bruce mayer, pe licensed electrical & mechanical engineer [email protected]

[email protected] • ENGR-11_Lec-05_Chp8_ParaMetric_Design.ppt1

Bruce Mayer, PE Engineering-11: Engineering Design

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 11

ParaMetric

Design



OutLine ParaMetric Design Design phase info flow Parametric design of a bolt Parametric design of belt & pulley Systematic parametric design Summary



Configuration Design

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 FlowSpecial Purpose Parts: Features Arrangements Relative dimensions Variable list Standard Parts: Type Variable list

ParametricDesign

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

DetailDesign

Product specificationsProduction drawingsPerformance Tests Bills of materials Mfg. specifications

ConFig Design



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 11

Real LifeApplication



Bruce Mayer, PEDir. System Engineering

19Feb02

3x00 S2-§19Seismic Protection

EarthQuake– Magnitude

8.0– Kurile Islands– 03Dec1995



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



BMayer



3x00 S2Testing: Tatsuno Japan, Dec01

S2-0200 Test SystemAL3120F, s/n 111001

3x00_S2S8_Tatsuno_PhotoDoc_0112.ppt



3x00 Seismic Loading & Geometry

BMayer



Loading Geometry Detail



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 Restoring Factor ofLine Direction Moment (N-m) Moment (N-m) SafetyR-S Y 6884 6966 1.01P-Q X 6884 8504 1.24

3x00_Seismic_Analysis_0202.xls



Bracket Stress Analysis Analysis Parameters

1. Assume Failure Pointat 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 Load4. Bolt Axial-PreLoad is negligible (Snug-Fit)5. Shear Load Per Restraint Point = 500lb/2.22kN6. Use Von Mises Yield Criteria: Ssy = 0.577Sy

Results

2.22 kN

Bolt Bolt Ssy Load Stress, Factor ofSize & Fcn Material (MPa) (MPa) SafetyM6 Connector SS-304 139.1 13.84 10.1M10 Anchor SS-304 139.1 4.74 29.4

3x00_Seismic_Analysis_0202.xls



ParaMetric Bolt Design From Analysis Determine Failure Mode

as AXIAL TENSILE YIELDING (E45) The Configuration Design Sketch

d

LTL

shank

head

threads

LoadLoad



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 Proof-Load divided by the supporting Material Area, A (Pa or psi)

Mathematically the Axial Stress Eqn

pppp ASFAFS



Use Engineering Analysis Using ENGR36 Methods Determine the

Bolt Load as 4000 lb (4 kip) Thus the “Functional

Requirement” for the Bolt lbs 4000pF To Actually Purchase a Bolt we need to

Spec a DIAMETER, d, and a length, L Find d Using the FR & Stress-Eqn

ppp S

AFAS lbs 4000lbs 4000



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 Boltwith Sp = 85 000 psi(85 ksi)



Bolt Grade DEFINES Bolt Size Use Sp and the FR to find the Bolt Area

22 in0470

inlb85000lb 4000 . AA

Relate A to d using Geometry 4

22 drAcircle

Since Bolts Have Circular X-Sections in245.0in047.04in047.0

4

222

2

dddA



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



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



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

22

22

inkip866

44dd

SdSF ppp

.

This ParaMetric Relationship can be displayed in a plot



ParaMetric Design of a Bolted Joint

0

2

4

6

8

10

12

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Bold Diameter (in)

Pro

of L

oad

(Kip

)

Bolt_Design_Parametr_d-F_0907.xls

PARAMETERS• Grade-5 Steel• Sp =85 ksidc NOT Feasible FEASIBLE

Functional Requirement



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



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



Reduction-FreeBolt 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

The “FORWARD” process• Use “Guess &

Check”

diameter d proof load >4000

d =0.1 in

area = 0.008 in2 load < 668

Need to change either

SIZE or MATERIAL



Before Next Example… Take

a Short BREAK



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



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



System Diagram

22r1r

c

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

Motor Pulley(driver)

Grinding Wheel Pulley(driven)

1

NOTE:d = 2r

NOTE:n → Spin Speed (RPM)



FreeBody Diagram of Drive Pulley

1r

2F

1F

1n T1

yB

xBx

y

Some Physics

211 FFrT

1TnP

290 1

21cosFFB x

290sin 1

21FFB y



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



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

Item Parameter Symbol Units LowerLimit

UpperLImit

1 Belt Torque Tb in-lb -- Tm

2 Belt Tension F1 lbs -- 35

3 Center Distance c in. small --



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


UpperLImit

1 Center Distance c in small --

2 Driven Pulley Dia.

d2 in -- --



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”


