ABSTRACT. Recently [1-2], the new calculation approach based on modal synthesis method is proposed for evaluation of structural and dry-friction damping effect on self-excited vibrations due to aero-elastic instability in the bladed turbine wheels. The method will be herein used to study a dry-friction damping of self-excited vibration of an industrial turbine wheel with 66 blades. The aerodynamic excitation arises from the spatially periodical flow of steam through the stator blade cascade. The self-excited aero-elastic forces of blades are described by Van der Pol model [3]. In [2], we considered Van der Pol model linked to absolute motion of the blades. In this paper, however, we will aim at the effect of Van der Pol model linked to relative motion between the blades. From the point of view of the theory of flutter of blade cascades, both motions can play important role for the occurrence of flutter. For evaluation of damping effect, the blade tie-boss couplings are applied on this particular turbine wheel. Therefore, neighboring blades are interconnected by rigid arms that are on one side fixed to one blade and are in friction contact on their free side with the other blade. Static normal contact forces are prescribed in contact point pairs at the initial state. Due to relative normal motions in contacts, the prescribed contact forces vary in time. Friction forces in contacts are driven by the modified Coulomb friction law. The proposed method as ROM is computationally efficient solution allowing many parameter designs, for example contact surface angles, of such a complex non-linear mechanical system. The paper will be aimed at the narrow frequency range of excitation and on the case when a slip motion is prevailing in the contacts. The effect of the angles of contact surfaces on the wheel dynamics and on level of self-excitation suppression will be discussed.

ABSTRACT. KSB supplied 6 variable speed pump sets (pump + coupling + motor) to pump wastewater from a storage tunnel to the local sewage treatment plant. The pumps have an operating speed range from n = 150 rpm to 326 rpm, with flow rates between Q = 1.95 m³/s to 3.8 m³/s. The motor drive is located at a different level on a separate platform. The connection between pump and motor is managed via a flexible coupling. The rotor is support by two roller bearings. At the top, drive end side, an axial, radial bearing is positioned and next to the impeller, non-drive end side, a double row radial bearing is installed. During commissioning, increased housing vibrations occurred at certain speeds and/or flow rates, which had to be reduced. To analyze the causes of the increased vibrations, a wide variety of measurements were carried out on site and then evaluated. For example, bump tests were carried out to determine the natural frequencies. In addition, casing vibrations and shaft measurements were measured during operation in order to determine possible excitation mechanisms. Since the measurement evaluations did not provide a clear picture, a finite element model of the pump with the adjacent components, pipeline and concrete block below the pump, was also created and a wide variety of dynamic analyzes were carried out. By comparing the measurement and the calculation, it was found that different mechanisms were responsible for the increased vibrations on the machine. Two causes were to be found within the pump and one with the system manufacturer. The concrete block below the pump was not dimensioned to be sufficiently stiff, so that it caused the entire structure to resonate in the operating speed range. Pump-side optimization measures were defined based on the modal results using finite element analyses. A new impeller design was developed, which produces lower hydraulic excitations with the large flow rate range. Furthermore, a more suitable roller bearing for the prevailing radial bearing loads was installed. The two optimizations on the pump side already reduced the housing vibrations to an acceptable level. However, since no changes could be made to the cast concrete block, the housing vibrations could not be reduced to a low level. An alternative control program had to be developed and implemented to bypass the resonance area of the overall structure.

ABSTRACT. Acoustic emissions of wind turbines are in general unwanted and manufacturers as well as drive train suppliers optimize their turbines towards quieter designs. However due to the ever-increasing turbine sizes and drive train power densities, problems with acoustic tonalities are difficult to predict during the design phase. Acoustic tonalities which exceed legal regulations may lead to restricted turbine operations and thus reduce yield. They arise for example from gear mesh vibration of planetary gearboxes, which are used in many wind turbine drive train designs. Passive or active vibration control measures at the drive train can be applied to reduce acoustic tonalities. The key to success of such mitigation measures is to understand which vibration modes of the drive train need to be reduced in order to achieve acoustic reductions.

