Multibody Dynamics With Abaqus

Prepared by Fuat Koro Energy & Chassis Systems

Presented byFuat Koro10/01/02


Multibody Dynamics

Flexible Multibody Dynamicsu Study of force and motion take

place simultaneouslyu Deals with non-linear structures

whose segments undergo largemotion coupled with deformations

MECHANICSKINETICS

KINEMATICS

DYNAMICS

STATICS

Rigid Multibody Dynamicsu Bodies are assumed to be

incapable of deforming in anymanner

u Relative displacements areassumed not to affect the systemresponse


Inertia Relief Analysis

u D’Alembert’s Principle:– Vector sum of all external forces and inertia forces acting on a rigid body is zero:

ΣF-MaG =0– Vector sum of all external moments and inertia torques acting on a rigid body is

zero:

ΣMG-Ia = 0

u 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)– Perform component-level static finite element analysis


Inertia Relief Analysis


Time History of Loads


Force BalanceForces 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


Variable Valve Actuation Mechanism1- 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


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)

Val

ve L

ift (m

m)


Spring Dynamics


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 5.5220

5000

1 .104

1.5 .104

2 .104

2.5 .104

25000

3

rm3500

5.5235.5 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 .104Dynamic at 3500 rpm vs Quasistatic

104×

103×

rm3quasi3500

5.5235.5 t3500 tquasi3500,

Spring Reaction Moment at3500 rpm

•Filtered

•Quasistatic(Abaqus/Standard)

•Raw output(Abaqus/Explicit)


Spring Design

5.748 5.75 5.752 5.754 5.756 5.758 5.76 5.762 5.7640

5000

1 .104

1.5 .104

2 .104

2.5 .104

104

0

react

5.7635.75 time

5.75 5.752 5.754 5.756 5.758 5.76 5.762

5000

1 .104

1.5 .104

2 .104

2.5 .104

104×

5.75

bandpass

static

5.7635.75 time time, time1,

Spring Reaction Moment at7000 rpm

•Filtered

•Smoothed

•Quasistatic(AbaqusStandard)

•Raw Output(Abaqus/Explicit)


Analysis of Flexible Multibody Dynamics

u Elasto-Dynamics– Deformation is considered uncoupled from the rigid body motion

u 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

u Explicit dynamic finite element formulation– ABAQUS/Explicit


Felxible Multibody Dynamics

u The applications of flexible multibody dynamics systems can befound in various multibody systems with connected rigid andflexible segments:

– aircraft wings

– lightweight spatial structures

– biomechanical systems

– high-speed mechanisms


ABAQUS Approach

u Modeling objective dictates the level of refinement– idealized joints vs. contact modeling– deformable bodies vs. rigid bodies

u Kinematic constraints can be modeled using 2-node connectorelements

– 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

u Any component in the assembly can be modeled as rigid ordeformable

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

u Mass and inertia properties for rigid bodies can be user definedor they can be automatically computed by Abaqus if rigidcomponents are represented using finite elements


Variable Valve Actuation Mechanism


Flexible Multibody Animation


Mobility and Kinematic Constraints

u The number of degrees of freedom, also called the mobility ofthe 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:

HingeHinge

Join

Cylindrical

1 DOF


Resolving Overconstraints


Dynamic Response - Future Work

u Seating velocity– impact between valve and seat at valve closure

u Valve bounce, valve float, valve liftu Dynamic Stresses

– Stress amplification, Fatigue life impact

u Cam profile synthesisu Structural optimization

– System natural frequency

u Maximum speed - redline rpm

Multibody Dynamics With Abaqus

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