parametric design design phase info flow parametric design of a bolt parametric design of belt and...
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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.