This paper proposes two experimental approaches to identify acoustic-relevant drive train vibration modes. In the first approach, drive train vibration modes are measured during turbine operation using a set of accelerometers. In parallel the acoustic tonalities are measured using a synchronized microphone outside of the turbine. Acoustic-relevant drive train modes are identified with the help of similarities in acoustic and structural order tracks. A second approach uses active vibration actuators as shakers at the drive train to excite isolated drive train modes and measures the acoustic response outside the turbine using a synchronized microphone. This allows the calculation of structure-to-acoustic transfer functions, which again can give insights in acoustic-relevant vibration modes. The paper describes the approaches in detail and discusses their characteristic advantages and efforts.

ABSTRACT. The Lomakin effect influences the rotordynamic characteristics not only of seals but also of journal bearings with axial flow. Recent findings have shown that the corresponding pressure loss coefficient is circumferentially distributed. If this distribution is supplied to hydrodynamic lubrication film models it can improve the predictions of load bearing capacity and attitude angle in steady-state cases. Thus, in the present paper a dynamic case was studied to investigate the influence of the circumferentially distributed loss coefficient on rotordynamic coefficients. Three-dimensional CFD flow simulations in a rotating reference frame have been conducted to determine the loss coefficient distribution and to compute a set of linear rotordynamic coefficients. Additionally, two sets of computations have been conducted with the lubrication film model CAPM. For one computation a standard pressure loss formulation was used while the the other computation was supplied with the loss coefficient distribution determined by CFD. The results show generally a good agreement between the CFD and both CAPM results. Unfortunately, the model results determined with use of the loss coefficient distribution show no improvement compared to the standard formulation. However, a physically consistent and accurate treatment of the boundary conditions allows better analyses and improvements of other model aspects.

ABSTRACT. Dynamic simulations of rotor systems supported on journal bearings require a solution for the Reynolds equation at every time step. Such simulations for high-speed rotors can be time-consuming. A novel method is demonstrated in this paper where the pressure variation along the bearing length is represented by a basis function satisfying the boundary conditions at the bearing ends. The basis function can be a polynomial or an exponential function whose coefficients are functions of the bearing length (L) to diameter (D) ratio. The same basis function is used as a test function to reduce the dimension of the Reynolds equation to 1D using the Galerkin method. The reduced differential equation is solved using the pseudospectral method (PSM). The computational effort required for solving the reduced equation is on par with short/long bearing theories. Bearing forces and peak dynamic pressure generated within the bearings as predicted by this equation are compared with the solution of the two-dimensional Reynolds equation solved using the MATLAB PDE toolbox. In the end, the dynamic response of a turbocharger rotor supported on finite-length full-floating journal bearings is simulated using this reduced equation and also compared with the results obtained using short bearing theory and 2D Reynolds equation solution for bearings. The approach demonstrated in this work can also be extended for pressure calculations in gas and thrust bearings.

ABSTRACT. Fluid film cavitation may strongly affect the vibration and stability behavior of rotors supported in hydrodynamic journal bearings. Different cavitation effects are distinguished in literature. Considering hydrodynamic bearings, cavitation is mainly caused by surrounding air, which is sucked into the bearing gap and also by outgassing of dissolved gases. Diverse physical and numerical approaches have been suggested in order to incorporate fluid film cavitation in the Reynolds equation. Here, a mass-conserving 2-phase cavitation method is applied, where a nonlinear relationship is used to describe the dependency between density and pressure of the oil/gas-mixture. Different 2-phase modelling approaches are presented and compared. Run-up simulations with a rotor/bearing co-simulation model are carried out to investigate the dynamics and especially the bifurcation behavior of rotor/bearing systems including a 2-phase cavitation approach. The numerical model for the rotor/bearing system consists of a multibody subsystem for the rotor and several finite element subsystems for the fluid films. Diverse high-speed rotor/bearing systems are analyzed, namely systems with single oil film bearings and systems with full-floating ring bearings. The influence of the cavitation parameters on the nonlinear vibration behavior of the rotor/bearing system is investigated. The different cavitation approaches are also compared with respect to numerical efficiency.

