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Lecture 20

AER 403 Lecture 20: AER 403 W20
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5 Pages
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Department
Aerospace
Course Code
AER 403
Professor
Fengfeng Xi

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AER 403 W20
Motion transmission isolation
• )n motion transmission isolation, there is no internal vibration source.
The excitation is the external support motion.
• (ence we need to look at the support motion vibration. |X/Y|=
[+ξ/)2]/[(1−/)2)2+(2ξ/)2]
when/n>> ,amplituderatio<,X/Y=//n 0
• This means that the isolation system requires a small n.
• A small n can be realized by a soft spring and/or a relative heavy
base.
• A typical example is an optical table which is made of marble
supported by an air cushion system.
• Looking at the equation of motion
md2x/dt2 = -k(x-y) - c(dx/dt-dy/dt)
md2x/dt2 + cdx/dt + kx = ky+ cdy/dt
Equivalent transmitting force through spring & damper
22, | 17
Motion transmission isolation
• /n>> , > X/Y=//n 0 Transmitting force is used
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to overcome the inertia force. • /n=, =
X/Y=1
Transmitting force is used
to overcome the spring and damping force. • /n=, =9
X/Y= /ξ+ 1/2
22,
| 18
Optical table
22, | 19
Transmissibility & isolation efficiency
• Transmissibility
|X/Y| |output amplitude / input amplitude|
• )solation efficiency [Y-X)/Y]×100%
• Decibel p.
dB = 20 log (X/Y)
Example
|X/Y| = 0.1 [(1-0.1)/1]100%=90% 20 log 0.1 = -20 dB
|X/Y| = 0.015 [(1-0.015)/1]100%=98.5% 20 log 0.015 = -36 dB
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Description
AER 403 W20 Motion transmission isolation In motion transmission isolation, there is no internal vibration source. The excitation is the external support motion. Hence we need to look at the support motion vibration. |X/Y|= [1+(2/)2]/[(1(/)2)2+(2/)2] when/n>> 2,amplituderatio<1,X/Y=1/(/n)2 0 This means that the isolation system requires a small n. A small n can be realized by a soft spring and/or a relative heavy base. A typical example is an optical table which is made of marble supported by an air cushion system. Looking at the equation of motion md2x/dt2 = -k(x-y) - c(dx/dt-dy/dt) md2x/dt2 + cdx/dt + kx = ky+ cdy/dt Equivalent transmitting force through spring & damper 22, | 17 Motion transmission isolation /n>> 2, >120 X/Y=1/(/n)2 0 Transmitting force is usedto overcome the inertia force. /n=0, =0 X/Y=1 Transmitting force is used to overcome the spring and damping force. /n=1, =90 X/Y= (1/2)2+1 1/2 22, | 18 Optical table 22, | 19 Transmissibility & isolation efficiency Transm
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