MULTIOBJECTIVE OPTIMIZATION OF AUTOMOTIVE VEHICLE GAGE PANEL - - PowerPoint PPT Presentation

International Conference on Vibration Problems – 2011, September 5-8, 2011, Prague, Czech Republic

Anatolijs Melnikovs* anatolijs.melnikovs@inbox.lv Alexander Janushevskis* Janis Auzins* Anita Gerina-Ancane** Janis Viba**

*RTU - Riga Technical University Machine and Mechanism Dynamics Research Laboratory M M D Z P L

6, Ezermalas, : +371 67089396 Riga, LV-1006 Fax: +371 67089746 Latvia

www.mmd.rtu.lv/zpla.htm janush@latnet.lv ** Riga Technical University, Institute of Mechanics

M I

MULTIOBJECTIVE OPTIMIZATION OF AUTOMOTIVE VEHICLE GAGE PANEL

INTRODUCTION

Frontal view of gage panels

• f AMOPLANT vehicles:

*Pictures from AMOPLANT Ltd page: http://www.amoplant.lv

1) 2) 3) RIGA OLD TOWN* *

Manufacturing requirements:

• Vibrostability of gage panel (Frequency range 10

– 250 Hz; acceleration level 50 m/s2)

• Gage panel shock resistance (acceleration level

100 m/s2)

3D GEOMETRICAL MODEL OF INITIAL DESIGN OF GAGE PANEL (GP)

The 3D geometrical model consists of 18 parts:

6 deformable bodies and 12 rigid bodies

Calculated inertial properties of GP:

Mass = 1.024189 [kg] Volume = 0.000778 [m3] Surface area = 0.730695 [m2] Center of mass: [ m ] X = 0.053455 Y = 0.031768 Z = -0.036300 Principal axes of inertia and principal moments of inertia: [kg] *[m2] Ix = (0.999996, -0.002695, 0.000849) Px = 0.003885 Iy = (-0.000739, -0.539488, -0.841993) Py = 0.011049 Iz = (0.002727, 0.841989, -0.539488) Pz = 0.013953

FINITE ELEMENT MODEL OF GAGE PANEL

The FE mesh: curvature based mesh

max elements size = 9 mm, min element size = 1.8 mm, element size growth ratio =1.5

GP materials: >ABS 2020 plastic >Alloy steel Model meshed with second-order tetrahedral elements Parabolic solid element STATIC ANALYSIS.The FE mesh consists of ~ 210,000 nodes, ~147,000 elements, ~630,000 DOF

STATIC ANALYSIS OF GP: MAXIMAL STRESSES FROM IMPACT LOAD

Von Mises stresses distribution due to vertical acceleration GP most loaded parts (von Mises stress > 0.9 [MPa] a = 100 m/s^2

STATIC ANALYSIS OF GP: DISPLACEMENTS and STRAINS FROM IMPACT LOAD a = 100 m/s^2 GP displacements from vertical acceleration GP strains from vertical acceleration

FREQUENCY ANALYSIS OF GP OF INITIAL DESIGN

Mode No. Freq (Hertz)

1

99,393

2

150,81

3

222,08

4

230,9

5

264,6

6

317,71

7

363,23

8

395,18

9

446,07

10

478,14

11

529,14

12

560,59

13

591,11

14

608,39

15

640,98

Directional Mass Participation

FREQUENCY ANALYSIS OF GP. MODES ANIMATION

> Modal damping ratio is assumed 0.03

HARMONIC ANALYSIS OF GP

f(t) = A sin (ω t + α) > Frequency range 10<ω<700 [Hz] > Multi-Degree-of-Freedom system: > Total DOF = 392 000

The peak steady state response of GP due to base excitations:

Amplitudes of vertical displacements at the defined points of GP

HARMONIC ANALYSIS OF GP

TIME HISTORY ANALYSIS OF GP

Polyharmonic load on GP: Transient behavior of GP at characteristic points:

Von Mises stress at the center of GP bracket Velocity of the GP at the center point Displacement of the GP at the center point

∑

+ ⋅ + + ⋅ = )) cos( ) sin( ( ) (

2 2 1 1

β α t w A t w A C t f

i

RANDOM VIBRATIONS OF GP

Statistical loads on GP:

PSD of von Mises stress at the center of GP bracket Acceleration power spectral density (PSD)

> The frequency range 10< ω<500 [Hz] > 15 lower modes are taken to account

RANDOM VIBRATIONS OF GP

PSD of vertical displacements at the defined points of GP

RANDOM VIBRATIONS OF GP

PSD of vertical acceleration at the defined points of GP

SUSTAINABILITY ANALYSIS OF GP

MULTIOBJECTIVE OPTIMIZATION OF GP BRACKET

Geometry modeling by SolidWorks (SW) Design of Experiments by EDAOpt¹ Initial GP design 1.Design variables 2.Constraints FEM calculations by SW Simulation

