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

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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

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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.

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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

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

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

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

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

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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

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

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

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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)

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Body orientation

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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

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Multibody simulation: kinematic analysis of a suspension

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Geometric modelling

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Constraints, Loads, Forces

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Assembly

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

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Dynamic analysis and Post- processing

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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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