F. Pichler - Multibody dynamics of jointed flexible structures - Phd Thesis, Technische Universität Graz, Austria, 2018
Complex mechanical structures are often an assembly of substructures which are connected by some type of joints, like screwed joints, crimp connections and others. The nonlinear contact and friction forces, which act on the involved surfaces of such joints, may influence the global and local dynamic behavior significantly.
In multibody dynamic simulations, linear flexible bodies are often considered via model order reduction techniques like component mode synthesis. Such reduction methods do not allow an accurate computation of the local deformations inside the latter mentioned joints. Consequently, unrealistic contact and friction forces lead to questionable results in terms of deformations and stresses.
In this thesis, a complete strategy for the efficient and accurate consideration of nonlinear joint forces within flexible multibody dynamics is presented.
For this purpose, the jointed structure is considered as one flexible body in a multibody system. Furthermore, the equations of motion of a flexible multibody system are extended by the vector of generalized joint forces. A computational efficient formulation of these generalized joint forces and the associated terms in the system's Jacobian is derived.
A problem-oriented extension of common reduction basis with so-called joint modes is introduced in order to enable an accurate approximation of the joint deformations. Three different approaches for the computation of these joint modes are presented. All three methods are based on the use of trial vector derivatives and were investigated with respect to the number of required joint modes for accurate results. An accuracy comparable to the finite element method was achieved by a number of joint modes which is up to 95% lower than the number of nodal degrees of freedom inside the joint. Joint modes computed by a stiffness weighted proper orthogonal decomposition of all trial vector derivatives are recommended for practical application. Furthermore, an optimized computation of these joint modes for preloaded structures has been developed.
For the realistic representation of dry friction joint properties different contact and friction models are reviewed. These models have been rated in terms of numerical efficiency and other criteria. Based on different numerical studies, a joint adapted exponential contact penalty model and a three-parameter Coulomb-type friction model are recommended.
In conclusion, the presented strategy permits efficient multibody simulation of jointed flexible structures with a result quality in terms of displacements and stresses comparable to the finite element method. Two exemplary applications from the field of automotive engineering confirm the practical relevance of the presented strategy.