# 2.72 Elements of Mechanical Design

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2.72 Elements of Mechanical Design
Spring 2009
2.72
Elements of
Mechanical Design
Lecture 13:
Gear failure prevention
Quiz
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Activity at end: Optional/Extra credit
Images removed due to copyright restrictions.
Please see images of very large and very small gears, such as:
Topics
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http://mems.sandia.gov/gallery/images_gears_and_transmissions.html
http://www.cage-gear.com/large_gear_cutting.htm
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None!
2
Selection vs. design of gears
It is rare to custom DESIGN a gear.
Many gear selection programs…
Anybody can read S/M and plug in #s
BASIC considerations to select gears:
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Ensure geometric compatibility (e.g. equal pitch and same type)
Avoid low-cycle failure (e.g. root stress)
Avoid high-cycle failure (e.g. pitting)
Focus on what is important
3
A failure…
4
How to model the gear teeth…
W
Wr
Wt
Wt
F
l
rf
t
a
x
l
Figure by MIT OpenCourseWare.
t
Figure by MIT OpenCourseWare.
5
Gear
manufacturing
Gear manufacturing - Hobbing
Please see digtos. &quot;GEAR HOBBING M20/32 CITIZEN CINCOM.&quot;
7
Gear manufacturing - Shaping
9
Selection vs. design of gears
Why do we care about gear tooth surface finish
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What affects the finish on the gear surfaces?
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How good could it be?
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How much would it cost?
Why do we care about the tooth geometry at the root
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What affects the quality of the fillet at the root?
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How good could it be?
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How much would it cost?
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Perspective
Failure modes
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Tooth bending/shear
Contact failure
Science modeling
→
Engineering modeling
American Gear Manufacturers Association (AGMA)
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Example
Single pressure angle
Full-depth teeth
Others
11
Calculating stresses
σ bending
Pd K m K B
= Wt K o K v K s
(U.S. units)
F J
1.9
Dynamic factor, kv
1.8
Qv = 5
1.7
Qv = 6
1.6
Qv = 7
1.5
1.4
Qv = 8
Qv = 9
1.3
Qv = 10
1.2
Qv = 11
1.1
1.0
&quot;Very accurate gearing&quot;
0
2000
4000
6000
8000
10,000
Pitch line velocity, Vt, ft/min
Figure by MIT OpenCourseWare. Adapted from Fig. 14-9 in Shigley &amp; Mischke.
σ contact = C p
Km C f
(Wt K o K v K s )
(U.S. units)
dp F I
Incredibly uninteresting, plug-chug &amp; ‘non-scientific’
12
Gear failure
at the root
Bending
Basic stress calculation
Stress near the tooth root, model tooth as a cantilever
Mc
σ=
I
Wt P
σ=
FY
6 Wt L
σ=
F t2
Root
P: Diametral pitch
Y: Lewis form factor
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~&frac14; to &frac12; for φ = 20o
f( # of teeth )
Conservative:
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Implies that one tooth carries the load
14
Basic stress calculation
Stress near the tooth root, model tooth as a cantilever
M c
σ =
I
Wt P
σ=
FY
6 Wt L
σ=
F t2
W
Wt
F
Wr
Wt
l
t
P: Diametral pitch
Y: Lewis form factor


~&frac14; to &frac12; for φ = 20o
f( # of teeth )
rf
a
l
x
t
Figure by MIT OpenCourseWare.
Figure by MIT OpenCourseWare.
http://www.oilanalysis.com/Backup/200101/Gear3.jpg
Conservative:
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Implies that one tooth carries the load
15
Dynamic effects
How to incorporate dynamic effects
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⎛
a + V
K
v = ⎜⎜
⎝
a
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V = pitch line velocity
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Kv depends on fab
b
c
⎞
⎟⎟
⎠
For rough estimates
Wt P
σ = KV
FY
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This is for English units, for SI is different
16
Allowable bending stress
Allowable bending stress number, St kpsi
These types of plots are associated with conditions
50
St = 102 HB + 16 400 psi
40
St = 77.3 HB + 12 800 psi
30
St = αt . Hb + Ct
20
10
150
200
250
300
350
Brinell hardness, HB
400
450
Figure by MIT OpenCourseWare. Adapted from Fig. 14-2 in Shigley &amp; Mischke.
17
Allowable bending stress
σ all
S t YN
=
(U.S. units)
S F KT K R
σ all
St YN
=
(SI units)
S F Yθ YZ
Elements of the equations:
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St
YN
KT
KR
SF
Allowable bending stress
Stress cycle life factor
Temperature factors
Reliability factors
AGMA factor of safety
Allowable stresses for:
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10 million stress cycles
99 percent reliability
18
Gear failure
at the surface
Fatigue
High cycle failure: Pitting
Images removed due to copyright restrictions. Please see any photos of surface pitting in gears, such as:
http://commons.wikimedia.org/wiki/File:Roue_creuse_03.jpg
20
Avoiding high cycle failure: Stress variables
Equivalent modulus
1
Ee =
2
2
1 − v1 1 − v21
+
E1
E2
Half contact width
2Wt d1 d 2
b=
π L Ee (d1 + d 2 )
υ = 0.333
Watch out! The book
switches meaning of F here…
Maximum contact pressure
2Wt
q=
π bL
Image from Wikimedia Commons, http://commons.wikimedia.org
21
Allowable contact stress [ANSI/AGMA 2001-D04 and 2101-D04]
Allowable contact stress number, Sc
1000 lb/in2
S c = α c ⋅ H b + Cc
175
Sc = 349 HB + 34 300 psi
150
125
Sc = 322 HB + 29 100 psi
100
75
150
200
250
300
350
400
450
Brinell hardness, HB
22
Figure by MIT OpenCourseWare. Adapted from Fig. 14-5 in Shigley &amp; Mischke.
Allowable contact stress
σ c,all
SC Z N C H
=
(U .S . units )
S H KT K R
σ c,all
S C Z N ZW
=
(SI units)
S H Yθ YZ
Elements of the equations:
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SC
ZN
CH
KT
KR
SH
Allowable contact stress
Stress cycle life factor
Hardness ratio factors for pitting resistance
Temperature factors
Reliability factors
AGMA factor of safety
Allowable stresses for:



10 million stress cycles
99 percent reliability
23
Exercise
Gears
General machine design
Activity: Refit lathes for the mfg. shop
Study the lathes in the shop…
1. What types of failures do we have?
2. Calcs/sims/tests need to augment Shigley/Mischke:
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Gearing
Belts
Friction elements
3. Worst case consequence of these kinds of failures:
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Pitting failure
Tool break/failure
Fatigure
25
Exercise
Windmill gear boxes
Windmill failures: Catastrophic
October 26, 2009.
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Wind energy overview: Lakawona
http://i124.photobucket.com/albums/p7/NBBooks/WTGTurbinesGettingLargerSM.jpg
http://i124.photobucket.com/albums/p7/NBBooks/WTGUSWindResources.jpg
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http://www.clipperwind.com/pdf/liberty_brochure.pdf
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Activity: Extra credit - As a group
You are tasked to build a windfarm off Cape Cod
1. Shigley/Mischke is not perfectly suited to cover gear
needs in this application. Why/how?
2. What calculations/simulations/tests would you do to
augment Shigley/Mischke?
3. What happens if you have pitting failure and what