Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems Ali Moghadasi Alexander Held Robert Seifried * Institute of Mechanics and Ocean Engineering Hamburg University of Technology Eißendorfer Straße 42, 21073 Hamburg Germany Email: robert.seifried@tuhh.de In recent years, topology optimization has been used for op- timizing members of ﬂexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for ﬂexible multibody systems is pre- sented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between ﬂexible members in a multibody system using revolute joints is seen in many ap- plications. Moreover, the modeling accuracy of the bearing area is shown to be inﬂuential on the shape of the optimized structure. In this work, the ﬂexible bodies are incorporated in the multibody simulation using the ﬂoating frame of ref- erence formulation, and their elastic deformation is approx- imated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints us- ing Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Fur- thermore, an application example of a ﬂexible multibody sys- tem with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization re- sult is performed with an equivalent system which is modeled with nonlinear ﬁnite elements. Keywords: ﬂexible multibody system, revolute joint, bearing domain, ﬂoating frame of reference, topology opti- mization 1 Introduction A critical issue in the design and utilization of machines such as industrial robots and mechanism is the energy con- sumption. One way to improve the energy efﬁciency is to reduce the moving masses in a dynamic system. However, this often results in the loss of stiffness of components and unacceptable elastic deformations and vibrations. In high- speed or high-precision systems, these deformations might deteriorate the required performance and accuracy. * Address all correspondence to this author. In order to reduce the mass of the members of multi- body system without hindering its performance, different optimization techniques have been proposed and adopted. Shape optimization of ﬂexible multibody systems has been investigated in [1–4]. In [5] the topology optimization of ﬂexible multibody systems is discussed which are modeled using nonlinear ﬁnite element methods. An alternative ap- proach is investigated in [6–8], where the ﬂoating frame of reference formulation is used to incorporate the ﬂexible bod- ies in the multibody system. Using a nonlinear ﬁnite element approach for ﬂexible multibody system, the incorporation of unilateral contact in the bearings is possible through contact elements. However, this approach often requires very high computation time, which is specially crucial in optimization application. Alter- natively, the ﬂoating frame of reference formulation can be used, in which the motion of the ﬂexible body is described by a body-related frame that undergoes large nonlinear mo- tions and rotations with respect to the inertial frame of refer- ence. Additionally, small linear deformations of the ﬂexible body are described with respect to the body-related frame using global shape functions. Limiting the number of global shape functions to a small set which describes the body de- formation sufﬁciently well, the computational effort of the dynamic simulation is reduced. This is especially favorable in an optimization process where the dynamic simulation needs to be performed in every iteration. However, due to the linear approximation of the elastic body deformation, the modeling of unilateral contact, as it occurs in bearings, is not trivial. The modeling and analysis of joints in multibody sys- tems and the effects of clearance have been comprehensively studied for different types of bearings and can be found among others in [9–15]. Depending on the bearing type be- tween ﬂexible bodies, different nonlinear phenomena can oc- cur in the contact area. For example, in a clearance joint, effects such as friction, impact and separation of contact sur-