PSI - Issue 45

Aditya Khanna et al. / Procedia Structural Integrity 45 (2023) 12–19 Khanna and Young / Structural Integrity Procedia 00 (2019) 000 – 000

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4

API Standard 618 (5th Edition, 2007), corresponds to acceptable vibration levels for well-designed and newly commissioned systems. Vibration levels in Zones A and B (i.e., below the B/C limit) are considered acceptable for long-term operation, whereas vibration levels in Zone D (i.e., above the C/D limit) are considered severe enough to warrant urgent correction or machine shutdown. As seen in Fig. 3b, the constant velocity ISO criteria are more conservative than the frequency-dependant empirical criteria at frequencies above 20 – 30 Hz. Since the natural frequencies of well-designed piping systems and small-bore connections often exceed 20 – 30 Hz, it is of great practical interest to determine which screening approach (constant velocity or frequency-dependant velocity) is more appropriate for pressure vessel nozzles and other similar small-bore connections.

Table 2. ISO/EFRC piping and small-bore connection vibration limits for various evaluation zones

Frequency range

A/B

B/C

C/D

Displacement (mm, RMS) Velocity (mm/s, RMS) Acceleration (m/s2, RMS)

2 – 10 Hz

0.202 12.67 15.92

0.302

0.454

10 – 200 Hz

19.0

28.5

200 – 1000 Hz

23.58

35.81

Wachel Correction

100

A/B B/C C/D

10

10

API "Design"

ISO/EFRC Limits

Velocity (mm/s RMS)

Displacement (mils P-P)

1

1

1

10

100

1000

1

10

100

(b)

(a)

Frequency (Hz)

Frequency (Hz)

Fig. 3. (a) ISO/EFRC vibration velocity limits for pipeline and small-bore connection vibrations, and (b) comparison against EI guidelines in displacement domain.

Locations at which the vibration exceeds the “Acceptable” limit but is below the “Danger” limit represent a grey area for vibration severity assessment. Geometry-specific vibration criteria can reduce the conservatism of vibration screening in this grey area and avoid the need for more costly analysis, e.g., strain gauging or computational modelling, in many instances. Several geometry-specific vibration criteria have been obtained in the past for beam like pipe configurations, for e.g., in the papers by Bifano et al. (2018) and Wachel et al. (1990). However, further work needs to be done in this area for other common piping geometries. The parametric FE study presented in the current work aims to address the gap in available assessment methods for cantilevered nozzles and other small-bore fittings attached to relatively thin-walled pipes and pressure vessels. While vibration criteria already exist for cantilever beams, pressure vessel nozzles are more akin to cantilevers on torsional spring supports. Due to the comparable wall thicknesses of the nozzle and the parent vessel, the transverse modes of the nozzle are accompanied by the flexure of the vessel shell (see Fig. 1). It is worth pointing out that the criteria reviewed previously, and the geometry-specific criteria developed in the present work, relate to resonant vibration at the fundamental transverse (bending) modes of the pipe geometry. Caution must be exercised when using these criteria to assess vibration at off-resonant frequencies, i.e., forced excitation below or above the fundamental natural frequency. Fig. 4 shows the dynamic stress per unit vibration at off-resonant conditions normalised by the dynamic stress per unit vibration at resonant conditions for a fixed-free beam. For forced excitation of cantilever beams below the first natural frequency (including the limiting case of static loading), the dynamic stress per unit displacement is relatively steady and slightly less than the dynamic stress per unit displacement at resonance. Hence, displacement is a better indicator of dynamic stresses than velocity when