Flow Induced Vibration , Noise in Pipes

 

Piping vibrations

Vibration of process plant piping can be a significant risk to asset integrity and safety. This is often due to flow induced vibration (FIV) and acoustic induced vibration (AIV), and is related to the flow of the main process fluid through the piping system.
Other possible sources of piping vibration include:

• Mechanical vibration and pulsations from compressors and pumps;
• Flow induced pressure pulsations related to the pipework configuration and other components and features in the flow;
• Valve configuration and operation;
• Cavitation and flashing across valves in liquid service.

Flow induced vibration

Flow induced vibration is the result of turbulence in the process fluid, which occurs due to major flow discontinuities such as bends, tees, partially closed valves, and small bore connections. The high levels of broadband kinetic energy created downstream of these sources is concentrated at low frequencies, generally less than 100 Hz, and can lead to excitation of vibration modes of the piping and connected equipment. The extent of this problem depends on the piping design, support configuration and stiffness, valve operation, and other related factors which determine the severity of the resulting vibration.

Acoustic induced vibration

A relief or control valve on piping systems in gas service, or other pressure reducing devices, can generate high levels of high frequency acoustic energy, an effect commonly referred to as acoustic induced vibration. In addition to high noise levels arising external to the piping, this excitation can result in high frequency vibration of the pipe wall, with the potential for high dynamic stresses at welded features such as supports and small bore connections. This in turn can lead to the possibility of fatigue cracking within a relatively short period of time (minutes or hours).

Flow induced pulsation

Flow induced pulsation (FIP) can be caused by dead leg branches in pipework, which can be excited as acoustic resonances with discrete frequencies. These resonances can induce large shaking forces in the pipework, leading to integrity and safety risks.

Causes of flow-induced vibration

Flow-induced vibration of pipelines and piping can be caused by a number of mechanisms including:
• Pumps and compressors which could produce pressure pulsations, exciting a response in nearby piping
• Fluctuating flow past obstructions or objects in the flow (for example, thermowells or other intrusions in the flow) and piping dead legs
• Multiphase flow – for cases with multiple phases flowing (for example, gas and liquid), specific multiphase flow regimes and flow frequencies through piping may drive vibration (for example, slug flows where packets of liquid impact the walls of the pipe at bends, elbows and obstructions)
• Rapid changes in flow conditions or fluid properties caused by opening valves, cavitation or other large pressure variations leading to changes in state, for example, flashing of liquids to vapor.

Air Flow Induced Vibrations & Noise in Fans

Industrial blowers, HVAC systems, cooling fans, and exhaust systems all make Vibration & Noise that can cause damage to the equipment ,discomfort or even a strong annoyance. For each of these products, the main source of Vibration & noise is often the turbulent flow producing acoustic waves, known as aeroacoustics and Flow induced Vibrations . Aeroacoustics noise and Flow induced Vibrations are complex and sensitive multi-disciplinary science involving airborne and structure borne acoustics, aerodynamics and structure vibration and deformation.
Flow-induced vibration can cause catastrophic failure of a structure if its natural frequencies “lock in” with the shedding frequencies of the flow. Short of catastrophic failure, flow-induced vibration can reduce equipment performance and lead to failure through fatigue. Engineers must understand the sources of this vibration, along with related amplitudes and frequencies, to produce designs that can withstand them.

