This thesis presents the static and dynamic performance data for a 5 pad tilting pad bearing in both the load-on-pad (LOP) and the load-between-pad (LBP) configurations over a variety of different loads and speeds. The bearing tested was an Orion Advantage with direct lubrication exhibiting these specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametrical clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to observe any frequency effects on the dynamic stfffnesses. It was found that under most test conditions the direct real part of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency. This frequency dependency is caused by pad inertia, pad flexibility, and fluid inertia. The observed frequency dependency can be accounted for with the addition of an added mass matrix to the conventional [K][C] matrix model to produce a frequency independent [K][C][M] model. This method eliminates the often debated question over whether a stability analysis should be performed at the running speed or at the first natural frequency. Substantially large added mass terms in the loaded direction were found that approached 60 kg. Some conditions for the LBP bearing exhibited unloaded direct mass coefficients that were at or near zero, which would lead to a frequency dependent [K][C] model to be used instead. The whirl frequency ratio was found to be zero at all test conditions. Static data were also recorded which included pad temperatures, attitude angle, eccentricity, static stiffness and power loss. Some cross coupling in the form of deviation from the loaded axis was evident from the locus plots; however, the cross coupled stiffness coefficients were found to be very small relative to the direct stiffness coefficients. Both static and dynamic experimental results were compared to theoretical predictions via a bulk flow analysis. Most parameters were modeled well including the static eccentricity e dynamic direct stiffness coefficients Kxx and Kyy, which were slightly over predicted. However, the direct damping coefficients Cxx and Cyy were significantly over predicted.

This thesis presents the static and dynamic performance data for a 5 pad tilting pad bearing in both the load-on-pad (LOP) and the load-between-pad (LBP) configurations over a variety of different loads and speeds. The bearing tested was an Orion Advantage with direct lubrication exhibiting these specifications: 5 pads, .282 preload, 60% offset, 57.87° pad arc angle, 101.587 mm (3.9995 in) rotor diameter, .1575 mm (.0062 in) diametrical clearance, 60.325 mm (2.375 in) pad length. Dynamic tests were performed over a range of frequencies to observe any frequency effects on the dynamic stfffnesses. It was found that under most test conditions the direct real part of the dynamic stiffnesses could be approximated as quadratic functions of the excitation frequency. This frequency dependency is caused by pad inertia, pad flexibility, and fluid inertia. The observed frequency dependency can be accounted for with the addition of an added mass matrix to the conventional [K][C] matrix model to produce a frequency independent [K][C][M] model. This method eliminates the often debated question over whether a stability analysis should be performed at the running speed or at the first natural frequency. Substantially large added mass terms in the loaded direction were found that approached 60 kg. Some conditions for the LBP bearing exhibited unloaded direct mass coefficients that were at or near zero, which would lead to a frequency dependent [K][C] model to be used instead. The whirl frequency ratio was found to be zero at all test conditions. Static data were also recorded which included pad temperatures, attitude angle, eccentricity, static stiffness and power loss. Some cross coupling in the form of deviation from the loaded axis was evident from the locus plots; however, the cross coupled stiffness coefficients were found to be very small relative to the direct stiffness coefficients. Both static and dynamic experimental results were compared to theoretical predictions via a bulk flow analysis. Most parameters were modeled well including the static eccentricity e dynamic direct stiffness coefficients Kxx and Kyy, which were slightly over predicted. However, the direct damping coefficients Cxx and Cyy were significantly over predicted.

This thesis provides experimental frequency dependent stiffness and damping coefficient results for a high-speed, lightly loaded, flexible-pivot tilting-pad bearing, with a load-on-pad configuration. Test conditions include four shaft speeds (6000, 9000, 13000 and 16000 rpm), and bearing unit loads from 172 kPa to 690 kPa. The results show that the bearing stiffness is a quadratic function of the frequency of vibration; hence their frequency dependency can be modeled by added-mass terms. The additional degrees of freedom introduced by the pads and the influence of the inertial forces generated in the fluid film account for this frequency dependency. The conventional frequency-dependent stiffness and damping model for tilting-pad bearings is extended with an added-mass matrix to account for the frequency dependency. This approach allows the description of the bearing dynamic characteristics with frequency-independent stiffness, damping and added-mass matrices. Experimental results are compared with predictions from the Reynolds equation and from a bulk-flow Navier-Stokes model. Both models produce good predictions of the stiffness and damping coefficients. However, results show that the bulk-flow model is more adequate for predicting the direct added-mass terms because it accounts for the fluid inertial forces. A bulk-flow solution of the Navier-Stokes equations that includes the effects of fluid inertia should be used to calculate the rotordynamic coefficients of a flexible-pivot tilting-bearing. Static performance measurement results are also detailed. Results include pad metal temperatures, eccentricity-ratios and attitude-angle as a function of bearing load, and estimated power losses.

