Vibration analysis of piping connected with shipboard equipment

Vibration analysis of piping connected with shipboard equipment Radharaman Tripathi 1 *, Tushar A. Jadhav 1 , Mahesh K. Gaikwad 2 , Mithul J. Naidu 3 , Aishwarya B. Gawand 4 , Duran Kaya 5 , Sachin Salunkhe 6 , 7 , Robert Cep 8 and Emad Abouel Nasr 9 1 Department of Mechanical Engineering Sinhgad College of Engineering, Savitribai Phule Pune University, Pune, Maharashtra, India, 2 Department of Mechanical Engineering, Jayawantrao Sawant College of Engineering, Savitribai Phule Pune University, Pune, Maharashtra, India, 3 Faculty of Mechanical Engineering, Tolani Maritime Institute Pune, Indian Maritime University, Pune, India, 4 Department of Engineering Sciences, Jayawantrao Sawant College of Engineering, Savitribai Phule Pune University, Pune, Maharashtra, India, 5 Gazi University Project Coordination and Implementation Research Center, Ankara, Türkiye, 6 Department of Biosciences, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India, 7 Department of Mechanical Engineering, Gazi University Faculty of Engineering, Ankara, Türkiye, 8 Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, Ostrava, Czechia, 9 Department of Industrial Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia The piping system connected with the shipboard equipment may be subjected to excessive vibration due to harmonic base excitation produced by hydrodynamic force imposed on the propeller blades interacting with the hull and by other sources. Vibration design aspects for shipboard pipework are often ignored, which may cause catastrophic fatigue failures and, consequently, leakage and spillage in the sea environment. Without dedicated design codes, the integrity of shipboard equipment against this environment loading can be ensured by testing as per test standard MIL-STD-167-1A (2005). However, in many cases, testing is not feasible and economically viable. Hence, this study develops an FE-based vibration analysis methodology based on MIL-STD-167-1A, which can be a valuable tool to optimize the testing requirement without compromising the integrity of these piping systems. The simulated model dynamic properties are validated with experimental modal testing and Harmonic response analysis result confirm that a mitigating solution option can be verified by a FE based vibration analysis to mitigate the vibration problem. KEYWORDS vibration, shipboard equipment, piping, mechanical resonance, modal, harmonic analysis 1 Introduction Excessive vibration in the piping system in the oil and gas and shipping industry is the biggest threat to safe and reliable operation since it can cause catastrophic fatigue failure without prior warning. Excessive vibration can pose severe issues related to safety, environment, and cost, i.e., it can cause uncontrolled leakage from piping flanges and, consequently, spillage in the seawater. The spillage of hydrocarbon liquids in the seawater can seriously threaten the sea environment and ecology. This study focuses on developing an approach for vibration analysis of piping systems connected with shipboard equipment to mitigate excessive vibration. Consequently, this will ensure environmental sustainability around the sea and nearby areas. OPEN ACCESS EDITED BY Govind Vashishtha, Wrocław University of Science and Technology, Poland REVIEWED BY Maan Singh Rathore, Indian Institute of Technology Roorkee, India Sumika Chauhan, National Institute of Technology Delhi, India *CORRESPONDENCE Radharaman Tripathi, [email protected] RECEIVED 05 March 2024 ACCEPTED 22 April 2024 PUBLISHED 15 May 2024 CITATION Tripathi R, Jadhav TA, Gaikwad MK, Naidu MJ, Gawand AB, Kaya D, Salunkhe S, Cep R and Abouel Nasr E (2024), Vibration analysis of piping connected with shipboard equipment. Front. Mech. Eng 10:1396170. doi: 10.3389/fmech.2024.1396170 COPYRIGHT © 2024 Tripathi, Jadhav, Gaikwad, Naidu, Gawand, Kaya, Salunkhe, Cep and Abouel Nasr. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Mechanical Engineering frontiersin.org01 TYPE Original Research PUBLISHED 15 May 2024 DOI 10.3389/fmech.2024.1396170 However, the contrary, most of the piping design codes focus mainly on static loadings like temperature and pressure. Hence, accurate analysis and subsequent calibration of appropriate vibration reduction simulation ensure the integrity and continuous operation of the plant. The vibration in piping mainly depends on three aspects, i.e., magnitude and frequency of excitation force (e.g., flow disturbance or pressure pulsation), system’s modal characteristics (natural frequency, mode shape, and damping), and fluid-structure interaction. In most cases, improper system modal characteristics are a prominent cause of the piping system’s vibration, especially when excitation and natural frequency are very close. Hence, realistic estimation of modal characteristics is vital to generate accurate results from the simulated Finite element model. Several simulations and experimental studies have been conducted to validate the mitigation options for troubleshooting excessive vibration. Atkins Kenneth et al. (2004). Discussed the various mitigating options for controlling the vibration in piping