mech4301 2008 lecture 5 case studies ch 61/22 mech4301 2008 materials selection in mechanical design...
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MECH4301 2008 Lecture 5 Case Studies Ch 6 1/22
MECH4301 2008 Materials Selection in Mechanical Design
Lecture 5
Materials Selection Without Shape (2/2): Case studies
Chapters 5 and 6
Cross Sectional Shape is
kept constant
MECH4301 2008 Lecture 5 Case Studies Ch 6 2/22
Review of Lecture 4: Materials for a stiff, light beam
2/1
2/15
ECLS12
m Chose materials with largest M=
2/1E
Material Index• Material choice
• Area = b2 What can be
varied ? {
I = second moment of area:12b
I4
Beam (solid square section)
b
b
L
FFunction
m = mass A = area
L = length = density
b = edge length S = stiffness I = second moment of area E = Young’s modulus
Stiffness of the beam, S:
3L
IECS
δ
FS
Constraint
LbLAm 2Minimise mass, m, where:Goal
Eliminate b
MECH4301 2008 Lecture 5 Case Studies Ch 6 3/22
CE
SLb
34 12
L
mb 2
2/1
2/15
ECLS12
m
I = second moment of area:12b
I4
3L
IECS δ
FS
LbLAm 2
Eliminating the free variable
2/1E
1
2
3
4
5
6
MECH4301 2008 Lecture 5 Case Studies Ch 6 4/22
Demystifying Material Indices (beam, elastic bending)
2/11
1
2/15
1
12
EC
LSm
2/12
2
2/15
2
12
EC
LSm
2
1
1
2/11
2/12
2
1
2
M
ME
Em
m
For given shape, the reduction in mass at constant bending stiffness equals the ratio between the reciprocal of the material indices.Same applies to bending strength.
mass, Material 1
mass Material 2
MECH4301 2008 Lecture 5 Case Studies Ch 6 5/22
Case studies Chapter 6
• Materials for light slender table legs
• Materials for small/light springs
• Materials for flywheels
• Materials for oars
• Short-term thermal insulation
• Materials for spark plug insulators
This lecture
Read these at home
MECH4301 2008 Lecture 5 Case Studies Ch 6 6/22
Materials for lightweight/slender table legs
p. 114
MECH4301 2008 Lecture 5 Case Studies Ch 6 7/22
Materials for table legs
legs are stiffness-limited,
minimum weight, designs
Specification
leg: light, stiff column
Minimum weight; slender
• Stiffness S specified
• Cost within reason
• Toughness adequate
• Cross-section area• Material
Material limits, set by constraints
2/1lc m.MPa15K Fracture toughness
Function
Objectives
Constraints
Free variables
2/1EM
Material index, p. 509, set by function/objective
Minimise
modulus
density
MECH4301 2008 Lecture 5 Case Studies Ch 6 8/22
Mass m = A L (1)
(3) 4
2/1
2
EL
Pm c
Critical condition for bucklingp. 483; (n = 1)
(2) 4 2
43
2
2
L
ER
L
IEPc
1/2
1M E
Maximise M1 for minimum mass
Table legs: Derivation of M. I. for minimum mass
Combine (1) and (2) to eliminate A
I is the second moment of area
Check on p. 509
Failure mode?
MECH4301 2008 Lecture 5 Case Studies Ch 6 9/22
P 509
MECH4301 2008 Lecture 5 Case Studies Ch 6 10/22
Slender legs?
E2M Maximise M2 to minimise cross section
Critical condition for bucklingp. 483; (n = 1)
Solve for R
MECH4301 2008 Lecture 5 Case Studies Ch 6 11/22
Materials for light / slender legs
CFRP best option
Selection line of gradient 0
Selection line of gradient 2
EM
ρM
2/1E
Foams are a good option !
MECH4301 2008 Lecture 5 Case Studies Ch 6 12/22
Materials for springs
Small springs: minimum volume Light springs:
minimum mass page 126
Images from: http://www.mech.uwa.edu.au/DANotes/springs/intro/intro.htmlhttp://www.ftexploring.com/lifetech/flsbws2.html
MECH4301 2008 Lecture 5 Case Studies Ch 6 13/22
22 EW
V
EM small
2
Material for a spring of minimum volume Cross section of given shape
Volume V = LA A=V/L
minimise V for given W….?
