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Rotordynamic simulations with nonlinear hydrodynamic bearing forces require a solution of the Reynolds equation at every time step. As a computationally efficient alternative to the standard numerical methods, a semi‐analytical solution based on the scaled boundary finite element method (SBFEM) was developed recently. Through a discretization of the hydrodynamic pressure (dependent variable) along the circumferential but not the axial coordinate, the partial differential equation is transformed into a system of ordinary differential equations. This system of differential equations is referred to as SBFEM equation and can be solved exactly if the influence of shaft tilting is neglected. In common numerical models, this influence can be taken into account without difficulties, but as far as this semi‐analytical approach is concerned, shaft tilting complicates the equations substantially. Therefore, previous studies on the SBFEM solution of the Reynolds equation were conducted without consideration of this effect. The formulation presented in the work at hand no longer requires this simplification. The terms representing the influence of shaft tilting in the SBFEM equation are handled by the perturbation method. The pressure field is expressed by a series expansion, where the solution of order k$k$ correlates to the kth$k\mathrm{th}$ power of a perturbation parameter chosen proportional to the tilting angle. The differential equation governing the kth$k\mathrm{th}$ solution contains lower‐order solutions on its right‐hand side, implying a recursive computation of the series from lowest to highest order. A universal expression for the general solution is formulated, where only the coefficients and the maximum power of the axial coordinate differ for every k$k$. This allows the implementation of a general algorithm with no inherent limitation regarding the maximum order of perturbation. For verification, the pressure fields computed by the proposed method are compared to a numerical reference solution, showing that the series converges to the correct result for the investigated set of parameters. [ABSTRACT FROM AUTHOR]

An accurate model of a foil bearing supported rotor needs to cover rotor dynamics of the shaft, structure dynamics of the foil as well as hydro‐ and thermo dynamics in the fluid film. The paper addresses the incorporation of tilting motions of the shaft and its influence on the foil deflection, which in turn results in a more accurate prediction of the stability threshold of the rotor‐bearing system. [ABSTRACT FROM AUTHOR]

The numerical effort of transient rotordynamic simulations is often dominated by the computation of nonlinear hydrodynamic bearing forces. These forces are described by the Reynolds equation and need to be computed at every time step. Usually, numerical models, analytical approximations, or look‐up table techniques are employed, depending on the desired tradeoff between accuracy and computational cost. In recent studies, a semi‐analytical approach based on the scaled boundary finite element method (SBFEM) has been developed as an efficient alternative to these methods. The partial differential equation is transformed into a system of ordinary differential equations, leading to an eigenvalue problem. Here, the numerical effort can be further decreased by means of a modal reduction, which is investigated in this study. The shaft eccentricity determines the smoothness of the hydrodynamic pressure field and is identified as an adequate indicator as to what subset of eigenvalues and eigenvectors should be considered in the solution. [ABSTRACT FROM AUTHOR]

It is a well‐known fact, that hydrodynamically supported systems are prone to nonlinear vibrations. Their exact simulative prediction with respect to frequency and amplitude is complicated by the fact that different system properties interact. The paper at hand outlines an approach that takes all relevant influences like rigid body motions, elastic deformations, nonlinear relation between fluid film pressure and bearing kinematics as well as temperature increase due to power loss or adjacent heat sources into account as detailed as necessary. Both journal and thrust bearings are considered as they contribute to the system's stiffness and damping capabilities. The approach is applied to self‐excited pad vibrations of tilting pad thrust bearings as well as the run‐up simulation of a turbocharger rotor under different axial loads. Both models are validated against measurements. [ABSTRACT FROM AUTHOR]

The force response of squeeze film dampers and hydrodynamic bearings is significantly influenced by the occurence of cavitation inside the lubricant films. The viscosity of the occuring mixture of oil and air bubbles is vastly different than that of pure lubricant and therefore changes the pressure build‐up and thereby the stiffness and damping properties of the lubrication films. To accurately predict the force response of a squeeze film damper, the cavitation and its effect on the pressure build‐up therefore has to be taken into account. Well known cavitation algorithms for lubrication problems, like the Elrod algorithm or the two‐phase‐model, neglect the transient nature of outgassing and assume instantaneous bubble formation and collapse. In the presented paper, a transient bubble dynamics model based on the Rayleigh‐Plesset‐Scriven equation is utilised instead and its effect on the rotordynamic behaviour of a turbocharger rotor is examined based on fully transient multi body dynamics simulations. [ABSTRACT FROM AUTHOR]

