# Vehicle Dynamics & Safety: Multibody System Simulation tools based on MultiBody approach are widespread in vehicle design and testing.

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Vehicle Dynamics & Safety: Multibody System Simulation tools based on MultiBody approach are widespread in vehicle design and testing

F M What is a Multibody System? System consisting of rigid or flexible parts connected by joints and undergoing large displacement: mechanisms, vehicles, trains …. Vehicle Dynamics & Safety: Multibody System

Multibody Approach What is the MB approach? The MultiBody approach consists in the automatic writing of the equation of motion of a MB system, starting from a description of the system itself. Different systems can be analyzed by the same software, as opposed to a dedicated approach.

MB System of different topologies must be analyzed Constraints must be reproduced System Forces must be modelled Rigid as well as deformable bodies must be available Multibody System

Topology of MB System A MB system can have an open chain (left, robot) or a closed chain (right, slider-crank mechanism) structure

Constraint must be modelled Constraints reduce the system d.o.f: Gruebler Formula: dof=6*n_body-n_constr Constraints

System forces Bodies exchange forces also through springs, dampers or more sophisticated elements (like tyres….)

Deformable bodies FEM discretization, followed by modal analysis and choice of relevant modes

MultiBody System coordinates To define the position of a MB system a reduced set of indipendent coordinates (joint) can be used or an extended/full set (body coordinates) of dependent coordinates

Joint coordinates Four bar linkage: 3 coordinates and 1 dof Two scalar constraint equations

Body coordinates Four bar linkage: 9 coordinates and 1 dof Eight scalar constraint equations

Body coordinates Body position in 3D is described by position of one point ( 3 dof, centre of mass) and by orientation (3 angles). Euler or Cardan conventions are used. In vehicle dynamics Roll(x)-Pitch(y)-Yaw(z)

Body orientation

Multibody simulation: classes of problems Kinematic analysis: position, velocity acceleration when no dof exists (forces have no influence on motion….) Dynamic analysis: nonlinear, linear (small oscillations, frequency response) Sensitivity/parametric analysis Optimization

Multibody simulation: kinematic analysis of a suspension

Geometric modelling

Assembly

Kinematic analysis Position, velocity and acc. analysis. Range of motion, workspace, collisions …

Dynamic analysis and Post- processing

Modellistica e Simulazione dei Sistemi Meccanici Testi di consultazione: A. Shabana, Dynamics of Multibody Systems, Wiley. G. Legnani, Robotica industriale, Casa Editrice Ambrosiana. Esercitazioni Le esercitazioni consistono nella risoluzione numerica di problemi tramite Matlab e ADAMS. Modalità desame Lesame consiste in un colloquio orale

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