ISSN 2395-1621 Finite Element Analysis Based Optimization of Expansion Joint with Fatigue Analysis #1 Harshal R. Aher, #2 Dr. A.G. Thakur, #3 Vinaay Patil 1 harshal.aher@rediffmail.com 2 ajay_raja34@yahoo.com 3.cae@vaftsycae.com 1 Mechanical Department, Pune University * Second Company Vaftsy CAE, Pune ABSTRACT Expansion joint or movement joint is an assembly designed to safely absorb the heat induced during expansion and contraction of materials, to absorb vibration, to hold parts together, or to allow movement due to ground settlement.thus its main function is to reduce deformation stresses which produce by pressure vessel. Expansion joints form the key component for distribution of thermal stresses in a pressure vessel. However the joint has to be also structurally safe in addition to being flexible. Expansion joints must accommodate cyclic and long-term structure movements in such a way as to minimize imposition of secondary stresses in the structure. This can be achieved through material changes and design changes. Use of Finite Element Analysis (FEA) and conduct a series of trial runs and try to identify the design for the expansion joint also determining the critical area where maximum stress is developed and perform fatigue analysis on the final design. Finally the validation is done on that critical area by strain gauge and ultra-sonic testing machine. ARTICLE INFO Article History Received :18 th November 2015 Received in revised form : 19 th November 2015 Accepted : 21 st November, 2015 Published online : 22 nd November 2015 Keywords Pressure Vessel, Expansion joint, thermal stress, FEA I. INTRODUCTION Bellows have a function to absorb regular or irregular expansion and con-traction in piping system, it is widely used as the element of expansion joint in various piping system, aerospace, micro electromechanical and industrial system. Bellows are special structures that require high strength as well as good flexibility. Most industrial piping system often suffer excessive deformation, displacement, heat expansion, vibration, and other causes are responsible for the failure.a expansion joint is a flexible connector fabricated of natural or synthetic elastomer, fabrics and, where necessary, metallic reinforcements. They provide stress relief in piping systems caused by thermal and mechanical vibration and/or movement. It can also be used to overcome problems of noise. Rubber, as a material of construction in the expansion joint, has superior noise and vibration eliminating qualities over all other types of material. The standard expansion joint is of the spool-type with a single arch and flanged ends. The movement capability of the expansion joint is dependent upon the arch. If greater expansion or contraction is required than can be absorbed by a single arch, then a multiple arch joint can be used with up to four arches. Elastomeric expansion joints are suitable for both pressure and vacuum systems. Note, multiple arched constructions are not suitable for vacuum applications unless specifically designed for that service.
Fig.1 Expansion joint II. OBJECTIVE The objective is to use Finite Element Analysis (FEA) and conduct a series of trial runs and try to identify the design for the expansion joint. Secondly to undertake FEA based material selection analysis and to perform fatigue analysis on the final design. Also develop and validate a three dimensional model of expansion joint and to predict the developed stresses using FEA package and to correlate the experimental analysis results with simulation analysis results.this project is sponsored by Vaftsy CAE, pune. III. LITERATURE REVIEWS 1) Sudeep Zirmire & Prof.R.S.Tajane (2014) presented in Analysis and Weight Optimization of Butane Separator Using Finite Element Analysis, that the analysis of current separator design using FEA. Also understand the complex interaction of low temperature and pressure. Establish safety norms for the vessel, and determine critical areas for inspection. In this different types of element size is consider for design. The optimum design is found which means the value of stress is lower than permissible stress. 