shaft design flow chart
DESCRIPTION
NotesTRANSCRIPT
![Page 1: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/1.jpg)
ME2 Design & Manufacture
Shaft Design
![Page 2: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/2.jpg)
Shafts
PLAIN TRANSMISSION
STEPPED SHAFT
MACHINE TOOL SPINDLE
RAILWAY ROTATING AXLE
NON-ROTATING TRUCK AXLE
CRANKSHAFT
![Page 3: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/3.jpg)
CIRCLIPS
GEAR PULLEY
KEY
KEY
SHAFT HUBHUB
FRAME
WOODRUFF
PROFILED
![Page 4: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/4.jpg)
P. Childs, 2014, Mechanical Design Engineering Handbook
Chapter 7
TRANSVERSELOAD
LOADTRANSVERSE
TRANSVERSELOAD
TORSIONALLOAD
AXIALLOAD
LOADTORSIONAL
AXIALLOAD
TWISTDUE TO
TORSIONALLOAD
DEFLECTION DUE TOBENDING MOMENT
![Page 5: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/5.jpg)
Shaft Design Procedure Flow Chart for Shaft Strength & Rigidity (Beswarick 1994)
DETERMINEEXTERNAL LOADS
CHOOSE PRELIMINARYSHAFT DIMENSIONS
IDENTIFY CRITICALSHAFT SECTIONS
INTERNAL FORCESAND MOMENTS
COMBINEDSTRESSES
SET FACTOROF SAFETY
COMPARE FACTOREDSTRESSES WITH
MATERIAL STRENGTH
IS SHAFT SECTIONSATISFACTORY
SPECIFY SHAFT
TRANSVERSE FORCES,AXIAL FORCES ANDBENDING MOMENTS
DIRECT STRESS
CHOOSE MATERIAL
STRENGTH MODULUS
DEFLECTION
SHEAR FORCES ANDTWISTING MOMENTS
SHEAR STRESS
NO 1st OPTIONNO 2nd OPTION
YES
DETERMINE DETERMINEDETERMINE
DETERMINE
DETERMINE
DETERMINE
DETERMINE
DETERMINE
![Page 6: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/6.jpg)
Determine External Loads
• Shaft rotational speed?
• Power or torque to be transmitted by the shaft?
• Belt / Chain tension?
• Gear & Pinion loading?
![Page 7: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/7.jpg)
Choose (Preliminary) Shaft Dimensions
• Determine dimensions of components mounted on shaft
• Specify locations for each device
• Specify the locations of the bearings / support
• Propose a general form or scheme for geometry
• Size restrictions
• (Easily) available materials and/or components
![Page 8: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/8.jpg)
Identify Critical Shaft Sections
Free Body Diagram:
• Determine magnitude of torques throughout shaft
• Determine forces exerted on shaft
![Page 9: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/9.jpg)
Identify Critical Shaft Sections
• Where are the loads applied?
• Where are the dimensions smallest?
• Where are the stresses / deflections large?
• Stress-raisers?
– Slots, holes & keyholes
– Sharp corners
– Rough surfaces
![Page 10: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/10.jpg)
Determine Internal Loads
Produce shearing force and bending
moment diagrams so that the
distribution of bending moments in
the shaft can be determined.
