Dynamics & Vibration 3

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conference time (CEST, Berlin)
Modal Analysis of Planetary Gearsets
27/10/2021 10:40 conference time (CEST, Berlin)
Room: J
J. Haslinger (MathConsult GmbH Kompetenzzentrum Ind. Math., AUT); G. Offner, M. Sopouch, B. Zinkiewicz (AVL List GmbH, AUT)
J. Haslinger (MathConsult GmbH Kompetenzzentrum Ind. Math., AUT); G. Offner, M. Sopouch, B. Zinkiewicz (AVL List GmbH, AUT)
This contribution deals with modal analysis - the computation of eigenfrequencies and eigenmodes - of a multibody systems, which is based on the linearization of the equation of motions at a loaded state. Special emphasis is taken on transmission systems of automotive applications, especially the modal analysis of planetary gearsets (PGS). In general, the multibody system representing the PGS consists of rigid and/or flexible bodies. These bodies are interconnected by nonlinear elements (joints), which represent forces and moments from radial and axial bearings and from gear interactions. In order to obtain the standard quadratic eigenvalue problem which has to be solved for eigenvalues and mode shapes, a linearization by a first order Taylor approximation is used. The linearization includes the FEM based body mass, damping and stiffness matrices in case of an elastic body. Additional terms may result from linearization of the inertia forces and the joint forces. The linearization of the joint forces and moments yields contributions to the linearized stiffness and damping matrices. Most parts of the linearization of the equations of motion are computable analytically, especially the linearization of the inertia forces. For joint types, where no explicit and a rather simple functional relationship is given, as for instance inner and outer gearing in the PGS, the partial derivatives of the joint forces with regard to node positions and velocities are approximated by the method of finite differences. A standard finite difference method for computing the joint stiffness matrix is rather time consuming. Therefore, an approach will be presented, which halves the number of gear joint evaluations when taking the geometrical properties of the joint into account. Furthermore, the desired properties of the stiffness matrix as symmetry and positive definiteness are enforced. They allow the selection of the most suitable eigenvalue solver for this class of matrices which further reduces the overall computation time compared to solving a general eigenvalue problem. The approach is applied to a typical engineering task of a PGS, which consists of the central sun gear, the ring gear (fixed in the gearbox housing) and three planets. Gear meshes are taken into account by contact models resolving all relevant details of the multi-flank-contact. The effect of the helix angle on the eigenfrequency distribution is investigated in detail.
modal analysis, eigenfrequencies, mode shapes, linearization, automotive application, transmission system, planetary gearsets
conference time (CEST, Berlin)
Fast Thermal Heat-Up Simulation of Hydrodynamic Lubricated Journal Bearings
27/10/2021 11:00 conference time (CEST, Berlin)
Room: J
N. Lorenz (MathConsult GmbH Kompetenzzentrum Ind. Math., AUT); G. Offner (AVL List GmbH, AUT); D. Jaitner (AVL Deutschland GmbH, DEU)
N. Lorenz (MathConsult GmbH Kompetenzzentrum Ind. Math., AUT); G. Offner (AVL List GmbH, AUT); D. Jaitner (AVL Deutschland GmbH, DEU)
Hydrodynamic journal bearings are key components in internal combustion engines, transmissions, as for instance those in wind turbines, and geared aircraft turbofans. The prediction of their reliability, durability and economy, but also friction loss power and wear are highly important. In particular the thermal behaviour of the bearing and its surroundings has a direct impact on friction and lubrication in the bearing. The lubricant properties are influenced by its thermal conditions on one hand. On the other hand, the thermal conditions are influenced by the mixed lubricated contact conditions as well. These interactions require a coupled modelling approach, which combines the component flexibility and its interaction with load carrying capacity as well as the thermal behaviour. In this work a thermo-elasto-hydrodynamic contact model is presented, which computes the temperature distribution within the thin viscous lubrication film and the temperature in the neighbouring bearing shell and journal structures. The oil film temperature is solved by using an averaged 2D energy equation; it considers temperature and pressure dependent density, cavitation because of partly filled gaps, energy transport due to conduction and convection, thermal expansion, internal friction as well as asperity friction caused by the direct contact of bearing structures. The bearing shell and journal structure temperatures are based on the three-dimensional thermal conduction equation with material dependant properties and contain the heat source due to dry asperity contact. Different types of boundary and interface conditions can be applied to the model, in order to have a flexible modelling approach for a wide range of applications. A heating acceleration algorithm was developed based on the coupled thermal model. This acceleration algorithm reduces the simulation time from the initial start temperature to the steady operating temperature in a comparably very short time.
Engineering simulation, heat transfer, journal bearings, thermo-elasto-hydrodynamic, flexible multi-body dynamics, mixed-lubrication, asperity friction, temperature equation