On E - chart, select with a line of gradient 2. Search on bottom right corner.
Elastic energy W
W = ½FL= ½ A L = ½ V L/L = ½ V= ½ V 2/E
Solving for V:
F = A A = V/L = /EL/L =
maximise
Goal: minimise V for given amount of elastic energy stored, W
F F
L
MECH4301 2008 Lecture 5 Case Studies Ch 6 14/22
E
2M
Selection line of gradient 2
spring of minimum volume
On E - chart, select with a line of gradient 2.
Search on bottom right corner (low E, high ).
CFRP & steels
elastomers
MECH4301 2008 Lecture 5 Case Studies Ch 6 15/22
Index ?
22 EW
Vm
22 EW
V
2
222
MMME
21
M
E
Solving Mlight for E:
On E/ vs / chart, select with line of gradient 2.
Search on bottom right corner (low E/, high /).
For minimum mass m = V
Material for a spring of minimum mass Cross section of given shape
For minimum Volume V
E
M light
2
EM small
2
Three materials properties in a single index: separate ?
MECH4301 2008 Lecture 5 Case Studies Ch 6 16/22
/
)/(E
2Mspring of minimum mass
CFRP
Exercise 5.7, Truck suspension
On E/ vs / chart, select with line of gradient 2. Search on bottom right corner (low E/, high /).
elastomers
Metals moved back and down. They are good for small springs, but they don’t get selected for light springs.
MECH4301 2008 Lecture 5 Case Studies Ch 6 17/22
Table B.3 p. 510
MECH4301 2008 Lecture 5 Case Studies Ch 6 18/22
Using CES to sort materials: Exercise 5.3
MECH4301 2008 Lecture 5 Case Studies Ch 6 19/22
From Lecture 4: Materials for a strong, light beam
L
mA
m = massA = areaL = length = densityMf = bending strengthI = second moment of areaE = Youngs ModulusZ = section modulus
Beam (shaped section).
Bending strength of the beam Mf:
Combining the equations for A, Mf and Z gives:
** Zy
IM
mf
3/2*
3/26
LMm f
LAm
Chose materials with largest
3/2*
Minimise mass, m, where:
Function
Objective
ConstraintL
FArea A
8
2bhZ
Eliminate free variable, A
MECH4301 2008 Lecture 5 Case Studies Ch 6 20/22Density (kg/ m^3)100 1000 10000
Tensi
le s
trength
(M
Pa)
1
10
100
1000
Wood, typical along grain
Magnesium alloys
Silicon carbide
CFRP, epoxy matrix (isotropic)
Bamboo
Polyamides (Nylons, PA)
Magnesium alloys
Rigid Polymer Foam (HD) Aluminum alloys
Titanium alloys
Rigid Polymer Foam (MD)
Flexible Polymer Foam (LD)
Stainless steel Low alloy steel
High carbon steel
GFRP, epoxy matrix (isotropic)
Selection line gradient1.5
Alumina
CES chart
3/2*
M
density
elastic
limit
Slope 1.5
Search region
MECH4301 2008 Lecture 5 Case Studies Ch 6 21/22
Using CES to sort materials. Q 5.3 light strong beam
Name density Elastic limitStage 1: Index
Rigid Polymer Foam (HD) 170 - 470 1.2 - 12.42 8.706e-3
Aluminum alloys 2500 - 2900 58 - 550 0.012
Flexible Polymer Foam (MD) 70 - 115 0.43 - 2.95 0.012
Stainless steel 7600 - 8100 480 - 2240 0.013
Rigid Polymer Foam (MD) 78 - 165 0.65 - 5.1 0.013
Flexible Polymer Foam (LD) 38 - 70 0.24 - 2.35 0.016
Bamboo 600 - 800 36 - 45 0.017
Titanium alloys 4400 - 4800 300 - 1625 0.017
GFRP, epoxy matrix (isotropic) 1750 - 1970 138 - 241 0.017
Silicon carbide 3100 - 3210 400 - 610 0.02
Rigid Polymer Foam (LD) 36 - 70 0.45 - 2.25 0.02
Polyamides (Nylons, PA) 1120 - 1140 90 - 165 0.022
Magnesium alloys 1740 - 1950 185 - 475 0.024
Flexible Polymer Foam (VLD) 16 - 35 0.24 - 0.85 0.025
Wood, typical along grain 600 - 800 60 - 100 0.026
CFRP, epoxy matrix (isotropic) 1500 - 1600 550 - 1050 0.054
Highest M = CFRP & wood
Foams=> The good: beam is light , The
bad? beam too thick.
