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Advances in Mechanical Engineering

Volume 2012 (2012), Article ID 413583, 8 pages

http://dx.doi.org/10.1155/2012/413583

## Comparative Modal Analysis of Gasketed and Nongasketed Bolted Flanged Pipe Joints: FEA Approach

^{1}Faculty of Mechanical Engineering, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi 23640, Pakistan^{2}Department of Mathematics, COMSATS Institute of Information Technology, Lahore 54000, Pakistan

Received 4 April 2012; Revised 30 October 2012; Accepted 1 November 2012

Academic Editor: Marco Ceccarelli

Copyright © 2012 Muhammad Abid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

It is widely known that resonance can quickly lead to failure in vibrating bolted flanged pipe joints. Condition monitoring is performed time to time in some industries for smooth operation of a system, whereas mostly trial-and-error tests are performed to control vibration. During all this process, the inherent design problems are not considered. A bolted flange joint in piping system is not a simple problem, being the combination of flange, gasket, bolts, and washers. The success of a bolted flanged pipe joint is defined by the “static mode of load” in the joint. However, it has been recognized that a “dynamic mode of load” governs in a gasketed bolted flanged pipe joint, which leads to its failure due to flange rotation, providing flange yielding, fatigue of bolts, and gasket crushing. This paper presents results of detailed 3D finite element and mathematical modal analysis under bolt up to determine natural frequencies and mode shapes of gasketed flanged joints with and without raised face in comparison to the nongasketed flange joint.

#### 1. Introduction

Since the advent of bolted flanged pipe joints and their applications in industries, leakage is the major causes of their failure. The problem becomes worst under dynamic loading applications such as in mill digester pipes during transfer of pulp. Traditional gasketed flanged joints are claimed to be problematic even during bolt up due to “dynamic mode of load” [1–6]. This is concluded due to the flange rotation, flexibility of gasket hence bolt loosening and leakage [1, 2, 4]. For large diameter flanges, with bolts diameter more than 18 mm, use of hammering for bolt tightening provides worst effect resulting in gasket crushing and flange yielding [1, 2, 4]. This not only increases maintenance, but also damages the joint permanently. This shows that inherent flange design problem is not considered. To avoid and control flange rotation, raised face of the flange in many industrial applications is machined [1, 2].

Keeping in view the above mentioned problems, associated with the conventional gasketed joints used in industry, several alternatives to these require consideration. For this, a nongasketed joint, concluded as an alternative for its “static mode of load,” during experimental and analytical studies by [1–4], is analyzed using detailed comparative 3D finite element modal analysis in comparison to the conventional gasketed joints with and without raised face to observe behaviour of both the joints in detail under applied bolt-up conditions. Natural frequencies and mode shapes for both the joints are determined. Results of both the FEA and mathematical analysis are compared. A flange size of 4 inch, 900# Class is used in this study

#### 2. Finite Element Analysis

##### 2.1. Material Properties

Material properties given in Table 1 are linear, isotropic as modal analysis ignores nonlinearities. Young's modulus and density for a modal analysis must be specified. Material properties for flange are as per ASTM A105 [7], for bolts are as per ASTM A193-B7 [7] and for gasket is as per ASTM A182 [7].

##### 2.2. Finite Element Modelling

Parametric 3D finite element analysis is performed to analyze behaviour of gasketed and nongasketed joint styles. During modelling symmetry of both geometry and loading is considered and angular portion of flange (22.5 degree rotation of main profile or 1/16th part) and gasket with a bolt hole and half portion of bolt are modelled. In nongasketed joint, second flange is replaced with a symmetry plate, whereas in gasketed joint, half thickness of gasket is modelled due to the symmetry of the geometry and loading conditions and gasket is modelled as a solid ring. For the gasketed joint without raised face, raised face is not modelled as in many industrial applications, this is machined to avoid or control any flange rotation [1, 2]. Half portion of bolt is modelled due to plane symmetry of the bolt. Flange joint models for gasketed joint with and without raised face and nongasketed joints are shown in Figures 1(a)–1(c), respectively.

##### 2.3. Element Selection and Meshing

###### 2.3.1. Solid Structural

Solid structural elements (SOLID45) being a lower order element is used for modelling of different components, that is, flange, bolt, symmetry plate (for nongasketed joint), and gasket (for gasketed joint only).

###### 2.3.2. Contact Elements

For both the joints, “surface-to-surface” contact elements are used, therefore both the flange faces are of same element type. Three-dimensional “surface-to-surface” CONTA173 contact elements, in combination with TARGE170 target elements are used between the flange face and symmetry plate (for nongasketed joint) and gasket (for gasketed joint) surface, the top of the flange, and the bottom of bolt head to simulate contact distribution.

###### 2.3.3. Meshing

Adaptive meshing is used throughout in the regions of high stress distribution, that is, flange fillet, bolt-hole region, bolt head, shank corner, symmetry plate (for nongasketed joint), and gasket (for gasketed joint). Front areas of the model are meshed first and then the same meshing pattern of meshed area is swept over the volumes (Figures 1(a)–1(c)).