UpperLImit

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



Analysis/Solution Game Plan1. Calc Buffing Wheel Diameter, d2

2. Calc Motor Torque, Tm

3. Calc (F1 – F2)

4. DECIDE Best Estimate for Ctr-Dist, c1

5. Calc Angles of Wrap, φ1 & φ2

6. Calc F1 by Friction Reln (c.f. ENGR36)

7. Calc F2

8. Calc The Initial belt Tension, Fi



Analysis Check Ctr Dist Mechanically The SPEED RATIO Sets

the DiaMeter Ratio - use to find d2

in 6in 23in 2600

18002

2

1

2

2

1 dddd

nn

Thus the MINIMUM Center Distance

in 4in 3in 12in 6

2in 2

2221

ddcmin



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)

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

nPTTnP m



Analysis Check Ctr Dist With Consistent Units Calc Tm

Now by PHYS4A or ENGR36

lbin 5217mN 9791 srad 60smN 373

..mT

21

1211211 FrTFFFrTFFrT m

m

Next Find Reln between F1 & F2 by ENGR36 Pulley-Friction Analysis

ff

eFFe

FF 1

22

1



Analysis Check Ctr Dist In This Case We assume that ≈100% of

the Motor Power is Transmitted to the DRIVE Pulley; Thus

Subbing for Tm & F2 in Torque Eqn

lbin 5217180018001 .bmbmbmm TTTTnTnT

f

bbf

bff

bb

er

TFrT

eF

rT

eFF

eF

rTFF

rTF

11

111

11

1

1

11

1

112

11



Analysis Check Ctr Dist Now by GeoMetry & TrigonoMetry

We can now (finally) Construct an eqn to express F1 as function of c

crr 12

1 arcsin2180

ce

F

in 1in 3230

1

11in 1

lbin 5217

arcsin.

.



Analysis Check Ctr Dist Now use the F1 = u(c) Eqn to Check the

4.5 inch estimate

Since 36 lbs EXCEEDS the 35 lb Max Tension for the belt we must ITERATE

lbs 033611in 1

lbin 5217in 54

in .54in 22

1 ...

arcsin

f

e

F



Analysis Check Ctr Dist Increase c to 5¼ inches

Since 34.53 lbs is LESS than the Rated Max for the belt, the 5.25” design works• But is 5.25” the BEST?

lbs 533411in 1

lbin 5217in 54

in .255in 22

1 ...

arcsin

f

e

F



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



4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 632

33

34

35

36

37

38

Center Distance, c (in)

Bel

t Ten

sion

, F1

(lb)

Flat Belt Tension as Function of Center Distance

FR = Fmax =35 lb

cmin = 4.9757 in



The MATLA

B C

ode% 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 inchesc = [4:.01:6];%% F1 = f(c) by anonymous functionF1 = @(z) 17.52./(1-1./(exp(0.3*(pi-2*asin(2./z)))))%% Make F1 Plotting VectorF1plot = F1(c);%% Make Horizontal line on (c, F1) plotFmax =[35, 35];cmax = [4,6]%% Plot F1 as a funcition of cplot(c,F1plot, cmax,Fmax)%%Make Function to ZERO to find CminF35 = @(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

>> F9 = F1(9)F9 = 31.6097

Calc the “Factor of Safety” for Belt-Tearing 111

lbs 1.63lbs 35

9 .

n

FFn

design

allowable



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

At Load F1 = (Fi + ΔF) & F2 = (Fi − ΔF) Thus the Fi Calc

lbs 11415217631

1122

11 ...

rTFFF

rTF mm

lb 85222

1146312

21 ...

FFF i



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



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



DPs NOT Always Continuous DPs can be DISCRETE or BINARY

Type of value Example Variable Valuesnumerical 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)



ParaMetricDesign

Summary

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 eqnsguess, ask someone,use experience, BrainStorm

calculateExperiment (test)

calculate/determine satisfactionUse Weighted Satisfaction Calcimprove “best” candidate



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



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.



All Done for Today

EngineeringIS

TradeOffs



Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 11

Appendix



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



The Taguchi Philosophy

bruce mayer, pe licensed electrical & mechanical engineer [email protected]

Documents

pe engineering

engineering designbruce

dimensions materials

n s j o h n s o n c

test systemal3120f

dec01 s2

lateral loading criteria

center of gravity consult