model accounts for the compressibility and viscosity-temperature characteristic of air. In the model of MWFBs, the temperature of the air at the inlet is estimated from the mixture of fresh air and the recirculating flow. The shaft is assumed to be isothermal. However, for the temperature prediction for BTFBs, the developed model is improved for more accurate results by taking into consideration more factors, such as effects of the cooling air, thermal expansion of the bearing components and the change of the bump foil elasticity due to the increase in temperature. Furthermore, the calculation of the fluid flow within the air film is also modified, because the top foil is recognized to detach from the bump strip in the region of the subambient pressure. The predicted results of both the two types of gas foil bearings show good agreement with published experimental data.

The calculated temperature profile shows that the highest temperature in the air film occurs a little downstream of the minimum film thickness and closer to the top foil than the shaft along the radial direction. An obvious increase of the predicted bearing load is noted if the bearing temperature is taken into account during the calculation. And the predictions also show that the effects of journal speed, rather than the bearing load, is more significant on the temperature increase of bearings. The ambient temperature affects the bearing performance mainly by changing the radial clearance of foil bearings through the thermal expansion of components.

Finally, parametric studies of the number of bumps, the size of bumps, the thickness of foils, and the material of foils are performed on the prediction of the bearing load and the nonlinear orbit simulations. The results demonstrate that more bumps provide much higher load capacity, but lower threshold speed for instability. In general, we can advance the performance of bump-type foil bearings with larger length ratio of the segment and the bump ( ls/lo), thicker foil thickness ( tf), higher bump height ( hb) and larger elastic modulus ( E), although the threshold speed for instability will slightly decrease.

学位請求論文は,Prediction of Static and Dynamic Performance and Thermohydrodynamic Analysis of Gas Foil Bearing(フォイル軸受の静特性、動特性及び温度特性の解析手法に関する研究)と題し,全8章から構成されている.

空気軸受の一種であるフォイル軸受は,すべり軸受やころがり軸受と比較して,小型,軽量であること,オイルポンプやオイルクーラーなどの補機が不要なことから,航空機のAPUやマイクロガスタービン等の高速回転機械に用いられてきた.しかしながら,ターボチャージャーのように軸径が細く,高温下で使用される高速回転機械への適用を促進するためには,熱の影響の考慮と負荷容量の増大および高速運転領域での安定性の向上が必須である.この問題に対処するため,マルチワウンド型フォイル軸受やバンプ型フォイル軸受などが提案されてきた.しかしながら,従来の研究の多くは,プロトタイプの開発研究が中心であり,設計に利用可能な計算手法は提案されてはいない.

このような背景の元に,本論文は,マルチワウンド型フォイル軸受とバンプ型フォイル軸受の性能評価のための計算手法を提案するもので,軸受の静特性および動特性と温度特性について評価を行い,既存の実験データとの比較を通して,計算手法の妥当性を検証したものである.

第1章は,「緒論」と題し,関連する研究についての概観と本論文中で展開されている研究の位置付けについて述べている.

第2章は,「フォイルの局所変形を考慮したマルチワウンド型フォイル軸受の数値解析モデル」と題し,静特性の計算手法について述べている.支配方程式の解法にあたっては流体系と構造系を連成させる必要があるが,ここでは弱連成計算手法が適用されている.なお,圧力分布を与えるレイノルズ方程式は差分法で,フォイルの局所変形は有限要素法によって計算されている.

第3章は,「ロバット則の重み関数を用いたマルチワウンド型フォイル軸受の熱流体解析」と題し,マルチワウンド型フォイル軸受を対象として,流体と構造の連成に加えて熱の影響も考慮して解析している.具体的には,第2章で用いた方程式にエネルギー方程式を加え,作動流体の温度依存性を考慮したレイノルズ方程式を解いて,軸受内部の温度分布を求めている.なお,計算を高速化するために,ロバット則の重み関数を用いたアルゴリズムを採用していることに特徴がある.

第4章は,「バンプ型フォイル軸受のリンク・ばねモデル」と題し,バンプフォイルとトップフォイルの2層構造を有するバンプ型フォイル軸受の静特性の評価法を提案している.この方法は,リンク・ばねモデルによって,バンプフォイルの弾性効果,バンプ間の相互作用力,トップフォイルとバンプの間に作用する摩擦力,トップフォイルの局所変形の4つの要因をすべて考慮していることに特徴がある.計算結果から,負荷容量を最適にする隙間幅が存在することが明らかになった.

第5章は,「バンプ型フォイル軸受の動特性」と題し,平衡位置周りの2次元微小振動に関する解析を行い,周波数依存性のある弾性係数,減衰係数を計算によって求め,安定性評価につなげている.

第6章は,「バンプ型フォイル軸受の熱流体解析」と題し,バンプ型フォイル軸受の静特性に及ぼす熱の影響について検討している.この解析では,軸受隙間の空気層の温度依存性に加えて,熱によるフォイルの材料定数の変化,熱膨張による軸受隙間幅の変化,固体部分での熱伝導,および空気層と固体部分での熱伝達の影響も考慮されている.計算の結果,熱膨張による軸受隙間幅の変化の影響を無視できないことが明らかになった.

第7章は,「バンプ型フォイル軸受の静特性および非線形安定性の解析事例」と題し,バンプ型フォイル軸受で支えられた回転軸の運動軌跡を計算によって求め,安定限界を求めることに成功している.これにより,バンプの個数,バンプの大きさ,フォイルの厚さ,フォイルの材質が負荷容量と安定限界に与える影響を計算によって評価できることが明らかになった.

第8章は,結論と題し,本研究で得られた知見について纏めて述べている.

以上を要約すると,本論文は,研究対象として,マルチワウンド型フォイル軸受とバンプ型フォイル軸受を取り上げ,計算によって,軸受の静特性および動特性と温度特性について評価を行ったものであり,これらの研究成果により,小型高速回転機械に適用されるフォイル軸受の設計法の確立に貢献した.本研究は,機械工学,特に機械機能要素学の発展に貢献するところが大きい.

よって,本論文は博士(工学)の学位請求論文として合格と認められる.