Rotors in fluid-film bearing supported turbomachinery are known to develop elliptical orbits as a result of rotor-bearing interactions, mass unbalance within the rotor, gravitational bending of the shaft and external excitation. In synchronous whirl, where the speed at which the shaft travels about the orbit is equal to the rotational speed of the rotor, temperature gradients may develop across the journal as a result of viscous shear in the bearing's lubricant film. This thermal gradient leads to bending of the shaft in a phenomenon known as The Morton Effect. Such thermally induced bending causes further growth of the elliptical orbit resulting in further bending leading to excessive vibration levels and premature bearing failure. This analysis examines the development of the Morton Effect in medium-speed turbochargers typical to shipboard propulsion engines and the effect that bearing clearance has on thermal stability. Floating ring and tilting pad journal bearings are considered with a single stage, overhung centrifugal compressor and an overhung axial turbine. Results indicate a correlation between bearing clearance and thermal stability in the rotor-bearing system. A model for the aerodynamic force generated as a result of interaction between air exiting a centrifugal compressor and the compressor's annulus in a turbocharger is then developed and applied to the rotor-bearing systems. Results suggest little correlation between this aerodynamic force and the development of the Morton Effect. / Master of Science

This thesis documents the results of high pressure testing of hole-pattern annular gas seals conducted at the Texas A&M University's Turbomachinery Laboratory. The testing conditions were aimed at determining the test seals sensitivity to pressure ratio, inlet fluid preswirl, rotor speed, and rotor to seal clearance. The rotordynamic coefficients showed only small changes resulting from the different pressure ratios tested. Only the damping terms at the lower frequencies showed some influence. One other notable result from the testing of different pressure ratios is that the seals were tested in a choked flow condition, and there was not a significant change in the seal behavior when the seals transitioned to the choked condition. The inlet fluid preswirl only had a notable effect on the cross-coupled stiffness in the larger clearance tests. These results lead to the conclusion that a swirl brake could have some rotordynamic value, but only if the seals have sufficiently large clearance. Conversely this also means that if hole-pattern seals are being implemented with a small clearance, then a swirl brake would not be an effective way to improve the rotordynamic stability of the system. The only significant effect that the rotor speeds had on the rotordynamic coefficients were that the cross-coupled coefficients increased as the rotor speed increased. This is the expected result because as the rotor speed increases there is a greater shear force on the gas as it passes through the seal resulting in more fluid circumferential velocity, which results in stronger cross-coupled coefficients. The changes in clearance resulted in drastic changes in the magnitude of the coefficients. The smaller clearance yielded much higher coefficients than the larger clearance. All of the rotordynamic coefficients were predicted well by ISOTSEAL. The code was found to do a good job predicting the seal leakage as well. This gives more credence to the coefficients and leakage that ISOTSEAL predicts.

Comprehensive modeling of gas foil bearings (GFBs) anchored to reliable test data will enable the widespread usage of GFBs into novel turbomachinery applications, such as light weight business aircraft engines, hybrid fuel cell-turbine power systems, and micro-engines recharging battery packs for clean hybrid electric vehicles. Pressurized air is often needed to cool GFBs and to carry away heat conducted from a hot turbine in oil-free micro turbomachinery. Side end pressurization, however, demonstrates a profound effect on the rotordynamic performance of GFBs. This dissertation presents the first study that devotes considerable attention to the effect of side end pressurization on delaying the onset rotor speed of subsynchronous motions. GFB performance depends largely on the support elastic structure, i.e. a smooth foil on top of bump strips. The top foil on bump strips layers is modeled as a two dimensional (2D), finite element (FE) shell supported on axially distributed linear springs. The structural model is coupled to a unique model of the gas film governed by modified Reynolds equation with the evolution of gas flow circumferential velocity, a function of the side end pressure. Predicted direct stiffness and damping increase as the pressure raises, while the difference in cross-coupled stiffnesses, directly related to rotor-bearing system stability, decreases. Prediction also shows that side end pressurization delays the threshold speed of instability. Dynamic response measurements are conducted on a rigid rotor supported on GFBs. Rotor speed-up tests first demonstrate the beneficial effect of side end pressurization on delaying the onset speed of rotor subsynchronous motions. The test data are in agreement with predictions of threshold speed of instability and whirl frequency ratio, thus validating the model of GFBs with side end pressurization. Rotor speed coastdown tests at a low pressure of 0.35 bar evidence nearly uniform normalized rotor motion amplitudes and phase angles with small and moderately large imbalance masses, thus implying a linear rotor response behavior. A finite element rotordynamic model integrates the linearized GFB force coefficients to predict the synchronous responses of the test rotor. A comparison of predictions to test data demonstrates an excellent agreement and successfully validates the rotordynamic model.

