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The turbocharger industry is booming recently, and there is an urgent need for new evaluations of the overall design. As the oil prices continue to rise, along with the new emissions regulations strictly enforced for the in-road as well as the off-road vehicles, the transition to turbocharged engines, and especially for diesel engines, has become irresistible. Higher power, smaller engines, reduced emissions, and overall better efficiency are the main concerns. By means of the recent development in the computational tools, a new era of the product development has emerged. Most diesel engine turbochargers incorporate floating-ring bearings that use the engine's oil for lubrication. The high-speed turbocharger is known to have subsynchronous vibrations at high amplitudes for a wide speed range that could reach 150,000 rpm. The bearing fluid-film whirl instability is the main source of the subsynchronous vibration. The nonlinear reaction forces inside the bearings are usually causing the rotor to whirl in a limit cycle but may become large enough to cause permanent damages. Additionally, the lubrication oil may leak at higher rates through the seals into the engine or the exhaust emissions. This dissertation investigates methods for improving the dynamic stability of the high-speed automotive turbochargers, especially designed for heavy-duty diesel engines that are used for example in heavy machinery, trucks, tractors, etc. The study utilizes the available modern computational tools in rotor-dynamics in addition to the locally developed supportive computer codes. This research is a major part of the turbocharger dynamic analysis supporting the current extensive experimental tests in the Virginia Tech Rotor Dynamics Laboratory for the product development of different high-speed diesel engine turbochargers. The study begins with the method of enhanced-performance hydrodynamic bearings. The aim is to modify the inner surface of the bearing for better dynamic characteristics. The finite-element model of the turbocharger rotor shaft with linearized bearing dynamic coefficients is developed. The system is solved for eigenvalues and eigenvectors in order to evaluate the dynamic stability. The first phase of the study demonstrated that there are two modes of instability that persist during much of the operating speed range, and one of the modes exhibits serious subsynchronous vibration levels at the higher speeds. The first unstable mode builds up at very low speeds forming a conical shape, where both rotor shaft ends whirl forward out-of-phase. The second unstable mode has a cylindrical shape with slight bending, where both rotor ends whirl forward in-phase. The outcome of the study is that the inner surface of the bearing has direct influence on the turbocharger dynamic stability. However, a fixed hydrodynamic bearing may not give total linear stability of the system if it is used without additional damper. The second method is to analytically design flexible damped bearing-supports in order to improve the dynamic characteristics of the rotor-bearing system. The finite-element model of the turbocharger rotor with linearized bearing dynamic coefficients is used to solve for the logarithmic decrements and hence the stability map. The design process attempts to find the optimum dynamic characteristics of the flexible damped bearing-support that would give best dynamic stability of the rotor-bearing system. The method is successful in greatly improving the dynamic stability of the turbocharger and may also lead to a total linear stability throughout the entire speed range when used besides the enhanced-performance hydrodynamic bearings. The study also presents a new method for improving the dynamic stability by inducing the turbocharger rotor unbalance in order to suppress the subsynchronous vibrations. The finite-element model of the turbocharger rotor with floating-ring bearings is numerically solved for the nonlinear time-transient response. The compressor and the turbine unbalance are induced and the dynamic stability is computed. The turbocharger model with linearized floating-ring bearings is also solved for eigenvalues and eigenvectors to predict the modes of instability. The linear analysis demonstrates that the forward whirling mode of the floating-ring at the compressor end becomes also unstable at the higher turbocharger speeds, in addition to the unstable forward conical and cylindrical modes. The numerical predictions are also compared to the former experimental results of a typical turbocharger. The results of the study show that the subsynchronous frequency amplitude of the dominant first mode is reduced when inducing either the compressor or the turbine unbalance at a certain level. In addition to the study of the stability improvement methods, the dissertation investigates the other internal and external effects on the turbocharger rotor-bearing system. The radial aerodynamic forces that may develop inside the centrifugal compressor and the turbine volutes due to pressure variation of the circulating gas are numerically predicted for magnitudes, directions, and locations. The radial aerodynamic forces are numerically simulated as static forces in the turbocharger finite-element model with floating-ring bearings and solved for nonlinear time-transient response. The numerical predictions of the radial aerodynamic forces are computed with correlation to the earlier experimental results of the same turbocharger. The outcomes of the investigation demonstrated a significant influence of the radial aerodynamic loads on the turbocharger dynamic stability and the bearing reaction forces. The numerical predictions are also compared to the former experimental results for validation. The external effect of the engine-induced vibration on the turbocharger dynamic stability is studied. The engine-induced excitations are numerically simulated as time-forcing functions on the rotor-bearings of the turbocharger finite-element model with floating-ring bearings in order to solve for the nonlinear time-transient response. The compressor radial aerodynamic forces are combined to the engine-induced excitations to numerically predict the total nonlinear transient response. The results of the study show that there are considerable amplitudes at the engine-excitation frequency in the subsynchronous region that may also have similar amplitude at the second harmonic. Additionally, the magnitudes of the engine-induced vibration have an effect on the turbocharger dynamic stability. The numerical predictions are compared to the former experimental tests for turbocharger dynamic stability. / Ph. D.