2) Brijeshkumar. M. Patel(2013) presented in Design, Manufacturing and Analysis of Metal Expansion Bellows here FE analysis for metal expansion bellows by the solid works software has been carried out. Here he have done the finite element analysis (FEA) of metal expansion bellows with and without the inner liner / sleeves and its values are validated with the theoretical design data values. The displacement and strain occurs in conventional bellows are much larger, finally the factor of safety of internal liners bellows are approximately double than the conventional bellows. Hence the bellows with inner liner gives very good results and performance than the conventional bellows. The un-reinforced of U-shaped bellows are defined as the flexible element of an expansion joints consisting of one or more convolutions and the end tangent with the ratio of length of the bellows to the diameter of the bellows must be with no more than five plies. These equations are based on elastic shell theory and consider the parameters involved for bellows of the U shaped configuration & the bellows most sensitive effective parameters which affect the final shape of the convolution. Solid Works Simulation uses the displacement formulation of the finite element method to calculate component displacements, strains, and stresses under internal and external loads. 3) G. Wang & K.F. Zhang (2006) presented in Superplastic forming of bellows expansion joints made of titanium alloys this is used to complex SPF method of applying gas pressure and compressive axial load is developed for the first time. It can be used to manufacture large diameter U type bellows expansion joints made of titanium alloys. Welded pipes that were bent by hot bending with a set of specific dies and were welded by PAW are used in tubular blanks of SPF process. A multi-layer die structure is adopted to determine the final shape of convolutions. The forming load route is divided into three steps in order to obtain optimum thickness distribution. This technology can also be used to fabricate stainless steel bellows expansion joints. The material performances of titanium alloys namely service temperature, cycle stress, and corrosion resistant are very suitable for making bellows expansion joints. However, because of their large deformation resistance, severe springback, low plasticity and formability at room temperature. A bellows expansion joint of titanium alloys has excellent corrosion-resistant performance and can be used to match a press vessel of titanium alloys and replace that of stainless steel and anticorrosion alloy. Description Material Bellow modulus IV. PARAMETERS TABLE I GIVEN PARAMETERS Sr. Parameter Notation Value No. s 1 Internal Pressure P 0.1 MPa 2 External Pressure P0 Atmospheri c 3 Process Volume Vp 410 cu m Expected Stagnant Vs 30 cu m 4 Volume 5 Buffer Volume Vb 50 cu m 6 Vessel radius R 3 m 7 Temperature T 150 C 8 Nozzle Diameter Dn 0.25 m 9 Number of nozzles NON 4 10 Drain Nozzle Dd 0.3 m 11 Head type - Ellipsoidal 12 Support Saddle Saddle 13 Support Ht H 2.5 m TABLE II MATERIAL PROPERTIES Poisson s ratio 0.29 Values SA 516 Grade 70 200 GPa allowed stress 137.8951
Fig.4 Meshing V. DIMENSIONS (From ASME SECTION VIII ) 1. Thickness of shell = 12 mm 2. Diameter of shell = 6000 mm 3. Thickness of nozzle = 6 mm 4. Diameter of nozzle = 250 mm 5. Thickness of reinforcing pad = 6 mm 6. Diameter of reinforcing pad = 589 mm 7. Thickness of Ellipsoidal head = 12 mm C. Boundary Conditions:- A pressure of 0.32 MPa is applied to all internal surfaces of the pressurized section and acceleration of 9810mm/s² is applied and fixed support is given to both saddles shown in Figure 7. From the resulting analysis output, the maximum total deformation occurs at various stages, and its value should be less than the maximum allowable total deformation he temperature condition on the pressure vessel i e C is given and fixing both the saddles otal deformation occurs in the pressure vessel found to be 77.599 mm. Fig.2 Final dimensions VI. FEA PROCESS FOR PRESSURE VESSEL A. Modelling:- The first step of pre-processing is to generate the 3-D model of the given component which is compatible to import in the solver. The 3-D model of the Pressure vessel is created in Ansys 14 work bench.the modelling of pressure vessel is shown in Figure 2. These files were used for analysis further process. Fig.5 Boundary conditions Fig.6 Total deformation Fig. 3 Model of pressure vessel B. Meshing:- The meshing is done with mesh size of 100 mm for cylinder and 25mm mesh size for other parts such as both saddle support, nozzle and reinforcement pad. The mesh is not over fined. Also Map faced meshing is done for removing non regularity in meshing which affects the end results. Fine mesh is done to get the accurate values of stresses in those regions. This can be viewed in Figure 3, the mesh type is Quadrilateral-mesh. (Nodes-68416 & Elements-68095.) By fixing one end of the saddle and free displacement of other one in axial direction is applied. Also all other same loading conditions are applied i.e dead weight, internal pressure and temperature condition shown in Figure 4.8. The total deformation occurs is more which 109.09 mm is so the expansion joint is required to reduce this deformation stresses shown in figure. So there is requirement of expansion joint to reduce the deformation stress. Fig. 7 Total deformation (fix one end) VII. DESIGN OF EXPANSION JOINT
