CHAIR OF

MULTIBODY

DYNAMICS

The rotordynamic properties of systems with hydrodynamic bearings are affected crucially by the nonlinear bearing forces. Regarding fast-rotating, lightly-loaded rotors, this causes subsynchronous self-excited oscillations with potentially high amplitudes, which can reduce the durability of the components, cause critical noise emissions, and affect the energy efficiency of the machine. To reduce expensive test bench experiments and time-consuming iterations in the product development process, the design has to be based on precise simulative analyses of the operating behavior under consideration of the nonlinear interactions between the bearing forces and the shaft vibrations. To this end, the equation of motion of the elastic shaft is incorporated into a time integration scheme and coupled with the Reynolds equation, which describes the pressure generation in hydrodynamic bearings. Hence, each time step of the simulation includes a solution of the Reynolds equation, for which numerical methods, analytical approximations, and look-up tables are employed. While numerical methods lead to considerable and often inacceptable computational times, analytical solutions are only possible in conjunction with substantial simplifications. The look-up table approach, to some extent, offers a tradeoff between these two extremes, while the modeling depth is usually limited, since the interpolation effort increases with every considered physical effect.

A promising basis for the development of a novel, numerically efficient solution without the substantial limitations of analytical methods or look-up table techniques is the semi-analytical Scaled Boundary Finite Element Method (SBFEM). The fundamentals for solving the Reynolds equation with the SBFEM have been derived in preliminary work, but the potential of the approach has not been exploited yet, which is the objective of this project. In order to further reduce the numerical effort, high-order shape functions need to be employed in combination with an automatic, adaptive mesh refinement as well as coarsening and a transformation of the Reynolds equation in a manner that smoothens the solution is analyzed. Another strategy worth investigating is to avoid the repeated solution of eigenvalue problems within the time integration scheme. This requires that the eigenvalue problem is differentiated with respect to the parameters of the shaft displacement and developed into a series prior to the rotordynamic simulation. In order to improve the modeling depth of the SBFEM solution compared to the preliminary work, strategies for incorporating mass-conserving cavitation models as well as shaft tilting need to be investigated. In the last step, the developed methodology is to be verified and analyzed with regard to its efficiency. To ensure a realistic context, this is done within the framework of a rotor dynamics or MBS formulation, whereby complex technical overall systems can also be simulated.

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This project is a cooperation between the Chair of Multibody Dynamics and the Chair of Computational Mechanics with one research assistant from each partner. The core objective of the project is the development of a practical simulation methodology for calculating the noise emissions of engines and their psychoacoustic evaluation. This makes it possible to directly trace the effects of structural modifications (stiffness, mass distribution) and tribological system parameters (bearing clearances, viscosity, deaxialization and filling level) back to the excitation mechanisms and the internal structure-borne sound paths and to preventively combat them in terms of acoustic optimization through design and tribological measures. This purely virtual engineering approach is intended to do entirely without real prototypes and thus enable an acoustic evaluation early on in the engine development process. In this way, design measures to improve acoustic quality can be implemented in coordination with the development groups of adjacent subject areas without negatively influencing other important design criteria such as performance, pollutant emissions or total mass.
In contrast, passive measures to combat noise emissions through insulation, for example, are generally cost-intensive, as they require additional material as well as additional assembly steps and therefore have an impact on the production process. At the same time, this runs counter to the idea of lightweight construction, reduced consumption and environmental friendliness and leads to additional installation space being required, which is usually a very scarce resource in the development of modern engines and automobiles. The fundamental problem with these insulation measures, which are being used more and more frequently these days, is their symptomatic approach, which combats the effect but ignores the causes of the acoustic disturbance.
The holistic methodology that is the focus of this project, on the other hand, makes it possible to directly analyze and combat the cause of the disruptive noise emissions. In addition, the psychoacoustic evaluation of the sound emission allows it to be categorized into disturbing and less disturbing sound emissions. In this way, the design can be specifically modified so that the resulting noise is classified as more pleasant by people; after all, a quiet noise can still be perceived as more disturbing than a loud one.
This text was translated with DeepL

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The aim of this project is to develop an efficient methodology for mapping the non-linear properties of hydrodynamic journal bearings in transient rotor dynamics simulations. This requires an efficient solution of the Reynolds equation, for which the semi-analytical Scaled Boundary Finite Element Method (SBFEM) is used. In this way, the calculation times are to be reduced compared to conventional, numerical methods, without the need to simplify the boundary conditions as in analytical approximations.

