12. VIBRATION ISOLATION
12.1 Introduction
High vibration levels can cau machinery failure, as well as objectionable
noi levels. A common source of objectionable noi in buildings is the
vibration of machines that are mounted on floors or walls. Obviously, the best
畑山政子place to mount a vibrating machine is on the ground floor. Unfortunately (but
fortunately for noi control consultants), this is not always possible. A typical problem is a rotating machine (such as a pump, AC compressor, blower, engine, etc) mounted on a roof, or on
a floor above the ground floor. The problem is usually most apparent in the immediate vicinity of
the vibration source. However, mechanical vibrations can transmit for long distances, and by
very circuitous routes through the structure of a building, sometimes resurfacing hundreds of feet from the source. A related problem is the isolation of vibration-nsitive machines from the normally occurring disturbances in a building (car or bus traffic, slamming doors, foot traffic, elevators…). Examples of nsitive machines include surgical microscopes, electronic equipment, lars, MRI units, scanning electron microscopes, and computer disk drives.
Figure 1 shows a common example of a vibration source, a large reciprocating air conditioning compressor weighing 20,000 pounds, mounted on a roof. Annoying noi levels at multiples of
the compressor rotational frequency, predominantly 60 and 120 Hz, were measured in the rooms directly below the compressor. For whatever reason (don’t get me started…), the architect cho to mount this unit at the middle of the roof span, at the midpoint between supporting columns. Also, this type of compressor (reciprocating) is notorious for high vibration levels. Centrifugal
or scroll type compressors are much quieter, but more expensive (you get what you pay for!). Figure
1. A reciprocating air conditioning compressor and chiller mounted on a flexible roof, Note the straight conduit on the left which bypass the isolators and directly
transmits vibration into the roof
A vibration problem can also be nicely described by the same source – path – receiver model we previously ud to characterize the noi control problem.
by the machine, such as unbalance, torque pulsations, gear
tooth meshing, fan blade passing, etc. The typical occur at
frequencies which are integer multiples of the rotating
frequency of the machine.
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Path: the structural or airborne path by which the disturbance
is transmitted to the receiver
Receiver: the responding system,
generally having many natural
frequencies which can potentially be
excited by vibration frequencies
generated by the source. (Murphy
says the natural frequency of the
plantedsystem will always coincide with an
excitation frequency.)
Any or all of the areas can be attacked to solve the problem. The best choice for a given
application will be dictated by the laws of physics, your ingenuity, and $.
References: Sources of additional information on vibration isolation include:
• Manufacturer’s technical data – check the web or catalog data sheets, some suppliers include:
o Mason Industries
o Barry Controls
o Kinetics
• ASHRAE (American Society of Heating, Refrigeration and Air Conditioning Engineering) Applications Handbook, 1999. See Appendix
• Handbook of Acoustical Measurements and Noi Control, Cyril M. Harris, McGraw Hill, 1991.
• Noi and Vibration Control Engineering, L. Beranek editor, John Wiley and Son, 1992,
pp 429-450
12.2 Possible Solutions
The best solution to a vibration problem is to avoid it in the first place. Intelligent design is far more cost effective than building a bad design and having to repair it later. The intelligent solution to any vibration problem involves the following steps:
1) Characterize the system parameters (mass, stiffness, damping) by experimental methods,
manufacturers data, or a combination of both.
2) Model the system dynamics using a simple lumped parameter model
a) identify natural frequencies, look for coincidence with excitation frequencies
b) if excitation forces and frequencies are known, system respon can be calculated
3) U the model to asss the effect of changes in system parameters
Vibration Solutions - Source
1) Relocate machine – place machine on as rigid a foundation as possible (on grade is best)
and as far as possible from potential receivers
2) Replace machine with a higher quality or different type of machine that is quieter (and
probably more expensive)
企业产权3) Change the operating speed of the unit to avoid coinciding with structural resonances
4) Balance rotating elements,
5) Add a tuned vibration absorber
6) U active vibration control
Vibration Solutions - Path
Minimizing the vibration transmission generally involves using isolator springs and/or inertia
blocks. The basic principle is to make the natural frequency of the machine on its foundation as
far below the excitation frequency as possible. The mathematics for this ca, and isolator
lection procedures are discusd in the next ctions.
