Parametric Design

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

Configuration Design

ConfigurationDesign

ConfigurationDesign

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

ParametricDesign

ParametricDesign

Design variable valuese.g. Sizes, dimensions Materials Mfg. processesPerformance predictionsOverall satisfactionPrototype test results

DetailDesignDetailDesign

Product specificationsProduction drawingsPerformance Tests Bills of materials Mfg. specifications

Parametric Design of a Bolt

d

LTL

shank

head

threads

tensileforce

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

pF

pS

pp SAF

However, bolt proof load is constrained

t o b e g r e a t e r t h a n t h e 4 , 0 0 0 ( l b s ) d e s i g n l o a d , o r lbs4000pF ( 8 . 2 )

B y s u b s t i t u t i n g ( 8 . 1 ) i n t o t h e c o n s t r a i n t e q u a t i o n ( 8 . 2 ) , w e o b t a i n : lbs4000pSA ( 8 . 3 )

Finding a feasible area

R e a r r a n g i n g ( r e a r r a n g i n g = “ j u g g l i n g ” )

pS

A000,4 ( 8 . 4 )

)(lbs/in000,85(lbs)000,4

2A ( 8 . 5 )

2lbs/in047.0A ( 8 . 6 )

Determining the diameter

s u b s t i t u t i n g , w e f i n d t h a t

22

in047.04

d ( 8 . 8 )

a n d f u r t h e r , t h a t

22 in0598.0)4(047.0

d ( 8 . 9 )

in.245.0d ( 8 . 1 0 )

nominal (standard) size 0.25 in

Fp versus d

0

2000

4000

6000

8000

10000

12000

0 0.1 0.2 0.3 0.4 0.5

diameter d (in)

Fp

(lbs

)

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 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?)

Systematic Parametric Design - without “juggling”

Determine best alternative

Predict Performance Check Feasibility: Functional? Manufacturable ?

Generate Alternatives

Formulate Problem

Analyze Alternatives

Evaluate Alternatives

Re-Design

Re-Specify

Select Design Variables Determine constraints

Select values for Design Variables

all alternatives

feasible alternatives

best alternative

Refine Optimize

refined best alternative

diameter d proof load >4000

d =0.1 in

area = d proof load >4000

Belt Design Problem

22r1r

c

1111 n,,d,r 2222 n,,d,r

Motor Pulley(driver)

Grinding Wheel Pulley(driven)

1

Free Body Diagram of motor pulley/sheave

1r

2F

1F

1nT1

yB

xBx

y

Formulating the parameters

Determine the type of parameterSolution evaluation parameters SEPsDesign variables DVsProblem definition parameters PDPs

Identify specifics of each parameterName (parameter/variable)Symbol Units Limits

Table 8.1 Solution Evaluation Parameters

Parameter Symbol Units Lower Limit Upper Limit 1 belt torque Tb lb-in Tm - 2 belt tension F1 lbs - 35 3 center distance c in. small -

think “function

”

Satisfaction w.r.t. Belt Tension

1.0

3530Belt Tension (lbs)

0.0

Satisfaction

Satisfaction w.r.t. Center distance

1.0

20Center distance c (in.)

Satisfaction

0.05

Table 8.2 Design Variables

Design Variable Symbol Units Lower Limit Upper Limit 1 center distance c in. small - 2 driven pulley diameter d1 in. - -

Think “form”

Table 8.3 Problem Definition Parameters

Parameter Symbol Units Lower Limit Upper Limit 1 friction coefficient f none 0.3 0.3 2 belt strength Fmax lbs - 30 3 motor power W hp ½ ½ 4 motor pulley diameter d1 in. 2 2

think “givens”

Parameter values: can be non-numeric, and discrete!

Type of valueExample Variable

Values

numerical length 3.45 in, 35.0 cm

non-numericalmaterialmfg. processconfiguration

aluminummachinedleft-handed threads

continuous height 45 in, 2.4 m

discretetire sizelumber size

R75x152x4, 4x4

discrete (binary)

zinc coatingsafety switch

with/withoutyes/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, circuitsmechanics of materials

Conduct experiments

Physical Principles (Table 4.3)

Conservation of energy Archimedes’ principle Ohm’s law Conservation of mass Bernoulli’s law Ampere’s law Conservation of momentum

Boyle’s law Coulomb’s laws of electricity

Diffusion law Gauss’ law Newton’s laws of motion Doppler effect Hall effect Newton’s law of gravitation

Joule-Thompson effect Photoelectric effect

Pascal’s principle Photovoltaic effect Coriolis effect Siphon effect Piezoelectric effect Coulomb friction Thermal expansion effect Euler’s buckling law Hooke’s law Newton’s law of

viscosity

Poisson effect/ratio Newton’s law of cooling Heat conduction Heat convection Heat radiation

Analytical relationships

ioio

oi

tf

NNddSR

PP

rVNF

IMFrT

maFmaF

//

0

0

System of equations ( for belt analysis)

Analysis spreadsheetProblem Definition Parameters

Parameter Sym. Units Value

friction coefficient f none 0.3

belt strength Fmax lbs 35

Motor power W hp 0.5

Motor speed n1 rpm 1800

Motor pulley diameter D1 inches 2

Design Variables

Variable Sym. Units Lower Value Upper

Driven pulley diameter d2 inches - 6 -

center distance c inches 4.0 4 12

Performance Calculations Constraint

Eng. Characteristic Sym. Units Value Type Value Condition

motor torque Tm lb-in 17.51

grinding wheel speed n2 rpm 600 = 600 Satisfied

angle of wrap Φ1 degrees 120.0

belt tension-taut F1 lbs 37.5 <= 35 Unsatisfied

belt tension-slack F2 lbs 20.0

initial belt tension Fi lbs 28.8

belt torque Tb lb-in 17.51 >= 17.51 Satisfied

input

output

function

form

givens

Satisfying the belt tension constraint

Which c value is the best?

Overall Satisfaction, Q = weighted rating!

520

2040

3035

3560 1

c

.F

.Q (8.34)

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

Belt-Puley System Satisfaction Curves

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25

Center Distance c (in.)

Sat

isfa

ctio

n

Belt Tension

Compactness

Overall Satisfaction

Systematic Parametric Design

Determine best alternative

Predict Performance Check Feasibility: Functional? Manufacturable ?

Generate Alternatives

Formulate Problem

Analyze Alternatives

Evaluate Alternatives

Re-Design

Re-Specify

Select Design Variables Determine constraints

Select values for Design Variables

all alternatives

feasible alternatives

best alternative

Refine Optimize

refined best alternative

read, interpretsketchrestate constraints as eq’ns

guess, ask someoneuse experience

calculateexperiment

calculate/determine satisfactionselect 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 methodsTaguchi MethodProbabilistic 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.