Engineering 11
ParaMetric
Design
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-11: Engineering Design
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
OutLine  ParaMetric Design
 Design phase info flow
 Parametric design of a bolt
 Parametric design of belt & pulley
 Systematic parametric design
 Summary
Engineering-11: Engineering Design
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Configuration Design
Abstract embodiment
Physical principles
Material
Geometry
Configuration
Design
Architecture
Special Purpose Parts:
Features
Arrangements
Relative dimensions
Attribute list (variables)
Standard Parts:
Type
Attribute list (variables)
Engineering-11: Engineering Design
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Information Flow
Parametric
Design
Design variable values
e.g. Sizes, dimensions
Materials
Mfg. processes
Performance
predictions
Overall satisfaction
Prototype test results
Engineering-11: Engineering Design
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ConFig Design
Special Purpose Parts:
Features
Arrangements
Relative dimensions
Variable list
Standard Parts:
Type
Variable list
Detail
Design
Product specifications
Production drawings
Performance Tests
Bills of materials
Mfg. specifications
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Engineering 11
Real Life
Application
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
3x00 S2-§19
Seismic Protection
Bruce Mayer, PE
Dir. System Engineering
19Feb02
Engineering-11: Engineering Design
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EarthQuake
– Magnitude 8.0
– Kurile Islands
– 03Dec1995
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
3x00 Seismic Protection Analysis Plan
 Measure/Calc Weight and Center of Gravity
 Consult S2/§19 for Lateral Loading Criteria (0.63g)
 Consult Mechanical Design Drawing for Seismic
Structural-Element Location & Configuration
 Use Newtonian Vector Mechanics to Determine
Force & Moment Loads
 Use Solid-Mechanics Analysis to Determine
Fastener (Bolt) Stresses
 Use Mechanical-Engineering &
Materials Properties to determine
Factors of Safety
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
BMayer
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
3x00 S2Testing: Tatsuno Japan, Dec01
3x00_S2S8_Tatsuno_PhotoDoc_0112.ppt
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
3x00 Seismic
Loading & Geometry
BMayer
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Loading Geometry Detail
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
OverTurning Analysis
 Analysis Parameters:
1. Worst Case → SHORTEST Restoring-Moment
Lever-Arm
–
Lever Arms= 582mm, 710mm, 776mm (see slides 4&5)
2. Vertical (resisting/restoring) Acceleration of 0.85g
per SEMI S2 §19.2.4
3. Horizontal (overturning) Acceleration for non-HPM
equipment of 0.63g per §19.2.2
 Results → Safe From Overturning WithOUT
Restraints (but not by much!)
Pivot
Axis
OverTurning
Line Direction Moment (N-m)
R-S
P-Q
Y
X
6884
6884
Engineering-11: Engineering Design
Restoring
Moment (N-m)
Factor of
Safety
6966
8504
1.01
1.24
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
12
3x00_Seismic_Analysis_0202.xls
Bracket Stress
Analysis
2.22 kN
 Analysis Parameters
1. Assume Failure Point
at M6 or M10 Bolts
2. FOUR (4) Angle Brackets With
a total of 8 Connecting & Anchor Bolts, Resist Shear
3. Two Bolts Per Point, Each Bolt Bears 50% of Load
4. Bolt Axial-PreLoad is negligible (Snug-Fit)
5. Shear Load Per Restraint Point = 500lb/2.22kN
6. Use Von Mises Yield Criteria: Ssy = 0.577Sy
 Results
Bolt
Size & Fcn
M6 Connector
M10 Anchor
Engineering-11: Engineering Design
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3x00_Seismic_Analysis_0202.xls
Ssy Load Stress, 
Bolt
Material (MPa)
(MPa)
SS-304
SS-304
139.1
139.1
13.84
4.74
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Factor of
Safety
10.1
29.4
ParaMetric Bolt Design
 From Analysis Determine Failure Mode
as AXIAL TENSILE YIELDING (E45)
 The Configuration Design Sketch
L
head
Load
d
shank
Engineering-11: Engineering Design
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LT
Load
threads
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Use Engineering Analysis
 Force Load, Fp, That Causes a
“Permanent Set” in a specific-sized Bolt
is Called the “Proof Load” (N or lbs)
 The “Proof Stress”, Sp, is the ProofLoad divided by the supporting Material
Area, A (Pa or psi)
 Mathematically the Axial Stress Eqn
S p  Fp A  Fp  AS p
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Use Engineering Analysis
 Using ENGR36 Methods Determine the
Bolt Load as 4000 lb (4 kip)
 Thus the “Functional
F

