shafts-06 - Mechanical Engineering at the University of ... · PDF fileShaft Fatigue Failure....
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1 Shafts Shafts in general Fatigue Deflection Critical Frequencies Shafts shoulders, keys, bending, torsion, deflection Shaft Power P=Tω Power = (Torque)(Angular Velocity) W = (Nm)(radians/s) 1 hp = 745.7 W Stresses in Shafts normal, bending, alternating,σ a normal, bending, mean, σ m shear, torque, alternating, τ a shear, torque, mean, τ m Fatigue Data Static Torsion Reversed Torsion Shaft Fatigue Failure
Transcript of shafts-06 - Mechanical Engineering at the University of ... · PDF fileShaft Fatigue Failure....
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ShaftsShafts in generalFatigueDeflectionCritical Frequencies
Shafts
shoulders, keys, bending, torsion, deflection
Shaft Power
P=Tω
Power = (Torque)(Angular Velocity)
W = (Nm)(radians/s)
1 hp = 745.7 W
Stresses in Shafts
normal, bending, alternating,σa
normal, bending, mean, σm
shear, torque, alternating, τa
shear, torque, mean, τm
Fatigue Data
Static Torsion Reversed Torsion
Shaft Fatigue Failure
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Shafts
shoulders, keys, bending, torsion, deflection
Shaft Design StrategyIdentify critical points along shaft
Find Ma, Mm, Ta, Tm
Find kf, kfs, kfm, kfsm
Find Sf (as a function of dshaft)Solve for dshaft (iterative)
General: Fluctuating Bending & Torsion
( ) ( ) ( ) ( )31
2222
43
43
32
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡+
++
=ut
mfsmmfm
f
afsaff
S
TkMk
S
TkMkNd
π
Some General Rules of Shaft DesignLength/positioning
Keep length as short as possible, avoid overhangs/cantilevered sections
Hollow shaftsGive greater stiffness/mass and higher natural frequency (but have greater cost and diameter)
Stress concentrationsLocate where bending moment is low, use generous radii
Deflection RulesGears
deflection less than 0.005 in., relative slope differ by less than 0.03 degrees
Bearingsdeflection important for sleeve/journal bearingsslope important for roller bearings
Natural FrequenciesBending
LateralWhirl
TorsionalNatural Frequency
first natural frequency > 3x(forcing frequency)
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Lateralassumes external excitation
set potential energy equal to kinetic energy
weighteachat
weighteachat
deflectionweightSUM
deflectionweightSUMgravityFrequencyNatural
)*(
)*( 2⋅=
∑
∑
=
=⋅= n
iii
n
iii
nw
wg
1
2
1
δ
δω
Shaft Whirl
2
2
)/(1)/(
n
ne ωω
ωωδ−
=
Whirl
2
2
)/(1)/(
n
ne ωω
ωωδ−
=
Bending Frequency StrategyFind maximum static deflection
static, but be realistic
Find ωn using Lateral Deflection
Find ω/ωn
Torsional Frequency StrategyFind Im of masses (usually ignore shaft)Find torsional spring constant, kt
Find J for each sectionkt,section=GJ/LFind 1/kt,total = 1/k1 + 1/k2 + 1/k3 + …
m
tn I
k=ω
Shaft CalculationsSee Examples on Norton CD