The meshing is done with mesh size of 100 mm for expansion joint. The mesh is not over fined. This can be viewed in Figure 3, the mesh type is Quadrilateral-mesh. (Nodes-68698 & Elements-64095.)The material used for pressure vessel is SA 299B (Carbon steel plate). Fig. 8 Expansion join TABLE IIII MATERIAL PROPERTIES FOR EXPANSION JOINT Material Inner Diameter of expansion joint (Db) Young modulus Operating pressure Allowable stress (S) SA 299B 6000 mm 179 GPa 0.32 MPa 158 Mpa Allowable Equivalent stress 3 x S = 474 MPa TABLE IIIV FINAL DIMENSIONS EXPANSION JOINT Convolution Pitch (A+B) 3000 mm convolution height (w) 1.33 x D D = 2000 mm bellows thickness (t) 70 mm outside bellows radius 1000 mm (ra) inside bellows radius 1250 mm (rb) C. Boundary Conditions:- Fig. 10 meshing A pressure of 0.32 MPa is applied to all internal surfaces of the pressurized section including internal surface of expansion joint and acceleration of 9810mm/s² is applied and free displacement support is given to saddles shown in Figure. From the resulting analysis output, the maximum total deformation occurs at various stages, and its value should be less to avoid additional deformation stress he temperature condition on the pressure vessel i e C is also applied otal deformation occurs in the pressure vessel found to be 34.35 mm which is shown in figure and equivalent stress is found to be430 MPa which is less than allowable stress which is 474 MPa. A. Modelling:- The next step is to generate the 3-D model of expansion joint with in the given component of pressure vessel. The 3- D model of the expansion joint is created in Ansys 14 work bench by editing previous model, keeping the overall length same and just adding expansion joint in center position. The modeling of expansion joint is shown in Figure 2.and cut section is taken for further analysis to reduce time Fig.11 Boundary conditions Fig.12Equivalent stress Fig. 9 modelling of expansion joint B. Meshing:-
B. Trial considering thickness 60 mm :- The reduction in shell thickness of expansion joint from 65 mm to 60 mm is applied and then repeting previous boundary conditions there is formation of new equivalent stress which is 446 MPa which is less than allowable equivalent stress which is 474 MPa and total deformation found to be 35.819 mm shown in figure. Fig. 13 Total deformation VIII. OPTIMIZATION In this optimization is done by trial and error method changing thickness of expansion joint. Design optimization is a technique that seeks to determine an optimum design. By optimum design, It mean, one that meets all specified requirements but with a minimum expense of certain factors such as weight, surface area, volume, stress, cost, etc. in other words, the optimum design is usually one that is as effective as possible. Virtually any aspect of design can be optimized: dimensions, shape (fillet radii), and placement of supports and cost of fabrication, natural frequency, material property, and so on. The ANSYS program offers two optimization methods to accommodate a wide ransge of optimization problems. A. Trial I considering thickness 65 mm:- The reduction in shell thickness of expansion joint from 70 mm to 65 mm is applied and then repeting previous boundary conditions there is formation of new equivalent stress which is 438 MPa which is less than allowable equivalent stress which is 474 MPa and total deformation found to be 34.987 mm shown in figure. Fig.16 Equivalent stress (60 mm thickness) Fig.17 Total deformation (60 mm thickness) Fig. 14 Total deformation (65 mm thickness) C. Trial considering thickness 50 mm:- The reduction in shell thickness of expansion joint from 60 mm to 50 mm is applied and then repeting previous boundary conditions there is formation of new equivalent stress which is 520 MPa which is more than allowable equivalent stress which is 474 MPa and total deformation found to be 38.501 mm shown in figure.the above analysis result shows that the design is unsafe for the shell thickness 50mm. So optimum thickness for expansion joint is 60 mm, were the equivalent stress is found to be 446 MPa which is less than allowable stress which is 474 MPa also total deformation is found to be 35.816 mm. Fig. 15 Equivalent stress (65 mm thickness)