##### 2.4. Boundary Conditions

###### 2.4.1. Gasketed Joint

The flanges are free to move in either axial or radial direction, this provides flange rotation and the exact behaviour of stress in flange, bolt, and gasket. Symmetry conditions are applied to gasket lower portion, both sides of gasket, bolt cross-sectional area, both sides of flange ring and attached pipe. Bolts are constrained in radial and tangential direction at the centre nodes Figures 1(a) and 1(b). A displacement of UY = −0.00267 is applied in the bolt to achieve a preload of 35% (254 N/mm^{2}) of the yield strength of the bolt (723 N/mm^{2}) as per achieved max strain in the bolt at applied torque of 505 N-m [1–4].

###### 2.4.2. Nongasketed Joint

Symmetry plate is constrained in axial direction (-direction) only and is free to move either in radial or tangential direction. Bolt is constrained along centre nodes at the bottom surface in and -direction and is free to elongate in the -direction (Figure 1(c)). A nominal preload of about 70% (448 N/mm^{2}) of the yield strength of the bolt (640 N/mm^{2}) is applied in the bolt [1–6].

##### 2.5. Solution

Modal analysis is performed using ANSYS software [8]. Flow chart showing all steps involved in modal analysis in ANSYS are shown in (Figure 2). In ANSYS, Block Lanczos full extraction method is used for large symmetric eigenvalue problems, for the faster convergence rate. After full extraction mode, boundary conditions (load and constraints) are applied on the model and solution is obtained for first eight modes. In a modal analysis, the term “expansion” means writing mode shapes to the results file. To review mode shapes in the postprocessor, ten to twelve modes are extracted for comparison of results.

#### 3. Comparative Modal Analysis Results and Discussion

From Model Analysis simulation in ANSYS, behaviour of each individual component and overall joint is observed. Critical mode where all individual components vibrate at same frequency for resonance phenomenon leading to complete joint failure is predicted. In plots, parts crossing each other do not really mean, rather they are an exaggeration. In fact, in modal analysis, if any part actually touches another part while vibrating, then failure is possible in the structure [9]. Resonant frequencies and mode shapes obtained for first twelve modes using Block Lanczos (full mode extraction method) are given in Table 2 and plotted in Figure 3. FEA results are also verified with the mathematical modal analysis [10, 11] results. At mode-1 resonant frequency of gasketed joint without and with raised face observed is 120 and 168 Hz, which shows that joint with raised face, is more stable. Whereas, for the nongasketed joint, lowest resonant frequency is 349, which is 2.9 and 2.1 times more than the gasketed joint with and without raised face to excite and proves the stability of nongasketed joints. In model analysis mostly first frequency is of more importance as observed from simulation as initial modes in both the gasketed joint styles showed crushing of gasketed, flange rotation with bolt shearing all the dynamic mode of load which is not desirable. In comparison due to no gasket in nongasketed joints a static mode of load is concluded. Various mode shapes obtained by using full mode extraction option are discussed and are shown in the the USUM plots following.

##### 3.1. Gasketed Joint without Raised Face (Figures 4 and 5)

Results for all modes are discussed; however, plots for mode 1–4, 9-10, X1, and X2 are only shown here.(i)Mode-1: Vibration of the flange with a maximum displacement of 1.51 mm observed in all displacements plots (UX, UY, and USUM). Due to flange rotation gasket crushing and shear in bolt and flange is observed, resulting in dynamic mode of load and joint failure.(ii)Mode-2: Maximum displacement of gasket (14 mm) and gasket rotation is observed in USUM plot. (iii)Mode-3: Bolt bending and flange rotation observed in all displacements plots (UX, UY, and USUM) with maximum displacement of 1.18 mm. Due to flange rotation gasket crushing and shear in bolt and flange is observed.(iv)Mode-4: Maximum displacement of 18 mm at gasket is observed in UX, while flange swinging and sliding on gasket is observed in all plots. (v)Mode-5: Gasket vibration and sliding in and out and crosses the bolt showing damage to the gasket with maximum displacement of 21 mm observed in all displacements plots (UX, UY, and USUM). (vi)Mode-6: Maximum displacement of 1.10 mm near hub top portion in pipe and flange sliding over gasket is observed in all displacements plots (UX, UY, and USUM).(vii)Mode-7: A large bending with maximum displacement of 2.09 mm in bolt observed in all displacements plots (UX, UY, and USUM). (viii)Mode-8: Gasket rotation is observed in all displacement plots (UX, UY, and USUM).(ix)Mode-9: Maximum displacement is 1.16 mm vibration of the flange is observed in all displacements plots (UX, UY, and USUM). Gasket crushing is observed due to flange rotation and shear in flange and bolt. This behavior is due to dynamic mode of rotation and causes leakage or failure of sealing.(x)Mode-10: Maximum displacement is at gasket and gasket sliding is observed.(xi)Mode-X1: At this selected mode flange and bolt rotation is observed. A 2.44% difference in FEA and mathematical model resonant frequencies is observed. Maximum displacement of 1.29 mm is observed near the pipe hub. (xii)Mode-X2:At this selected mode flange and bolt rotation is also observed. Whole joint is vibrating with it resonant frequency, and the overall maximum displacement is 4.38 mm. Also flange swinging is observed in - plane. This case is very critical in terms of vibration because all parts of flange are vibrating with its natural frequencies and resonance may lead to failure.

