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Metal expansion bellows are a mechanical device for absorbing energy or displacement in structures. It is widely used to deal with vibrations, thermal expansion, and the angular, radial, and axial displacements of components. The main objective of this paper is to perform numerical analysis to find various characteristics of stresses in U-shaped metal expansion bellows as per the requirement. Jan 29, 2017 Metal Bellows Design Software Solutions (MBDSS) Version. This ensures your customized solution based on EJMA and ASME: All of the formula calculation and values are based on EJMA Latest version 9th Edition and ASME. EJS is a member of EJMA. The bellows membrane design for all three categories are similar. The EJMA bellows fatigue curve is a best fit curve based on data that was available, so it provides an expected average cycle life. The ASME curve was developed also using bellows fatigue data, but it provides design margins consistent with ASME pressure equipment codes.
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Numerical Investigations on Characteristics of Stresses in U-Shaped Metal Expansion Bellows
1Department of Mechanical Engineering, M. E. Society’s College of Engineering, Pune, Maharashtra 411001, India
2Department of Mechanical & Materials Technology and Department of Technology, S.P. Pune University, Pune 411007, India
3Department of Mechanical Engineering, G.S.M. College of Engineering, Pune, Maharashtra 411045, India
Received 5 May 2015; Revised 23 July 2015; Accepted 6 August 2015
Academic Editor: Yuanshi Li
Copyright © 2015 S. H. Gawande 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
Metal expansion bellows are a mechanical device for absorbing energy or displacement in structures. It is widely used to deal with vibrations, thermal expansion, and the angular, radial, and axial displacements of components. The main objective of this paper is to perform numerical analysis to find various characteristics of stresses in U-shaped metal expansion bellows as per the requirement of vendor and ASME standards. In this paper, extensive analytical and numerical study is carried out to calculate the different characteristics of stresses due to internal pressure varying from 1 MPa to 2 MPa in U-shaped bellows. Finite element analysis by using Ansys14 is performed to find the characteristics of U-shaped metal expansion bellows. Finally, the results of analytical analysis and finite element method (FEM) show a very good agreement. The results of this research work could be used as a basis for designing a new type of the metal bellows.
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1. Introduction
Metal bellows are structural component in which a wavy shape is formed on the surface of a circular tube to introduce elastic property. Expansion joints used as an integral part of heat exchangers or pressure vessels shall be designated to provide flexibility for thermal expansion and also to function as a pressure-containing element. Normally metal bellows are used as an expansion joint in shell and tube heat exchanger. It deals with vibrations, thermal expansion, and angular, radial, and axial displacements of components. Its present applications are in AC equipment, industrial plants, hose pipes, vacuum systems, and aerospace equipment.
Limited amount of research work has been carried out by some researchers working in the area of the expansion joint for shell and tube heat exchanger. Their work has been reported by performing industrial survey (namely, Alfa Laval India Ltd., Pune) and exhaustive literature review through earlier published research work, journal papers, and technical reports. Many design formulae of bellows can be found in ASME code [1]. And the most comprehensive and widely accepted text on bellows design is the Standards of Expansion Joint Manufactures Association, EJMA [2]. Number of pilot and test experiments have been performed for analysis of AM350 steel bellows by Shaikh et al. [3]. As bellows are exposed to marine atmosphere for more than 13 years which leads to pitting effect, hence the determination of dynamic characteristics of beam finite elements by manipulating certain parameters on commercial software was done by Broman et al. [4]. In comparison with semianalytical, methods have potential of considering axial, bending, and torsion degrees of freedom at the same time, and the rest are modeled by finite elements in which experimental results are also verified. The effect of the elliptic degree of Ω-shaped bellows toroid on its stresses is investigated by Li [5]. In addition, Becht IV [6] has investigated the fatigue behavior of expansion joint bellows. The results of Ω-shaped bellows with elliptic toroid calculated stresses correspond to experiments. The elliptic degree of Ω-shaped toroid affects the magnitude of internal pressure-induced stress and axial deflection-induced stress. It especially produces a considerable effect on the pressure-induced stress. To maintain the fatigue life of toroid bellows, during manufacturing process toroid elliptic degree must be reduced. EJMA stresses for unreinforced bellows are evaluated by Becht IV [6]. Using linear axisymmetric shell elements parametric analysis is conducted. Finite