Methods are presented for parameter identification of an annular gas seal on a flexiblerotor test rig. Dynamic loads are applied by magnetic bearings (MBs) that support the rotor. MB forces are measured using fiber-optic strain gauges that are bonded to the poles of the MBs. In addition to force and position measurements, a finite element (FE) rotor model is required for the identification algorithms. The FE rotor model matches free-free characteristics of the test rotor. The addition of smooth air seals to the system introduces stiffness and damping terms for identification that are representative of reaction forces in turbomachines. Tests are performed to experimentally determine seal stiffness and damping coefficients for different running speeds and preswirl conditions. Stiffness and damping coefficients are determined using a frequency domain identification method. This method uses an iterative approach to minimize error between theoretical and experimental transfer functions. Several time domain approaches are also considered; however, these approaches do not produce valid identification results. Stiffness coefficients are measured using static test results and an MB current and position based model. Test results produce seal coefficients with low uncertainties for the frequency domain identification method. Static test uncertainties are an order of magnitude larger, and time domain attempts fail to produce sealIn addition to the primary identification research, an investigation of the relationships between MB force, strain, and magnetic field is conducted. The magnetic field of an MB is modeled using commercial FE software. The magnetic field model is used to predict strain measurements for quasi-static test conditions. The strain predictions are compared with experimental strain measurements. Strain predictions agree with experimental measurements, although strain is typically over-predicted. coefficient measurements.

Rotor-bearing system characteristics, such as natural frequencies, mode shapes, stiffness and damping coefficients, are essential to diagnose and correct vibration problems during system operation. Of the above characteristics, accurate identification of bearing force parameters, i.e. stiffness and damping coefficients, is one of the most difficult to achieve. Field identification by imbalance response measurements is a simple and often reliable way to determine synchronous speed force coefficients. An enhanced method to estimate bearing support force coefficients in flexible rotor-bearing systems is detailed. The estimation is carried out from measurements obtained near bearing locations from two linearly independent imbalance tests. An earlier approach assumed rotordynamic measurements at the bearing locations, which is very difficult to realize in practice. The enhanced method relaxes this constraint and develops the procedure to estimate bearing coefficients from measurements near the bearing locations. An application of the method is presented for a test rotor mounted on two-lobe hydrodynamic bearings. Imbalance response measurements for various imbalance magnitudes are obtained near bearing locations and also at rotor mid-span. At shaft speeds around the bending critical speed, the displacements at the rotor mid-span are an order of magnitude larger than the shaft displacements at the bearing locations. The enhanced identification procedure renders satisfactory force coefficients in the rotational speed range between 1,000 rpm and 4,000 rpm. The amount of imbalance mass needed to conduct the tests and to obtain reliable shaft displacement measurements influences slightly the magnitude of the identified force coefficients. The effect of increasing the number of rotor sub-elements in the finite-element modeling of the shaft is noted. Sensitivity of the method and derived parameters to noise in the measurements is also quantified.

Comprehensive modeling of gas foil bearings (GFBs) anchored to reliable test data will enable the widespread usage of GFBs into novel turbomachinery applications, such as light weight business aircraft engines, hybrid fuel cell-turbine power systems, and micro-engines recharging battery packs for clean hybrid electric vehicles. Pressurized air is often needed to cool GFBs and to carry away heat conducted from a hot turbine in oil-free micro turbomachinery. Side end pressurization, however, demonstrates a profound effect on the rotordynamic performance of GFBs. This dissertation presents the first study that devotes considerable attention to the effect of side end pressurization on delaying the onset rotor speed of subsynchronous motions. GFB performance depends largely on the support elastic structure, i.e. a smooth foil on top of bump strips. The top foil on bump strips layers is modeled as a two dimensional (2D), finite element (FE) shell supported on axially distributed linear springs. The structural model is coupled to a unique model of the gas film governed by modified Reynolds equation with the evolution of gas flow circumferential velocity, a function of the side end pressure. Predicted direct stiffness and damping increase as the pressure raises, while the difference in cross-coupled stiffnesses, directly related to rotor-bearing system stability, decreases. Prediction also shows that side end pressurization delays the threshold speed of instability. Dynamic response measurements are conducted on a rigid rotor supported on GFBs. Rotor speed-up tests first demonstrate the beneficial effect of side end pressurization on delaying the onset speed of rotor subsynchronous motions. The test data are in agreement with predictions of threshold speed of instability and whirl frequency ratio, thus validating the model of GFBs with side end pressurization. Rotor speed coastdown tests at a low pressure of 0.35 bar evidence nearly uniform normalized rotor motion amplitudes and phase angles with small and moderately large imbalance masses, thus implying a linear rotor response behavior. A finite element rotordynamic model integrates the linearized GFB force coefficients to predict the synchronous responses of the test rotor. A comparison of predictions to test data demonstrates an excellent agreement and successfully validates the rotordynamic model.