请长假理由Vibration Solutions – Receiver
1) Change the natural frequencies of the system to avoid coinciding with excitation
frequencies. This can be accomplished by adding stiffeners (which rais the natural frequency) or by adding mass (which lowers the natural frequency)
2) Add structural damping
12.3 Vibration Isolators
Consider a vibrating machine, bolted to a rigid floor (Figure 2a). The force transmitted to the
floor is equal to the force generated in the machine. The transmitted force can be decread by adding a suspension and damping elements (often called vibration isolaters) Figure 2b , or by
adding what is called an inertia block, a large mass (usually a block of cast concrete), directly attached to the machine (Figure 2c). Another option is to add an additional level of mass (sometimes called a ismic mass, again a block of cast concrete) and suspension (Figure 2d).
Figure 2. Vibration isolation systems: a) Machine bolted to a rigid foundation b)
Supported on isolation springs, rigid foundation c) machine attached to an
inertial block d) Supported on isolation springs, non-rigid foundation (such as a floor); or machine on isolation springs, ismic mass and cond level of isolator springs
If we consider only the vertical motion, the ca shown in Figure 2b can be described
mathematically by a single degree of freedom, lumped element system.
)(.
..t F kx x c x m =++ Equation 1
where:
m = mass of system k = stiffness c = viscous damping
x(t) = vertical displacement F(t) = excitation force
If we neglect damping, the vertical motion of the system, x(t) can be shown to be:
m k r t r k F t x n n O ==−=ωωωω :re whe sin 1)(2
Equation 2 The system has a natural, or resonant frequency, at which it will exhibit a large amplitude of motion, for a small input force. In units of Hz (cycles per cond), this frequency, f n is:
m
k f n n ππω212== Equation 3 In units of RPM (revolutions per minute), the critical frequency is
m
k f RPM n critical π26060== The force transmitted to the floor is:kx F T =
The ratio of transmitted force to the input force is called transmissibility, T
Y
X r F F T O T =−==112 Equation 4 This same equation can also be ud to calculate the respon of a machine X to displacement of the foundation, Y .
The effectiveness of the isolator, expresd in dB is:
INERTIA BLOCK SEISMIC MASS
不应该的英文T E 1log 1010
= Equation 5 The effectiveness of the isolator, expresd in percent is:
% Isolation = 100*)1(T − Equation 6
The transmissibility as a function of frequency ratio is shown in Figure 3. Vibration isolation (defined as T<1) occurs when the excitation frequency is > 1.4 f n . For minimum transmissibility (maximum isolation), the excitation frequency should be as high above the natural frequency as possible. The transmissibility above resonance has a slope of –20 dB/decade.
The transmissibility including the effect of damping is:
普及英语
ratio damping critical 2 :where )2()1()2(12222
==
+−+=n
m c r r r T ωξξξ Equation 7
Typical values for damping ratio, ξ are .005 -.01 for steel, and .05-.10 for rubber
The inclusion of damping has the greatest effect in the vicinity of resonance, decreasing the vibration amplitude. A curious effect of damping is that it results in incread amplitude at frequencies > 1.4 f n .
Examples:
1) Calculate the transmissibility at 60 and 120 Hz for a 20,000 lb chiller unit supported by eight springs with 3” static deflection. Answer:坐月子可以刷牙吗
Frequency – Hz r T dB % Isolation
60 60/1.8 = 33.33 .0009 30.5 99.910% 120 120/1.8 .00022 36.6 99.978%
2) A surgical microscope weighing 200 lb is hung from a ceiling by four springs with
stiffness 25 lb/in. The ceiling has a vibration amplitude of .05mm at 2 Hz (a typical resonant frequency of a building). How much vibration does the microscope
experience? Answer: r = .903, |X/Y| = 5.45, X=.273 mm (we have amplification)