4000
lbs
p
Requirement” for the Bolt
 To Actually Purchase a Bolt we need to
Spec a DIAMETER, d, and a length, L
 Find d Using the FR & Stress-Eqn
4000 lbs
AS p  Fp  4000 lbs  A 
Sp
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Design DECISION
 We Now need to make a Design
Decision – We get to CHOOSE
• Bolt MATERIAL  Gives Proof Stress
• Bolt DIAMETER  Gives Supporting Area
 In this Case Choose
FIRST a Grade-5,
Carbon-Steel Bolt
with Sp = 85 000 psi
(85 ksi)
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Bolt Grade DEFINES Bolt Size
 Use Sp and the FR to find the Bolt Area
4000 lb
2
A
 A  0.047 in
2
85000 lb in
 Relate A to d
using Geometry
Acircle  r 2 
d 2
4
 Since Bolts Have Circular X-Sections
A
d 2
4
 0.047 in
Engineering-11: Engineering Design
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2
 d 
2

4 0.047 in 2


d  0.245 in
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Spec Bolt
 We can PICK any Grade-5 Bolt with a
Diameter >0.245”
• To Keep down the Bulkiness of the
Hardware choose d = ¼” (0.25”)
 Thus We Can Specify the Bolt as
• Grade-5
• ¼-20 x 6”
– CHOOSE Coarse Thread (the “20”)
– CHOOSE a Bolt Length of 6” based on size
of Parts Connected
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Forward & Inverse Analysis

As Design Engineers we Can
approach the quantitative Functional
Requriments (FR’s) in Two Ways
1. Forward ≡ Guess & Check
– Set the ENGR-Spec and then Check if the FR
is Satisfied (The Seismic Case)
 e.g; Guess a ½-12 Grade-2 bolt & chk Sp
2. Inverse
– Start with FR and Use Math & Science to
effectively DETERMINE the ENGR-Spec
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
ParaMeterization
 The Bolt Design Problem, After
Selecting Grade-5 Material, depends on
the Bolt DiaMeter as a PARAMETER
 The Bolt Proof Load as a Fcn of d
Fp  S p
 S p  2 
kip  2

