ABSTRACT. The complexity and intricate dynamics of rotating machines generally requires models with a high number of Degrees of Freedom (DOFs). In this way, any model must come with some reduction method, that reduces the dimensionality of the system while retaining the major dynamic characteristic of it. The existence of nonlinear effects often complicates even more the analysis, and they are often neglected in the model reduction by, for example, relying on linearized models. Taking this into account, this paper presents a nonlinear model reduction method to obtain Reduced Order Models (ROMs) to study rotating machines under nonlinear forces. The method is based on the idea of Nonlinear Normal Modes (NNMs) and the existence of Invariant Manifolds (IMs). These manifolds can be seen as an extension of the linear eigenspaces commonly used in modal analysis to reduce the dimensionality of dynamical systems. The basis of the method is the obtention of the manifolds, allowing the reduction of the model to a single nonlinear mode, thus essentially reducing the problem to integrating a single pair of equations. In addition, the method is applied on a rotor-bearing systems with two kinds of nonlinearities: a cubic nonlinearity and a hydrodynamic bearing.

ABSTRACT. Regarding aerodynamic bearings, mainly two basic types can be distinguished: air bearings with a rigid housing and air foil bearings with an elastic supporting structure.

Here, a modified bearing concept – called air ring bearing – is investigated, which may be considered as a further development of rigid air bearings or as a combination of the two basic bearing types.

The idea of air ring bearings is to insert a ring-shaped bearing bushing between the shaft and the foil structure. Alternatively, a viscoelastic supporting structure (e.g. an elastomer) can be applied to connect the bushing ring with the housing. In the first case, external dissipation is mainly generated by dry friction; in the latter case viscous damping is used to provide external dissipation.

Due to the external friction/damping generated by the ring mounting structure, rotor systems with air ring bearings can be operated above the linear threshold speed of instability so that stable self-excited vibrations with moderate amplitudes can be achieved in the complete speed range.

Here, a detailed transient co-simulation model for rotor systems with air ring bearings is presented. The rotor is represented by a multibody model; the air films of the two bearings are represented by two nonlinear time-dependent finite element systems. The multibody model and the two finite element subsystems are solved simultaneously by means of an explicit sequential co-simulation technique.

Due to the high nonlinearities, the system shows interesting vibration and bifurcation effects, which are investigated in detail with the help of run-up simulations.

ABSTRACT. Most turbocharger rotors in vehicles are operated within oil-lubricated fluid film bearings. However, for high performance and reduced friction losses a ball bearing system is superior. But there are several technical challenges that needs to be mastered in order to design, build and produce a reliable product for series applications. Examples are high temperatures and temperature ranges due to the exhaust gases and different surrounding conditions in combination with tight clearances and furthermore the huge rotational speeds at which these machines are typically operated. In particular for the latter mentioned, vibrations, inherent to rotating devices, are gaining on importance. They frequently come along with either high dynamical loads, which could lead to a failure of the bearing or overall system, generate noise or both.

Besides hardware testing simulation is utilized to cope with the systems behaviour and investigate the source as well as the vibration characteristics. To do this, a flexible rotor model of the turbocharger is coupled to a non-linear ball bearing model considering the specific geometry and number of balls, for example. Additionally, and in contrast to many other rotating machines operated in two separate bearings, a single bearing cartridge design is used here. Run-up simulations within time-domain are performed and compared with measurements to validate the model. Furthermore, parametric studies are utilized to investigate the sensitivities and show the capability and robustness of the system to withstand loads under different operating conditions.

ABSTRACT. The behavior of rotors depends on a variety of factors that are described by geometric and physical parameters. Because of different reasons values of some of them can be uncertain (e.g. stiffness or damping parameters of contact connections, parameters of unbalance loading, etc.). Several approaches making it possible to treat such problems have been developed (the worst scenario method, the probabilistic approaches like the Monte Carlo method, the fuzzy number approach, the sensitivity approaches, etc.). Application of the fuzzy approach requires to specify interval of values, which the uncertain quantity can take, and to assign the degree of membership, the magnitude of which ranges between 0 and 1, to each value from this interval. To do this the database of knowledge (e.g. values arranged in the form of a histograms) or experience of persons solving the problem are needed. The degree of membership approaching to one indicates high probability of the uncertain quantity value while the degree of membership approaching to zero means that probability of the corresponding value is low. The fuzzy numbers approach requires to perform interval analyses for the chosen membership levels, the same for all uncertain quantities, which makes it possible to construct corresponding intervals of the individual results (e.g. deflection in some direction, natural frequencies, stability parameters, etc.).