This project was initiated to more fully understand the dynamic stability of an automotive turbocharger rotor-bearing system using both linear and nonlinear analyses. The capabilities of a commercial Finite Element Analysis (FEA) code (computer program) were implemented in the investigation process. Several different hydrodynamic journal bearings were employed in the study of the turbocharger linearized dynamic stability. The research demonstrates how the linear analysis of a turbocharger rotordynamics can be very beneficial for the design evaluation and maintenance purposes. / Master of Science

Overall losses in swash plate type axial piston machines are mainly defined by three tribological interfaces. These are swash plate/slipper, piston/cylinder and cylinder block/valve plate. Within a research project, funded by the German Research Foundation, a combined approach of experimental research and simulation is chosen to acquire further knowledge on the cylinder block/valve plate contact. The experimental investigations focus on the friction torque within the contact and the measurement of the cylinder block movement in all six degrees of freedom. Simultaneously a simulation model is created focusing on the main physical effects. By considering the results of the experimental investigations significant physical effects for the simulation model are assessed. Within this paper a first comparison between experimental results and the simulation is presented, showing that for a qualitative match the implemented effects (mainly the fluid film, solid body movement, solid body contact, surface deformation) are sufficient to model the general behaviour of theinvestigated pump.

"Two most important events in the history of lubrication theory are attributed to Reynolds and Sommerfeld. Reynolds derived the governing equations for lubricating films in simplifying the Navier-Stokes equations considering thin-film effects. Sommerfeld obtained a closed form analytical solution to the Reynolds equation for the long bearing (one-dimensional case) with fixed constant eccentricity which results in a point symmetric pressure profile compared to an arbitrary (ambient) level. In attempting to reconcile with experimental evidence, Gumbel advanced the argument that sub-ambient pressure in a fluid film is not possible. On the basis that the fluid film would rupture, he put forth that the sub-ambient portion of the Sommerfeld solution should be discarded, a proposition that is commonly recognized as the half-Sommerfeld solution (of Gumbel). Ever since Gumbel suggested this improvement, much interest remains regarding the physical process of rupture in bearing lubricating films. In lubrication literature, cavitation is used interchangeably with rupture to indicate a condition in which an abundance of a gas phase, essentially ambient air, is present in a portion of the bearing clearance. A cogent two-phase morphology for addressing cavitation in long bearings is postulated in order to predict time-dependent fluid behavior from an initial state that is a generalization of Gumbel’s half-Sommerfeld solution. The ultimate steady-state is presumed to satisfy the hypothesis of Swift and Stieber that an ambient condition is reached by the rupture point at an unspecified location simultaneously with a vanishing pressure gradient. A trans-rupture continuity equation, as proposed by Olsson, determines a formula for the speed of a moving rupture point requiring a specific model of the two-phase flow in the rupture region. Employing an adhered film model, sequential application of Olsson’s equation to the rupture points of the intermediate states between the half-Sommerfeld and Swift-Stieber states renders an interpretation of a time-dependent progression towards a steady-state solution. Closed form analytical formulas, which readily combine to provide an exact solution to the Reynolds equation are derived with the start (formation point) of the full-film other than the customary bearing maximum gap and with the rupture point at any assigned intermediate location. Each valid solution for an intermediate state yields an invariant flux that must satisfy a window of constraints to exclude the possibility of sub-ambient pressures. A complete set of such valid solutions exists for each fixed eccentricity and can be depicted as a contour plot of the invariant flux with formation and rupture points as coordinates. The method can readily be extended to two-dimensions, offering a promising alternative to the Elrod cavitation algorithm, which is commonly used in more comprehensive bearing analyses."