connected with a reciprocating compressor, and they also discussed the multiple constraints to get the realistic value of modal parameters from the finite element model. Alexandre et al. (2018) discussed an F.E. analysis methodology for assessing the fatigue life of welded components based on a realistic simulated stress and Stress life (S-N) approach from British Standard BS-7608. Beauvais Romain et al. (2021) tested a piping system and established a non-intrusive acceleration measurement technique to identify the internal sound pressure level within a piping loop. Pulsation-induced vibration problems can be easily diagnosed based on this approach. Richard and Jacquelin. (2021) determined a procedure for incorporating the underlying wall pressure fluctuations in a finite element model to determine the fatigue life of a piping system. They studied the manual assessment method based on energy institute Guidelines (2008) and the experimental method to verify and validate the F.E. analysis results. Baldwin and Simmons. (1986) studied flow-induced vibration in safety relief valves (SRVs) in high-energy piping systems. They developed an analytical design procedure based on the Strouhal number, Mach number, and stub dimensions to eliminate the vibration problem in the existing system. Cicero et al. (2016) studied the effect of thermal cutting methods (oxyfuel, plasma, and laser cut technologies) on the fatigue behavior of structural steels. Then, the S-N resultsobtainedwereusedtoderivethe corresponding BS7608 design classes. El-Borgi et al. (2021) established the F.E. model updating technique to minimize errors between the analyzed and measured responses. This model updating procedure was established iteratively by tuning the parameters associated with the assumed boundary conditions for the simulation until the computational F.E. model can replicate the system’s actual behavior. Gao and Hongquari (2020). Proposed an improved FEM approach for vibration analysis of a pipeline system subjected to multi-excitation, i.e., a pipeline subjected to both hydraulic pump pressure fluctuation and base excitation from the engine. Haapaniemi Heikki et al. (2002) focused on the correlation between the simulated finite element model and modal testing measurement. The technique of Output-only modal analysis was established and verified to get the modal parameters of piping even when the system is FIGURE 1 Geometry of piping connected with a vertical loop. TABLE 1 Natural frequency of original pipe structure. Mode Frequency (Hz) 127 2 66.8 3 102 4 104.5 5 127 6 144 Frontiers in Mechanical Engineering frontiersin.org02 Tripathi et al. 10.3389/fmech.2024.1396170 in use. Jiang and Zhu. (2018) simulated a piping system model in FEA software. Based on the experimental modal testing, the simulated model was tuned to reflect the realistic boundary condition and modal properties. The simulated results comply with exploratory testing; hence, experimental modal testing can be used to calibrate the model for vibration analysis. Jiang et al. (2013). Describe an expert system for online monitoring and diagnosis of realistic vibration faults in reciprocating compressor systems with the help of facts and rules logic. Kedar Bhagwat and Gulave. (2017) proposed a method to reduce the acoustic and flow-induced vibrations in the piping system. Liu et al. (2020) developed and demonstrated an approach of vibration analysis for troubleshooting the severe vibration problem in the compressor station yard pipeline. The field vibration test verified the computer model. The best solution was based on the increasing natural frequency of the system by additional support constraints. Moon Seong-In et al. (2011) developed test specifications for components, which were FIGURE 2 First mode shape; Mode 1, f1 = 27 Hz. FIGURE 3 Second mode shape; Mode 2, f2 = 66.8 Hz. Frontiers in Mechanical Engineering frontiersin.org03 Tripathi et al. 10.3389/fmech.2024.1396170 FIGURE 4 Effect of separation margin on amplification factor. FIGURE 5 Excitation displacement on the F.E. model. Frontiers in Mechanical Engineering frontiersin.org04 Tripathi et al. 10.3389/fmech.2024.1396170 applied to predict fatigue life for the unit brackets at the initial product design stage using a vibration fatigue technique. Noh Byeongwook et al. (2006) studied the fatigue strength of loadcarrying cruciform fillet welded joints for geometric or structural stress in the welded joint. The structural stress concentration factor for 1 mm below the surface was calculated by finite element analysis and compared to the basic fatigue resistance curve offered by BS7608 (2014).Martin et al. (2012) presented two methods for extracting the modal properties of the compressor yard pipeline based on experimental testing and the finite element method, respectively. The modal testing verified the simulated results. Tison and Atkins. (2001) presented various methods to mitigate vibration in reciprocating compressor piping systems. They explained the multiple limitations for getting accurate modal characteristics by computer simulation, e.g., natural frequencies. Wachel et al. (1986) conducted dynamic pressure and vibration measurements