Applicability of the fuzzy number approach was tested by means of computer simulations. The investigated rotor was supported by hydrodynamic bearings. Some parameters of the rotor and its loading were considered to have uncertain values. The direct integration of the motion equation or the trigonometric collocation method were applied to determine the rotor steady state response. The goal of the analysis was determination of the rotor maximum radial displacement.

The approach to analyzing the rotor systems with uncertain parameters based on application of the fuzzy numbers has some advantages. It does not require knowledge of the probability density function of the individual uncertain parameters and corresponding generators of random numbers. If the number of the uncertain parameters is not too large, the number of performed simulations can be considerably lower than those if the Monte Carlo method were applied.

ABSTRACT. Large rotating systems are commonly operated in the subcritical speed range. Elevated vibration levels are de- tected when the rotating speed or one of its integer multiples equals one of the natural frequencies of the system. Subcritical resonances may also be caused by non-integer multiples of the rotating speed, mainly due to roller element bearings. In flexibly supported rotor systems with asymmetric stiffness, the horizontal and vertical natural frequencies are separated. In large rotating systems, the operating speed range is often limited by the subcritical resonances. In this paper, a semi-active control method based on control of the foundation stiffness is presented. Modification in the foundation stiffness of the rotor system results in a corresponding change in the natural fre- quencies. This principle is used in the developed method to choose an optimal foundation stiffness for each rotating speed of the rotor system. The presented method is validated with a rotor model based on experimental dimen- sions. The vibration response of the model employing the foundation stiffness optimization is evaluated in the subcritical speed region. With the optimal foundation stiffness, the subcritical resonances caused by multiple rotor bending modes can be avoided in a given speed range. The extent of the resonance-free range depends on the control range of the foundation stiffness. In the light of the presented results, the proposed semi-active foundation stiffness control can be applied to reduce the total vibration levels in rotating systems. The presented method can be applied in any rotating system where it is possible to modify the foundation stiffness during operation.

ABSTRACT. A gyroscopic rotor exposed to unbalance and internal damping is controlled with an active piezoelectrical bearing in this paper. The used rotor test-rig is modelled using an FEM approach. The present gyroscopic effects are then used to derive a control strategy which only requires a single piezo actuator, while regular active piezoelectric bearings require two. Using only one actuator generates an excitation which contains an equal amount of forward and backward whirl vibrations. Both parts are differently amplified by the rotor system due to gyroscopic effects which cause speed dependent different eigenfrequencies for forward and backward whirl resonances. This allows to eliminate resonances and stabilize the rotor system with only one actuator but requires two sensors. The control approach is validated with experiments on a rotor test-rig and compared to a control which uses both actuators.

ABSTRACT. The presented work focusses on the experimental investigation of a vibroacoustic metamaterial integrated into a spinning circular saw blade. Vibroacoustic metamaterials are a novel technology for broad band vibration reduction. Build from an array of local resonators a broad band vibration reduction characteristic in the frequency domain (so called stop band) can be achieved. A design of a vibroacoustic metamaterial suitable for the integration into a circular saw blade is elaborated and a numerical stop band prediction is performed. The resonators of the vibroacoustic metamaterial are integrated into the saw blade with a water jet cutting machine in terms of slots, forming flaps that are free to oscillate. The structural dynamic behavior of the saw blade with integrated vibroacoustic metamaterial is experimentally investigated on a rotor dynamic test bench and compared to that of a standard saw blade. The saw blades are excited by an automatic impulse hammer and the resulting out-of-plane vibrations are measured with a laser-vibrometer at two different radii. Measurements are carried out at different rotational speeds up to 1800 rpm. Up to rotational speeds of 1000 rpm a stop band characteristic in the frequency range of 1900 – 2500 Hz is observable.

