Bernhard Schweizer

Numerical Approach for Solving Reynolds Equation With JFO Boundary Conditions Incorporating ALE Techniques

Calculating the fluid flow and pressure field in thin fluid films, lubrication theory can be applied, and Reynolds fluid film equation has to be solved. Therefore, boundary conditions have to be formulated. Well-established mass-conserving boundary conditions are the Jakobsson-Floberg-Olsson (JFO) boundary conditions. A number of numerical techniques, which have certain advantages and certain disadvantages, have been developed to solve the Reynolds equation in combination with JFO boundary conditions. In the current paper, a further method is outlined, which may be a useful alternative to well-known techniques. The main idea is to rewrite the boundary value problem consisting of the Reynolds equation and the JFO boundary conditions as an arbitrary Lagrangian-Eulerian (ALE) problem. In the following, an ALE formulation of the Reynolds equation with JFO boundary conditions is derived. Based on a finite element implementation of the governing boundary value problem, numerical examples are presented, and pressure fields are calculated for a plain hydrodynamic journal bearing with an axial oil groove.

Dynamics of rotating thermoelastic disks with stationary heat source

Rotating disks are important components of car brakes or sawing units. In both cases, heat effects to be induced via stationary local contacts between pads and disk or workpiece and saw blade, respectively, influence the dynamic behavior and raise interesting problems in theory and practice. Therefore, the discussion of dynamic thermoelasticity in rotating disks with stationary heat sources is of basic interest to understand the interaction of temperature and displacement or stress fields in such structural elements. It will be analyzed here in detail for the case of an elastic disk for which there is a full (but weak) coupling of strain and temperature within the two applications mentioned. As a relatively general case, the combined excitation by a mechanical load and a simultaneously acting heat source will be examined.

Stabilized Implicit Cosimulation Method: Solver Coupling With Algebraic Constraints for Multibody Systems

In this manuscript, an implicit cosimulation method is analyzed, where the solvers are coupled by algebraic constraint equations. We discuss cosimulation approaches on index-2 and on index-1 level and investigate constant, linear and quadratic approximation functions for the coupling variables. The key idea of the method presented here is to discretize the Lagrange multipliers between the macrotime points (extended multiplier approach) so that the coupling equations and their time derivatives can simultaneously be fulfilled at the macrotime points. Stability and convergence of the method are investigated in detail. Following the stability analysis for time integration schemes based on Dahlquists test equation, an appropriate cosimulation test model is used to examine the numerical stability of the presented cosimulation method. Discretizing the cosimulation test model by means of a linear cosimulation approach yields a system of linear recurrence equations. The spectral radius of the recurrence equation system characterizes the numerical stability of the underlying cosimulation method. As for time integration methods, 2D stability plots are used to graphically illustrate the stability behavior of the coupling approach.

Impact Studies of Gears in Combustion Engines

Gears are commonly used design elements, typically used to convert torque. However, gears are also used in mechanisms or gear drives to transmit motion. Typical applications of gear drives are gear trains, used to drive the camshaft by the crankshaft in large-scale diesel engines. There, normally the transmitted rated torque is relatively small compared to the dynamical loads. They often introduce vibrations of the entire drive train, caused by gas forces or auxiliary devices. These dynamic loads cause the flanks of teeth to lift-off. The re-establishment of contact is mostly in the form of impacts and may occur on both sides of the teeth. Because of the noise induced by these impacts, this phenomenon is called gear hammering. In gear trains, the gears are often designed with thin gear bodies to reduce inertia effects and the total weight of the engine. As a result not only noise, but also endurance problems may arise due to the high peaks in the contact forces. Thus, the precise knowledge of the contact forces is necessary for the design process. However, contact forces between rotating gears are extremely difficult and expensive to measure. Therefore, the simulation of contact forces inheres great importance. Nowadays, the contact simulations are mainly done with commercial multibody packages, assuming rigid gears connected by elastic elements. These elastic elements somehow describe the contact stiffness as well as the elasticity of the gear bodies.

A contribution to the thermal modeling of bump type air foil bearings:Analysis of the thermal resistance of bump foils.

A detailed analysis of the effective thermal resistance for the bump foil of air foil bearings (AFBs) is performed. The presented model puts emphasis on the thermal contact resistances between the bump foil and the top foil as well as between the bump foil and the base plate. It is demonstrated that most of the dissipated heat in the lubricating air film of an air foil bearing is not conducted by microcontacts in the contact regions. Instead, the air gaps close to the contact area are found to be thin enough in order to effectively conduct the heat from the top foil into the bump foil. On the basis of these findings, an analytical formula is developed for the effective thermal resistance of a half bump arc. The formula accounts for the geometry of the bump foil as well as for the surface roughness of the top foil, the bump foil, and the base plate. The predictions of the presented model are shown to be in good agreement with measurements from the literature. In particular, the model predicts the effective thermal resistance to be almost independent of the applied pressure. This is a major characteristic property that has been found by measurements but could not be reproduced by previously published models. The presented formula contributes to an accurate thermohydrodynamic (THD) modeling of AFBs.