Lattice structures are lattice‐like assemblies that are inspired by organic systems. The structure inside is made up of cells whose edges form rod‐shaped elements. The size of the cells and the dimensions of the rods can influence the mechanical properties of the entire structure. For the use of lattice structures within engineering applications, stiffness and damping are important parameters. In monolithic designs, the outer contour or the material itself must be modified to change the stiffness and damping. In the case of a lattice structure, moreover, the structure of the inner cells can be adapted, resulting in greater flexibility [1]. Numerical simulations of the structural dynamic behavior will be used to optimize the damping, while heuristic methods are applied to account for the large parameter space. To adjust the simulation model, the damping is measured frequency‐dependent on a real structure which is subsequently used for model adjustment. [ABSTRACT FROM AUTHOR]

A particle damper is a passive damping technique, which is based on the high damping properties of granular materials. The energy dissipation rate of a particle damper depends on several factors, like the type of granular materials, filling ratios, particle size, and shape, etc. Out of all these factors, the type of granular materials used to design a particle damper plays a major role. Therefore, this contribution aims to investigate the influence of eleven different granular materials on vibration attenuation. Furthermore, the application of particle dampers for reducing the low‐frequency vibration amplitude of a wind turbine generator has been demonstrated. For this, two different approaches, namely the damping plate concept and the existing cavity concept have been introduced. It has been found that both concepts are capable of reducing the vibration amplitude tremendously. The material investigation has shown that rubber granulate can reduce the vibration amplitude of the test specimen significantly higher in comparison to the other materials by increasing the additional mass to the entire system marginally. The material test is independent of any particular application. Hence, the results can be used to reduce the vibration amplitude of any mechanical structure. [ABSTRACT FROM AUTHOR]

The aim of this work is to numerically calculate the effective cutting forces during orthogonal turn‐milling using the well‐known analytical approach introduced by Victor/Kienzle in connection with a multi‐body system. Starting with a routine that numerically computes the mill's infeed with the implemented dexel model, it is possible to reconstruct and follow the tool's outline and track caused by its rotation. Hence, the acting cutting forces can be determined. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a framework for modelling the deformation behaviour of friction welded hybrid structures. The constitutive model is developed for large deformations and nonlinear material behaviour. Moreover, to demonstrate the model's applicabilities, it was implemented into a finite element system (ABAQUS). Subsequently, the simulation results were critically evaluated using experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented to determine the vibrational behavior of an electric motor and the associated structure. Therefore, a holistic simulation approach is used, which takes into account the mutual influence of structural mechanics and electrodynamics. For this purpose, a multi body simulation (MBS) is extended so that electromagnetic loads can be considered, which are calculated by using the finite element method (FEM). In electric machines an undisturbed and constant magnetic field is of great importance. Even small variations of the air gap lead to changes in the magnetic field compared to the ideal geometry, which cause a change in the resulting torque and vibration excitation. Especially local and global asymmetric air gap changes due to load‐ and operation‐dependent deformations of the stator and rotor are problematic. Such deformations result on the one hand from the electromagnetically excited structural vibrations and on the other hand from the rotordynamic loads. For these reasons, it is necessary to consider the electro‐ and structural‐dynamic effects together. The developed method is presented on a simple generic motor to show the influence of the coupling. [ABSTRACT FROM AUTHOR]

Despite many advantages, hydrodynamic bearings tend to induce nonlinear vibrations on rotor systems at low external loads. The occurrence and also the amplitudes of these vibrations are very sensible to the operating conditions of the system such as occurrence of gaseous cavitation, oil viscosity (strongly dependent on oil temperature), bearing clearance (dependent on metal temperature and thermal expansion coefficients) or rotor imbalance. This contribution shows the calculation of nonlinear rotor oscillations with the help of a detailed transient 3D‐thermo‐hydrodynamic bearing model. Referring to experimental data of a real exhaust turbocharger with semi‐floating ring bearings, this holistic approach is used for a separate investigation of a) the influences of the temperature‐dependent oil viscosity in the lubricating films and b) the influences of temperature‐related changes in the lubricating gap on the nonlinear oscillations of the rotor. [ABSTRACT FROM AUTHOR]

Within a multi‐body simulation (MBS) a three‐dimensional FE model is employed to represent the nonlinear properties of rubber bushings. This is implemented via a sequential force‐displacement coupling between the two solvers. For a first material modelling approach of the elastomer, the modified Neo Hooke model is used in conjunction with the generalized Maxwell model. Later, however, a physically motivated material model will be used. First results for a single‐mass oscillator are presented and show the general functionality of the coupled approach. Since the use of FE models in MBS causes a significantly higher computational effort, it is necessary to realize the coupling between FEM and MBS as efficient as possible, which is also a future task. [ABSTRACT FROM AUTHOR]