ABSTRACT. Parametric excitation can occur on a rotor-bearing system with subharmonic or fractional frequency vibration response if the stiffness has a sudden change over a fraction of its orbit. This can be explained from the Jeffcott rotor model, simplified into the standard Mathieu Equation. This paper focus on the exactly half-speed subharmonic vibration phenomenon. A corresponding real case of fluid film bearing damage is then presented on a steam turbine generator. Vibration reached over full scale of 508 microns (20 mil pp) at generator drive end bearing and therefore tripped the machine. The major vibration component that tripped the unit was exactly half-speed subharmonic frequency at a level of over 500 microns. The root-cause was found to be due to bearing damage. Why the half-speed subharmonic vibration occurred at such a high level that tripped the machine is fully explained in this paper. Other vibration plots including orbit, spectrum, and shaft centerline are also presented for vibration diagnostics. Rubs occurred but were not believed to be the root-cause of half-speed subharmonic vibration.

ABSTRACT. This paper implements sensitivity and optimization analysis in an 8-DOF rotor-bearing system, consisting of two identical semi-floating ring bearings integrated with ring-shaped wire mesh dampers (WMDs), and a rotor carrying a disc mass at both ends, representing the compressor and turbine wheels. While the realistic geometric characteristics of the rigid rotor are fixed, the variation of WMD design variables and of operating conditions (oil temperature and unbalance phase) compose a Design of Experiment (DoE) process. The unique source of nonlinearity in the system is the bearing impedance forces, which are a combination of nonlinear oil film forces and of nonlinear WMD forces due to the varying stiffness and damping of the WMD throughout its operation (deformation). The considered WMD key design variables are the radial thickness, the relative density, the radial interference and the wire diameter, and they are methodically preselected, in order to cover a wide range of encountered WMD designs. The results show significant alternation in the synchronous and sub-synchronous dynamic response of the rotor and of the bearing rings, in the rotating speed range up to approximately 170 kRPM; this leads to a narrow acceptable design range. Furthermore, after conducting various statistical tests to the collected response data, significant correlation was presented between the maximum relative eccentricity ratio and three of the WMD design variables.

ABSTRACT. Modern Gas Turbine require a detailed and precise rotor dynamic design. As the engine size, power output and shaft length increase, the requirements against vibration magnitude and dynamic behavior getting more and more challenging. A key pre-requisite to have an excellent prediction of the operational behavior of the shaft train (especially in early design stages), is a) to have good numerical model which includes all relevant interfaces and substructures and b) to know the most sensitive parameters and components that determine and influence the overall dynamic behavior of the complete shaft train. This paper presents a case study with the objective to identify the most significant parameters and subcomponents of the powertrain, which have the highest impact on damping and eigenfrequencies of the powertrain using DOE statistical methods. The effort is based on a detailed mixed 3D / 1D numerical model including all significant interfaces and subcomponents. The modeling approach goes beyond today’s typical industrial approaches. The rotating part is based on todays standard 1-D models for rotors, blades and journal bearing. The stationary substructures, e.g. Gas Turbine and Generator stator and support, the concrete foundation and the soil and piles underneath the foundation, have been modelled using a 3D FE approach. Special attention has been paid regarding accurate and detailed representation of the interfaces, like foundation bolting, bearing connection, etc.. The 3D models have been reduced and attached to the rotating part using a Craig -Bampton substructure method. This allows a very economic throughput time without loosing accuracy. To minimize the number of calculation cases and to extract the dominating parameters (direct and interactions), statistical DOE methods have been applied extensively. The results of this study enable a robust rotor dynamic design of the shaft trains already in early design stages. The results enable as well to separate between important design parameters, i.e. need to be specified with tight tolerances and unimportant contributors, that allow a loose tolerance, which at the end reduces cost and risk. The paper will describe the models, the approaches, the DOE methods, the results, and learnings on the example of a GE H-class gas turbine power train.

