multibody dynamics with abaqus
TRANSCRIPT
Prepared by Fuat Koro Energy & Chassis Systems
Presented byFuat Koro10/01/02
Prepared by Fuat Koro Energy & Chassis Systems
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
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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
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Inertia Relief Analysis
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Time History of Loads
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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
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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
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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)
Val
ve L
ift (m
m)
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Spring Dynamics
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Spring Dynamics
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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 5.5220
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)
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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)
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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
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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
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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
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Variable Valve Actuation Mechanism
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Flexible Multibody Animation
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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
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Resolving Overconstraints
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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