Structural Optimization of the Rear Swingarm of Ducati ... · PDF fileswingarm of Ducati...

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

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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.

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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

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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

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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

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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]

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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

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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

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NON DESIGN SPACE

DESIGN SPACE

Finite element model (Design Space)

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Finite element model

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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

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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

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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.

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Feasible Model (Leyni test - Von Mises results)

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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.

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Thanks for the attention