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

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

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

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

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

However, bolt proof load is constrained

Finding a feasible area

Determining the diameter nominal (standard) size 0.25 in

Infeasible Proof Strength Versus Diameter Feasible minimum calculated required

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 F p 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?)

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

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

Free Body Diagram of motor pulley/sheave

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

Table 8.1 Solution Evaluation Parameters think “function”

Satisfaction w.r.t. Belt Tension Belt Tension (lbs) 0.0 Satisfaction

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

Table 8.2 Design Variables Think “form”

Table 8.3 Problem Definition Parameters think “givens”

Parameter values: can be non-numeric, and discrete! Type of valueExample VariableValues numericallength3.45 in, 35.0 cm non-numerical material mfg. process configuration aluminum machined left-handed threads continuousheight45 in, 2.4 m discrete tire size lumber size R75x15 2x4, 4x4 discrete (binary) zinc coating safety switch with/without yes/no, (1,0) not in book, (take notes?)

“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

Physical Principles (Table 4.3)

Analytical relationships

System of equations ( for belt analysis)

Analysis spreadsheet input output function form givens

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

Overall Satisfaction, Q = weighted rating!

Satisfaction Calculations increasing decreasing Qmax

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)

Maximum Overall Satisfaction - Qmax

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

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

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

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.