9 natural frequency

8/12/2019 9 Natural Frequency

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Introduction to Natural Frequency Testing

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INTRODUCTION

Every mechanical system has a series of natural frequencies, each of which has its

own damping characteristics. These natural frequencies will liedormantin a

system until they are excited by some external influence or forcing function.

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The vibration can be greatly amplified if a forcing function, such as unbalance or a

blade pass frequency (# blades X RPM) happens to be within the range of a

natural frequency. When such forcing frequencies coincide with (or closely

approach) a natural frequency, this is the condition known as resonance.


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DIFFERENCE BETWEEN NATURAL FREQUENCY, RESONANCE AND

CRITICAL SPEED

The termsnatural frequency, resonanceandcritical speedare often used

interchangeably, even by experienced vibration analysts. However, there are

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. ,operating at a resonant frequency, but this may or may not be a critical speed. It is

hoped the following definitions will help clarify the differences between each of these

important terms.


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a. Natural Frequency:

Reference 2 defines a natural frequency as The frequency of free vibration of a

system. The frequency at which an undamped system with a single degree of

freedom will oscillate upon momentary displacement from its rest position.In

addition, for a multiple degree-of-freedom system, the natural frequencies are

the frequencies of the normal modes of vibration. All machines and all

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structures have a number of natural frequencies. If forced to vibrate at one or

more of these natural frequencies, dynamic stresses of 10 to 100X higher

than those are inducedcompared to those which would be generated if these

same forces were input at other frequencies lower or higher than these

natural frequencies.

This only becomes a problem if they are excited(seeresonancebelow). For

example, when we perform impulse tests, we are not looking for resonant

frequencies, but for natural frequencies which the machine must avoid so that it

may not encounter resonance.


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Natural Frequency

Every machine will be vibrating at its natural frequency when it is exciting

by external force:

= 1/2

=

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2Pi 2PiFn = natural frequency , cpm

Gc = Gravity of earth , m/s2

K = Stiffness Kg/metreM = Mass , Kg/m/s2

Delta = Deflection, m


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b. Resonance:

Resonance is the condition which occurs when such forcing frequencies do in fact

coincide with one or more natural frequencies. These may be a natural frequencies

of the rotor, but often can be a natural frequency of the support frame, foundation or

even of drive belts. The piping on compressors can be a problem if they resonate.

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Forcing frequencies include those from sources such as unbalance, misalignment,

looseness, bearing defects, gear defects, belt wear, etc.

Therefore, it is important to point out resonances can be encountered not only at 1X

RPM,but at series of frequencies including 1X RPM, 2X RPM, 3X RPM, etc.

Reference 2 defines resonance as the condition of vibration amplitude and phase

change response caused by a corresponding system sensitivity to a particularforcing frequency. A resonance is typically identified by a substantial amplitude

increase, and related phase shift.


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Resonance - Characteristics

1. Lack of response to balance attempts: thus it is almost impossible to

balance the rotor having resonance problem. It is necessary to change

natural frequency or speed.

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. ,resonant direction be 5 to 15 times higher than other direction.

3. Phase Behavior in the resonant measuring direction: 90 degree change

of phase with almost 180 degree through resonant

4. Probable phase difference in measuring direction perpendicular to resonant

measuring direction: Noticeable phase difference else than 90 degreewhen measurement in horizontal compare to vertical direction.


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5. Frequencies at which resonance can occur:

Resonant Vibration = Forcing frequency vibration x Q

6. Resonance can suddenly occur on a long running machine never before

subjected to it:

For exam le bearin wear or sim le sleeve bearin re lacement which can

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cause a change in natural frequency. One can simply solve this type of

problem by proper installation of the bearings and checking for required

clearance specifications.

7. Possible effect of coupling changes:

Coupling changes can sometimes result in a different torsional natural

frequency, particularly if a different diameter coupling is used, or differenttype. Significant vibration occur in bearings on either side of the coupling.


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c. Critical Speed:

Reference 3 points out that critical speeds are a special case of resonance in

which the vibrating forces are caused by the rotation of the rotor. He also adds that

critical speed testing is often more complicated than resonance testing because

the natural frequencies encountered are functions of stiffness and mass which may

be dependent on machine speed. For example,in the case of a machine with an

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extended overhung rotor or in the case of general sleeve bearing machines, critical

speeds can change their frequency location due to changes in stiffness and/or

gyroscopic motion (unlike resonant frequencies for frames, foundations and rolling

element bearing machines which have fixed natural frequencies independent of

operating speed).

Similarly, Reference 1 defines critical speeds as in general, any rotating speed

which is associated with high vibration amplitude. Often, the rotor speeds whichcorrespond to natural frequencies of the system.Generally, good design practices

mandate that a machine should be designed not to operate within 20% of a critical

speed(not20% of any natural frequency).


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Critical Speed

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typically 20% or greater


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fn

fhfl

Q (amplification factor) = fn / (fh-fl)

Damping factor = 1

2Q

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= 0.707 An


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9 natural frequency

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