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## Parametric Design

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### Design variables DVs. Problem definition parameters PDPs. Identify specifics ... Design ... Probabilistic optimal design. Both methods use statistics and ... – PowerPoint PPT presentation

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Title: 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
Configuration Design
3
Information flow
Special Purpose Parts Features
Arrangements Relative dimensions Variable
list Standard Parts Type Variable list
Parametric Design
Design variable values e.g. Sizes, dimensions
Materials Mfg. processes Performance
predictions Overall satisfaction Prototype test
results
Detail Design
Product specifications Production
drawings Performance Tests Bills of materials
Mfg. specifications
4
Parametric Design of a Bolt
Configuration sketch
tensile force
shank
Mode of failure under investigation tensile
yielding
5
Tensile Force Causing a Permanent Set
proof load , cross section area A,
materials 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
minimum
calculated
required
10
What steps did we take to solve the problem?
• Reviewed concept and configuration 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
d 0.1 in
12
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 w.r.t. Belt Tension
17
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
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 (DVs)
f (PDPs)
• 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
eqns
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
• satisfy the constraints and
• maximize the customers 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.