![Page 11: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/11.jpg)
Shear and Moment Diagrams
𝑑2𝑦
𝑑𝑥2=𝑀
𝐸𝐼
𝑑𝑦
𝑑𝑥=
𝑀
𝐸𝐼𝑑𝑥 slope
𝑦 = 𝑀
𝐸𝐼𝑑𝑥 deflection
with: 𝑀 = 𝑉𝑑𝑥 and V = − 𝑞𝑑𝑥
M M+dM V V+dV
q
![Page 12: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/12.jpg)
R
1V
R
R
1H
gm gR
2H
2V
Ft
Fr
1T
m gp
T2
Combining Normal Stresses
Vertically
Horizontally
1VR
A
L1
B L2
L
R2V
C
3
rF g+m g mpg
80
BEARING
120
GEAR
BEARING
DRIVEBELT
100
GEAR
1HR
A
21L B L
tF
3
R2H
L
C
T
![Page 13: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/13.jpg)
Combining Normal Stresses
Vertical Bending Moments
Horizontal Bending Moments
1VR
A
L1
B L2
L
R2V
C
3
rF g+m g mpg
1HR
A
21L B L
tF
3
R2H
L
C
T
Vertically
Horizontally
A
5
B 3
C A
30
10
B C
![Page 14: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/14.jpg)
Combining Normal Stresses
Vertical Bending Moments
Horizontal Bending Moments
21110522 .BM
13030322
.CM
Combined:
I
cM
A
5
B 3
C A
30
10
B C
A
30.1
11.2
B C
![Page 15: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/15.jpg)
Normal stress & Shear stress
dx
dx
![Page 16: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/16.jpg)
Normal Stress or Shear Stress?
![Page 17: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/17.jpg)
Normal Stress or Shear Stress?
![Page 18: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/18.jpg)
![Page 19: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/19.jpg)
Shear stresses
• Shear stresses due to:
– Shear forces ( shear force diagram)
– Torque
• Power = Torque x Angular velocity
𝑃 = 𝑇 ∙𝑑𝜃
𝑑𝑡= 𝑇 ∙ 𝜔 = 𝑇 ∙ 2 ∙ 𝜋 ∙ 𝑓
• Shear stress: Torsion Formula 𝜏 =𝑇∙𝑟
𝐽
J: polar moment of inertia
r: radius
![Page 20: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/20.jpg)
Mohr's Circle
Combining and visualising the normal and shear stress components
x
y
txy
txy
tx'y' x'
• Normal stresses σx & σy and
shear stress τ known.
• Average normal stress
𝜎𝑎𝑣𝑔 =𝜎𝑥 + 𝜎𝑦
2
• Actual combined stress
𝑅 =𝜎𝑥 + 𝜎𝑦
2
2
+ 𝜏𝑥𝑦2
![Page 21: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/21.jpg)
Mohr's Circle
Combine and visualise the normal and shear stress components
• Normal stresses σx & σy and
shear stress τ are known.
• Average normal stress
𝜎𝑎𝑣𝑔 =𝜎𝑥 + 𝜎𝑦
2
• Actual combined stress
𝑅 =𝜎𝑥 + 𝜎𝑦
2
2
+ 𝜏𝑥𝑦2
• Principal stresses σ1 and σ2
t
avg
R
1 2
x y
txy
![Page 22: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/22.jpg)
http://moodlepilot.imperial.ac.uk/pluginfile.php/12151/
mod_resource/content/1/out/index.html
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Choose Material
• Maximum principal stresses
• Introduce safety factor
• Select a material to match design stress
– steel, low- or medium-carbon
– high quality alloy steel, usually heat treated (critical applications)
– brass, stainless steel (corrosive environments)
– aluminium (light weight)
– polyamide (Nylon®) or POM (Polyoxymethylene/Acetal, Delrin®)
small, light-duty shafts, electronics applications, food industry
eqyield n
![Page 24: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/24.jpg)
Typical Safety Factors
1.25 to 1.5 reliable materials under controlled conditions subjected to
loads and stresses known with certainty
1.5 to 2
2 to 2.5
2.5 to 3
3 to 4 well-known materials
under uncertain conditions of load, stress and environment
untried materials
under mild conditions of load, stress and environment
Growing uncertainty
![Page 25: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/25.jpg)
Fatigue - Correction Factors
with k < 1, and depending on:
• Surface
• Size
• Temperature
• Stress concentrations
• …
σe′ = k ∙ σe σe = 0.5 ∙ σuts
![Page 26: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/26.jpg)
Shaft Design Procedure Flow Chart for Shaft Strength & Rigidity (Beswarick 1994)
![Page 27: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/27.jpg)
• Analyse all the critical points on the shaft and
determine the minimum acceptable diameter
at each point to ensure safe design
• Determine the deflections of the shaft at critical
locations and estimate the critical frequencies
• Specify the final dimensions of the shaft
![Page 28: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/28.jpg)
Critical Deflections for Efficiency & Performance
• Gears:
– deflection < 0.13 mm
– slope < 0.03°.