Automotive turbochargers (TCs) increase internal combustion engine power and efficiency in passenger and commercial vehicles. TC rotors are usually supported on floating ring bearings (FRBs) or semi-floating ring bearings (SFRBs), both of which are inexpensive to manufacture. However, fluid film bearings are highly nonlinear components of TC units and contribute to the complex behavior (i.e. bifurcations and frequency jumps between a first whirl frequency and a second whirl frequency) of the entire rotor-bearing system (RBS). The frequency jump phenomenon concerns the TC manufacturing industry due to increased levels of noise generation. This thesis presents progress on assessing the effects of some bearing parameters and operating conditions on the RBS dynamic forced performance and the frequency jump phenomenon. A fluid film bearing model is integrated into a finite element rotordynamics computational model for numerical prediction of the TC linear and nonlinear (time transient) forced response. Since automotive TCs operate with variable rotational speed, predictions are conducted with shaft acceleration/deceleration. Over most of its operating speed range, TC rotor nonlinear response predictions display two subsynchronous whirl frequencies w1 and w 2 representing a conical mode and a cylindrical bending mode, respectively. At low shaft speeds w1 is present up to a shaft speed (Omega bifurcation), where there is a frequency jump from w1 to w 2. The second whirl frequency may persist up to the highest shaft speeds (depending on operating conditions). Results show during rotor deceleration the Omega bifurcation may be different from the one during rotor acceleration (hysteresis). Predictions show the following factors delay the Omega bifurcation: increasing oil supply pressure, decreasing oil supply temperature, and increasing shaft acceleration. Also, rotor imbalance distribution greatly affects Omega bifurcation and the shaft amplitude of total motion. Overall, this study shows the sensitivity of bifurcations and frequency jump phenomenon in TC nonlinear response due to various bearing parameters and operating conditions. Further analysis is required to generalize these findings and to assess the effect of other bearing parameters (i.e. clearances, outer film length, ring rotation, etc.) on this phenomenon. In addition further validation of the predictions against test data is required for refinement of the predictive tool.