Static performance and rotordynamic coefficients are provided for a rocker-pivot, tilting-pad journal bearing with 50 and 60 percent offset pads in a load-between-pad configuration. The bearing uses leading-edge-groove lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter, .0814 - .0837 mm (.0032 - .0033 in) radial bearing clearance, .25 to .27 preload, 60.325 mm (2.375 in) axial pad length. Operating conditions included loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the direct real dynamic stiffnesses were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, producing a frequency independent [K][C][M] model. The direct imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency independent direct damping coefficients. Compared to the 50 percent offset, the 60 percent offset configuration’s direct stiffness coefficients were larger at light unit loads. At high loads, the 50 percent offset configuration had a larger direct stiffness in the loaded direction. Negative direct added-mass coefficients were regularly obtained for both offsets, especially in the unloaded direction. Added-mass magnitudes were below 32 kg for all test cases. No appreciable difference was measured in direct damping coefficients for both pivot offset. A bulk-flow Navier-Stokes CFD code provided rotordynamic coefficient predictions. The following stiffness and damping prediction trends were observed for both 50 and 60 percent offsets. The direct stiffness coefficients were modeled well at light loads and became increasingly over-predicted with increasing unit load. Stiffness orthotropy was measured at zero and light load conditions that was not predicted. Direct damping predictions in the loaded direction increased significantly with unit load while the experimental direct damping coefficients remained constant with load. The direct damping coefficients were reasonably modeled only at the highest test speed of 16 krpm. Experimental cross-coupled stiffness coefficients were larger than predicted for both offsets, but were of the same sign and considerably smaller than the direct coefficients.

This thesis provides a comparison of experimental rotordynamic coefficients for laminar, smooth bushing oil seals to theoretical predictions from XLLubeGT and XLAnSeal. The experimental results come from a new test rig developed at the Turbomachinery Laboratory at Texas A&M University. The two software programs were developed to predict the static and dynamic characteristics of seals. XLLubeGT is a Reynolds equation based program while XLAnSeal is based on a bulk-flow Navier- Stokes model that includes temporal and convective acceleration terms. XLAnSeal was used to predict the added-mass terms of the seals since XLLubeGT assumes those terms to be zero or negligible. The data used for input into the two seals code was the actual measured conditions from the test rig. As part of the input parameters, inlet inertia effects and thermal gradients along the seal were included. Both XLLubeGT and XLAnSeal have the capability to analyze straight bore seals with different inlet and outlet clearances – essentially a tapered seal – but seal expansion caused by the radial differential pressure across the seal bushing was not included. Theoretical and experimentally determined dynamic characteristics include stiffness, damping, inertia terms and Whirl Frequency Ratio (WFR). Seal static characteristics are also reported. They include: leakage, shaft center line loci and Reynolds numbers. Test conditions include three shaft speeds: 4000, 7000 and 10,000 rpm, three test pressures: 21, 45 and 69 bar [300, 650, and 1000 psi] and multiple eccentricities from 0.0 to 0.7. The results for the dynamic characteristics show good correlation of the experimental data to the theoretical values up to an eccentricity of about 0.5. At higher eccentricities, the theory generally under-predicts the dynamic characteristics. Inertia terms are greatly under-predicted. The results for the static characteristics also show good correlation to the experimental data, but they also have a tendency to be under-predicted at higher eccentricities.

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Tato dizertační práce se zabývá dvěma případy interakce tělesa s tekutinou (FSI). První z nich se zabývá analýzou vzájemné interakce mezi rotorem čerpadla a kapalinou uvnitř těsnící spáry. Vliv těsnící spáry na dynamiku celého stoje je popsán pomocí dynamických parametrů, které jsou také označovaný jako přídavné účinky. V současnosti používané modely těsnících spár používají pro stanovení dynamických parametrů řadu zjednodušujících předpokladů. V této práci je prezentováno pět různých analýz dynamických parametrů těsnící spáry čerpadla na okysličovadlo. Každá z těchto pěti analýz používá jinou míru zjednodušení výpočetního modelu. V případě největšího zjednodušení je modelován pouze objem kapaliny uvnitř těsnící spáry. Nejkomplexnější analýza pro stanovení dynamických parametrů těsnící spáry používá pro výpočet model celého čerpadla s excentrickou polohou rotoru. Druhá část této dizertační práce definuje novou metodu pro řešení interakce kapaliny s pružným tělesem. Tato metoda využívá řešení inverzního problému kmitání. Přímý problém kmitání, který je také označován jako problém vlastních hodnot, používá jako vstupy pro řešení matice hmotnosti, tuhosti a tlumení, které jsou dohromady označovány jako koeficientové matice, na základě kterých je v nejobecnějším případě stanovena Jordanovská matice a také modální matice pravostranných a levostranných vlastních vektorů. Při řešení inverzního problému kmitání jsou stanoveny koeficientové matice na základě Jordanovské matice a modálních matic pravostranných a levostranných vlastních vektorů. Existují dva případy inverzního problému kmitání. V případě, že jsou známy všechny vstupní vlastní čísla a vlastní vektory, pak se jedná o tzv. plný problém. Naopak v případě, že alespoň 1 mód kmitání soustavy není znám, tak se jedná o tzv. částečný problém. V této práci je prezentováno 5 algoritmů pro řešení inverzního problému v kmitání. Nicméně pro každý typ inverzního problému kmitání je prezentován jeden univerzální algoritmus. Algoritmus pro řešení plných problémů byl poprvé prezentován v roce 1979 Otakarem Daňkem. Algoritmy pro řešení částečných problémů, které jsou prezentovány v této práci, jsou vůbec prvními algoritmy pro řešení tohoto typu inverzního problému kmitání. Univerzální algoritmus pro řešení částečných problémů je označován jako algoritmus pro řešení částečných problémů s volbou doplňkových vlastních hodnot. Aplikace těchto dvou univerzálních algoritmů pro řešení inverzního problému kmitání pro případ plných i částečných problémů je ukázána na řešení dvou případů interakce pružného tělesa s kapalinou.