The operating behavior of high-speed plain bearing rotor systems is significantly influenced by the non-linear bearing properties. A typical example of this is the occurrence of self-excited, sub-harmonic vibrations. These can impair the service life of the components and lead to increased power loss and critical noise emissions and must therefore be taken into account in the design. This requires a precise analysis of the dynamic behavior, which is often only carried out at a late stage of the product development process using test bench tests. If this reveals defects that require changes to the product to be rectified, the development time is extended and additional costs are incurred. To avoid this, dynamic simulations are increasingly being integrated into the product development process, which allow the operating behavior to be examined even before a prototype is manufactured. The decisive factor here is the realistic representation of the non-linear relationships between the dynamic and hydrodynamic subsystems in the simulation model. For this purpose, the equations of motion are embedded in a time-step method and coupled with the Reynolds equation, which describes the hydrodynamic pressure build-up in the journal bearing. The Reynolds equation is usually solved numerically or based on characteristic maps, as closed analytical solutions are only known for highly simplified cases. A two-dimensional discretization of the lubrication gap is required for the numerical solution, which, in conjunction with the high number of time steps, entails a considerable computational effort. In turn, the map approach is only possible or useful with a limited modeling depth, as each physical effect taken into account increases the interpolation effort. In order to create an efficient alternative to conventional methods, a semi-analytical solution is being developed in this project. The resulting reduction in computing times should contribute to time and cost savings in industrial and scientific applications. The developed methodology is based on the SBFEM and, in contrast to the numerical solution methods, only requires a one-dimensional discretization. The original partial differential equation is converted into an ordinary differential equation system, which can be solved using an exponential approach. To further improve efficiency, the SBFEM solution is combined with various strategies to reduce the required number of degrees of freedom.
This text was translated with DeepL

View project in the research portal

This project is a cooperation between the Junior Professorship of Fluid-Structure Coupling in Multibody Systems and the Chair of Computational Mechanics with one research assistant per partner. The core objective of the project is the development of a practical simulation methodology for the calculation of noise emissions from engines and their psychoacoustic evaluation. This makes it possible to directly trace the effects of structural modifications (stiffness, mass distribution) and tribological system parameters (bearing clearances, viscosity, deaxialization and filling level) back to the excitation mechanisms and the internal structure-borne sound paths and to preventively combat them in terms of acoustic optimization through design and tribological measures. This purely virtual engineering approach is intended to do entirely without real prototypes and thus enable an acoustic evaluation early on in the engine development process. In this way, design measures to improve acoustic quality can be implemented in coordination with the development groups of adjacent subject areas without negatively influencing other important design criteria such as performance, pollutant emissions or total mass.
In contrast, passive measures to combat noise emissions through insulation, for example, are generally cost-intensive, as they require additional material as well as additional assembly steps and therefore have an impact on the production process. At the same time, this runs counter to the idea of lightweight construction, reduced consumption and environmental friendliness and leads to additional installation space being required, which is usually a very scarce resource in the development of modern engines and automobiles. The fundamental problem with these insulation measures, which are being used more and more frequently these days, is their symptomatic approach, which combats the effect but ignores the cause of the acoustic disturbance.
The holistic methodology that is the focus of this project, on the other hand, makes it possible to directly analyze and combat the cause of the disruptive noise emissions. In addition, the psychoacoustic evaluation of the sound emission allows it to be categorized into disturbing and less disturbing sound emissions. This allows the design to be specifically modified so that the resulting noise is perceived as more pleasant by people; after all, a quiet noise can still be perceived as more disturbing than a loud one.
This text was translated with DeepL

View project in the research portal