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There are three characteristics of motion which are all related by the natural frequency of vibration for steady state harmonic vibration: displacement, velocity and acceleration. Of these, which is the best indicator for cyclic stress (or strain) which in turn is related to fatigue damage? As it turns out, it is velocity.
One may think that is should be displacement since stress is proportional to displacement, but the same displacement can result in different stresses in different piping systems. The same displacement will generally cause a higher stress in a stiffer piping system than in a more flexible piping system.
You can understand why velocity is the best indicator if you consider energy concepts. Vibration is a transfer between kinetic and potential energy. The maximum kinetic energy is at the point with maximum velocity, which is when the displacement is zero (that is also where the acceleration zero, it is switching from accelerating to decelerating). The maximum potential energy is when the displacement is maximum as the potential energy is the energy stored as a result of system displacement (that is also where acceleration is maximum).
Kinetic energy is proportional to velocity squared. Potential energy is proportional to the area under the stress strain diagram, which for a linear elastic system, is the strain times elastic modulus (which is the stress), times the strain, divided by two. So, the potential energy for a linearly elastic system is proportional to the strain squared. Since the kinetic energy must equal the potential energy, the velocity squared is proportional to the strain squared so velocity is proportional to strain and thus also proportional to stress (again, for an elastic system).
The simplest vibration screening rules use velocity as it makes the assessment relatively insensitive to the piping system layout. However, there are additional factors to consider which affect the vulnerability of a piping system with respect to fatigue failure due to vibration, such as the presence of high stress risers (an example of which is an un-reinforced stub in branch connections).
It is useful to have a screening rule for evaluation of piping vibration in order to determine if the vibration is potentially harmful (can lead to damage or fatigue failure) or if it is simply a nuisance and can be accepted without doing a more detailed assessment or anything to mitigate it. A very useful screening rule is provided in ASME OM-3, “Requirements for Preoperational and Initial Start-up Vibration Testing of Nuclear Power Plant Piping Systems;” however, it is first important to understand when it is appropriate to use this rule. It is not uncommon to have people use tools they are familiar with to address problems the tools are not suited for, yielding meaningless results.
To understand where the OM-3 screening rule is applicable, it is useful to understand different categories of piping vibration. The first division is transient versus steady state. The screening rule is for steady state vibration where fatigue failure with the accumulation of many cycles is the concern. There are many types of transient pipe vibration, for which other assessment tools would need to be used. There are many types of transient pipe vibration for which other assessment tools would need to be used. These include things like pressure wave water hammer due to events such as rapid valve closure, pump start-up or trip, collapse of vapor bubbles in subcooled liquid lines, opening a valve into a closed liquid system with a trapped gas bubble in it, slug flow such as slugs of steam condensate and natural gas liquids, and occasional wind-induced votex shedding.
Steady state vibration occurs primarily from two sources: 1) mechanically induced vibration of a driver (such as a compressor) that in turn vibrates the pipe, and 2) flow-induced vibration caused by the pressure pulsing or by flow turbulence and cavitation. These two sources of vibration can be exacerbated by acoustic resonance and/or by mechanical resonance. An example of mechanically induced vibration is associated with fluid solids equipment and coke drums whose low frequency vibration causes the connected pipe to vibrate in turn. An example of flow-induced vibration is excitation from the pressure pulsations from reciprocating pumps and compressors.
A second division is high frequency versus low to mid frequency vibration. The screening rule is for beam type pipe vibration, where the pipe is flexing like a beam, which is generally at frequencies below about 50 hertz. In high cycle vibration, the walls of the pipe may be rippling in shell vibration modes. Application of criteria based on beam behavior – such as the OM-3 crieria or even conventional piping dynamic analysis tools – to high cycle vibration is simply inappropriate. Examples of sources of high frequency vibration include broadband excitation caused by pressure let down and single frequency excitation caused by acoustic resonance. Other screening rules such as those based on sound are more appropriate for these conditions.
The OM-3 screening rule is a maximum peak velocity of 0.5 inch/second. The peak velocity will occur at the location where vibratory displacement is also maximum. It may require taking a number of measurements at different locations in the piping system to locate where the peak velocity is occurring. Note that peak is maximum amplitude, not a range. Range is maximum minus minimum amplitude.
Velocity is actually the best measurement for assessing the level of dynamic stress in a piping system because, for an elastic system, velocity is proportional to dynamic stress. This can be developed from an understanding that vibration is a transfer between potential and kinetic energy.
The rule is generally very conservative and simplified methods are provided in ASME OM-3, which for a great majority of piping systems will permit higher peak velocities. The screening rules make conservative assumptions with respect to having high stress risers in the system and large lumped masses such as heavy valves. If the vibrating piping system fails to pass the screening criteria, there are additional, less conservative methods in OM-3 that consider more of the system characteristics.
https://www.youtube.com/watch?v=7_AiV12XBbI
Posted by Chuck Becht on Thursday, 25 July 2013 in Piping
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