ABSTRACT. In modern turbomachinery, the performance and reliability is often limited by shaft vibrations induced by fluid film forces and moments of (i) plain or (ii) profiled annular seals. Therefore, these narrow annuli are mainly responsible for the overall system behaviour, i.e. safe operation and maintenance intervals. However, many studies focus only on the characteristics from the forces due to the translational motion, although the influence of the rotordynamic tilt and moment coefficients is well known. Therefore, these additional coefficients are much less researched. Especially, for profiled seals, the availability of reliable experimental data for validation purpose is rare. To overcome this fact, a test rig is operated at the Chair of Fluid Systems at the Technische Universität Darmstadt. The generic experiments presented here investigate the force and moment characteristic of plain, symmetrically profiled and non-symmetrically profiled annular seals within the relevant parameter range for turbulent flows in pumps. The investigations focus on the influence of the annulus length as well as the pressure difference across the annulus.

ABSTRACT. The increasing necessity of developing models that can more accurately represent real-life applications, supporting the evolution of methods of condition monitoring, fault diagnoses, and fault analysis, has driven researchers to develop accurate and refined models to improve the prediction of systems’ operational conditions, as well as methods for reliable identification. In this context, this work investigates ball bearing faults in different states, using Support Vector Machines (SVM) to perform fault identification and classification. The contact model between balls and raceways considers elastohydrodynamic (EHD) lubrication. To introduce this theory in the complete rotor equations, the EHD reduced model is applied to represent reactions force in the bearings system nodes. Next, a multilevel numerical integration algorithm solves the EHD equations obtaining the displacements, the velocities, and the forces for each contact. The restoring non-linear force parameters are calculated using the Levenberg–Marquardt optimization algorithm. Moreover, the ball bearings are assembled in the rotor with a gearbox and a flywheel. The equations are then solved, outputting the vibration signals for different configurations of faulty and healthy bearings. The defects are modeled according to their bearing location, which can be in the inner race, outer race, or in a single rolling ball element. Their fault profile is a sinusoidal function, limited by the spall depth and width, approaching a more realistic ball trajectory. This project uses the SVM for identifying and classifying the bearings’ conditions using simulated noisy vibration signals, recognizing specific patterns that may indicate the existence of faults. Due to the noise and its eventual impact on the time response, data processing can be necessary to reduce its influence, preserving as much information as possible. Hence, the fast kurtogram (FK) is proposed for identifying the optimal frequency range and signal frequency resolution pair to improve the identification process.

ABSTRACT. The dynamic pressure generated within journal bearings can be predicted using the Reynolds equation and it is generally coupled to rotor equations of motion for predicting their dynamic behavior. Such simulations for high-speed rotating machinery require high computational efforts. Many different methods exist in the literature to efficiently solve the Reynolds equation for a plain journal bearing (without any features like oil feed holes or grooves). The database approach is one of these methods where the Reynolds equation is non-dimensionalized and transformed into a partial differential equation that only depends on two independent parameters. These parameters are functions of bearing dimensions, lubricating oil viscosity, rotor state variables, and rotational speed. A database of bearing forces can be created by considering different sets of values for these two parameters within their finite range. Such a database can be used to predict bearing forces using multivariate interpolation. The authors extended this approach to consider oil feed holes in the journal bearings by introducing two additional parameters. The Reynolds equation expressed in terms of these four parameters is solved using the MATLAB PDE toolbox to generate the database. The vibration response of a turbocharger rotor supported on a semi-floating journal bearing consisting of oil feed holes is investigated using the proposed database approach. The oil feed holes modeling improved the predictability of sub-synchronous vibrations when compared with experimental results. In the end, the impact of a different number of oil feed holes on the turbocharger rotordynamics response is also presented.