• Rolling element bearings:
– non self aligning - slope < 0.04°
– self aligning - slope < 2.5° - 3°
![Page 29: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/29.jpg)
Shaft-Hub Connection
• Power transmitting components such as gears, pulleys and sprockets need to be mounted on shafts securely and located axially.
• In addition a method of transmitting torque between the shaft and the component is required.
• The hub of the component contacts with the shaft and can be attached to, or driven by the shaft by
– keys
– pins
– set screws
– press and shrink fits
– splines
– taper bushes
![Page 30: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/30.jpg)
Shaft-Hub Connection after Hurst (1994)
Pin
Gru
b
scre
w
Cla
mp
Pre
ss fit
Shrink f
it
Splin
e
Key
Taper
Bush
High torque capacity x x x
Large axial loads x x x x
Axially compact x x x
Axial location provision x x
Easy hub replacement x x x
Fatigue x x x x
Accurate angular
positioning x x x x ()
Easy position
adjustment x x x x x
![Page 31: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/31.jpg)
Example: What to do
when a shaft deflects too much
Choose the appropriate answer(s) from:
Use High Grade Steel, such as 30CrNiMo8
Increase the diameter of the shaft
Add bearings for extra support
Reduce the load bearing length of the shaft
![Page 32: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/32.jpg)
Some general design considerations
IE
LF
3
3
Overhung layout
More robust layout
![Page 33: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/33.jpg)
Ø=0.04 m
140 N 130 N 150 N
=0.15 m L 1
=0.08 m =0.14 m L 2
L 3
=0.07 m L 4
Example
![Page 34: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/34.jpg)
Example
• As part of the preliminary design of a machine shaft, a check is to undertaken to determine the deflections
• The components on the shaft can be represented by three point masses.
• Assume the bearings are stiff and act as simple supports.
• The shaft diameter is 40 mm and the material is steel with a Young’s modulus of 200 GPa.
![Page 35: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/35.jpg)
Example
=0.15 m
O
x
1 R
L 1
Ø=0.04 m
R 2
=0.08 m
140 N 130 N
=0.14 m L 2
1 W
L 3
2 W
150 N
=0.07 m L 4
3 W
![Page 36: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/36.jpg)
Solution
Macaulay's Method
• Resolving vertical forces:
R1+R2=W1+W2+W3.
• Clockwise moments about O:
W1L1+W2(L1+L2)-R2(L1+L2+L3)+W3(L1+L2+L3+L4) =0
• Hence 321
43213212112
LLL
)L+L+L+(LW+)L+(LW+LWR
![Page 37: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/37.jpg)
Solution cont.
• Calculating the moment at XX:
MXX = -R1x + W1[x-L1] + W2[x-(L1+L2)] - R2[x-(L1+L2+L3)]
• Relation between bending moment and deflection
• This equation can be integrated once to find
the slope θ = dy/dx
and twice to find the deflection y.
x
x
Mxx Vxx
Mdx
ydEI
2
2
![Page 38: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/38.jpg)
Solution cont.
MXX = -R1x + W1[x-L1] + W2[x-(L1+L2)] - R2[x-(L1+L2+L3)]
x
x
Mxx Vxx
Mdx
ydEI
2
2
1
2
32122
2122
11
2
1 CLLLx2
RLLx
2
WLx
2
W
2
xR
dxMdx
dyEI
2
2
CxCLLLx6
RLLx
6
WLx
6
W
6
xR
xMdEIy
1
3
32123
2123
11
3
1
Note that in Macaulay's Method
terms within square brackets to be ignored
when the sign of the bracket goes negative.