  d  66.8 2   d
4
in 

 4 
d
2
 This ParaMetric Relationship can be
displayed in a plot
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
ParaMetric Design of a Bolted Joint
12
PARAMETERS
• Grade-5 Steel
• Sp =85 ksidc
NOT Feasible
10
FEASIBLE
Proof Load (Kip)
8
6
4
Functional Requirement
2
0
0.00
0.05
0.10
Bolt_Design_Parametr_d-F_0907.xls
Engineering-11: Engineering Design
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0.15
0.20
0.25
0.30
0.35
Bold Diameter (in)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
0.40
Inverse Analysis ReCap
 The Steps used to Find Bolt Diameter
•
•
•
•
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 (stretching) yield
• Determined that a variable (proof load) was
“constrained” to a Maximum value by its Function
• Obtained analytical relationships for Fp and A
• “Reduced” those equations to “find” a value  d
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Reduction Limitations
 Many times such an Orderly Physical
Reduction is NOT Possible
• Science & Math may not provide clear
guidance; e.g.,
– There is NO Theory for Turbulent Flow
– Many Times Design-Engineering is AHEAD of
the Science; e.g., the First Planar Transistor
• We have 10000+ possible Decisions
– Not Sufficient time to do ALL of them
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Formulate
Problem
Re-Specify
Re-Design
Reduction-Free
Bolt Design
Select Design Variables
Determine constraints
diameter d
proof load >4000
Generate
Alternatives
Select values for Design Variables
all
alternatives
Analyze
Alternatives
Predict Performance
Check Feasibility: Functional? Manufacturable ?
 The
“FORWARD”
Determine best alternative
process
Need to change
feasible
alternatives
Evaluate
Alternatives
best
alternative
d =0.1 in
Refine
Optimize
area = 0.008 in2
load < 668
either SIZE or
MATERIAL
• Use “Guess &
Check”
refined best
alternative
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Before Next Example…
 Take
a
Short
BREAK
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Example  Flat-Belt Drive Sys
 Functional Requirements for Buffing
Wheel Machine
• 1800 rpm, ½ HP Motor
• 600 rpm Buff Wheel Speed
 Constraints
• Belt/Pulley
CoEfficient of Friction = 30%
• Max Belt Tension = 35 lb
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Example  Flat-Belt Drive Sys
 Goals
• Slip-before-Tear for
Belt (FailSafe)
• DRIVE Pulley
(motor side) to Slip
Before Driven Pulley
• High Power Efficiency
• Compact System
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
System Diagram
Motor Pulley
(driver)
Grinding Wheel Pulley
(driven)
r1 ,d1 ,1 ,n1
r2 ,d 2 ,2 ,n2
1
r1
NOTE:
n → Spin
Speed (RPM)
Engineering-11: Engineering Design
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r2
c
2
NOTE:
d = 2r
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
FreeBody Diagram of Drive Pulley
y
F2
 Some
Physics
T  r1 F 1 F 2 
r1
n1
1
Bx
By
T
x
P  Tn1
1 

B x  F1  F2 cos 90  
2

1 

B y  F1  F2 sin  90  
2

F
1
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Solution Evaluation Parameters
 The SEP’s are those Quantities that we
can Measure or Calculate to Asses How
well the Design meets the System
CONSTRAINTS and GOALs
 In This case
• Tb  Check for Belt SLIPPING (ENGR36)
• F1  Check for Belt BREAKING
– Manufacturer’s Data
• c  Check for COMPACT System
– Our (or Customer) Judgement
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Summarize SEPs




If Belt SLIPS then Tb < Tmotor
If Belt BREAKS then F1 > 35 lbs
If System is compact then c ≈ “small”
Summarize SEPs in Table
Parameter
Symbol
Units
1
Belt Torque
Tb
in-lb
--
Tm
2
Belt Tension
F1
lbs
--
35
3
Center Distance
c
in.
small
--
Engineering-11: Engineering Design
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Lower Upper
Limit LImit
Item
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Design ParaMeters (Variables)
 Design ParaMeters, or Variables, are
those quantities that are under the
CONTROL of the DESIGN ENGINEER
 In This Case there are Two DPs; the
Center-Distance & Driven-Pulley Dia.
 Summarize DPs in Table
Parameter
Symbol
Units
1
Center Distance
c
in
small
--
2
Driven Pulley Dia.
d2
in
--
--
Engineering-11: Engineering Design
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Lower Upper
Limit LImit
Item
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Problem Definition ParaMeters
 PDP’s are those quantities that are
Fixed, or “Given” by the Laws of
Physics or UnChangeable System
Constraints. In this Case the “Givens”
Parameter
Symbol
Units
1
Friction Coefficient
f
--
0.03
0.3
2
Belt Strength
Fmax
lbs
--
35
3
Motor Power
W
Hp
½
½
4
DRIVE Pulley Dia.
d1
in.
2
2
5
Driven Pulley Spd
n2
rpm
600
600
Engineering-11: Engineering Design
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Lower Upper
Limit LImit
Item
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis/Solution Game Plan
1.
2.
3.
4.
5.
6.
7.
8.
Calc Buffing Wheel Diameter, d2
Calc Motor Torque, Tm
Calc (F1 – F2)
DECIDE Best Estimate for Ctr-Dist, c1
Calc Angles of Wrap, φ1 & φ2
Calc F1 by Friction Reln (c.f. ENGR36)
Calc F2
Calc The Initial belt Tension, Fi
Engineering-11: Engineering Design
35
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Mechanically The SPEED RATIO Sets
the DiaMeter Ratio - use to find d2
n1 d 2
1800 d 2



 d 2  32 in   6 in
n2 d1
600 2 in
 Thus the MINIMUM Center Distance
cmin
d1 d 2 2 in 6 in
 