to diagnose the exact cause of vibration. Test measurement verified the mitigation solution for troubleshooting a complex vibration problem in piping connected with a reciprocating pump. Wang Qiang et al. (2016) investigated the dynamic strain measurement FBG sensors, confirming the excellent correlation with simulated results for modal parameters like natural frequencies. Fiber Bragg sensors are helpful for the health monitoring of small-bore hydraulic piping due to smaller additional mass. Adil and Alaeddin. (2010) presented a study to understand the effect of the high speed of a ship on the shipboard vibration, which can be unpleasant to passengers and crew members and additionally can cause malfunction and fatigue failure of the shipboard equipment and structures. The current study demonstrates the methodology for vibration analysis of piping systems subjected to mechanical or base excitation. The excitation mechanism, like mechanical excitation due to connected reciprocating equipment and base excitation due to the ship, can generate a high vibration level, which can cause catastrophic fatigue failure. A dedicated design code for the shipboard piping system is not available. Hence, test standard MIL-STD-167-1 can guide the design and vibration analysis of the shipboard equipment’spipeworkwithouta design code. A finite element model has been generated based on design parameters to generate dynamic characteristics and results. Experimental modal testing hasbeenconductedtovalidatethe modal properties. These modal properties can calibrate the simulated model to develop realistic results and validate the mitigation options. In this regard, the paper is organized as follows. Section 2 presents modal and harmonic response analysis of a finite element model of a piping loop system. Section 3 offers the experimental modal testing by modal hammer and FFT analyzer, which validate the piping system’s fundamental mode and corresponding natural frequency. Finally, Section 4 provides some concluding remarks regarding the finite element analysis methodology to generate accurate results and optimize the testing requirements. 2 Modal and harmonic response analysis The piping with a vertical pipe loop is used at the ship, in the skid of reciprocating machinery or other equipment, where a loop is provided to absorb the thermal displacement or due to adjacent piping layout space constraints. In this study, an F.E. model of a piping system was generated in the ANSYS workbench based on the design parameters shown in Figure 1. This piping system consists of a vertical loop with four elbows, and the piping system material is Stainless steel. The F.E. model contains 47,719 nodes and 7,938 elements. The model’s mesh was created with sweep mesh, mostly Solid element Solid 186. The Fixed support boundary condition was kept at the start and end of the piping Loop model to simulate the stiff connection on the connected equipment. 2.1 Modal analysis of original pipe structure Modal analysis determines a mechanical structure’s vibration characteristics (mode shape, natural frequency), e.g., a piping FIGURE 6 Output displacement results: original pipework. Frontiers in Mechanical Engineering frontiersin.org05 Tripathi et al. 10.3389/fmech.2024.1396170 Loop. The natural frequency and mode shapes depend on the distribution of mass and stiffness in a piping system and boundary conditions considered in an F.E. simulation. Hence, to generate accurate results, calibration of simulated results is often required by experimental modal testing. Afixed beam can represent the geometry (shown in Figure 1) as a 4-D system if each pipe element resembles a point element in a beam. This assumption holds when a straight pipe does not deform significantly in a radial direction. It is valid for various pipinginstallationsintheplantsysteminwhichflexibility is FIGURE 8 S-N curve for nominal stress as per BS7608[22]. FIGURE 7 Output stress results: original pipework. Frontiers in Mechanical Engineering frontiersin.org06 Tripathi et al. 10.3389/fmech.2024.1396170 introduced by elbow elements only. Hence, this vertical pipe loop configuration can be idealized by 4-degree freedom system, where each axis is collinear to the bisector of each elbow. The extracted natural frequencies based on F.E. modal analysis are listed in Table 1. Figure 2 shows the first mode shape of the piping loop system, which indicates maximum deformation in a Lateral direction(Y) at the center of the piping loop. The second mode shape in Figure 3 represents the bending mode in the longitudinal l(Z) direction. Other modes are second-order or complex vibration modes, which maintain a separation margin of more than 50% with the excitation frequency, and significant dynamic response is not expected for these modes mentioned in section 2.2. 