Isolation Models Comparison
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CHAPTER 9 VIBRATION CONTROL : VIBRATION ISOLATION . Comparison of Vibration Isolation Models ISOLATION OF VIBRATORY FORCE Isolation with Rigid Foundation (Force Harmonic motion) ISOLATION OF VIBRATORY MOTION (Harmonic Motion of the Base) Rotating Unbalance Force transmitted to foundation: Force Transmissibility, n r T r r r r r T c m k c k F F T where 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 0 Displacement transmitted to foundation: Ratio of displacement of the mass to the displacement of the base 2 2 2 2 2 c m k c k Y X 2 1 2 1 2 2 2 2 r r r T D Force transmitted to foundation due to rotating unbalance: 2 1 2 2 2 2 2 2 c M k c k me F T 2 1 2 1 2 2 2 2 r r r T R t me kx x c x M sin 2 The isolation efficiency (IE) is given by: IE=(1-TR) X 100%. vibration isolation requires > √: Tr can be reduced by decreasing the natural frequency of the system and by decreasing the damping ratio. However, since vibration isolation requires > √2the machine should pass through resonance during start-up and run-down. Some damping is therefore essential to avoid infinitely large amplitudes at resonance. damping reduces the maximum force transmitted to the foundation if: < √2 damping increases the maximum force transmitted to the foundation if: > √2 t F kx x c x m o sin
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Transcript of Isolation Models Comparison
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CHAPTER 9 VIBRATION CONTROL : VIBRATION ISOLATION . Comparison of Vibration Isolation Models ISOLATION OF VIBRATORY FORCE
Isolation with Rigid Foundation (Force Harmonic motion)
ISOLATION OF VIBRATORY MOTION (Harmonic Motion of the Base)
Rotating Unbalance
Force transmitted to foundation: Force Transmissibility,
nr
Tr
rrr
rT
cmk
ck
F
FT
where21
21
222
2
2222
222
0
Displacement transmitted to foundation: Ratio of displacement of the mass to the displacement
of the base
22222
cmk
ck
Y
X
21
21222
2
rr
rTD
Force transmitted to foundation due to rotating unbalance:
2
1
222
22
2
cMk
ck
me
FT
21
21222
2
rr
rTR
tmekxxcxM sin2
The isolation efficiency (IE) is given by: IE=(1-TR) X 100%.
vibration isolation requires > : Tr can be reduced by decreasing the natural frequency of the system and by decreasing the damping ratio.
However, since vibration isolation requires > 2the machine should pass through resonance during start-up and run-down. Some damping is therefore essential to avoid infinitely large amplitudes at resonance.
damping reduces the maximum force transmitted to the foundation if: < 2
damping increases the maximum force transmitted to the foundation if: > 2
tFkxxcxm o sin