NUMERICAL AND EXPERIMENTAL INVESTIGATIONS ON PRELOAD EFFECTS IN AIR FOIL JOURNAL BEARINGS

A detailed elastogasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The two-dimensional pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. The assembly preload is calculated by simulating the assembly process of top foil, bump foil, and shaft. Most advantageously, there is no need for the definition of an initial radial clearance in the presented model. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the elastic foil structural stiffness (in particular for moderate shaft displacements) and the bearing damping. It is observed that the effect of the fluid film on the overall bearing stiffness depends on the assembly preload: For lightly preloaded bearings, the fluid film affects the overall bearing stiffness considerably, while for heavily preloaded bearings the effect is rather small for a wide range of reaction forces. Furthermore, it is shown that the assembly preload increases the friction torque significantly.

Nonlinear Oscillations of High-Speed Rotor Systems in Semi-Floating Ring Bearings

Semi-floating ring bearings are preferred to be incorporated in high-speed rotor systems since they usually provide a better vibration and damping behavior than full-floating ring bearings. Nevertheless, such rotor bearing systems can show whirl/whip instabilities as well which lead to subsynchronous oscillations in addition to synchronous oscillations due to unbalance. Moreover, a critical bifurcation can take place into a regime of subsynchronous oscillations with extremely high amplitudes which resembles Total Instability known from investigations of full-floating ring bearings. To illustrate the various types of subsynchronous oscillations, different rotor models are investigated under the influence of semi-floating ring bearings. First, transient run-up simulations are performed to outline the nonlinear phenomena. Then, the stability and bifurcation behavior is analyzed in detail by using the methods of numerical continuation.

Error estimation approach for controlling the macro step-size for explicit co-simulation methods

This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model and an electrical lumped-element circuit is demonstrated. The multiphysics, multirate and multiscale problem requires a consistent formulation and framework to tackle the challenging transient effects occurring at both system and device level.Micro Abstract Shell elements for slender structures based on a Reissner-Mindlin approach struggle in pure bending problems. The stiffness of such structures is overestimated due to the transversal shear locking effect. Here, an isogeometric Reissner-Mindlin shell element is presented, which uses adjusted control meshes for the displacements and rotations in order to create a conforming interpolation of the pure bending compatibility requirement. The method is tested for standard numerical examples.Powered by TCPDF (www.tcpdf.org) This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Niiranen, Jarkko; Khakalo, Sergei; Balobanov, Viacheslav

Efficient Thrust Bearing Model for High-Speed Rotordynamic Applications

The dynamic behavior of rotor systems is influenced by thrust bearings. Therefore, a time-efficient model of oil-lubricated thrust bearings is introduced within this contribution. The areas of application for this bearing model are multibody simulations and more specifically high-speed rotordynamic systems. The Reynolds equation is solved at each pad of the bearing for the calculation of the fluid-film forces and moments, where the effect of misalignment of the shaft is also considered. For the solution of Reynolds equation the weak formulation is used, i.e. the Galerkin approach. This optimized bearing model results in heavily reduced simulation times especially if they are compared to the relatively large simulation times needed in co-simulations. The applied procedure can be easily implemented into commercial software and is flexible for investigating any bearing geometry and number of pads. Finally, the effect of the thrust bearing is studied in run-up simulations on an example rotor-bearing system.

Analytische Berechnung der integralfreien Terme aus den Somigliana-Identitäten

Unter Anwendung der Kugelgeometrie wird eine neue Methode beschrieben, mit der die integralfreien Terme aus den Somigliana-Identitaten fur drei-dimensionale Kontinua mit nicht glatten Randern analytisch berechnet werden konnen. Fur diese Terme aus der Somigliana-Verschiebungsidentitat und der Somigliana-Spannungsidentitat werden Berechnungsformeln entwickelt, die nur noch Transformationen von speziellen Tensorfunktionen enthalten, so das insbesondere keine Integrationen mehr durchzufuhren sind. Die erzielten Ergebnisse sind auf andere Probleme der Randelementmethode ubertragbar. New analytical formulas are derived for calculating the integral free terms of both the 3-D Somigliana displacement and the Somigliana stress identity with non-smooth boundary. The basis of the approach is to incorporate spherical geometry. Computation of the formulas is easy because the integration is replaced by simple tensor-function transformations. It is possible to apply the results to other problems associated with the Boundary Element Method.