In this paper, a method for vibration analysis of electric engines and associated structure is presented. For this purpose, a multi‐body simulation (MBS) is extended in such a way that electromagnetic loads can be considered using the finite element method (FEM). Subsequently, the determined loads lead to an excitation of the structural vibrations and a sound radiation of the engine, which is analyzed at selected operating points. A test rig will be used to validate the implemented method. Finally, different design variations of the engine are evaluated with respect to their acoustic behavior. The developed method is not limited to the presented application, but it can be applied to any system with electric drives. [ABSTRACT FROM AUTHOR]

A semi‐analytical solution of the Reynolds equation for hydrodynamic bearings in rotordynamic simulations is investigated, which is based on the Scaled Boundary Finite Element Method (SBFEM). The numerical efficiency of this approach is compared to the Finite Element Method (FEM), considering linear as well as higher‐order shape functions. It is observed that the SBFEM requires significantly less computational time than the FEM, especially with respect to high‐order formulations. [ABSTRACT FROM AUTHOR]

Present‐day research in the field of product development are increasingly focused on the efficient use of energy and raw material resources. In the light of this context, the design principle of consistent lightweight construction is gaining more and more importance. One possible approach is the targeted combination of different materials with favourable technological properties in hybrid structures. Against this background, the rotary friction welding (RFW), is particularly advantageous allowing the joining of dissimilar materials, like aluminium and steel in order to create such lightweight structures. The purpose of the paper at hand, is to present a framework for modelling the elastoplastic behaviour of those manufactured structures under the assumption of large deformation and non‐linear material behaviour. Moreover, the presented model was implemented into a finite element analysis program (ABAQUS), in order to simulate a tensile test of a friction welded lightweight structure. Subsequently, the simulation results were critically evaluated using experimental data. [ABSTRACT FROM AUTHOR]

A numerically efficient, semi‐analytical solution of the Reynolds equation for hydrodynamic journal bearings is developed based on the Scaled Boundary Finite Element Method. The pressure field is discretized along the circumferential coordinate of the lubrication gap, while an analytical formulation is used in the axial direction. A system of inhomogeneous ordinary differential equations is obtained, which is solved under consideration of the boundary conditions. The solution is verified, and its numerical efficiency is investigated in comparison to an FEM solution. [ABSTRACT FROM AUTHOR]

The vibration behaviour of fast rotating rotors is significantly influenced by the bearing properties. Lubricant film induced excitations can cause sub‐synchronous rotor oscillations known as oil‐whirl and oil‐whip phenomena. The non‐linear bearing properties depend primarily on the lubricant properties, kinematics of bearing partners and especially on the occurrence of cavitation. Outgassing processes lead to a two‐phase flow consisting of gas and oil, which can influence the bearing stiffness and damping respectively and consequently the rotor response behaviour. In this contribution, the oscillations of a semi‐floating ring supported turbocharger rotor are investigated under the influence of lubricant film cavitation. For this purpose, run‐up simulations are carried out under the assumption of mass‐conserving cavitation according to the two‐phase model and compared with measurements. In order to illustrate the influence of outgassing processes, a comparison is made with non‐mass‐conserving cavitation theory according to the assumptions of Half‐Sommerfeld. [ABSTRACT FROM AUTHOR]

Different oil‐film‐induced instabilities have to be accounted for when designing rotor systems supported by hydrodynamic bearings. Because the system's behaviour is strongly dependent on the thermal state, this contribution presents an approach for calculating the thermo‐hydrodynamic behaviour of a bearing‐rotor‐system. It incorporates a solution of the three‐dimensional energy equation for the fluid film and accounts for heat conduction through the surrounding parts of the bearing. The simulation model is validated with the help of experimental data and improvements are pointed out compared to an isothermal approach. [ABSTRACT FROM AUTHOR]

In this paper an experimental method for determining the frequency‐dependent stiffness and damping properties is presented. The aim is to obtain valid input parameters for a simulation model that considers the most important effects of typical damping materials without the necessity of poroelastic material formulations, which require at least five different input parameters. These parameters are difficult and expensive to determine experimentally. Moreover, the determination procedure is not very robust and the results can easily vary [1]. Additionally, such parameters are often phenomenological without having a physical meaning. For these reasons, it is promising to use a simpler material model based on frequency‐dependent stiffness and damping parameters within numerical simulations in order to be able to predict the acoustic behavior of complex systems with different damping and insulation treatments sufficiently. [ABSTRACT FROM AUTHOR]

Although the use of combustion engines will decrease in passenger cars due to ecological reasons, turbochargers (TC) as typical applications with floating ring bearings will furthermore be applied in other applications like combined heat and power plants, ships or emergency backup generators for data processing service center and similar systems. Thus, the development of TC concerning rotor‐ and hydrodynamics is an important task, which leads due to the non‐linear behaviour to the necessity of advanced simulations for improving the performance. [ABSTRACT FROM AUTHOR]