ABSTRACT. Lighter casing and stator are the favourable features for the gas turbine product design to be cost competitive and better manufacturability. However, a light and flexible stator is very challenging in the rotor dynamics due to rotor and flexible support interaction. The operational margin to the critical speeds and the stability maybe compromised by the flexible support of the stator structure. A slim spoke frame stator for the power turbine (PT) of a new industrial gas turbine was proposed for optimisation of cost and manufacturability. The frequency response function (FRF) modal test of the stator at the front and rear bearing locations is simulated by finite element (FE) analysis. The simulated FRF results are used to evaluate the static and dynamic support stiffness of the stator. The result of the dynamic support stiffness of the stator showed far less than the API 616 standard recommended bearing support stiffness in the speed range of the PT rotor. A more sophisticated full rotor/stator FE model is developed using axisymmetric 2D multi-harmonic element and full 3D element respectively for the rotor and stator modelling. The full FE model enable to catch all the dynamics of the rotor-bearing-stator system and to quickly perform rotordynamic design analysis. The superelement representation of the rotor and stator are used. The super element which is based on the component modal synthesis (CMS) approach greatly save the analysis time but with little loss of computational accuracy. The effect of the flexible stator analysed by the full FE analysis and FRF derived support dynamic stiffness are compared. The stability and unbalance response analyses are performed by full rotor/stator FE model. The results are assessed according to the design criteria for the rotordynamics. The effects of the slim stator are also investigated. In conclusion with a sophisticated FE model of the rotor/stator and bearing along with their supper element dimension reduced representation, the viability of the design of the PT rotor with slim spoke frame can be quickly assessed and verified.

ABSTRACT. The rotors of modern turbomachines, such as microturbines and turbocompressors, operate at very high rotational speeds. This is beneficial in terms of the flow system and allows high efficiencies to be achieved, but at the same time high speeds can cause dynamic problems and advanced bearing systems must be used. The mechanical, thermal, and electrical loads that act on the rotating systems of such machines require very detailed analyses, because, at high speeds, some components must operate slightly below the limits of their technical capacities.

This article presents the results obtained from an experimental study carried out on a 30-kilowatt prototype gas microturbine with a nominal speed of 100 krpm. An unconventional bearing system, which consists of two super-precision ball bearings and a single gas foil bearing, was used for the rotor of this machine. The function of the foil bearing is to support the overhung end of the shaft where the rotor disk of the gas microturbine and compressor is located. Such a bearing was chosen because of the operating conditions. In addition to the high rotational speed, the bearing node, which is located directly next to the gas turbine, is exposed to high temperatures of up to 500°C. The experimental examination of the microturbine prototype was conducted under laboratory conditions and included several start-up tests, a test carried out at constant speed, and rotor rundowns. The vibration level of the casing (near the bearings) and the temperature of the selected components were monitored during the tests. Based on the obtained characteristics, the dynamic state of the machine was evaluated and some modifications to the bearing system were proposed. The analysis of the vibrations that occur in the resonance area has shown that an additional foil bearing significantly reduces the vibration level, and reduces the risk of damage to the machine as it passes through critical speeds. The results presented in this paper may be of interest to other researchers and engineers who are involved in the development of high-speed turbomachines, especially gas microturbines.

ABSTRACT. Aircraft engines for civil and military applications are designed to avoid excessive vibrations, which may limit their mechanical integrity as well as their performance. In the concept phase, it is a common practice to shift some critical speeds of the en-gine, which occur usually due to rigid or flexural (bending) vibration modes of the ro-tors, into speed ranges that might have a lighter impact on the engine vibrations. Squirrel cages (SQCs) are usually used to this end. They provide a softer support to the rotors, giving the possibility of shifting rigid body as well as flexural modes. In this work, a detailed end-to-end approach for robust engine dynamics is presented and applied to a realistic dual-spool aircraft engine.

At the first step, a stochastic optimization approach is applied to the rotor dynamic model of an aircraft engine in order to identify the optimal stiffness values of the SQCs. The aim of this optimization is to avoid rigid body modes in certain speed ranges as well as to avoid flexural modes. At this step, the influence of SQC stiffness on the critical speeds of the system is evaluated. According to pre-defined criteria, the suitable SQC stiffness value or ranges of SQC stiffness values are obtained, which will be used as the 3D SQC geometry design goal in the next step.