Fan Stall
Stall is aerodynamic phenomenon which occurs when a fan operates beyond its performance limits and flow separation occurs around the blade.
The angular relationship between the air flow impinging on the blade of a fan and the blade itself is known as “the angle of attack”. In axial flow fan, when this angel exceeds a certain limit, the air flow over the blade separates from the surface and centrifugal force then throws the air outwards, towards the rim of blades. This action causes a build up of pressure at the blade tip, and this pressure increases until it can be relived at the clearance between the tip and the casing. Under this condition the operation of the fan becomes unstable, vibration sets in and the flow starts to oscillate. The risk of stall increases if a fan is oversized or if the system resistance increase excessively.
Rotating Stall
This is a special case of stall that normally only occurs in backwardly inclined and airfoil centrifugal fans. Most observers also report that inlet box dampers are involved. Variable inlet vanes do a good job of preventing rotating stall because they provide a more stable flow path for the air through the wheel. These fans are encased in a scroll type housing that helps generate the fan’s pressure. The pressure around the periphery of the fan wheel varies relative to how near it is to the fan outlet (where it is highest). These fans have several blades, typically 9 to12.
Rotating stall typically occurs in fans which are severely throttled (inlet box damper typically less than 30% open).Most researchers have reported that the frequency of travel of this rotating stall occurs at about two-thirds of the fan rotational RPM(x). Some have observed two traveling cells at once generating a four-thirds rotational frequency. There are other reports of rotating stall ranging from two-thirds and even higher harmonics (2/3x, 4/3x, 6/3x, 8/3x, …). If these exciting frequencies coincide with the natural frequencies of the wheel or housing, resonance occurs and damage can result. This frequency will show up in both sound and vibration measurements. Rotating stall is among the most destructive of instabilities in the fan.
Surge
In concept, a system in surge is like an oscillator. The energy imparted to the air alternates between creating kinetic energy (high velocity in the duct) and potential energy (compressing the air in the plenum). The positive slope on the fan curve allows large amplification of this oscillation to occur. In extreme conditions, the air can temporarily blow back through the inlet.In a fixed system, the frequency of the surge is constant.
Usually the frequency is low enough that you can count the number of cycles per minute since it is quite audible. Most severe reports occur at a frequency below 300 cpm. One researcher reported that this effect seems to disappear at frequencies above 450 cpm.The frequency of surge can be be calculated for simple systems:
Frequency (Hz) = 175 * Square Root [Duct-area /(Plenum-volume * Duct-length)]

Vibration Data Types

Acquiring vibration data is only part of the challenge of vibration measurement; the other part is the analysis of the data acquired. It’s important to understand the types of wave forms associated with vibration analysis, the important differences between them and when it is appropriate to use each type of vibration analysis tool. Here’s a quick overview of some of the basics.

Time Domain Vibration Analysis

Vibration analysis starts with a time-varying, real-world signal from a transducer or sensor. Analyzing vibration data in the time domain (amplitude plotted against time) is limited to a few parameters in quantifying the strength of a vibration profile: amplitude, peak-to-peak value, and RMS, which are identified in this simple sine wave.

Fast Fourier Transform (FFT)

The fast Fourier transform (FFT) is an efficient algorithm used to compute a discrete Fourier transform (DFT). This Fourier transform outputs vibration amplitude as a function of frequency so that the analyzer can understand what is causing the vibration. The frequency resolution in an FFT is directly proportional to the signal length and sample rate. To improve the resolution, the time of the recording must be extended, but be careful of a changing vibration environment.

Spectrogram

A spectrogram takes a series of FFTs and overlaps them to illustrate how the spectrum (frequency domain) changes with time. If vibration analysis is being done on a changing environment, a spectrogram can be a powerful tool to illustrate exactly how that spectrum of the vibration changes.

Power Spectral Density

A power spectral density (PSD) takes the amplitude of the FFT, multiplies it by its complex conjugate and normalizes it to the frequency bin width. This allows for accurate comparison of random vibration signals that have different signal lengths. For this reason, PSDs are typically used to describe random vibration environments like those specified in military and commercial test standards.

Octave band

Analyzing a source on a frequency by frequency basis is possible but time consuming . The whole frequency range is divided into sets of frequencies called bands. Each band covers a specific range of frequencies. For this reason, a scale of octave bands and one-third octave bands has been developed. A band is said to be an octave in width when the upper band frequency is twice the lower band frequency. A one-third octave band is defined as a frequency band whose upper band-edge frequency (f2) is the lower band frequency (f1) times the cube root of two.

Vibration Spectrum : Mixing Frequencies

When two frequencies are present in a machine and a cause and effect relationship is not present, the high frequency will be riding the low frequency and the Fast Fourier Transform (F’FT) will yield spectral lines at frequency one and frequency two. If there is a cause and effect relationship and the two frequencies can mix together, the result is amplitude modulation. Without getting mathematical, amplitude modulation is a time varying amplitude. Amplitude modulation is caused when the equipment has some form of non linearity. This non linearity permits the amplitude of the two signals to add together when the signals are in phase, or subtract when the signals are out of phase. With amplitude modulation, the carrier frequency will be the frequency with the highest amplitude. The envelope of the varying amplitude will be the difference between the two frequencies. An FFT of these signals can yield spectral lines at frequency one, and frequency one plus and/or minus frequency two.

