Vehicle Dynamics & Safety: Multibody System

Simulation tools based on MultiBody approach are widespread in vehicle design and testing

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• 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 modelledConstraints 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 coordinatesFour 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

Constraints, Loads, Forces

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 d’esame• L’esame consiste in un colloquio orale