At the second step, the 3D SQC geometries are identified, which not only fulfil the stiffness requirements from the first step but also satisfy the HCF fatigue life re-quirements. At this step, 3D FEM simulations are used to evaluate fully parametrized SQC geometries w.r.t. stiffness values and stresses. The respective Haigh diagram is drawn and the margin to the Goodman line is discussed. This analysis process chain is coupled with a numerical optimization method in order to find the optimal SQC geometry.

Various state-of-the-art machine learning techniques are used to support and speed up SQCs design process, including correlations analysis/variable screening, surro-gate models and numerical optimization techniques. Finally, optimal SQC designs are identified and analyzed.

ABSTRACT. Aerodynamic foil bearings (AFB) are a type of bearings predominantly used for high-speed, oil-free applications. Offering many advantages in regard to friction loss at high speeds, stability and price they do lack in load capacity as well as start-up and coast-down friction wear.

Characteristic friction losses for sliding-contact bearings are often described using the Stribeck curve [1]. Typically, a preloaded foil bearing has comparatively high friction torque in the boundary and mixed lubrication regime, i.e., in the lower speed range, in contrast to its fully lifted-off friction torque. This leads to most of the wear being exerted in these two regimes. The friction loss of AFBs has been studied experimentally by many authors, e.g., [2]. In order to predict the friction and consequently the lifespan of an AFB the start-up and coast-down regimes are being modelled in such a way that allows for accurate, efficient simulation and later optimisation of lift-off speed and wear characteristics.

The proposed simulation method applies the Kirchhoff-Love plate theory to the top-foil mapping [3]. This system of differential equations is coupled with the underlying bump or spring foil in order to simulate the displacement due to the pressure build up. Consequently, this coupled system allows for simulation from almost zero rpm to full speed making use of a no impingement condition for rotor and foil. The underlying simulation model makes use of the finite difference method for spatial discretization and a temporal explicit Runge-Kutta method.

Difficulties to overcome are the smooth combination of various friction regimes across the sliding surfaces as well as the synchronous coupling of Reynolds-, deformation- and kinematic equations. Moreover, the modelling of the boundary conditions at the free edges of the simulated top-foil has proven to be sensitive to the approach used.

Resulting gaps between the rotor and top foil as well as corresponding forces due to foil displacements can be taken as an input for further friction calculations. The results can be compared to various test datasets in order to validate the method.

[1] Richard Stribeck. `Die wesentlichen Eigenschaften der Gleit- und Rollen- lager' [2] Marcel Mahner et al. `An experimental investigation on the infuence of an assembly preload,[...]'. In: Tribology International 137 (2019) [3] R. Szilard. Theories and Applications of Plate Analysis[...]. Wiley, 2004.

ABSTRACT. See attached pdf-file!

ABSTRACT. A detailed 2D finite element (FE) model of a three-pad air foil journal bearing is presented using commercial FE software in this paper. A mechanical preload is introduced within the FE model of the bearing by adopting an assembly procedure of bump and top foils in the bearing sleeve. A periodic force is applied quasi-statically on the rotor shaft along the bearing radial direction to estimate the foil structure stiffness and damping characteristics (static hysteresis). The presence of air film is ignored initially. The static hysteresis curve obtained from the FE model is compared with the test data. A good agreement is achieved between the simulation results and measurements. Static hysteresis curves obtained with different assembly preload of foils are compared with each other, which showed an increase in foil structure stiffness and damping with an increase in the amount of preload. The next step includes the linearization of the steady-state compressible Reynolds equation for the thin air film present between the shaft and the bearing surface with suitable approximations, which is solved numerically using a finite difference scheme. A long-bearing assumption is made during the solution procedure, reducing the Reynolds equation to one dimension. The accuracy of approximated Reynolds equation is verified by comparing the load-carrying capacity results obtained through the direct and approximated Reynolds equation while coupling both equations with a simple elastic foundation model. The approximated Reynolds equation is then coupled with the FE model of the bearing. Coupled fluid-structure simulations with different amounts of preload are performed in order to investigate its effect on the pressure distribution over the bearing surface and the load-carrying capacity of the bearing.