Successive robust design optimization of an electronic connector

Successive robust design optimization of an electronic connector Dirk Roos dynardo dynamic software and engineering GmbH Ralf Hoffmann & Thomas Liebl Tyco Electronics AMP GmbH

Design for Six Sigma Six Sigma is a concept to optimize the manufacturing processes such that they automatically produce parts conforming with six sigma quality Design for Six Sigma is a concept to optimize the design such that the parts conform with six sigma quality, i.e. quality and reliability are explicit optimization goals 2 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Robust Design Optimization Objective function and additional stochastic constraints 3 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Successive Robust Design Optimization Material limit Limit state function 4 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Process integration reads and writes parametric data to and from all ASCII input of any external solver reads binary parametric data from ABAQUS odb format reads and writes parametric data to EXCEL, CATIA and ANSYS Workbench ANSYS Workbench reads and writes parametric data to and from many CAD software in order to explore a wide range of responses based on a limited number of actual solutions: Autodesk Inventor, CATIA SolidWorks, Solid Edge, Mechanical Desktop, Unigraphics and Pro/ENGINEER 5 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Process integration CAD / PDM ANSYS Workbench Structural Mechanics - Fluid Dynamics - Heat Transfer - Electromagnetics An adaptable multi-physics design and analysis system that integrates and coordinates different simulation tasks Sensitivity Robustness Optimization Reliability Robust Design 6 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Workflow Optimization, Robustness & Reliability Analysis Tyco Electronics CAD-Model (UG;ProE) CAD-Parameter CAD Plug In ANSYS - Workbench Parameter exchange 3D Tolerance Simulation (CeTol) Kinematic Model With rigid body Statistical function ofer geometric parameter Input datas from CeTol into Design Explorer / OptiSlang Process datas Result: statistical function of functional parameter Mathematical model to perform forecast of Robustness & Reliability Geometry-Tolerance Analysis and comparison with manufacturing 7 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Connector Problem description 8 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008 Basic Design Idea: 2 rows with double contacts (2x 10 Contact points) Contact reliablity increased due to parallel contact points Problem description: Contact of each spring and all other springs influenced to each other Contact force influenced by Body deformation Status quo: Optimization and Robustness Analysis by Design Explorer Question: optimized Design to meet contact force > 1N Reliability of optimized Design