##### 3.2. Gasketed Joint with Raised Face (Figures 6 and 7)

Results for all modes are discussed; however, plots for mode 1–4, 9-10, X1, and X2 are only shown here.(i)Mode-1: Vibration of flange is observed from all displacements (UX, UY, and USUM) with maximum displacement of 1.24 mm in UY resulting in gap at the inside diameter.(ii)Mode-2: Flange rotation in UX and UY shows gasket crushing. Maximum displacement of 1.93 mm observed at the bolt head.(iii)Mode-3: Bolt bending and flange rotation showing gasket crushing observed in all displacements plots with maximum displacement 1.03 mm.(iv)Mode-4: Gasket sliding observed in UX, while flange swinging and sliding on gasket is observed in UY and USUM plots with maximum displacement of 0.91 mm.(v)Mode-5: Gasket slides in and out and crosses the bolt causing damage to the gasket. Bending in bolt also observed in all the displacements plots with maximum displacement of 7.96 mm.(vi)Mode-6: Maximum displacement of 1.51 mm near hub top portion in pipe and flange sliding over gasket observed in all displacements plots.(vii)Mode-7: Large bending in bolt observed in all displacements plots with maximum displacement of 2.09 mm in bolt.(viii)Mode-8: Maximum displacement of 1.12 mm near hub top portion in pipe and bending in bolt observed in UX plots and flange rotation and bolt bending observed in UY and USUM. (ix)Mode-9: Maximum displacement of 2.642 mm at pipe inner radii and large bending in bolt shank is observed in all displacement plots. (x)Mode-10: Maximum displacement of 1.26 mm in flange hub and bending in bolt observed.(xi)Mode-X1: Flange and bolt rotation observed from all displacement plots. A negligible 2.41% difference between FEA and mathematical calculated resonant frequencies is observed. At this frequency the maximum displacement is in the pipe near the hub.(xii)Mode-X2: Flange and bolt rotation observed from all displacement plots. Whole joint structure is under vibration and overall displacement is 4.39 mm. Flange swinging is observed in UX plot in - plane. This case is very critical in term of vibration because all part of flange is vibrating with its natural frequencies; hence, resonance may occur at this frequency. A negligible 0.01% difference between FEA and mathematical calculated resonant frequencies is observed.

##### 3.3. Nongasketed Joint (Figures 8 and 9)

Results for all modes are discussed; however, plots for mode 1–4, 8–11 are only shown here.(i)Mode-1 and 2: No flange movement observed in flange. A maximum displacement in the middle of the bolt shows its excitation only in all the displacements plots.(ii)Mode-3 and 4: Excitation initiation in flange and pipe observed with no gap between flange surfaces, showing negligible small pipe bending. However, obvious bolt excitation still concluded.(iii)Mode-5, 6 and 7: Pipe bending at top portion and minimum at flange pipe fillet with negligible flange movement observed. Bolt bending also observed in all the displacement plots.(iv)Mode-8: An obvious excitation in flange and bolt observed, with almost zero separation between flange surfaces.(v)Mode-9: Bolt displacement movement in UY observed with almost static flange joint behaviour.(vi)Mode-10: An obvious bolt excitation observed with almost static flange joint behaviour.(vii)Mode-11: Excitation of complete flange joint observed with almost static flange joint behaviour.

#### 4. Conclusion

(i)A dynamic “mode of load” in both the gasketed joint styles, that is, with and without raised face is concluded. Flange rotation providing measurable gap resulting in loss of contact at the inside diameter between gasket and the flange, bolt bending and gasket crushing at different modes is concluded. This may provide ultimately leakage and joint failure. This overall dynamic behaviour of gasket joint is also concluded due to the additional gasket mass and its heavy weight, providing lowest frequency and maximum displacement. For the gasketed joint without raise face, first two resonant frequencies are less than the rest of the flange styles, concluding its critical behaviour for failure. However, in comparison to gasketed joint with raised face it becomes stable after third frequency.(ii)No flange rotation, so no gap and no loss of contact in nongasketed flange joint for any mode shape concluded its “static mode of load.”(iii)Overall, from comparative modal finite element analysis, nongasketed flange joint, due to its light weight, compact dimensions, and inherent static mode of load is concluded the best choice and an alternative to the conventional gasketed joint for leak-free conditions.

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