2.2 Effect of separation margin on the dynamic response The amplification factor represents the amplification of static response under a dynamic condition, which depends on the ratio of excitation to natural frequency and the damping factorinthesystem.Theamplification factor for a simple dynamic system is shown in Eq. (1).Itshowsthatthe amplification factor reduces sharply with a ±20% separation margin. It can be seen in Figure 4 that for a separation margin of 40%, the amplification factor is 1.5 or less, which can go up to 20 without a separation margin for a critical damping ratio of 0.025. The amplification factor can be higher for lower damping values, i.e., for a 0.01% damping ratio, the amplification factor is 50.Amplification Factor (A.F) for Steady-state harmonic excitation AF 1  1−ω ωn  2  +2ξω ωn  2 (1) where, ω= Excitation frequency, ω n = Natural frequency, ξ= Critical damping ratio. Hence, it shows that the accurate estimation of natural frequency is an essential step of dynamic analysis to derive accurate results from F.E. analysis. The sufficient TABLE 2 The natural frequency of pipework with the damper. Mode Frequency (Hz) 1 63.8 2 103.5 3 104.5 4 129 5 136 6 169 FIGURE 9 F.E. Model for pipework with the damper. Frontiers in Mechanical Engineering frontiersin.org07 Tripathi et al. 10.3389/fmech.2024.1396170 separation margin between excitation and natural frequencies can maintain a dynamic response close to the static response. 2.3 Harmonic response analysis of original pipework Modal results are linked to Harmonic analysis; a periodic excitation determines the structure’s response under a steadystate sinusoidal loading at a given frequency in harmonic response analysis. Harmonic response analysis mainly checks the excessive dynamic response due to mechanical resonance. This magnifies structural response in a lightly damped system when driven with a sinusoidal input at its natural frequencies. The paper will expose the piping system to prescribed frequency, and amplitude ranges to reveal critical response prominences or potential deficiencies. MIL-STD-167-1A(2005) provides dynamic excitation force for shipboard equipment testing for hydrodynamic force imposed on the propeller blades interacting with the hull and by other sources. This standard provides an environment vibration amplitude sufficiently large for a selected frequency range to avoid malfunctioning shipboard equipment and connected piping systems on Naval Ships. Exploratory vibration and variable frequency tests specify the excitation frequency range and single excitation amplitudes to determine the presence of response prominence. Response prominence mainly represents a resonance or other distinct maximum in the form of transmissibility. In most cases, transmissibility greater than 1.5 is sufficient to classify a maximum as a response prominence, and for these systems, endurance testing is required. It is evident from Figure 4 that a separation margin of 40% or more can bring the transmissibility or amplification factor value to less than 1.5 and may omit the requirement of endurance testing. MIL-STD-167-1A(2005) specifies the excitation frequency range and vibration amplitude as 4–33 Hz and 0.012 inches for exploratory vibration tests. This vibration amplitude is equal to 1.3 g acceleration at 33 Hz. Hence, on the conservative side, a 0.024-inch (0.6096 mm) excitation force in the lateral direction and excitation frequency range of 0–33 Hz has been considered for the harmonic response analysis (refer to Figure 5). This may cover more severe environmental conditions associated with ships of higher speed. The analysis result shows an amplitude of dynamic displacement and stress of 11.23 mm and 319 MPa (at 27 Hz), respectively, for a damping factor of 0.015. Displacement profile and stress contour FIGURE 10 Comparison of natural frequencies. TABLE 3 Comparison of natural frequency original vs. modified system. Mode no. Original Pipe(Hz) Pipe with support (Hz) 1 16.1 16.2 2 43.7 44.3 3 55.1 56.2 4 55.9 56.3 5 64.2 66.0 6 66.0 66.4 Frontiers in Mechanical Engineering frontiersin.org08 Tripathi et al. 10.3389/fmech.2024.1396170 for original pipework are shown in Figures 6,7respectively. It is equal to the transmissibility factor or response prominence of 18.4. The BS7608[22] provides the basic design S-N curve to a particular structural detail class based on the type of stress for assessment (e.g., nominal, hot spot, or shear stress), local stress concentration, stress direction, residual stress, size and shape of discontinuity on piping, etc. The weld classes D and F2 are common in the piping system, representing the pipe without discontinuity and pipe with welded discontinuity, like shoe support and small-bore connection. The allowable endurance limit for weld class D & F2 is 80 and 35 MPa peak to peak (P-P), respectively, as per BS-7608. The standard basic design S-N curve is shown in Figure 8. It shows that with current support, the piping system will be subjected to fatigue failure, and this excessive vibration is required to be mitigated. This high transmissibility can be reduced by providing a restraint that increases the system’s natural frequency by shortening the free span length. The force required to restrain the pipework can be calculated based on a piping system’s inertial force (mass x acceleration) at a particular frequency. FIGURE 11 Output displacement: modified pipework. FIGURE 12 Output stress results: modified pipework. Frontiers in Mechanical Engineering frontiersin.org09 Tripathi et al. 10.3389/fmech.2024.1396170