This thesis compares experimental static and dynamic force characteristics for a two-axial-groove bearing and a pressure-dam bearing without a relief track. The thesis also compares experimental results to predictions from a numerical analysis. The tested pressure-dam bearing has s θ= 130°, ' k =3.4~4.2, and d L − =0.75. The test results show that eccentricity for both bearings decreases as Sommerfeld number increases. However, the pressure-dam bearing maintains a minimum eccentricity of about 0.5 at high speeds. The results also show that the attitude angle for both bearings increases as Sommerfeld number increases. The maximum attitude angle for the axial-groove bearing is 90° at noload. However, the attitude angle for the pressure-dam bearing increases above 90° at no-load as speed increases. A dynamic test shows that the pressure-dam bearing has higher direct stiffness and damping at high Sommerfeld number because of the increase in eccentricity. However, as Sommerfeld number decreases, the difference between stiffness and damping coefficients of both bearings diminishes. The dynamic test also shows that both bearings have significant added mass coefficients in the laminar flow region that decrease as eccentricity increases. The estimated axial-groove bearing whirlfrequency ratio (WFR) from experimental results is 0.45. The WFR of the pressure-dam bearing reduces to 0.41 at high Sommerfeld numbers. Numerical analysis shows that the pressure-dam bearing can have lower WFR if the dam arc length is increased to 150°. Numerical analysis also shows that stability can be improved further by adding a relief track. Generally, the numerical analysis under predicts the bearings’ eccentricity and dynamic force coefficients with better agreement at low Sommerfeld numbers.

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 dissertation presents an experimental and theoretical study of subsynchronous rotordynamic instability in rotors caused by interference and shrink fit interfaces. The experimental studies show the presence of strong unstable subsynchronous vibrations in two different rotor setups with interference and shrink fit interfaces that were operated above their first critical speeds. The unstable vibrations occur at the first natural frequency of the rotor-bearing system. The instability caused complete wreckage of the test rig in one of the setups showing that these vibrations are potentially dangerous to the safe operation of rotating machines. The two different rotor setups that are studied are a single-disk rotor mounted on a uniform diameter shaft and a two-disk rotor with an aluminum sleeve shrink fitted to it at the outer surface of the two disks. In the single-disk rotor, an adjustable interference arrangement between the disk and the shaft is obtained through a tapered sleeve arrangement, which acts as the interference fit joint. The unstable sub-synchronous vibrations originate from slippage in the shrink fit and the interference fit interfaces that develop friction forces, which act as destabilizing cross-coupled moments when the rotor is operated above its first critical speed. The unique contribution offered through this work is the experimental validation of a physically correct model of internal friction which models the destabilizing mechanism as a system of cross-coupled internal moments at the shrink fit interface. The dissertation describes stability simulations of various test rotor setups using the correct internal moments model. A commercial finite-element based software called XLTRCTM is used to perform rotordynamic simulations for stability studies. The method of stability study is the computation of eigenvalues of the rotor-bearing system. A negative real part of the eigenvalue indicates instability. The simulations include the test rotors that were experimentally observed as stable and unstable with shrink and interference fit interfaces in their assemblies. The dissertation also describes the simulations of various imagined rotor configurations with shrink fit interfaces, and seeks to explain how configurations differ on rotordynamic stability depending upon several rotor-bearing parameters such as geometry and elastic properties, as well as upon the amount of internal friction parameters, which differ from configuration to configuration.

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.

Historical attempts to measure forces in magnetic bearings have been unsuccessful as a result of relatively high uncertainties. Recent advances in the strain-gauge technology have provided a new method for measuring magnetic bearing forces. Fiber optic strain gauges are roughly 100 times more sensitive than conventional strain gauges and are not affected by electro-magnetic interference. At the Texas A&M Turbomachinery Laboratory, installing the fiber-optic strain gauges in magnetic bearings has produced force measurements with low uncertainties. Dynamic flexibility transfer functions exhibiting noticeable gyroscopic coupling have been identified and compared with results of a finite element model. The comparison has verified the effectiveness of using magnetic bearings as calibrated exciters in rotordynamic testing. Many applications including opportunities for testing unexplained rotordynamic phenomena are now feasible.

To reduce manufacturing cost and time, a hole-pattern seal incorporating holes of larger diameter (12.19 mm (0.48 inches)) has been proposed. Experimental leakage and rotordynamic coefficients for this new seal design are presented. This experimental data was compared to theoretical results generated by ISOTSEAL a program developed by Kleynhans and Childs. Finally, the performance of this new hole-pattern seal was compared to a hole-pattern seal tested by Wade. The experiments are configured to investigate the influence of changes in pressure ratio, preswirl, rotor speed, and clearances on seal characteristics. Due to stator stability issues, the peak inlet pressures had to be varied to allow for testing. Consequently, to study the effect of inlet preswirl and clearance, data were non-dimensionalized or normalized. Cross-coupled coefficients were relatively frequency-independent while direct coefficients were functions of excitation frequency. For all test cases, the seal developed negative direct stiffness at low frequencies. Tests showed that pressure ratio had minimal effect on rotordynamic coefficients. Non-dimensional cross-coupled stiffness increased with increasing preswirl causing the seal to become less stable with increasing preswirl. Cross coupled stiffness increased with increasing running speed. Two clearances: 0.1 mm (4 mils) and 0.2 mm (8 mils) were tested. The results demonstrated that non-dimensionalized stiffness is greater for the smaller clearance. The larger clearance develops larger normalized direct damping values, and has enhanced stability. Rotordynamic predictions are poor for cross-coupled coefficients. Generally, ISOTSEAL over-predicts direct stiffness and under-predicts direct damping. Negative stiffness was not predicted by ISOTSEAL. Predictions do improve for the smaller clearance. ISOTSEAL does a good job of predicting non-dimensional leakage. Non-dimensionalized direct and effective stiffness were greater for the "old" hole-pattern seal tested by Wade. However, the "new" seal generally developed greater normalized direct damping and exhibited a lower cross-over frequency. Non-dimensionalized leakage was greater for the seal tested here. Production of this new seal proved to be more difficult than originally thought. The price of the new seal cost approximately the same as an original hole-pattern seal.

Historical attempts to measure forces in magnetic bearings have been unsuccessful as a result of relatively high uncertainties. Recent advances in the strain-gauge technology have provided a new method for measuring magnetic bearing forces. Fiber optic strain gauges are roughly 100 times more sensitive than conventional strain gauges and are not affected by electro-magnetic interference. At the Texas A&M Turbomachinery Laboratory, installing the fiber-optic strain gauges in magnetic bearings has produced force measurements with low uncertainties. Dynamic flexibility transfer functions exhibiting noticeable gyroscopic coupling have been identified and compared with results of a finite element model. The comparison has verified the effectiveness of using magnetic bearings as calibrated exciters in rotordynamic testing. Many applications including opportunities for testing unexplained rotordynamic phenomena are now feasible.

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.