PSI - Issue 45

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

14

3

reason, the widely adopted Energy Institute (EI) guidelines (2nd Edition, 2008), which are based on previous empirical charts and stress calculations on several categories of small-bore fitting geometries, are expressed in the units of root mean squared (RMS) velocity. However, severe vibration of pipe spans and smallbore fittings most often occurs due to resonance at the fundamental bending mode, which is characterized by sinusoidal (single tone) vibration at the fundamental natural frequency of the item. Hence, the vibration criteria are often expressed interchangeably in the units of peak-peak displacement, RMS velocity, or 0-peak acceleration. The older SWRI “Marginal” and “Danger” limits, when expressed in units of RMS velocity , are almost identical to the EI “Concern” and “Problem” limits, as shown in Fig. 2. The older “Correction” limit, sometimes known as the Wachel Correction Line, lies approximately half- way between the “Marginal” and “Danger” limits and is a useful indicator of vibration levels requiring corrective action or further assessment. Based on experience, pipe vibration levels above the EI “Concern” limit but below the Wachel “Correction” limit generally result in acceptable dynamic stresses.

100

Danger

100

Correction

10

10

Marginal

Velocity (mm/s RMS)

Displacement (mils P-P)

1

1

1

10

100

1

10

100

(a)

Frequency (Hz)

(b)

Frequency (Hz)

Fig. 2. Pipe vibration criteria as per (a) the SWRI design chart from the 1970s (broken lines), and (b) the more recent EI guidelines (solid lines).

While the SWRI and EI guidelines hypothesise that the allowable vibration velocity is proportional to the square root of the dominant vibration frequency (i.e., the allowable displacement is proportional to the inverse square root of frequency), semi-empirical criteria based on stress calculations on common piping configurations (including an international standard) recommend constant-velocity vibration limits, i.e., allowable displacement inversely proportional to frequency. Some of the constant-velocity vibration criteria available in open literature are reviewed in Table 1. These criteria are mostly in agreement and recommend a screening limit of around 25 mm/s 0-Peak (18 mm/s RMS) for small-bore fittings.

Table 1. Constant-velocity criteria for pipes, and small-bore connections.

Screening (Acceptable) Vibration Level

Reference

Comments

mm/s RMS

mm/s 0-Peak

ISO Standard 20816-8 (2018) EFRC Guidelines (3rd Ed., 2012)

Pipes, small-bore fittings, and pulsation dampers (10 – 200 Hz) Cantilever small-bore fittings Typical small-bore fittings Typical continuous piping Small- bore fittings (≤ 300 Hz)

19.0

27.0

Harper (2014)

18.0 21.0 28.0 14.0 25.0

25.0 30.0 40.0 20.0 35.0

Hamblin (2003)

Jacimovic and D’Agaro (2020)

Main pipes (≤ 300 Hz)

The ISO standard 20816-8 (2018) for reciprocating compressor systems, arising from the European Forum for Reciprocating Compressors (EFRC) guidelines (3rd Edition, 2012), provides a three-tier vibration severity chart (Table 2 and Fig. 3) to assist with decision making. The A/B limit, which is close to the “design” curve specified by