For example, suppose gear mesh frequency is modulated by gear speed, gear mesh frequency is 1200 Hz, and gear speed is 20 Hz. An FFT of this signal would then yield spectral lines at 1200 Hz, 1200 + 20 = 1220 Hz, and/or 1200 – 20 = 1180 Hz.

Descriptions of these frequencies are:
1. 1200 Hz is gear mesh frequency.
2. 1220 Hz is gear mesh frequency plus gear speed. This is a sum frequency.
3. 1180Hz is gear mesh frequency minus gear speed. This is a difference frequency.
4. The difference between 1200and 1220Hz, or 1200and 1180Hz is 20 Hz, and this is also a difference frequency.
5. The source of excitation, or the problem shaft or gear is usually expressed as a difference frequency.

Vibration Time Wave form : Multiple Frequencies-Non Linear System(Frequency Modulation)

Frequency modulation is a time-varying frequency,as opposed to amplitude modulation, which is a time-varying amplitude. The lower frequency is the carrier, and the higher frequency is the modulator. The modulator is normally an excited frequency, and the source of excitation is normally the speed of the rotating unit.
Pulse Excited Natural Frequency

Frequency Modulation

Frequency modulation can be a series of high frequency bursts similar to a pulse, or the high frequency can occur periodically with a low frequency. Since the frequency response of an accelerometer is best at high frequencies, such problems may be best measured in acceleration. Frequency modulation occurs most often in impacts, such as defects on the inner race of cylindrical roller bearings, or when two shafts are rotating very close to each other. Frequency modulation can occur in screw compressors, vacuum pumps, and blowers when one shaft is bent enough to permit an impact once each revolution.

One last comparison should be noted to clarify the differences between a high frequency
riding a low frequency, amplitude modulation, and frequency modulation.

1. High frequency riding a low frequency - No looseness is present. High and low frequencies may be exact multiples of each other. No mixing of signals occurs. Changes in the phase have little or no effect.

2. Amplitude modulation - High frequency is the carrier; low frequency is the modulator. Signals go into and out of phase.

3. Frequency modulation - Low frequency is the carrier; high frequency is I the modulator.

Vibration Time Wave form : Multiple Frequencies-Non Linear System (Pulse)

A pulse is caused by a hit or an impact. Pulses fall into one of three categories: empty pulses, frequency modulation, and amplitude modulation.This occurs when excited or generated frequencies are not present. It is called empty because it contains no generated or excited frequencies. A pulse is identified by a series of spectral lines. The repetition rate of the pulse is equal to the difference frequency between the spectral lines. The empty pulse has a low level spectral line at shaft speed, and the amplitude increases with each succeeding harmonic.
Empty Pulse

Frequency modulation is a time-varying frequency. This frequency modulation can appear as a series of bursts or beats. Generated or excited pulses are usually caused by a once-per-revolution impact or excitation.
Generated or Excited Pulse

Vibration Time Wave form : Multiple Frequencies-Non Linear System (Sum and Difference Frequencies ) .

Another type of amplitude modulation occurs when one component is eccentric. One example of sum and difference frequencies is gear eccentricity. When one gear is eccentric or out of round, the amplitude of gear mesh frequency increases when the high place or places go into mesh. If the gear has only one high place, the signal amplitude will be higher once each revolution. In either case, amplitude modulation is caused by the eccentric gear. The associated spectra contain a spectral line at gear mesh frequency with side bands of gear speed. If the gear has more than one high place, then the difference frequency between the gear mesh frequency and the side bands is equal to the number of high places times the speed of the problem gear. If two high places are present, the difference frequency is two times gear speed. Three high places would generate a difference frequency of three times gear speed, four high places would generate four times gear speed, etc.

If the eccentric gear has not caused looseness, side bands will occur at gear mesh frequency
plus gear speed or multiples of gear speed. In other words, the side bands will be on the high side of gear mesh frequency. The frequencies add, in this case, because the phase relationship between the carrier and the modulator is constant. As stated earlier, the machine is behaving in a linear manner.
One Revolution of Gear with Four Eccentricities.

Sum and Difference Frequency with No Phase Shift.

Sum and Difference Frequency with Phase Shift.