element analysis is carried out using commercial code. Meridional stresses due to internal pressure and displacement are accurate. Bellows-forming process is done after evaluating effective parameters by Faraji et al. [7]. FEM results are compared with analytical solutions. Faraji et al. [8] used a commercial FEM code, ABAQUS Explicit, to simulate manufacturing process of metal bellows. Forming of different shapes of tubular bellows using a hydroforming process is proposed by Kang et al. [9]. The conventional manufacturing of metallic tubular bellows consists of four-step process: deep drawing, ironing, tube bulging, and folding. In their study, single-step tube hydroforming combined with controlling of internal pressure and axial feeding was proposed. These reviewed papers show that there is need for rigorous analysis and forming parameters of bellows. It is stated that the Ω-shaped bellows have much better ability to endure high internal pressure than common U-shaped bellows. Metal bellows have wide applications in piping systems, automotive industries, aerospace, and microelectromechanical systems. Kang et al. [10] have developed a microbellows actuator using microstereo lithography technology. Numerous papers have dealt with various aspects of bellows except for forming process. Broman et al. [4] have determined dynamic characteristics of bellows by manipulating certain parameters of the beam finite elements. Jakubauskas and Weaver [11] have considered the transverse vibrations of fluid-filled double-bellows expansion joints. Jha et al. [12] have investigated the stress corrosion cracking of stainless steel bellows of satellite launch vehicle propellant tank assembly. Zhu et al. [13] have investigated the effect of environmental medium on fatigue life for U-shaped bellows expansion joints. However, few papers have shown the manufacturing process of the metal bellows. Wang et al. [14] have developed a new process for manufacturing of expansion joint bellows from Ti-6Al-4V alloys with high degree of spring back. Wang et al. [14] have used gas pressure instead of fluid pressure, because the process was done in high temperature ambient. Kang et al. [10] have investigated the forming process of various shapes of tubular bellows using a single-step hydroforming process. Lee [15] has carried out parametric study on some of the forming process parameters of the metal bellows by finite element only. He has mentioned that, in general, metal bellows are manufactured in four stages: deep drawing, ironing, tube bulging, and folding.
From the literature survey, it is seen that a number of researchers have worked on study and applications of different types of bellows under various working conditions, their comparison, and manufacturing processes, and few are working on fatigue life enhancement. But investigations on need for selection of proper material of bellows for given application, their proper design, stresses induction, fatigue life analysis, and prediction of failure and investigations on various characteristics of different bellows and vibration effect are essential.
2. Problem Formulation and Objective
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As per literature and industrial survey, it is seen that bellows are one of the most important elements in the expansion joint and have the function to absorb regular as well as irregular expansion and contraction of the system. Bellows require high strength and good flexibility, which can be achieved by good design and proper manufacturing method. The design referred to from EJMA requires proper configuration selection which makes it difficult. The metal bellows are manufactured with different methods like forming, hydroforming, bulging, drawing, and deep drawing, which depend on applications. The materials used for bellows are normally stainless steel; in rare cases Inconel and aluminum are also used. Different shapes of bellows are U-shaped, semitoroidal, S-shaped, flat, stepped, single sweep, and nested ripple. As per discussion with experts working in the same field, it is observed that the concept of study in this paper needs detailed understanding of proper design and investigations on selection of materials, shapes, vibration effect, joining of bellows to shell, stresses, flow analysis, fatigue life analysis, and prediction of failure. Hence this work focuses on selection of materials of bellows for the given application, their proper design, and determination of characteristics of stresses of bellows, fatigue life analysis, and prediction of failure.
3. Determination of Characteristics of Stresses of Bellows by Analytical Analysis
Metal expansion bellows are a very distinctive component of a piping system. They must be designed strong enough to accommodate the system design pressure as well as flexible enough to accept the design deflections for a calculated number of occurrences, with a minimum resistive force. In order to understand the static and dynamic behavior of metal expansion bellows as shown in Figure 5, it is necessary to study the selection of materials of bellows for the given application, basic fundamental, their proper design, and working. The different mechanical properties and design parameters for bellows under consideration are shown in Table 1.