Tests are performed on a flexure-pivot-pad tilting-pad bearing with a series integral squeeze film damper in load-between-pads configuration, with both active and locked damper. The damper effects are negated when locked, resulting in a flexure-pivot-pad bearing only. Experimental tests provide static performance data and dynamic stiffnesses from which rotordynamic coefficients are extracted. The following two excitation schemes are implemented: (1) multi-frequency, single direction excitation and (2) single-frequency, rotating load excitation (or "circular excitation"). The XLTRC2 Rotordynamics Software Suite provides stiffness and damping coefficient, eccentricity, and power loss predictions for the locked damper bearing. Test conditions include the rotor-speed range of 4000-12000 rpm and the unit-load range of 0-862 kPa (0-125 psi). Dynamic tests utilizing the multi-frequency excitation for the locked and active damper bearing configurations both show that the real portion of the dynamic stiffness is well modeled by a quadratic curve fit, and the imaginary portion representing the damping is a linear function of excitation frequency. This means that frequency independent coefficients can be obtained when an added mass term is included. While stiffness coefficients are lower for the active damper bearing, damping coefficients remain almost constant between the locked and active damper configurations. A simulation shows that, although the damping coefficients do not change significantly, the reduced stiffness provided by the damper results in greater effective damping. Static performance tests for the locked and active damper bearing indicate low cross-coupling, as shown by the eccentricity and low attitude angle measurements. Pad metal temperature measurements show a smaller temperature differential along the pad arcs for the active damper bearing, than observed for the locked damper case. Frictional power loss is estimated based on lubricant temperature rise and does not differ significantly for the two bearing configurations.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Dynamic analyses of a flexible rotor supported by fluid film radial bearings on elastomeric suspension are performed using the Finite Element Method. The response to the unbalance and the stability behavior are obtained for different types of damping devices configuration and viscoelastic materials. The stiffness and damping coefficients of the hydrodynamic bearings are evaluated through the Short Bearing Theory. The properties of the elastomers, as a function of the frequency at a given temperature, are obtained from tests conducted in the Laboratory of Mechanical Systems of the School of Mechanical Engineering in the Federal University of Uberlândia. Dissipative elastomeric devices have strong influence on the dynamic behavior of the rotor. It is observed that with the suitable choice of the damper, the amplitude of the unbalance response may be reduced. The threshold speed of stability is increased with the use of elastomeric dampers for the most analyzed cases. / Análises dinâmicas de um rotor flexível apoiado por mancais radiais de filme fluido montados em uma suspensão elastomérica são realizadas utilizando o Método dos Elementos Finitos. A resposta ao desbalanceamento e o comportamento da estabilidade são obtidos para várias configurações de dispositivos amortecedores e para diferentes materiais viscoelásticos. Os coeficientes de rigidez e de amortecimento dos mancais hidrodinâmicos são obtidos através da Teoria de Mancais Curtos. As propriedades dos materiais viscoelásticos, determinadas em função da frequência a uma dada temperatura, são obtidas através de ensaios conduzidos no Laboratório de Sistemas Mecânicos da Faculadade de Engenharia Mecânica da Universidade Federal de Uberlândia. Os dispositivos dissipativos elastoméricos possuem forte influência no comportamento dinâmico do rotor. Observa-se que, com a escolha adequada da configuração do amortecedor, a amplitude da resposta ao desbalanceamento pode ser reduzida. A velocidade limite de estabilidade é aumentada com o emprego dos amortecedores elastoméricos para a maioria dos casos analisados. / Doutor em Engenharia Mecânica

This master´s thesis solves the problem of stationary viscous flow of incompressible fluids in thin layers of fluid film lubrication in fixed pad thrust bearings. The parametric computational model of oil domain was created for investigation the distribution of pressure, velocity and thermal fields together with the determination of the basic parameters as axial force, heating up and friction loss. Subsequently this model was applied for investigation influence of uneven bearing clearance. The problem task was solved by final volume method in Ansys CFX 12.0 software.

This thesis investigated the heat transfer of internally oil cooled rotors in permanent magnet electric machines which are, among other things, used in hybrid vehicles or zero emission vehicles. The magnets become sensitive and can be demagnetized at high working temperatures, hence the need of cooling. The scope of this work included CFD simulations in STAR-CCM+. Three different 3D multiphase models simulating the oil propagation in the rotor were performed. A Lagrangian multiphase model combined with a fluid film model was the most suitable model for simulating the spray of the oil and the film thickness along the inner rotor wall. It was noticed that periodic boundaries caused problems for the fluid film model, therefore a complete geometry was preferred over a truncated model. The 3D solutions provided thicker film thicknesses than the analytical solutions from the fluid film thickness theory. The maximum analytical thickness was of the same order of magnitude as the surface average film thickness provided by the multiphase models. This thickness was assumed to be constant when used as the base for the fluid region in the 2D one-phase models.The study showed that aluminum was the most suitable rotor material due to its high conductive capacity, which provided a more even distribution of the temperature in the solid and hence resulted in lower overall temperatures. The cooling power increased linearly with the volumetric flow rate, however the heat transfer coefficient decreased for the higher flow rates. A volumetric flow rate of 10dl/min was recommended. A 2D model was compared to a preliminary experiment and showed that these were not correlated. The conclusion was that more experiments and simulations are needed in order to confirm the validity of the 2D model.