When a gear or geared shaft system is loose, the looseness causes the modulator to subtract from the carrier because the two frequencies are out of phase. When the two frequencies are in phase, they add. Looseness causes an out-of-phase condition. Eccentricity is an in-phase condition.
If gear eccentricity has caused looseness (non linearity) associated with the problem gear, side band scan occur on both sides of gear mesh frequency. If looseness is the more severe problem, the amplitudes of the side bands will be higher on the low side of gear mesh frequency. If eccentricity is the more severe problem, the amplitudes of the side bands will be higher on the high side of gear mesh frequency. If looseness is the only problem, then the side bands occur only on the low side of gear mesh frequency.
The frequencies subtract when looseness is present because the phase relationship between the signals is not constant, which means the machine is acting in a nonlinear manner.
The principles described for gear mesh frequency apply to other generated frequencies such as blade or vane pass frequencies, bearing frequencies, frequencies from multiple defects, and frequencies from bars or corrugations on press rolls.

Vibration Time Wave form : Multiple Frequencies-Non Linear System (Amplitude Modulation ) .

Two or more independent frequencies can be mixed together if a machine has some form of non linearity or other problem. There are many forms and degrees of frequency mixing. Examples of amplitude modulation, sum and difference frequencies, pulses, and frequency modulation are discussed in the following sections.

Amplitude Modulation :
Amplitude modulation occurs when two frequencies are added together algebraically. Frequencies will not add in a machine that behaves in a linear manner. Therefore, a problem must exist before amplitude modulation can occur. There are several forms of amplitude modulation; one form is a beat. A beat occurs when the amplitudes of two frequencies are added together.

When the amplitudes of the two frequencies go into phase, they add together. Then, as the two frequencies go out of phase, the amplitudes subtract until they are 180 degrees out of phase. The two frequencies continue to go into and out of phase, forming a time varying amplitude signal called a beat.

Beat-Amplitude Modulation of Two Frequencies.

Amplitude modulation also occurs when two frequencies are not exact multiples

Two Similar Frequencies with Second Harmonic.

Beat of Two Similar Frequencies.

Vibration Time Wave form : Multiple Frequencies - Linear system

High Frequency Riding a Low Frequency :
When two independent frequencies are present in a linear system, they cannot add together in amplitude or frequency. When this occurs, the two frequencies mix, and the high frequency will ride the low frequency, At first glance, amplitude modulation appears to be present.

High frequency riding on low frequency

Since harmonics are not present and the high frequency is riding the low frequency, there is not
a cause and effect relationship. The two signals are generated independently. It is important to note that a high frequency which is an exact multiple of a low frequency will cause the amplitude of the high frequency peaks to be the same in each period of the low frequency. A high frequency that is not a multiple will cause the amplitude of the high frequency peaks to vary during each period of the low frequency.

Vibration Time Wave Form : Square Wave

A special case to note is a single frequency with only odd harmonics present. The harmonics tend to cancel each other out, except for one positive and one negative peak per time period of the fundamental. The peaks have an amplitude equal to the sum of all the amplitudes added together.
A special case of odd harmonics is has only odd harmonics, and every other odd harmonic is
180 degrees out of phase. The resultant signal is a square wave. The amplitudes correspond to the amplitude of the fundamental divided by the harmonic number.

Single Frequency with Only Odd Harmonics.

Note that the signal is not exactly square, but has ripples. This is due to the fact that a limited number of odd harmonics are contained in the signal. A true square wave contains all odd harmonics, which cannot be truly simulated on a computer as a sum of the cosine functions.

Single Frequency with Only Odd Harmonics.

It may appear impossible for a piece of equipment to generate a square wave, but it is possible to generate a signal with square wave features. This can occur in a motor if the motor has a loose mount. If the mounting bolts are loose, the motor will tend to move up and down. If the motor moves up and is stopped by the mounting bolt, and then moves down and is stopped by the motor support, a square wave can be generated. If clipping occurs on both the top and bottom of a signal and the clipping is significant,the result will resemble a square wave.

Vibration Time Wave form : Clipping

CLIPPING :
A signal is said to be clipped when a slight amount of the positive or negative signal is flattened. The upper signal is an undistorted time signal. The lower signal is clipped at the bottom.

Clipped Signal

a clipped time signal and a spectrum from a motor
1800 RPM Belt Driving a Fan.

Such a signal can be generated when a machine goes against a stop in one direction and cannot move further in that direction for a small period of time. As the cycle continues, the machine moves away from the stop in a relatively linear manner. The signal is distorted because the time period for the negative and positive portion is not the same. Clipping is also a “form of distortion. The frequency spectrum contains very little harmonic content, because in order for harmonic content to be generated, the signal distortion must be repeatable.