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ME317 dfM at Stanford ©2006 K. Ishii Design for Manufacturability ME317 dfM Robust Design Fundamentals Kos Ishii, Professor Department of Mechanical Engineering Stanford University ishii@stanford.edu http://me317.stanford.edu “Robust means product & process insensitive to noises” Genichi Taguchi, 1985

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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

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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)

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

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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

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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

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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

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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

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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

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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 )

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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

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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

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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!

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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

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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: +0.0001 inch Width b: +0.001 inch Length L: +0.005 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

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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

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

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

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ME317 dfM at Stanford ©2006 K. Ishii An Example Cookie A0 = 8; x = 0.2; y = 0.1 2 4

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

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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

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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

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

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ME317 dfM at Stanford ©2006 K. Ishii nVariations (Simulated with DoE matrix*) 0.00015” in tip relief 1.5 degrees in roll angle Shaft misalignment of 0.0005” Torque variations of 25% * L8 is one type of DoE matrix, to be explained in next lecture Helical Gear Example

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