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1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 1
Stefano Verzelli, Simone Di Piazza
DUCATIMOTOR HOLDING S.p.A.
Structural Optimization of the
Rear Swingarm of Ducati
HyperMotard
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 2
Summary
•Introduction
•Topology optimization problem
•Boundary conditions
•Material properties
•Finite element model
•Topology optimization analysis and results
•Conclusions
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 3
Introduction
Today the use of structural optimization methods can be very useful to obtain a proper and efficient solution. These methods can reduce the development process and improve the quality of the final product. Solutions that in the past were generated with several loops by designers and engineers, now can be found easily using FE optimization tools.
This presentation shows the methodology used to design the swingarm of Ducati Hypermotard.
Using Altair OptiStruct, Ducati has developed an efficient structure with a high stiffness to weight ratio, respecting the constraints given by the stylists.
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 4
During the Topology Optimization process, the material is considered to be porous. A relative density 0<ρ<1 is associated to each element, representing the contribution of this element to the stiffness of the component.
In order to satisfy the design constraints and the objective of the optimization, according to the load cases, the elements’density are variously distributed on the model.
The purpose of the optimization process is to obtain the most efficient configuration for the component’s structure.
The results of the analysis sometimes need to be interpreted in order to have a feasible component.
The Topology Optimization Problem
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 5
Boundary ConditionsTwo different load cases were used for this optimization:
• Fatigue test (Leyni test bench)• Bending and Torsional Stiffness
The Leyni test was simulated using the following scheme:
125.025°
97.787°
Rocker
Reaction rod
Rear swingarm
Fma
FaShock absorber
Radial runoutSwingarm pivot
Rear wheel pin
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 6
Boundary Conditions (Bending Stiffness)
Bending Stiffness has been evaluated using the following formula:
[N/mm]|| Y
K F yBending =
Vehicle coordinate system
Y
Fy
y
x
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 7
Boundary Conditions (Torsional Stiffness)
Torsional Stiffness has been evaluated using the following formula:
Fy
Rear wheel hub lenght Lb
yz
Vehicle coordinate system
Rigid elements
Δz2
l
e
Δz1 α
B
ZZ
L
yTorsion
LK F
21180
*Δ−Δ
=π
[Nm/deg]
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 8
The material used for the simulation is an aluminium alloy (EN AC 42100 UNI EN 1706) with the following mechanical properties:
E = 72400 MPaν = 0.33ρ = 2.7 e-6 Kg/mm3
σY = 210 MPa
Accordingly with these values we have used a fatigue limit underreversed stress of 70 MPa.
Material properties
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 9
Finite element modelThe model counts 486102 nodes and 1830077 linear tetra elements: rigid elements were used to simulate hinges and to apply loads.
hingesBending/torsional beam
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 10
NON DESIGN SPACE
DESIGN SPACE
Finite element model (Design Space)
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 11
Finite element model
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 12
Topology OptimizationThe purpose of the topology optimization was to maximize swingarmtorsional stiffness, minimizing its mass.It was necessary to try several different analysis setup, changing design constraints, manufacturing constraints and objective.
AnalysisManufacturing
ConstraintsDesign Constraints Objective
1 Use of MINDIM controlUpper Boundary limits on Bending&Torsion Stiffnesses
Upper Boundary Von Mises Leyni testminimize mass
2Use of DISCRETE = 3.0 and
CHECKER 1 controlsUpper Boundary limits on Bending&Torsion Stiffnesses
Upper Boundary Von Mises Leyni testminimize mass
3Use of DISCRETE = 3.0 and
CHECKER 1 controlsUpper Boundary limit on MASS minimize WCOMP
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 13
Results – Analysis 1
Vertical distribution of material
Horizontal distribution of material
AnalysisManufacturing
ConstraintsDesign Constraints Objective
1 Use of MINDIM controlUpper Boundary limits on Bending&Torsion Stiffnesses
Upper Boundary Von Mises Leyni testminimize mass
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 14
Results – Analysis 2
Horizontal distribution of material
Vertical distribution of material
AnalysisManufacturing
ConstraintsDesign Constraints Objective
2Use of DISCRETE = 3.0 and
CHECKER 1 controlsUpper Boundary limits on Bending&Torsion Stiffnesses
Upper Boundary Von Mises Leyni testminimize mass
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 15
Results – Analysis 3
Vertical distribution of material
Horizontal distribution of material
Vertical distribution of material
AnalysisManufacturing
ConstraintsDesign Constraints Objective
3Use of DISCRETE = 3.0 and
CHECKER 1 controlsUpper Boundary limit on MASS minimize WCOMP
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 16
Feasible Model
vertical wall
horizontal wall
The optimization results were combined in order to obtain a morefeasible topology for the rear swingarm.A new model has been constructed, based on this interpretation.The following images shown the new F.E.M. model in detail.
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 17
Feasible Model (Leyni test - Von Mises results)
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 18
Conclusions
•Optistruct allowed us to find the most efficient design, satisfying the stylistic constraints;
•Stiffness results (bending & torsional) are fully satisfying and reached the desired targets;
•Resulting part mass was only 4.8kg;
•The component is stressed uniformly below material limits with asuitable safety factor;
•Topology optimization allowed us to reduce the design time.
1st European HyperWorks Technology Conference – Berlin, Germany October 23-24, 2007 19
Thanks for the attention