Connector Problem description ProE CAD model (with 36 design CAD parameters) ANSYS Workbench model (with 10 contact force response parameters) 9 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Connector Problem description ProE CAD model (with n=36 design CAD parameters) ANSYS Workbench model (with 10 contact force response parameters) Design Explorer only reduced model possible Study single spring DX / optislang Study reduced model DX Study full model optislang 10 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Model single spring Ansys Workbench Simulation Model single spring with Input Geometry Parameter and Result Force Reaction @ Tab (front; rear) most important aim: set up workflow CAD-ANSYS- optislang 11 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Model single spring Comparison Results Design Explorer <-> optislang Response Surface Design Optimization DOE-Design sample type m Goal Driven Opimization d_y1 d_y2 F1 RSO F1 diff F2 RSO F2 diff F1/F1 targ F2/F2 targ CCD CCD Auto Defined 0.271 0.241 3.00 2.93 102.3% 2.98 3.490 85.4% 97.8% 116.3% CCD G-optimized 0.279 0.253 3.09 2.79 110.6% 3.080 2.790 110.4% 93.0% 93.0% Opt Space Filling Auto Defined 0.281 0.256 3.34 2.87 116.4% 3.05 3.030 100.7% 95.7% 101.0% Opt Space Filling full quadratic 0.279 0.253 3.09 2.79 110.8% 2.99 3.198 93.5% 92.8% 106.6% ARSM OptiSlang CCD Aadaptive 0.278 0.254 3.00 3.00 100.0% 3 3.000 100.0% 100.0% 100.0% 12 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Design Explorer Analysis Design Explorer Analysis of Connector with reduced parameter model Input Parameter: (outside and inner springs linked together) Response Parameter: 13 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Design Explorer Analysis of Connector with reduced parameter model Optimization reduced parameter model Target: F > 3N (1N+3s) ( y3=0.01 ) Design Explorer Analysis 14 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Design Explorer Analysis Design Explorer Analysis of Connector with reduced parameter model Robust Design Analysis; Reliability Estimation DOE Central Composite Design mean s UGW OGW F1ov 5.08 0.71 0.82 9.34 F2ov 1.58 0.47-1.23 4.40 F3ov 0.58 0.39-1.75 2.91 F4ov 1.92 0.51-1.16 5.01 F5ov 5.87 0.72 1.53 10.20 F1oh 1.34 0.68-2.75 5.44 F2oh 2.08 0.62-1.65 5.81 F3oh 2.35 0.59-1.21 5.92 F4oh 1.98 0.65-1.91 5.87 F5oh 1.00 0.65-2.91 4.90 100.00% 95.00% 90.00% 85.00% 80.00% 75.00% 70.00% 65.00% 60.00% 55.00% 50.00% 100.00% 95.00% 90.00% 85.00% 80.00% 75.00% 70.00% 65.00% 60.00% 55.00% 50.00% Probability Function front contact all >=4 >=3 >=2 >=1 Probability Function rear contact all >=4 >=3 >=2 >=1 Reliability Target failed 15 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Iterative RDO with optislang ProE CAD model (with n=36 design CAD parameters) ANSYS Workbench model (with 10 contact force response parameters) ANSYS Workbench finite element model with mean number of nodes of 35.660 Mean calculation time 1 hour @ 2 Xeon 2.66 GHz CPU 16 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 1 - Robustness analysis n=31 random CAD parameters Global variance-based robustness analysis Advanced latin hypercube sampling with N=90 parallel finite element calculations Calculation time 20 hours with Distributed calculation of ANSYS Workbench on 8 Xeon 2.66 GHz CPUs 17 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 1 - Robustness analysis First global variancebased robustness evaluation Identification of n=15 most important design parameters 18 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 1 - Robustness analysis Performance critical contact force F3o_v With failure probability of 89 %! Large Number of numerical outliers 19 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 2 - Optimization n=15 most important CAD design parameters Deterministic optimization Minimal distance function approach defines optimal weighted objectives with objective term definition & scaling & weights Target contact forces are result from six sigma analysis based on the histograms 20 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 2 - Optimization Adaptive response surface method with D-optimal linear DOE N=126 parallel finite element calculations Calculation time 25 hours with Distributed calculation of ANSYS Workbench on 8 Xeon 2.66 GHz CPUs 21 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 2 - Optimization Stagnation of the objective improvement after the 5th adaption Performance critical contact force F3o_v 22 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 3 feasible design search Introducing of constraints to obtain a feasible start design Using an Evolutionary Algorithm N=391 parallel finite element calculations Calculation time 80 hours 23 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 3 feasible design search Increasing the performance critical contact force F3o_v 1.6 N -> 2.3 N Decreasing of the non-critical contact force F2o_h 3.1 N -> 1.0 N 24 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 4 Design improvement Target: Increasing of the non-critical contact force F2o_h Adaptive response surface method with D-optimal linear DOE Start design is based on best design resulting the EA optimization Start design range only 20 % of the total design space N=172 parallel finite element calculations Calculation time 35 hours 25 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 4 Design improvement Increasing the non-critical contact force F2o_h 3.1 N -> 1.0 N -> 1.6 N All mean contact forces are larger than the limit state of 1 N! 26 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 5 - Robustness analysis n=36 random CAD parameters Global variance-based robustness analysis of the optimized design Advanced latin hypercube sampling with N=50 parallel finite element calculations Calculation time 10 hours 27 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 5 - Robustness analysis 28 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 5 - Robustness analysis Performance critical contact force F3o_v With failure probability 9 %! Contact force F2o_h with failure probability 1 %! 29 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Results Robustness Analysis Failure probabilities of the other contact forces lesser than 1% Design without numerical outliers 30 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 6 - Reliability analysis Identification of n=12 most important random parameters using coefficients of importance Defining the limit state condition for violation the minimal number of 10 contact forces More than 50% of the contact forces are lesser than 1N Using APDL command 31 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Step 6 - Reliability analysis Reliability analysis using ARSM with N=137 D-optimal design of experiment Adaptive sampling on the MLS surrogate model without samples in the unsafe domain Probability of failure is near zero Optimized design is an Six Sigma Design 32 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Results Variance and probability-based robust design optimization with n=36 random CAD parameters Increasing the performance critical contact force F3o_v according failure probability 89% -> 9% Failure probabilities of the other contact forces lesser than 1% System failure probability (more than 50% of the contact forces are lesser than 1) is near zero! (Six Sigma Design) Optimized design without numerical outliers N=950 parallel finite element calculations Total calculation time 1 week 33 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008

Benefits significance of robust design optimization Identify product design parameters that are critical to achieve a performance characteristic Quantify the effect of variations on product behavior and performance Adjust the design parameter to hit the target performance Reduces product cost Understanding potential sources of variations Minimize the effect of variations (noise) Qualify possible steps to desensitize the design to these variations More robust and affordable designs Cost-effective quality inspection No inspection for parameters that are not critical to performance 34 Weimarer Optimierungs- und Stochastiktage 5.0, 20./21. November 2008