ABSTRACT. The reduction of noise or more general vibration amplitudes is one major issue in large structures can be achieved with different methods. Preferable passive systems are used due to the reduced costs and easy application. Besides conventional concepts like viscous dampers or tuned mass dampers, particle dampers offer a broadband damping behaviour combined with a small increase of the overall mass of the system. The working principle of particle dampers is based on energy dissipation induced by frictional contact between the particles themselves as well as particle and surrounding structure. Several parameters influence the damping characteristic and thus allow for an optimization of the system. In the case of granular materials at least the filling ratio, the particle size and the particle shape define the frequency range, in which the damper works effective, and the amount of dissipated energy. As the usage in rotating systems superimpose centrifugal forces on the particle dampers the setup and chosen parameter for the usage in blades of a wind turbine or similar systems is quiet different to non rotating applications. Due to the centrifugal force the positioning of the granular materials in a damper cavity is affected and the resulting contact behaviour varies. In this contribution the influence of the centrifugal force on the damping behaviour of a granular particle damper in a blade structure is investigated. The vibration is measured with a laser vibrometer and a derotator, which is a special device to measure vibrations on rotating objects. This method can be used to determine the vibration modes of the rotating blades in a body-fixed reference frame.

ABSTRACT. A common problem in transient rotordynamic simulations is the numerical effort necessary for the computation of hydrodynamic bearing forces. Due to the nonlinear interaction between the rotordynamic and hydrodynamic systems, an adequate prediction of shaft oscillations requires a solution of the Reynolds equation in every time step. Since closed-form analytical solutions are only known for highly simplified models, look-up table techniques or numerical methods are usually employed. However, numerical solutions are computationally expensive, while look-up table approaches only provide a limited modeling depth. In previous studies, a semi-analytical solution of the Reynolds equation based on the scaled boundary finite element method (SBFEM) has been developed with the objective of reducing the numerical effort while maintaining an adequate modeling depth. Compared to the finite element method (FEM), the developed approach is efficient if a high accuracy (small discretization error) is desired. Since this has only been investigated for single calls of the Reynolds equation, the accuracy and efficiency are now evaluated by means of rotordynamic simulations. Moreover, a larger variety of reference solutions are considered, including the FEM, the finite volume method (FVM), and analytical approximations.

ABSTRACT. The presence of wall slip has a significant impact on the Stribeck curve for the infinite journal bearing. In this paper, Molecular Dynamics (MD) simulation is employed to calculate the slip length of Newtonian fluid confined between two iron smooth surfaces. MD simulations are accomplished by LAMMPS open-source software. The lubrication oil served in this research is polyalphaolefin base oil consisting of 1-Decane molecules. Results revealed that with decreasing temperature, the shear stress values, as well as dynamic viscosity, increase as an Arrhenius law. Besides, results indicate that slip length is increasing with decreasing gap height as an asymptotic expansion.

ABSTRACT. Supercritical carbon dioxide (S-CO2) cycles are of great interest in the scientific research especially considering the energy transition that is occurring. The S-CO2 high density and relatively low viscosity make it an interesting fluid for power generation. Moreover, CO2 is not toxic, it is not explosive, it is not a polluting gas, and is rather cheap compared to other working fluids used for power generation. Therefore, there is great interest in using S-CO2 thermodynamic cycles instead of organic Rankine cycles (ORCs) for waste heat recovery (WHR). For large heat sources, large flowrates of fluid can be obtained. Therefore, the development of axial flow expanders can allow large power generations. However, the blades are required to sustain high levels of aerodynamic loading derived from the physical characteristics of the S-CO2. In the presence of rotor eccentricities, the aerodynamic loading of free-standing blades is not constant tangentially and will promote the tangential vibration of the rotor. The dynamic phenomenon that arises is known as Alford force. The Alford force determines an increase of the vibration level of the machine and a higher risk of instabilities. In this paper, a preliminary investigation on the first stage of an axial expander is performed. Different correlations proposed in the literature are adopted to estimate the magnitude of the Alford force. A mono-dimensional code and a simplified computational fluid dynamics (CFD) model are adopted to obtain the parameters of the stage considered. For this preliminary investigation, free-standing blades are considered as a simplification. As a matter of fact, a similar phenomenon arises also for shrouded blades due to the non-homogeneous tangential pressure distribution. Nonetheless, the simplification adopted can give an insight on the magnitude of this phenomenon. The results obtained strongly depends on the correlation considered and, on the model, used to evaluate the stage parameters. However, the magnitude of the forces obtained is not negligible and highlights the necessity to further investigate this phenomenon.