• 1. Static analysis – impact loads
• 2. Dynamic analysis:

Harmony analysis Time history analysis

• 3. Frequency analysis
• 4. Sustainability analysis

Approximation,

• ptimization by EDAOpt¹

Responses

• 1. Optimal shape

geometry by SW

• 2. Checking results of
• ptimization by SW

Simulation

EDAOpt¹ - software for design of experiments, approximation and optimization developed in RTU

Optimal design variables

T k x

x F x F x F x F )] ( ),..., ( ), ( [ ) ( min

2 1

=

( )

≤ x g j

( )

= x hl

n

E x∈

The problem is stated as follows: subject to , j=1, 2,…, m, and , l=1, 2, …, e, where k is number of objective functions Fi; m is the number of inequality constraints; e is the number of equality constraints and is a vector of n design variables.

Random vibrations analysis

METHOD USED TO DEFINE CROSS SECTION SHAPE

1) Cross-section shape definition with B-spline knot points 2) 3D- shape creation through path curve Design parameters are NURBS knot points Ranges of Design Parameters: 3) Shape of the bracket (The same on the left bracket)

SHAPE DEFINITION OF BRACKET: 3 ≤ X 1 ≤ 9; 1.5 ≤ X 2 ≤ 6; 1.5 ≤ X 3 ≤ 4

2 1 3

The LH design of experiment is calculated with MSD (mean-square distance) criterion for 3 factors and 40 trial points

THE DESIGN OF EXPERIMENT

Second order local polynomial approximation: Weighted Least Squares Method

∑

∈ ∧

− × − =

X

N j j j j

x y y x x w

2

)) ( ( ) ( min arg

β

β

Approximation quality estimation with crossvalidation error coefficient

2 1 1 2

) ( 1 1 ) ) ( ( 1 % 100 y y n y x y n

i n i n i i i i Xrel

− − − =

∑ ∑

= = − ∧

σ

ε β β β β

∑ ∑ ∑ ∑

= = − = + = ∧

+ + + + =

d i i ij d i d i d i j j i ij i i

x x x x y

1 2 1 1 1 1

Gauss weight function

const u u w = − = ) ) ( 5 . exp( ) (

2

α α

APPROXIMATION OF RESPONSES

Constraints:

] X[ 2 ) ( ) ( ) (

2 3 1 2 3 2 2 2 1

MPa

vonMises

< − + − + − = σ σ σ σ σ σ σ 1) On maximal equivalent stresses in the GP brackets at the defined cross -section points: Cross -section check points: Y1;Y2;Y3;Y4;Y5 < X [MPa]

2) On GP eigenfrequencies Objective functions: 1) v -Volume of the GP 2) Displacements at check points 3) Parameters of environmental pollution MULTIOBJECTIVE OPTIMIZATION OF GP BRACKET

SHAPE OPTIMIZATION OF GP BRACKETS

Constraints: A)Y1;Y2;Y3;Y4;Y5 < 1.4; [MPa] B) Y1 < 1.2 [MPa] and all constraints active Objective functions: 1) v -Volume of the disk 2) max displacements at characteristic points 3) Parameters of environmental pollution

A) B)

Volume = 166880 [mm3] Volume = 167151 [mm3]

OPTIMIZATION OF GP BRACKET

Cross – sections of criterions surfaces and active constraints for variant B

RESULTS OF SHAPE OPTIMIZATION OF GP BRACKET

Initial design of GP Optimized design of GP

Von Mises stress distribution in considered cross-section

Mode No. Freq (Hertz) Initial New

1

99,393 122,65

2

150,81 166,47

3

222,08 233,24

4

230,9 254,51

5

264,6 270,28

6

317,71 367,86

7

363,23 409,5

8

395,18 418,51

9

446,07 488,53

10

478,14 516,69

FREQUENCY ANALYSIS COMPARISON

Initial design

HARMONIC ANALYSIS COMPARISON

Vertical displacements at the defined check points of GP

New design

• The first results of simulation and optimization of the

vehicle GP are presented

• The smooth easy technologically realizable shapes are
• btained by current approach
• The jagged forms are excluded from optimization process

and there's no need for the excessive computational resources

• The most time consuming step of the current approach is

implementation

• f

computer experiments with FEM analysis for building of metamodels of the GP responses. Then solution of several single objective problems and realization

• f

different aggregation strategies for multiobjective optimization are relatively easy, to obtain an acceptable final solution

CONCLUSIONS

Thanks for your attention!