2 2
2
2
 1 in  3 in  4 in
Engineering-11: Engineering Design
36
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Since we do NOT want the Pulleys to
RUB, Estimate c = 4.5 in.
 Next Calc Motor Torque using Motor
Power. From Dyamnics (PHYS 4A)
P  Tn  Tm  P n
 Need to take Care with Units
• ½ hp = 373 W = 373 N·m/s
• 1800 rpm = 60π rads/s
– Note that radians are a PURE Number
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 With Consistent Units Calc Tm
373 N  m s
Tm 
 1.979 N  m  17.52 in  lb
60 rad s
 Now by PHYS4A or ENGR36
Tm
T  r1 F 1 F 2   Tm  r1 F 1 F 2   F 1
F 2
r1
 Next Find Reln between F 1
F1
f
 e  F 2  f
F1 & F2 by ENGR36
F2
e
Pulley-Friction Analysis
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 In This Case We assume that ≈100% of
the Motor Power is Transmitted to the
DRIVE Pulley; Thus
Tm nm  Tb n1  Tm1800  Tb1800  Tm  Tb  17.52 in  lb
 Subbing for Tm & F2 in Torque Eqn
Tb
Tb F 1
F 1 Tb
F 1  F 2  F 1  f  F 1 f 
r1
r1 e
e
r1
Tb
1  Tb

 F1 1  f    F 1
1 

 e  r1
r1 1  f 
 e 
Engineering-11: Engineering Design
39
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Now by GeoMetry & TrigonoMetry
 r2  r1 
1  180  2 arcsin

 c 
 We can now (finally) Construct an eqn
to express F1 as function of c
17.52 in  lb
F 1




1
1 in 1  
 3 in 1 in   
0.3   2 arcsin
 

c


 e 

Engineering-11: Engineering Design
40
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Now use the F1 = u(c) Eqn to Check the
4.5 inch estimate
17.52 in  lb
F 1 4.5 in  
 36.03 lbs




1
1 in 1  
 2 in   
f   2 arcsin
 

4
.5
in



 e

 Since 36 lbs EXCEEDS the 35 lb Max
Tension for the belt we must ITERATE
Engineering-11: Engineering Design
41
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Increase c to 5¼ inches
F 1 4.5 in  
17.52 in  lb




1
1 in 1  
 2 in   
f   2 arcsin
 

5
.25
in


 e 

 34.53 lbs
 Since 34.53 lbs is LESS than the Rated
Max for the belt, the 5.25” design works
• But is 5.25” the BEST?
Engineering-11: Engineering Design
42
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Find the Best, or Minimum, Value of c
using the MATH-Processor software
MATLAB (c.f. ENGR25)
• PLOT F1(c) to see how F1 varies with c
– cmin at crossing pt for line F1 = 35 lbs
• Use the fzero function to precisely
determine cmin for F1 = 35 lbs
– See MATLAB file
Belt_Center_Distance_Chp8_Sp10.m
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Flat Belt Tension as Function of Center Distance
38
Belt Tension, F1 (lb)
37
36
35
FR = Fmax =35 lb
34
33
32
4
cmin = 4.9757 in
4.2
4.4
4.6
4.8
5
5.2
5.4
5.6
Center Distance, c (in)
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
5.8
6
Engineering-11: Engineering Design
45
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
The MATLAB Code
% Bruce Mayer, PE * ENGR11 * 03Jul09
% Plot & Solve for Belt Drive System Center Distance
% file = Belt_Center_Distance_Chp8_Sp10.m
%
clear % clear out memory
% c to range over 4-8 inches
c = [4:.01:6];
%
% F1 = f(c) by anonymous function
F1 = @(z) 17.52./(1-1./(exp(0.3*(pi-2*asin(2./z)))))
%
% Make F1 Plotting Vector
F1plot = F1(c);
%
% Make Horizontal line on (c, F1) plot
Fmax =[35, 35];
cmax = [4,6]
%
% Plot F1 as a funcition of c
plot(c,F1plot, cmax,Fmax)
%
%Make Function to ZERO to find Cmin
F35 = @(z) 35-17.52./(1-1./(exp(0.3*(pi-2*asin(2./z)))))
cmin = fzero(F35,5)
Analysis  Check Ctr Dist
 We “don’t want push it” by using a
design the produces Belt Tension that is
very close to 35 lbs.
 Try c = 9” 
Check F1(9) by MATLAB
 Calc the
“Factor of Safety”
for Belt-Tearing
Engineering-11: Engineering Design
46
>> F9 = F1(9)
F9 = 31.6097
Fallowable
n

