ME317 dfM at Stanford ©2006 K. Ishii Design for Manufacturability ME317 dfM Robust Design Fundamentals Kos Ishii, Professor Department of Mechanical Engineering Stanford University “Robust means product & process insensitive to noises” Genichi Taguchi, 1985

ME317 dfM at Stanford ©2006 K. Ishii Today’s Agenda nNext Four Lectures: ROBUST DESIGN 1. Robust Design Introduction--simple examples 2. Design of Experiments (DoE) / Taguchi Method 3. Variation Patterns / Confounding, Case Study 4. Robust Conceptual Design (Dr. Russell Ford) nToday: Robust Design Fundamentals  Concept of Robustness  DoE Basics  Cantilever Example: Using Analytical Models

ME317 dfM at Stanford ©2006 K. Ishii What’s Robustness? nSeek candidate design whose performance is insensitive to variation nFocus on variation that affect performance  Manufacturing variation  Deterioration of parts/materials  Environmental variables nIllustrative Examples  Kos’ Rectangular Cookie  Force Sensor (Cantilever Beam Structure)  Profile Modified Helical Gears  CD Pickup Mechanism (Dynamic Performance)

Robust Dimensional Fit nEXAMPLE  Design a hood hinge with excellent alignment  Low manufacturing and assembly cost nSOURCES OF VARIANCE  Manufacturing variation  Assembly errors

ME317 dfM at Stanford ©2006 K. Ishii Robustness Optimization nPeak vs. Robust Optimum Parameter X P R R h P l  R l P h Objective Function L Probability TIP ROOT START ROLL ANGLE AMT. OF RELIEF

ME317 dfM at Stanford ©2006 K. Ishii Robust Design Philosophy System--Parameter--Tolerance nSYSTEM DESIGN Function Requirements  System Configuration  Russell Ford’s Lecture nPARAMETER DESIGN System Configuration  Detailed Design  Hit Target Response while Minimize Variation nTOLERANCE DESIGN Detailed Design  Tolerance Specification  Tighten tolerances sensitive to performance variation but insensitive to cost

ME317 dfM at Stanford ©2006 K. Ishii Robust Design Approach nThe Principles of Parameter Design  Use a limited set of experiments to determine the design sensitivities  Design the product and process to minimize the sensitivity of the quality measures to noise nTolerance Design  Tightening tolerance induces higher control cost  Applied after parameter design  Tighten the tolerance of most sensitive variables

ME317 dfM at Stanford ©2006 K. Ishii Noise and Loss nControl Factors:  Designers have control, e.g., parameter set points nNoise Factor:  Designers do not have control  Need to minimize effects on performance nTypes of Noise Factors:  External (outer): environmental noise  Unit to Unit (product): mfg. variations  Deterioration (inner): changes in the product

ME317 dfM at Stanford ©2006 K. Ishii Example: Noise Factors nNoise Factors for braking distance of a car  External  wet or dry road  Unit-to-Unit Variation  friction characteristics of brake pads  Deterioration  wear of brake pads

ME317 dfM at Stanford ©2006 K. Ishii Loss Function nVarious Form of Loss Functions mm+² 0 m-² 0 Step mm+² 0 m-² 0 Quadratic nQuadratic Loss functions:  Nominal-is-Best: k(y-m) 2  Smaller-is-Best: ky 2  Larger-is-Best: k(1/y 2 )

ME317 dfM at Stanford ©2006 K. Ishii nMany forms of criteria (Nominal-is-Best Case)  Average Loss = S 2 = variance, m = target performance = mean Robustness Objective Criteria

ME317 dfM at Stanford ©2006 K. Ishii Robust Design Basics 1. Establish the concept configuration  Dr. Russell Ford’s Lecture 2. Define performance goals 3. Identify factors which influence performance  Classify into categories  Draw Cause-and-effect diagram  Select factors that form the basis of experiments nImportant to consider all possible factors  May need to identify significant factors and iterate nUtilize analytical / numerical models if available

ME317 dfM at Stanford ©2006 K. Ishii Force Sensor Example nStep 1: Design Concept  Cantilever Bar + Strain Gauge nStep 2: Robust objective  Hit the target stiffness!

ME317 dfM at Stanford ©2006 K. Ishii Identify pertinent variables nStep 3: Cause & Effects Diagram (Ishikawa Dia.)  List all the variables that influence performance  Classify significant control and noise parameters

ME317 dfM at Stanford ©2006 K. Ishii Factors in the Force Sensor Example nControl Factors: b, h, L ( L < 2 inch) nNoise Factors:  Thickness h: inch  Width b: inch  Length L: inch nGoal  Minimize variation on stiffness  Target Objective: K 0 =0.05 lb/in L±  L b±  b h±  h Material: Aluminum E = 1.25x10 7 psi Strain Gauge

ME317 dfM at Stanford ©2006 K. Ishii Closed Form Approach The “Rectangular Cookie” Problem nIf there is a closed form expression  Could lead to analytical solutions  E.g. for the force sensor: X Y A nVery simple example:  A = X Y  Target A0  Noise on X and Y  Find target X and Y that Minimize Variation

ME317 dfM at Stanford ©2006 K. Ishii Derive the Robustness Criteria nRelate performance variation to noise 0 1

ME317 dfM at Stanford ©2006 K. Ishii Find the robust optimum nFind the value of X that minimizes variation on A

ME317 dfM at Stanford ©2006 K. Ishii An Example Cookie A0 = 8;  x = 0.2;  y =

ME317 dfM at Stanford ©2006 K. Ishii How about Numerical Optimization nUse simulation and optimization methods 2 4

ME317 dfM at Stanford ©2006 K. Ishii Force Sensor Example Closed Form Approach nDefine a “cost function” = variation in K  VERY IMPORTANT STEP nMonotonicity Analysis of V  Determines L nUse expression for target K and relate b and h  Expression of V on one variable, b of h  Set dV/dh = 0 or dV/dh = 0 and find the optimum

ME317 dfM at Stanford ©2006 K. Ishii Robust Design of Helical Gears Using Computational Models nObjectives  Minimize transmission error  Indication of noise and vibration  Use gear profile modification nDesign variables in profile modification TIP ROOT START ROLL ANGLE AMT. OF RELIEF

Performance Contour Plots of Transmission Error Peak to Peak Transmission Error Weighted Objective Function

ME317 dfM at Stanford ©2006 K. Ishii nVariations (Simulated with DoE matrix*)  ” in tip relief  1.5 degrees in roll angle  Shaft misalignment of ”  Torque variations of 25% * L8 is one type of DoE matrix, to be explained in next lecture Helical Gear Example