Vehicle Dynamics & Safety: Multibody System Simulation tools based on MultiBody approach are widespread in vehicle design and testing
Vehicle Dynamics & Safety: Multibody System What is a Multibody System? System consisting of rigid or flexible parts connected by joints and undergoing large displacements: mechanisms, vehicles, trains. F M
Multibody Approach What is the MB approach? The MultiBody approach is a set of tools that allows the (automatic) writing/solution of the equations 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.
Multibody System MB Systems of different topologies must be analyzed Constraints must be reproduced System Forces must be modelled Rigid as well as deformable bodies/elements must be available
Topology of MB System A MB system can have an open chain (left, robot PUMA Programmable Universal Machine for Assembly) or a closed chain (right, slider-crank mechanism) structure
Constraints Constraint must be modelled Constraints reduce the system d.o.f: Gruebler Formula: dof=6*n_body-n_constr
Constraints Incastro: fixed joint Cerniera: revolute /pin /hinge joint Manicotto: collar Carrello: roller/rocker Pattino: slider C. sferica: spherical joint G. cardanico: Hookean/Universal joint
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 (zxz). 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.) Equilibrium position (static analysis) 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 Postprocessing
MSC ADAMS -MD Adams (Mech. Dynamics, later Multi- Domain ), now MSC Adams is a commercial software developed from a research software by Orlandea (1973 University of Michigan, Ann Arbor). -It s an acronym of Automatic Dynamic Analysis of Multibody Systems.
MSC ADAMS It consists of three main modules and several vertical application: Adams Pre for data input, modelling Adams Post for results analysis (graphs, animations..) Adams Solver for equations assembly and solution (static, kinematic, dynamic sim.) All these modules are integrated in ADAMS- View
MSC ADAMS Customized version for special purpose applications: ADAMS Car, Chassis, Driveline Solver modules (plugins): Linear (eigenmodes, eigenfrequency), Vibration (frequency response), Flex (flexible Bodies), Durability (computation of stresses in def. Bodies).
MSC ADAMS Adams Control allows the introduction of simple control systems in simulation. With Mechatronics ADAMS can be used for co-simulation with Matlab Simulink (or Easy5) Control system Mechanical system
MSC Adams The Adams/View Modeling database is a hierarchical (binary) database. Each object in the database has an object that owns it, called its parent, and many objects own other objects, called their children. The top level objects in the database are models, views, plots, and libraries containing such things as dialog boxes.
MSC Adams
Testi di consultazione: A. Shabana, Dynamics of Multibody Systems, Wiley. D. Negrut, ADAMS Theory in a nutshell G. Legnani, Robotica industriale, Casa Editrice Ambrosiana.