MULTIOBJECTIVE OPTIMIZATION OF AUTOMOTIVE VEHICLE GAGE PANEL - PowerPoint PPT Presentation

International Conference on Vibration Problems – 2011, September 5-8, 2011, Prague, Czech Republic MULTIOBJECTIVE OPTIMIZATION OF AUTOMOTIVE VEHICLE GAGE PANEL 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 M I ** Riga Technical University, Institute of Mechanics

RIGA OLD TOWN* INTRODUCTION Frontal view of gage panels of AMOPLANT vehicles: 1) 2) * 3) *Pictures from AMOPLANT Ltd page: http://www.amoplant.lv

Manufacturing requirements: • Vibrostability of gage panel (Frequency range 10 – 250 Hz; acceleration level 50 m/s 2 ) • Gage panel shock resistance (acceleration level 100 m/s 2 )

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 [m 3 ] Surface area = 0.730695 [m 2 ] Center of mass : [ m ] X = 0.053455 Y = 0.031768 Z = -0.036300 Principal axes of inertia and principal moments of inertia : [kg] *[m 2 ] 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

GP materials: FINITE ELEMENT MODEL OF GAGE PANEL >ABS 2020 plastic >Alloy steel The FE mesh: curvature based mesh max elements size = 9 mm, min element size = 1.8 mm, Model meshed with second-order element size growth ratio =1.5 tetrahedral elements STATIC ANALYSIS.The FE mesh consists of ~ 210,000 nodes, ~147,000 elements, ~630,000 DOF Parabolic solid element

STATIC ANALYSIS OF GP: MAXIMAL STRESSES FROM IMPACT LOAD a = 100 m/s^2 Von Mises stresses distribution due to vertical acceleration GP most loaded parts (von Mises stress > 0.9 [MPa]

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 Directional Mass Participation 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

FREQUENCY ANALYSIS OF GP. MODES ANIMATION

HARMONIC ANALYSIS OF GP The peak steady state response of GP due to base excitations: > Multi-Degree-of-Freedom system: > Total DOF = 392 000 > Frequency range 10< ω <700 [Hz] f(t) = A sin ( ω t + α ) > Modal damping ratio is assumed 0.03

HARMONIC ANALYSIS OF GP Amplitudes of vertical displacements at the defined points of GP

Transient behavior of GP at TIME HISTORY ANALYSIS OF GP characteristic points: Polyharmonic load on GP : ∑ ( ) ( sin( ) cos( )) = ⋅ + α + ⋅ + β f t C A w t A w t 1 1 2 2 i Velocity of the GP at the center point Von Mises stress at the center of GP bracket Displacement of the GP at the center point

RANDOM VIBRATIONS OF GP Statistical loads on GP : > The frequency range 10< ω <500 [Hz] > 15 lower modes are taken to account Acceleration power spectral density (PSD) PSD of von Mises stress at the center of GP bracket

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 The problem is stated as follows : min ( ) = [ ( ), ( ),..., ( )] T F x F x F x F x 1 2 k x ( ) ( ) 0 ≤ g j x 0 = h l x , j =1, 2,…, m , and , l =1, 2, …, e, subject to where k is number of objective functions F i ; m is the number of inequality constraints; e is the number of equality constraints x ∈ E n is a vector of n design variables. and Optimal design variables Initial GP design Approximation, 1.Design variables optimization by EDAOpt¹ 2.Constraints Responses 1. Optimal shape geometry by SW FEM calculations by SW 2. Checking results of Simulation Design of optimization by SW Experiments by 1. Static analysis – impact loads Simulation EDAOpt¹ 2. Dynamic analysis: � Harmony analysis � Time history analysis � Random Geometry modeling 3. Frequency analysis vibrations analysis by SolidWorks (SW) 4. Sustainability analysis EDAOpt ¹ - software for design of experiments, approximation and optimization developed in RTU

METHOD USED TO DEFINE CROSS SECTION SHAPE Design parameters are NURBS knot points 1 Ranges of Design Parameters: 3 ≤ X 1 ≤ 9; 1.5 ≤ X 2 ≤ 6; 1.5 ≤ X 3 ≤ 4 SHAPE DEFINITION OF BRACKET: 1) Cross-section shape definition with B-spline knot points 2 3 2) 3D- shape creation through 3) Shape of the bracket path curve (The same on the left bracket)

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

APPROXIMATION OF RESPONSES Second order local polynomial approximation: 1 − d d d d ∧ ∑ ∑ ∑ ∑ 2 = β + β + β + β + ε y x x x x 0 i i ij i j ij i 1 1 1 1 i = i = j = i + i = Weighted Least Squares Method Approximation quality estimation with crossvalidation error coefficient 1 n ∧ ∧ ∑ ∑ 2 ( ( ) − ) y x y arg min ( ) ( ( )) 2 β = − × − w x x y y x − i i i 0 j j j n β 100 % = 1 σ = i ∈ j N X Xrel 1 n ∑ 2 ( − ) y y Gauss weight function i 1 − n u = 1 i ( ) exp( 0 . 5 ( ) 2 ) α = − w α = u const

MULTIOBJECTIVE OPTIMIZATION OF GP BRACKET Objective functions: 1) v -Volume of the GP 2) Displacements at check points 3) Parameters of environmental pollution Constraints: 1) On maximal equivalent stresses in the GP brackets at the defined cross -section points: ( ) 2 ( ) 2 ( ) 2 σ − σ + σ − σ + σ − σ σ = < X[ ] 1 2 2 3 1 3 MPa vonMises 2 Cross -section check points: Y1;Y2;Y3;Y4;Y5 < X [MPa] 2) On GP eigenfrequencies

SHAPE OPTIMIZATION OF GP BRACKETS A) Volume = 166880 [mm 3 ] B) Volume = 167151 [mm 3 ] 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

OPTIMIZATION OF GP BRACKET Cross – sections of criterions surfaces and active constraints for variant B

RESULTS OF SHAPE OPTIMIZATION OF GP BRACKET Optimized design of GP Initial design of GP Von Mises stress distribution in considered cross-section

FREQUENCY ANALYSIS COMPARISON Mode No. Freq (Hertz) Initial New 122,65 1 99,393 166,47 2 150,81 233,24 3 222,08 254,51 4 230,9 270,28 5 264,6 367,86 6 317,71 409,5 7 363,23 418,51 8 395,18 488,53 9 446,07 516,69 10 478,14

HARMONIC ANALYSIS COMPARISON Initial design New design Vertical displacements at the defined check points of GP

CONCLUSIONS •The first results of simulation and optimization of the vehicle GP are presented •The smooth easy technologically realizable shapes are obtained 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 of computer experiments with FEM analysis for building of metamodels of the GP responses. Then solution of several single objective problems and realization of different aggregation strategies for multiobjective optimization are relatively easy, to obtain an acceptable final solution

Thanks for your attention!