![Page 39: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/39.jpg)
Boundary conditions
Assuming: deflection at the bearings is zero
• y(x=0) = 0 → C2 = 0
• y(x=L1+L2+L3) = 0 →
321
3
36
3
326
3
3216
1
211
LLL
LLLLLLC
WWR
321
3
36
3
326
3
3216211
LLL
LLLLLLLLLx
2
R
LLx2
WLx
2
W
2
xR
dx
dyEI
WWR2
3212
2
2122
11
2
1
xLLL
LLLLLLLLLx
6
R
LLx6
WLx
6
W
6
xREIy
WWR3
3212
3
2123
11
3
1
321
3
36
3
326
3
3216211
![Page 40: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/40.jpg)
Solving for deflections
Forces: W1=130 N, W2=140 N, W3=150 N,
Geometry: =4 mm,
Material E=200,000 MPa
Substitution of these values gives:
R1=79.2 N
R2=340.8 N
Deflections:
at x=0.15 m, y=5.110-3 mm
at x=0.29 m, y=2.810-3 mm
at x=0.44 m, y=-1.210-3 mm
=0.15 m
x
1 R
L 1
R 2
=0.08 m =0.14 m L 2
L 3
=0.07 m L 4
44744
mm57.12m102566.164
04.0
64
dI
Also check the slope of the shaft at the critical locations
![Page 41: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/41.jpg)
Hollow v Solid
0
20
40
60
80
100
0 20 40 60 80 100
Re
lati
ve P
ola
r M
om
en
t o
f In
ert
ia [
%]
Wall Thickness / Shaft Radius [%]
![Page 42: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/42.jpg)
Hollow v Solid
0
20
40
60
80
100
0 20 40 60 80 100
Re
lati
ve P
ola
r M
om
en
t o
f In
ert
ia [
%]
Relative Mass [%]
![Page 43: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/43.jpg)
Hollow v Solid
0
20
40
60
80
100
0 20 40 60 80 100
Re
lati
ve P
ola
r M
om
en
t o
f In
ert
ia [
%]
Relative Mass [%]
Danger of buckling?
![Page 44: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/44.jpg)
![Page 45: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/45.jpg)
![Page 46: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/46.jpg)
Some Concluding Remarks - I
Shaft Design Considerations
• size and spacing of components
• material selection, material treatments
• deflection and rigidity
• stress and strength
• frequency response
• assembly, manufacturing & servicing constraints
![Page 47: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/47.jpg)
Some Concluding Remarks – II
1. Minimize deflections and stresses: short shaft, overhangs only if necessary
– Deflection of cantilever beam > deflection of simply supported beam
for the same dimensions and loading)
– But think about assembly and serviceability
2. Stress-raisers (i.e. keys, sharp corners) should not be placed in critical regions:
– minimize effects with a radius (standard values!) or a chamfer.
3. Low carbon steel is often as good as higher strength steels since deflection is
typical the design limiting issue.
4. Limiting deflections
– Gears: deflection < 0.13 mm and slope < 0.03°.
– Rolling element bearings
non self aligning: slope < 0.04°
self aligning: slope < 2.5° (depending on model / configuration)
5. Hollow shafts have better stiffness to mass (specific stiffness) and higher natural
frequencies than solid shafts, but are more expensive and typically have a larger
diameter.
6. Natural frequency of shaft should be >> highest excitation frequency in service.
![Page 48: Shaft Design Flow Chart](https://reader034.vdocuments.site/reader034/viewer/2022042501/55cf91b0550346f57b8fb7fa/html5/thumbnails/48.jpg)
Q&A 27 Oct 2014
• Check the Forum!
– Important announcements
– ME1 Notes
– CAD models
• Sharepoint: Use it!
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