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Design for Manufacturability ME317 dfM Robust Parameter Design using the Design of Experiments

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Design for Manufacturability ME317 dfM Robust Parameter Design using the Design of Experiments

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    1. Design for Manufacturability ME317 dfM Robust Parameter Design using the Design of Experiments

    2. Robustness and DOE... “What do you do when you don’t have a good analytical model that relates the variables and output?”

    3. Agenda See ‘N Say Too difficult to develop a numerical model Must resort to experiments Robust Design: Design of Experiments DoE: Basics Orthogonal Arrays Fractional Factorials Inner / Outer Array Experiments Next Week (Please note sequence change) Conceptual Robust Design Robust Design Case Study / Confounding

    4. DoE Robustness Process 1. Establish the concept configuration 2. Define performance goals 3. Identify factors which influence performance 4. Set ranges of factors to study 5. Design a set of experiments Use orthogonal arrays to determine the effect of each factor on mean and variance Inner--Outer array to analyze environmental effects (often called Blocking) 6. Build Models required by plan, run tests 7. Analyze results by analysis of variance

    5. Robust Design by Experiments: Goal Use a limited set of experiments to determine the design sensitivities Design the product and process to minimize the sensitivity of quality measures to environment

    6. Factorial Experiments Analyze the effects of variables simultaneously Two-level factorial: monotonic and mostly linear Design of Experiments

    7. More Precisely... Taylor Series Expansion of Y around yo Y = f(A, B, C)

    8. Full Factorial Experiments Full Factorial Experiments Estimate all the main and interaction effects Number of experiments multiply Three factors at two levels: 23 = 8 Seven factors at two levels: 27 = 128

    9. Fractional Factorial Experiments Fractional Factorial Experiments Neglect higher order interactions mean + A + B + C + AB + BC + AC + ABC Interactions confounded with main effects can be dangerous Smaller number of experiments Three factors at two levels: 23-1 = 4 runs Seven factors at two levels: 27-4 = 8 runs

    10. Orthogonal Arrays For any pair of columns, all combinations of factor levels occur, and occur an equal number of times.

    11. Derive the Sensitivities using Orthogonality Add all 4 equations y0 is mean of Yi

    12. Taguchi’s Orthogonal Array Eight Run Orthogonal Array: up to 7 factors at two levels (27-4 runs)

    13. Three Level Arrays Nine Run Orthogonal Array: up to 4 factors at 3 levels (34-2 runs)

    14. Interaction Effects If value of A influences sensitivity of B Interaction! Need to consider factor AB

    15. A Numerical Example Three factors at two levels A = Ao + a B = Bo + b C = Co + c Identify range 90 < Ao < 110 8 < Bo < 12 0.8 < Co <1.2 Environment Variables (Blocks) a = + 1.0 b = + 0.1 c = + 0.01

    16. Plan the Experiment Assign columns Enter Values

    17. Let’s say we collected 4 data per trial (Production Setting) A = 90; B = 8.0; C = 0.8 Data 1: Y = 13.8 Data 2: Y = 13.9 Data 3: Y = 13.25 Data 4: Y = 15.26 Analysis of Mean and Variance Ymean Variance

    18. Systematic Study of Noise Effects Inner Array Factorial for Control Factors Outer Array Factorial for Environmental Factors Simulation of how environment affects each design Lab experiments with much tighter control

    19. L4-L4 Array Spreadsheet Template available on ME317 website

    20. Y (B1) = (Y1 + Y2) /2 = (14.064 + 25.98) /2 = 20.02 Y (B2) = (Y3 + Y4) /2 = (11.551 + 71.179) /2 = 41.365 Back to the Example Compute the Mean (Use Orthogonality)

    21. Mean Response All factors affect mean

    22. Variance Response Which factors affect variance?

    23. Four Types of Control Factors Classify based on effects to the response

    24. Strategy of Parameter Design Strategy Select levels of class I and II to reduce variations Select class III to adjust mean to target value Set class IV at the most economical level Big assumption: no significant interactions

    25. Strategy for the Example All Parameters affect the Mean Parameter C Affects Variance most (Category I) Set at C=C? for least sensitivity Parameter A Also affects Variance (Category I) Set at A=A? for least sensitivity Parameter B Little effect on Variance (Cat. III) Use this to adjust response

    26. What about See’N Say? Noise Factors Spring Stiffness Belt Tension Control Factors Rotor Ball Bearing Size (3) Friction Pad (3) Pad Placement (3) Rotor Pulley Diameter (3) Design of Experiments Full Factorial requires 81 prototypes! Actually made 9 prototypes. Caution: Beware of Confounding! This lecture ignored interactions DoE requires careful planning; Will address in next lecture

    27. HW#3 Steps 1 and 2 Apply Orthogonal Arrays to Force Sensor Analyze L4 inner and L4 outer Inspect L8 inner and L4 outer Use excel template on the web

    28. HW #3 Robust Design of a Helicopter Competition for longest flight time! Use DOE to optimize

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