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Design of Pressure VesselsInternally Pressurized Cylinders:Stresses in Thin-Walled Cylinders:
,
,
Stresses in thick-walled cylinder:
Externally Pressurized Cylinders:Stresses in thick-walled cylinder:
22
2
2 2
,max
22
2
2 2
2 2
,max 2 2
1
1
oi i
r
o i
r i
oi i
o i
i i o
o i
rp r
r
r r
p
rp rr
r r
p r r
r r
2 2
2 2 2
,max
2 2
2 2 2
2
,max 2 2
1
1
2
o o i
r
o i
r o
o o i
o i
o o
o i
p r r
r r r
p
p r r
r r r
p r
r r
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Rotating Cylinders:
Cylinder with Central Hole:
: mass denisty, kg/: rotational speed (rad/s)
Solid Shaft:
Recommended tolerances in millimeters for classes of fit:
Maximum and Minimum Shaft and Hub Diameters:
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Interference Fit:
Force and Torque:
Interference of press fit of hollow shaft to hub
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Fasteners and Power Screws
Power Screws: Pitch p: the distance from a point on one thread to the same point to
the adjacent thread.
: The thread angle.
Number of threads per inch n= 1/p
l= m*p, m: number of starts, l: lead
Helix angle ; l : lead The Tensile stress area:
The pitch diameter of an ACME power thread is: (in) (mm)
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Forces and Torque
Raising the Load:
Lowering the Load:
The power, in horse power:
The power, in watts:
Effieciency:
Self Locking Screws
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Strength of Steel Bolts:Proof strength: =0.8 * Yield strength
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UN Coarse and Fine Threads:
M Coarse and Fine Threads
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Design of Spur gearsSpur Gear Geometry:
Center distance: Circular pitch: Gear Ratio:
Diameteral pitch:
Module (m): Formulas for addendum, dedendum, and clearance (pressure angle, 20; full-
depth involute):
Loads on Gear Tooth
Bending Stresses in Gears
Modified Lewis Equation:
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AGMA Bending Stress Equation:
Application Factor
Size Factor
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Load Distribution Factor
Pinion Proportion Factor
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Pinion Proportion Modifier
Mesh Alignment Factor
Dynamic Factor
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Contact Stresses in Gears:
Gear Materials:
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Allowable Contact Stress:
Allowable Bending and Contact Stress:
Stress Modification Factors:
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AGMA recommends modifying the allowable bending stresses as follows:
AGMA recommends modifying the allowable contact stresses as follows:
Stress Cycle Factors, and :
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Reliability Factor:
Hardness Ratio Factor, :
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Power transmission and pinion speed relationship:
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Design of Helical GearNormal Circular Pitch:
Axial Pitch:
Equivalent Number of Teeth and Pressure Angle:
Helical Tooth Proportions:
Loads in Helical Gear:
AGMA Equations for Helical Gears:Bending Stress:
Pitting Resistance:
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Geometry Factors for Helical Gears:
Geometry factors Y and I for helical gears loaded at tooth tip.
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Design of Riveted and Welded Joints:Design of Riveted Joints:
Failure Modes for Fasteners in Shear:
Bending of Members:
Shear of Rivets (Single or Double):
Tensile Failure of Members:
Compressive Bearing Failure of Members:
Design of Welded Joints:
Fillet Weld:
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Shear Loading:
Bending Loading:
Electrode Properties:
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Design of Springs
Strength of Spring Materials
Deflection of Helical Compression Springs
Lengths and Forces in Helical Springs
Cyclic Loading
max 3 3
d w
Spring Index (meaure of coil curvature)
8 0.5 81
Transverse shear factor
K is replaced with curvature correction factor, K
4 1 0.615
4 4
d
d
w
DC
d
PD PDKd C d
K
CK
C C
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Design of Keys
310 for unpeened springs
465 for peened springs
se
se
S MPa
S MPa
1. Failure due to shear:
2. Failure due to compressive or bearing stress
design
The shear force acting on the Key
2
/ 2
The area for a key is . The design shear stress is
2
s
sy
s s
T TP
d d
A wl
SP T
A dwl n
design
The compression or bearing area of the key is
2
2
The compressive or bearing pressure is:
0.94
c
y
c s
lh TA
d
SP T
A dlh n
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Brakes and ClutchesThrust Disk Clutch
Uniform Pressure Model
Uniform Wear
Properties of Common Friction Materials
2 2o o iP p r r
2 3 32
23
o
i
r
oo o i
r
pT p r dr r r
3 3
2 2
2
3
o i
o i
r rPT
r r
2
o i
PT r r
2 a i o iP p r r r
2 2a i o iT p r r r
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Short-Shoe Brake
Band Brakes
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Design of Keys
1. Failure due to shear:
2. Failure due to compressive or bearing stress
design
The shear force acting on the Key
2
/ 2
The area for a key is . The design shear stress is
2
s
sy
s s
T TP d d
A wl
SP T
A dwl n
design
The compression or bearing area of the key is
2
2
The compressive or bearing pressure is:
0.94
c
y
c s
lh TA
d
SP T
A dlh n
h
h
h
d: shaft diameter
l: key length
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Failure Prediction for Multiaxial Stresses
I. Ductile Materials
Maximum Shear Stress Theory (MSST):Also known as Tresca Yield Theory
1 3 1 2 3,y
s
S
n
Distortion-Energy Theory (DET):Also known as von Mises Yield criterion