ABSTRACT. Within the framework of the conducted research, an active foil bearing was designed and tested. Typical gas foil bearings have a high starting torque. This is because the top foil must be clamped on the shaft during start-up. It is only at a sufficiently high speed that an air layer forms itself between the top foil and the rotating shaft, which, along with the self-adjusting shape of the bump foils, allows the bearing to operate. This article presents an innovative (one-of-a-kind) active foil bearing. The diameter of the bearing sleeve can be changed using an electric drive mounted in the bearing. These modifications allow the dynamic properties of the rotor to be controlled. It is also possible to reduce the starting torque by increasing the diameter of the bearing sleeve during start-up. The article presents the results of the friction torque tests conducted on the newly developed bearing with variable geometry. This paper shows the starting torque characteristics for bearings with different geometries.

ABSTRACT. High-speed rotors on gas foil bearings (GFBs) are applications of increasing interest due to their potential to increase the power to weight ratio in machines and also establish oil-free design solutions. The gas lubrication principles render lower (compared to oil) power loss and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at DN (Diameter [mm] X Rotating Speed [RPM]) values much lower than the one corresponding to the speed of sound [DN at c.a. 6.5e6], these being usually triggered through Hopf bifurcation of a fixed-point equilibrium (balanced rotor) or secondary Hopf bifurcation of periodic limit cycles (unbalanced rotor). In this work, an active gas foil bearing is presented as a novel configuration including a number of piezoelectric actuators which shape the foil through feedback control. At first, a finite element model for the thin foil mounted in a number of PZTs, is developed. Second, the gas-structure interaction is modelled through Reynolds equation for compressible flow. A simple physical model of a rotating system consisting of a rigid rotor and two identical gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the impedance forces from the gas to the rotor and to the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed depended equilibrium (balanced rotor). Further to that, linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability. Case studies include a small (30mm) and a large (100mm) bearing, which are referred as bearing D30 and bearing D100 respectively, both at operating range with upper bound of speed corresponding to DN = 6.5e6.

ABSTRACT. With increasing demand in sustainable and oil-free technology, air foil bearings grow in popularity. They are applicable in high speed turbomachinery and---by contrast to rigid air bearings---are more tolerant against manufacturing and assembly inaccuracies. A foil bearing consists of the bearing sleeve and the foil sandwich. In typical designs, an underlying, compliant foil is paired with a smooth top foil for better airflow. The main differences in the layout of journal and thrust bearings lie in the number of bearing pads and the kind of underlying foil. The most common include the bump foil, beam foil, metal meshes and the wing foil. In this study, a multi-pad bump-type foil thrust bearing with a taper-land height profile is investigated. A detailed thermo-elasto-hydrodynamic (TEHD) finite element model is used for the optimization of the bearing geometry. The model accounts for the deformations of the foils via a Reissner-Mindlin-type shell model. Deformations of the rotor are calculated via the Navier-Lame equation with thermoelastic stresses and centrifugal effects. The temperature of the top foil and the rotor are calculated with the use of heat diffusion equations. The temperature of the lubricating air film is obtained through a 3D energy equation. Film pressures are calculated with the 2D compressible Reynolds equation. Moreover, the surrounding of the bearing and runner disk is part of the thermodynamic model. The heat fluxes caused by dissipation in the lubricating air gap mainly enter the foil sandwich and the runner disk. Therefore, it is crucial to represent their thermodynamic behavior in the fully coupled model. Results display that the thermal bending of the runner disk is a key factor in performance reduction. This is a result of the direct coupling of the component deformations to the lubricating gap height and, therefore, the pressure generation inside the bearing. Besides the rotor disk deflections, the deformations of the bearing foils are of high importance for the calculation of the lubricating gap height. Due to the bump-type understructure, the top foil sagging effect is observed in simulation results. The combination of the line support and the air film pressure causes dents in the deformed top foil which in turn decrease the load capacity of the bearing. The study at hand showcases the influence of misalignment between the rotor and the bearing on the bearing performance.