Vehicle Dynamics

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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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Vehicle Dynamics Safety Multibody System

• What is a Multibody System?
• System consisting of rigid or flexible parts
  connected by joints and undergoing large
  displacement mechanisms, vehicles, trains .

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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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Multibody System

• 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

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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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Constraints
Constraint must be modelled Constraints reduce
the system d.o.f Gruebler Formula
dof6n_body-n_constr
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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