Parametric Design

1. Parametric Design • Design phase info flow • Parametric design of a bolt • Parametric design of belt and pulley • Systematic parametric design • Summary

2. Abstract embodiment Physical principles Material Geometry Special Purpose Parts: Features Arrangements Relative dimensions Attribute list (variables) Standard Parts: Type Attribute list (variables) Architecture Configuration Design Configuration Design

3. Information flow Special Purpose Parts: Features Arrangements Relative dimensions Variable list Standard Parts: Type Variable list Design variable values e.g. Sizes, dimensions Materials Mfg. processes Performance predictions Overall satisfaction Prototype test results Parametric Design Detail Design Product specifications Production drawings Performance Tests Bills of materials Mfg. specifications

4. Parametric Design of a Bolt Configuration sketch head tensile force shank threads Mode of failure under investigation: tensile yielding

5. Tensile Force Causing a Permanent Set “proof load” , cross section area A, material’s proof strength , then : (8.1)

6. However, bolt proof load is constrained

7. Finding a feasible area

8. Determining the diameter nominal (standard) size 0.25 in

9. Proof Strength Versus Diameter Infeasible Feasible calculated minimum required

10. What steps did we take to “solve” the problem? • Reviewed concept and configuration details • Read situation details • Examined a sketch of the part – 2D side view • Identified a mode of failure to examine – tensile yield • Determined that a variable (proof load) was “constrained” • Obtained analytical relationships (for Fp and A) • “Juggled” those equations to “find” a value – d Equation “juggling” is not always possible in design, especially complex design problems. (How do you “solve” a system of equations for a complex problem?)

11. Systematic Parametric Design - without “juggling” diameter d proof load >4000 d =0.1 in area = d proof load >4000

12. Motor Pulley (driver) Grinding Wheel Pulley (driven) Belt Design Problem

13. Free Body Diagram of motor pulley/sheave

14. Formulating the parameters • Determine the type of parameter Solution evaluation parameters SEPs Design variables DVs Problem definition parameters PDPs • Identify specifics of each parameter Name (parameter/variable) Symbol Units Limits

15. Table 8.1 Solution Evaluation Parameters think “function”

16. Satisfaction 1.0 0.0 Belt Tension (lbs) 30 35 Satisfaction w.r.t. Belt Tension

17. Satisfaction 1.0 0.0 Center distance c (in.) 20 5 Satisfaction w.r.t. Center distance

18. Table 8.2 Design Variables Think “form”

19. Table 8.3 Problem Definition Parameters think “givens”

20. Parameter values: can be non-numeric, and discrete! not in book, (take notes?)

21. “Formulating” the formulas (constraints) • Recall from sciences: physics, chemistry, materials • Recall from engineering: statics, dynamics, fluids, thermo, heat transfer, kinematics, machine design, circuits mechanics of materials • Conduct experiments

22. Physical Principles (Table 4.3)

23. Analytical relationships

24. System of equations ( for belt analysis)

25. Analysis spreadsheet givens form input function output

26. Satisfying the belt tension constraint Which c value is the best?

27. Overall Satisfaction, Q = weighted rating!

28. Satisfaction Calculations increasing decreasing Qmax

29. Function satisfaction results from form customer satisfaction = f (product function) product function = f (form) + givens SEP = f (DV’s) + f (PDP’s) Example: acceleration of a motorcycle customer satisfaction = f (how “fast” it goes) Acceleration = f (power, wt, trans.) + (fuel, etc)

30. Maximum Overall Satisfaction - Qmax

31. Systematic Parametric Design read, interpret sketch restate constraints as eq’ns guess, ask someone use experience calculate experiment calculate/determine satisfaction select Qmax alternative improve “best” candidate

32. Design for Robustness Methods to reduce the sensitivity of product performance to variations such as: • manufacturing (materials & processes) • wear • operating environment Currently used methods Taguchi Method Probabilistic optimal design Both methods use statistics and probability theory

33. Summary • The Parametric Design phase involves decision making processes to determine the values of the design variables that: • satisfythe constraints and • maximize the customer’s satisfaction. • The five steps in parametric design are: • formulate, • generate, • analyze, • evaluate, and • refine/optimize. • (continued next page)

34. Summary (continued) • During parametric design analysis we predict the performance of each alternative, reiterating (i.e. re-designing) when necessary to assure that all the candidates are feasible. • During parametric design evaluation we select the best alternative (i.e. assessing satisfaction) • Many design problems exhibit “trade-off" behavior, necessitating compromises among the design variable values. • Weighted rating method, using customer satisfaction curves or functions, can be used to determine the “best” candidate from among the feasible design candidates.