Fdesign
35 lbs
n9 
 1.11
31.6 lbs
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Analysis  Check Ctr Dist
 Finally for System SetUp Determine the
No-Load Belt PreTension, Fi
 First Find “Slack” Side Tension F2 
from previous analysis AT LOAD
Tm
Tm
17.52
F 1
 F 2  F 2 F 1
 31.6 
 14.1 lbs
r1
r1
1
 At Load F1 = (Fi + ΔF) & F2 = (Fi − ΔF)
Thus the
F 1 F 2 31.6  14.1
F i

 22.85 lb
Fi Calc
2
2
Engineering-11: Engineering Design
47
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Specify Design
 The Center Distance of 9” meets all the
Functional Requirements and the
System Goals (if 9” is a “compact” size)
 Thus Spec the Design
• Flat-Belt Drive System
• 2” DRIVE Pulley
• 6” Driven Pulley
• 9” Center Distance
• 23 lb No-Load Belt PreTension
Engineering-11: Engineering Design
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
TradeOffs
 Note that we encountered a “Trade-Off”
Between Compactness & Reliability
 In this case as c INCREASES
• Compactness DEGRADES
– Drive System becomes Larger
• Reliability IMPROVES
– Tearing/Stretching Tension becomes Less
 The “BEST” Value determined thru
TradeOff Consultations w/ the Customer
Engineering-11: Engineering Design
49
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
DPs NOT Always Continuous
 DPs can be DISCRETE or BINARY
Type of value
Example Variable Values
numerical
Length
material
mfg. process
non-numerical
Configuration
continuous
height
tire size
discrete
lumber size
zinc coating
discrete (binary)
safety switch
Engineering-11: Engineering Design
50
3.45 in, 35.0 cm
aluminum
machined
left-handed threads
45 in, 2.4 m
R75x15
2x4, 4x4
with/without
yes/no, (1,0)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Formulate
Problem
Re-Specify
Re-Design
Generate
Alternatives
ParaMetric
read, interpret
sketch
Design
restate constraints as eqns
guess, ask someone, Summary
Select Design Variables
Determine constraints
Select values for Design Variables
use experience, BrainStorm
all
alternatives
Analyze
Alternatives
Predict
Performance
calculate
Check
Feasibility:(test)
Functional? Manufacturable ?
Experiment
feasible
alternatives
Evaluate
Alternatives
calculate/determine
Determine
best alternative
satisfaction
Use Weighted Satisfaction Calc
best
alternative
Refine
Optimize
improve “best” candidate
refined best
alternative
Engineering-11: Engineering Design
51
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Summary  ParaMetric Design
 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,
• refine/optimize
Engineering-11: Engineering Design
52
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Summary  ParaMetric Design
 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 methods, using customer
satisfaction functions, can be used to determine
the “best” candidate from among the feasible
design candidates.
Engineering-11: Engineering Design
53
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
All Done for Today
Engineering
IS
TradeOffs
Engineering-11: Engineering Design
54
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Engineering 11
Appendix
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering-11: Engineering Design
55
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
Design for Robustness
 A “Robust” Design results in a product
whose (excellent) Function is
INSENSITIVE to Variations in
• Manufacturing (materials & processes)
• “Alignment”
• Wear
• Operating Environment
 Typically Uses Statistical Methods
• Monte Carlo, Taguchi, RSM, DoE, others
Engineering-11: Engineering Design
56
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt
The Taguchi Philosophy
Engineering-11: Engineering Design
57
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt