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Shaft Design
ENTC 463Mechanical Design Applications II
Next Thursday4/3/2008
Meet @ Thompson 009B
ENTC 463Mechanical Design Applications II
Allen to Hagan – 2:20 to 3:00 PMHigginbotham to Winniford– 3:00 to 3:35 PM
ATTENTION: MMET Students, the IAC members would like to meet YOU on April 11th !
WHO? IAC Members
WHAT? Meet and Greet
WHERE? 510, 5th Floor Rudder Tower
WHEN? April 11th 3:30-5:00pm
WHY? They will also be available to review your resume and help you improve it for potential employers. Please sign up with Courtney in THOM 117
Deadline to sign up is April 8th.
MMET IAC MeetingApril 11th 2008
STUDENTS NEEDED!!MMET Majors ONLY
Come join us for the 2008 Spring IAC MeetingGreat DOOR PRIZES!
I-POD NANO and much more!(Must Be Present to Win)
Sign up with Courtney in THOM 117
ENTC 463
• Lab 3 Due 4/10• Homework HW 12 Due 4/15
– Chapter 12 – 2, 4, 25, 27
Shafts
• Mott, Chapter 12• Why use shaft?
– To transmit power• Shaft geometry
– Cylinder, bar, beam (length and diameter)• Load acting on shaft
– Torsion (shear stress)– Bending (normal stress)
Shaft Design
Shaft Design
Shaft Design
• Given required power to be transmitted– Calculate torque, – Calculate forces, – Calculate stresses (if
geometry is known),– Select material
• Given required power to be transmitted– Calculate torque, – Calculate forces, – Determine shaft
diameter (if the material is known)
Shaft Design Procedure1. Develop the free body diagram; model the
various machine elements mounted on the shaft in terms of forces and torques
2. Develop the shear and moment diagram; identify bending moment (leads to normal stress) and torque (leads to shear stress)
3. Identify critical locations for stress analysis; calculate stresses (known diameter)
4. Determine diameter or select material based on failure theories
Forces Acting on Shaft
• Forces due to gear (spur gear)
gear) (helical tantan2
63000
ψφ
tx
tr
t
WWWWDTW
nhpT
==
=
=
Forces due to Gears
Forces Acting on Shaft
• Forces due to chain and sprocket
θθ
sincos
222
ccy
ccx
B
B
A
Ac
FFFF
DT
DT
DTF
==
===
Forces Acting on Shaft
• Forces due to V-belt and sheave
20.2
pulley andbelt flat For 2
5.121
DTF
DTF
FFF
B
B
B
≈
≈
−=
Example
• A chain is transmitting 100 kW with the chain speed at 6000 rpm and V = 50 m/s. The shaft material is AISI 1040 cold drawn. Determine the shaft diameter required.
Shaft Design Considerations
• Stress Concentration (fillet or key seat)1.5 < Kt < 2.5
• Combined tangential and radial load (3-D)– Two shear and moment diagrams
Wt
Wr
22yzxyy MMM +=
x
z
y
Stress Concentration
• Keyseats– Kt = 2.0 for profile keyseat– Kt = 1.6 for sled keyseat
• Shoulder fillets– Kt = 2.5 for sharp fillet– Kt = 1.5 for well-rounded fillet
• Retaining ring grooves– Kt = Kt = 3.0, or– Increase diameter by 6%
Forces Acting on A Shaft
Shear and Moment DiagramsFrom bottom look up Front view
Shaft Design/Analysis Example
( ) ( )( )
31
22
31
22
223
223
223
31
32
32
32
1616
:
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎟⎠
⎞⎜⎜⎝
⎛≥
⎟⎟⎠
⎞⎜⎜⎝
⎛+≥
≤+
≤+−−++
≤−
yy
y
y
y
y
ST
SMNd
TMSNd
NS
TMd
NS
TMMd
TMMd
NS
MSST
π
π
π
ππ
σσ
( )( )( )
( )
( )
( )223
22
1
223
22
1
34
34
1622
1622
16322
32642
TMMd
TMMd
dT
ddT
JTc
dM
ddM
IMc
xyxx
xyxx
xy
x
+−=+⎟⎠⎞
⎜⎝⎛−=
++=+⎟⎠⎞
⎜⎝⎛+=
===
===
πτσσσ
πτσσσ
ππτ
ππσ
Is this correct ?