This thesis documents the results of high pressure testing of hole-pattern annular gas seals conducted at the Texas A&M University's Turbomachinery Laboratory. The testing conditions were aimed at determining the test seals sensitivity to pressure ratio, inlet fluid preswirl, rotor speed, and rotor to seal clearance. The rotordynamic coefficients showed only small changes resulting from the different pressure ratios tested. Only the damping terms at the lower frequencies showed some influence. One other notable result from the testing of different pressure ratios is that the seals were tested in a choked flow condition, and there was not a significant change in the seal behavior when the seals transitioned to the choked condition. The inlet fluid preswirl only had a notable effect on the cross-coupled stiffness in the larger clearance tests. These results lead to the conclusion that a swirl brake could have some rotordynamic value, but only if the seals have sufficiently large clearance. Conversely this also means that if hole-pattern seals are being implemented with a small clearance, then a swirl brake would not be an effective way to improve the rotordynamic stability of the system. The only significant effect that the rotor speeds had on the rotordynamic coefficients were that the cross-coupled coefficients increased as the rotor speed increased. This is the expected result because as the rotor speed increases there is a greater shear force on the gas as it passes through the seal resulting in more fluid circumferential velocity, which results in stronger cross-coupled coefficients. The changes in clearance resulted in drastic changes in the magnitude of the coefficients. The smaller clearance yielded much higher coefficients than the larger clearance. All of the rotordynamic coefficients were predicted well by ISOTSEAL. The code was found to do a good job predicting the seal leakage as well. This gives more credence to the coefficients and leakage that ISOTSEAL predicts.

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery.

Internal friction has been known to be a cause of whirl instability in built-up rotors since the early 1900's. This internal damping tends to make the rotor whirl at shaft speeds greater than a critical speed, the whirl speed usually being equal to the critical speed. Over the years of research, though models have been developed to explain instabilities due to internal friction, its complex and unpredictable nature has made it extremely difficult to come up with a set of equations or rules that can be used to predict instabilities accurate enough for design. This thesis deals with suggesting improved methods for predicting the effects of shrink fits on threshold speeds of instability. A supporting objective is to quantify the internal friction in the system by measurements. Experimental methods of determining the internal damping with non-rotating tests are investigated, and the results are correlated with appropriate mathematical models for the system. Rotating experiments were carried out and suggest that subsynchronous vibration in rotating machinery can have numerous sources or causes. Also, subsynchronous whirl due to internal friction is not a highly repeatable phenomenon.

The present work investigates the nature of dry-friction whip and whirl through experimental and numerical methods. Efforts of the author, Dyck, Pavalek, and coworkers enabled the design and construction of a test rig that demonstrated and recorded accurately the character of multi-mode dry-friction whip and whirl. These tests examined steady state whip and whirl characteristics for a variety of rub materials and clearances. Results provided by the test rig are unparalleled in quality and nature to those seen in literature and possess several unique characteristics that are presented and discussed. A simulation model is constructed using the Texas A and M University (TAMU) Turbomachinery Laboratory rotordynamic software suite XLTRC2 comprised of tapered Timoshenko beam finite elements to form multiple degree of freedom rotor and stator models. These models are reduced by component mode synthesis to discard highfrequency modes while retaining physical coordinates at locations for nonlinear interactions. The interaction at the rub surface is modeled using a nonlinear Hunt and Crossley contact model with coulomb friction. Dry-friction simulations are performed for specific test cases and compared against experimental data to determine the validity of the model. These comparisons are favorable, capturing accurately the nature of dryfriction whirl. Experimental and numerical analysis reveals the existence of multiple whirl and whip regions spanning the entire range of frequencies excited during whirl, despite claims of previous investigations that these regions are predicted by Black's whirl solution, but are not excited in simulations or experiments. In addition, spectral analysis illustrates the presence of harmonic sidebands that accompany the fundamental whirl solution. These sidebands are more evident in whip, and can excite higher-frequency whirl solutions. Experimental evidence also shows a strong nonlinearity present in the whirl frequency ratio, which is greater than that predicted by the measured radius-toclearance ratio at the rub location. Results include whirl frequencies 250% of that predicted by the measured radius-to-clearance ratio.