What makes timber so
good?
3/2*
M
Materials sorted by
Index
MECH4301 2008 Lecture 5 Case Studies Ch 6 22/22
The End Lecture 5
MECH4301 2008 Lecture 5 Case Studies Ch 6 23/22
Material for a flywheel -- filament-wound GFRP
Case
RotorBurst shield
MECH4301 2008 Lecture 5 Case Studies Ch 6 24/22
Specification for a flywheel Specification
Flywheel
Maximum energy/wt
• Must not disintegrate
• Cost within reason
• Fr. Toughness adequate
• Material
Function
Objectives
Constraints
Free variables
MECH4301 2008 Lecture 5 Case Studies Ch 6 25/22
Material index and constraints for flywheels
Maximise energy/unit weight at maximum velocity
Energy
Mass
Must not fail
Energy/mass
Maximise
yM
Angular velocity
2
tR2
U42
tRm 2
y
22R8
3
21
83
2mU y
Density
Strength
Moment of inertia
Additional constraint: Fracture toughness > 15 MPa.m1/2
(1)
(2)
(3)
(4)
Linear on , quadratic on ω
MECH4301 2008 Lecture 5 Case Studies Ch 6 26/22
Table B.3 p. 510
yM
MECH4301 2008 Lecture 5 Case Studies Ch 6 27/22
Material for flywheels
ρyσ
Searchregion
MECH4301 2008 Lecture 5 Case Studies Ch 6 28/22
Material for flywheels
Density (typical) (Mg/m^3)1 10
Ela
stic
Lim
it (t
ypic
al)
(M
Pa
)
10
100
1000CFRP
GFRPLow alloy steels
Mg alloys
Nickel alloys
Copper alloys
Zinc alloys
Low carbon steel
Al alloys
Al-SiC Composite
Ti alloys
Lead alloys
Density (Mg/m3)
Strength - DensityAdditional constraint:
K1c > 15 MPa.m1/2
E
last
ic li
mit
(MP
a)
ρyσ
Searchregion
MECH4301 2008 Lecture 5 Case Studies Ch 6 29/22
Energy source
Gasoline
Rocket fuel
Flywheels
Advanced batteries
Lead-Acid battery
Springs, rubber bands
Comment
Oxidation of hydrocarbon - weight or oxygen not included
Less than hydrocarbons because oxidising agent forms part of fuel
Attractive but not yet proven
Battery technology near limit
Large weight for acceptable range
Much less efficient method of energy storage than flywheel
Energy density kJ/kg
20,000
5,000
up to 350
up to 350
45 - 60
up to 5
Flywheels postscript: Energy density of energy sources
MECH4301 2008 Lecture 5 Case Studies Ch 6 30/22
Potential Use Temperature as a Function of Working Time for Ultra-high Temperature Composites under Simulated Aero Convective Environment (*corresponds to static oxidation test)
Y. R. Mahajan, ARC-I, Hyderabad
Some possible materials for Exercise 5.9 fin for rocket
MECH4301 2008 Lecture 5 Case Studies Ch 6 31/22
HYPERSONIC TECHNOLOGY DEMONSTRATOR (HSTDV)HYPERSONIC TECHNOLOGY DEMONSTRATOR (HSTDV)
AUTONOMOUS AIRBREATHING SUSTAINED FLIGHT
AT HYPERSONIC SPEED WITH KEROSENE FUEL
Mach No. : 6.5Altitude : 32.5 kmFlight duration of cruise vehicle : 20 secs
Hypersonic Vehicle consists of : 1. LAUNCH VEHICLE (L.V.) 2. CRUISE VEHICLE (C.V.)CV encapsulated in the payload stage of LV.
Y. R. Mahajan, ARC-I, Hyderabad