Fatigue Failure Criterion
• Cyclic loading due to shaft rotation– Find mean and alternating stresses– Construct Mohr’s circles for mean stress and
alternating stress– Derive effective mean and alternating
stresses (based on MSST or DET)– Use Soderberg or Goodman for design and
analysis
Fatigue Failure of Shaft
3
3
16
0
32
dT
dM
xy
y
x
πτ
σπ
σ
=
=
±=
3
16
00:Mean
dT
mxy
my
mx
πτ
σσ
=
==
0
0
32:gAlternatin
3
=
=
=
mxy
my
ax dM
τ
σπ
σ
NSSK
dMdT
y
m
n
at
a
m
1''
':Soderberg
32'
32'
3
3
=+
=
=
σσ
πσ
πσ
1'
:sionsteady tor and bending reversedfully for equation ANSI/ASME
22
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
ys
m
n
a
Sτ
Sσ
ANSI Shaft Design Equation
For repeated reversed bending and constant torque
ANSI/ASME Shaft Equation
1'
:sionsteady tor and bending reversedFully 22
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
ys
m
n
a
Sτ
Sσ
1'
1'
1'
:factorsafety Consider
2222
22
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⇒=⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⇒
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
ys
m
n
a
ys
m
n
a
ys
m
n
a
SNτ
SNσ
NSτ
NSσ
Sτ
Sσ
ANSI / ASME Shaft Equation
13'
31'
1'
:n)for torsioshear (pure DET Use
22
2
222
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⇒
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+⎟⎟⎠
⎞⎜⎜⎝
⎛⇒=⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
y
m
n
a
y
m
n
a
ys
m
n
a
SNτ
SNσ
S
NτSNσ
SNτ
SNσ
13'
13'
:ionconcentrat stressConsider 2222
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⇒=⎟
⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
y
m
n
at
y
m
n
a
SNτ
SNσK
SNτ
SNσ
ANSI / ASME Shaft Equation
1
163
'
32
13'
16
32
2
3
2
322
3
3
=
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛⎟⎠⎞
⎜⎝⎛
+
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛⎟⎠⎞
⎜⎝⎛
⇒=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛⇒
==
==
yn
t
y
m
n
at
m
a
S
NdT
S
NdMK
SNτ
SNσK
dT
JTc
dM
IMcσ
ππ
πτ
π
31
22
43
'32
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛=
yn
t
ST
SMKNd
π
ANSI / ASME Shaft Equation
31
22
43
'32
sionsteady torandbendingreversedFully
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛≥
yn
t
ST
SMKNd
π
31
22
4332
Static
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎟⎠
⎞⎜⎜⎝
⎛≥
yy ST
SMNd
π
ANSI Shaft Design Equation
31
22
43
'32
sionsteady torandbendingreversedFully
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛≥
yn
t
ST
SMKNd
π
1'
:sionsteady tor and bending reversedFully 22
=⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛
ys
m
n
a
Sτ
Sσ
Can we use Soderberg or Goodman criterion?
Example 12-1 (p. 548)
• The system transmitting 200 hp from pinion P to gear A, and from pinion C to gear Q.
• The shaft rotating speed is 600 rpm.• Shaft material is AISI 1144 OQT 1000
Example (p. 549)• Free body diagram• Shear and moment diagrams• Torque at each segment• Calculate diameter for locations A, B, C, and D
(at both left and right)
A B C D
No momentTorque = 21000
No torque, no moment, vertical shear onlyNo torque
Shear and Moment DiagramsFrom bottom look up Front view
Design Examples
Design Example - Torque
Design Example - Forces
Design Examples – Shear and Moment
