Browsing by Author "Ebrahimi, Saeed"

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A contribution to computational contact procedures in flexible multibody systems
(2007) Ebrahimi, Saeed; Eberhard, Peter (Prof. Dr.-Ing.)
This thesis is devoted to computational contact procedures in flexible multibody systems. For this purpose, first in Chapter 1 contact problems in multibody systems together with some computational procedures were briefly introduced. Then, in Chapter 2 starting from kinematics and kinetics of rigid bodies, some basic concepts of flexible multibody dynamics including solution algorithms were explained. In this context, some common modeling strategies were briefly explained. Among all, the floating frame of reference has been used in this work to generate equations of motion. This approach is a widely-used method which introduces two kinds of variables for body reference motion and elastic deformations. Chapter 2 ended with giving some notes regarding symbolic and numerical derivation of equations of motion together with numerical integration methods. Some of the most frequently-used formulations for incorporating the contact constraints into the governing equations of motion were introduced briefly in Chapter 3. Among them, the penalty approach, the Lagrange multipliers approach, linear complementarity problem formulations and proximal point approach were mentioned. Contact and impact problem of planar flexible bodies in multibody systems were formulated in Chapters 4 and 5, respectively, yielding the linear complementarity problems. In Chapter 4, the available approach for planar rigid bodies was extended for planar flexible bodies. The major difference between both approaches was in the formulation of contact kinematics. It was also shown that our formulation approaches the LCP formulation developed for rigid bodies when the effect of deformations is ignored. Impact analysis was followed in Chapter 5 by formulating some other LCPs on position and velocity level. The formulations on position level for normal direction was done by imposing non-penetrability conditions through complementarity relations between normal gaps and normal impact forces. In doing so, at first kinematics of impacting bodies was described in terms of generalized coordinates. Some common integration approaches have been further used to find the required relations which represent generalized coordinates as functions of impact forces. Then, this formulation was appended to the formulation of tangential contact forces which was developed for continual contact in Chapter 4. For the velocity level formulation of normal impact, one deals with velocity of normal gaps and the generalized velocities instead of normal gaps and the generalized coordinates. In the case of impact, examples for both short and long impacts were considered. The results showed a good agreement between the results of our approach based on the formulations from the explicit Runge-Kutta approach on position and velocity level and also the RADAU5 approach with the results of FEM. It was shown that the formulations on both position and velocity level approach the precise results of FEM even for stiff planar deformable bodies provided that a proper number of eigenmodes of the FEM model is chosen for building the reduced model of deformable bodies. We also observed that selection of higher number of eigenmodes leads to the lower energy dissipation. Selection of higher eigenmodes allows a better adjustment of the shape of deformable bodies during impact which consequently leads to lower normal impact forces. As a result, the amount of released energy during the expansion phase of impact increases as a higher number of eigenmodes is considered. Then, the modeling of contact and impact of spatial flexible bodies using the Polygonal Contact Model (PCM) approach was explained in Chapter 6. PCM was originally an algorithm of contact of spatial rigid bodies based on the surface compliance approach. In Chapter 6 the extension of PCM as a general algorithm for contact of flexible bodies which establishes a more realistic modeling of many contact problems in multibody systems was explained. It can be summarized that with the extended PCM, contacts between elastic bodies can be considered at only moderate additional costs. As an application of contact modeling in multibody systems, Chapter 7 was devoted to the subject of contact in geared systems. First, the approach for contact modeling of meshing rigid gear wheels was briefly explained. Furthermore, it was extended by introducing some elastic elements between the teeth and the gear body of each gear wheel to consider partially elasticities.