Multibody Dynamics With Abaqus

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Prepared by Fuat Koro Energy & Chassis Systems

Presented by

Fuat Koro

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Multibody Dynamics

Flexible Multibody Dynamics

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Study of force and motion take

place simultaneously

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Deals with non-linear structures

whose segments undergo large

motion coupled with deformations

MECHANICS

KINETICS

KINEMATICS

DYNAMICS

STATICS

Rigid Multibody Dynamics

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Bodies are assumed to be

incapable of deforming in any

manner

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Relative displacements are

assumed not to affect the system

response

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Inertia Relief Analysis

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D’Alembert’s Principle:

– Vector sum of all external forces and inertia forces acting on a rigid body is zero:

Σ

F-Ma

_G

=0

– Vector sum of all external moments and inertia torques acting on a rigid body is

zero:

Σ

M

_G

-Ia = 0

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Analysis Steps:

– Select a component

– Identify worst case loading from motion simulation

– Extract forces from a rigid multibody dynamic analysis. (Abaqus, ADAMS,

DADS)

– Assign loads in Abaqus (inertia loads are in the form of gravity and rotational acceleration loads)

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Force Balance

Forces in x direction -3000 -2000 -1000 0 1000 2000

1.50E-02 1.70E-02 1.90E-02 2.10E-02 2.30E-02 2.50E-02 2.70E-02 2.90E-02

time spring.X joint.X rff.X roll.X body.X sum.X

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Variable Valve Actuation Mechanism

1- Cylinder head 2 - Output cam 3 - Coupler 4 - Rocker 5 - Double torsion spring 6 - Camshaft 7 - Rocker roller 8 - Cam 9 - Control shaft arm 10 - Control shaft 11 - Slide Pin 12 - Variable-Length Ground Link

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Valve Lift Curves

0 1 2 3 4 5 6 7 8 9 10 80 100 120 140 160 180 200 220 240

Camshaft Rotation (degrees)

V al ve L ift (m m )

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Spring Design

5.498 5.5 5.502 5.504 5.506 5.508 5.51 5.512 5.514 5.516 5.518 5.52 5.522 0 5000 1 .104 1.5 .104 2 .104 2.5 .104 25000 3 rm3500 5.523 5.5 t3500 5.5 5.502 5.504 5.506 5.508 5.51 5.512 5.514 5.516 5.518 5.52 5.522 5000 1 .104 1.5 .104 2 .104 2.5 .10104 4 Dynamic at 3500 rpm vs Quasistatic × 103 × rm3quasi3500 5.523 5.5 t3500 tquasi3500,

Spring Reaction Moment at

3500 rpm

•Filtered

•Quasistatic

(Abaqus/Standard)

•Raw output

(Abaqus/Explicit)

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Spring Design

5.748 5.75 5.752 5.754 5.756 5.758 5.76 5.762 5.764 0 5000 1 .104 1.5 .104 2 .104 2.5 .104 104 0 react 5.763 5.75 time 5000 1 .104 1.5 .104 2 .104 2.5 .104 104 × 5.75 bandpass static

Spring Reaction Moment at

7000 rpm

•Filtered

•Smoothed

•Quasistatic

(Abaqus

Standard)

•Raw Output

(Abaqus/Explicit)

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Analysis of Flexible Multibody Dynamics

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Elasto-Dynamics

– Deformation is considered uncoupled from the rigid body motion

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Component Mode Synthesis

– Dynamic substructuring using ABAQUS/ADAMS

– Linear finite element theory

» No nonlinearities due to geometry, materials and boundary conditions

– Moving reference frame approach

– Stress-stiffening effects can be incorporated if modes are extracted after a

nonlinear analysis

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Explicit dynamic finite element formulation

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Felxible Multibody Dynamics

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The applications of flexible multibody dynamics systems can be

found in various multibody systems with connected rigid and

flexible segments:

– aircraft wings

– lightweight spatial structures

– biomechanical systems

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ABAQUS Approach

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Modeling objective dictates the level of refinement

– idealized joints vs. contact modeling

– deformable bodies vs. rigid bodies

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Kinematic constraints can be modeled using 2-node connector

elements

– Connection types include basic and assembled kinematic pairs.

» BEAM,WELD,HINGE,UJOINT,CVJOINT,TRANSLATOR,CYLINDRICAL,PLANAR

» LINK,JOIN,SLOT,SLIDE-PLANE,CARTESIAN,RADIAL-THRUST,AXIAL

» ALIGN,REVOLUTE,UNIVERSAL,CARDAN,EULER,CONSTANT VELOCITY, ROTATION,FLEXION-TORSION

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Any component in the assembly can be modeled as rigid or

deformable

– Helps in understanding the impact of component stiffness in system response

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Mass and inertia properties for rigid bodies can be user defined

or they can be automatically computed by Abaqus if rigid

components are represented using finite elements

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Mobility and Kinematic Constraints

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The number of degrees of freedom, also called the mobility of

the device needs to be known to prevent overconstraints.

– Kutzbach criterion: m=3(n-1)-2j₁-j₂ (planar)

m=6(n-1)-5j₁-4j₂-3j₃-2j₄-j₅ (spatial)

– Planar 4-bar linkage example:

Hinge

Join

Cylindrical

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Dynamic Response - Future Work

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Seating velocity

– impact between valve and seat at valve closure

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Valve bounce, valve float, valve lift

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Dynamic Stresses

– Stress amplification, Fatigue life impact

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Cam profile synthesis

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Structural optimization

– System natural frequency