Fig.18 Total deformation (50 mm thickness) Fig.19 Equivalent stress (50 mm thickness) IX. EXPERIMENTAL ANALYSIS A. Strain gauge:- Strain gauges are intended for measure of strain. The results of such measurements may be used for statements for concerning the material stresses in the specimen, the nature and amount of forces acting on the specimen etc. However a strain gauge can only perform its task properly if the strain to be measure is transferred faultlessly and free of loss. For that purpose, an intimate connection required between strain gauge and object to be measured. The required intimate, plane connection between specimen and the strain gauge is performed by special adhesive. Other bonding agents and methods are limited to special application area, e.g. ceramic bonding agent for high temperature installation and spot welding for applications on steel construction. B. Ultra sonic testing:- In ultrasonic testing (UT), very short ultrasonic pulse-waves with centre frequencies ranging from 0.1-15 MHz and occasionally up to 50 MHz are transmitted into materials to detect internal flaws or to characterize materials. In ultrasonic testing, an ultrasound transducer connected to a diagnostic machine is passed over the object being inspected. The transducer is typically separated from the test object by a couplant (such as oil) or by water, as in immersion testing. However, when ultrasonic testing is conducted with an Electromagnetic Acoustic Transducer (EMAT) the use of couplant is not required. There are two methods of receiving the ultrasound waveform: reflection and attenuation. In reflection (or pulse-echo) mode, the transducer performs both the sending and the receiving of the pulsed waves as the "sound" is reflected back to the device. Reflected ultrasound comes from an interface, such as the back wall of the object or from an imperfection within the object. The diagnostic machine displays these results in the form of a signal with amplitude representing the intensity of the reflection and the distance, representing the arrival time of the reflection. In attenuation (or through-transmission) mode, a transmitter sends ultrasound through one surface, and a separate receiver detects the amount that has reached it on another surface after traveling through the medium. Imperfections or other conditions in the space between the transmitter and receiver reduce the amount of sound transmitted, thus revealing their presence. VI. CONCLUSION. 1) Modeling of Pressure vessel with Expansion joint is done in Ansys 14.5 Workbench. First of all weather design of pressure vessel is safe or not without expansion joint is checked. We found that deformation stress is more so there is requirement of expansion joint. 2) After design and modeling of expansion joint again analysis is done on same software, we found that design is safe also deformation stress is reduced. ACKNOWLEDGEMENT Thanks to Dr. A.G. Thakur sir and Mr. Vinaay Patilfor his valuable contribution for helpful guidance and support to bring this project to final stage. REFERENCES [1] Sudeep Zirmire and Prof.R.S.Tajane Analysis and Weight Optimization of Butane Separator Using Finite Element Analysis, IJREAT International Journal of Research in Engineering & Advanced Technology, Volume 2, Issue 3, June-July, 2014 [2] Brijeshkumar. M. Patel, Design, Manufacturing and Analysis of Metal Expansion Bellows, International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 2, Issue 3, May 2013 [3] G. Wang & K.F. Zhang (2006) Superplastic forming of bellows expansion joints made of titanium alloys, Journal of Sound and Vibration, 317 (2008) 112 126 [4] Hervandil Morosini & Sant Anna, A practical procedure to assess critical defects in pressure vessels subjected to fatigue loads, Engineering Fracture Mechanics 78 (2011) 1669 1683 [5] Jerzy Okrajni and Mariusz Twardawa, Description of the thermo-mechanical fatigue of thick-walled pressure vessels,procedia Materials Science 3 ( 2014 ) 918 923 [6] Ming-Hsien Lu & Jiun-Shya Yu, The effect of analysis model on the stress intensity calculation for the nozzle attached to pressure vessel under internal pressure loading, International Journal of Pressure Vessels and Piping 117-118 (2014) 9-16 [7] You-Hong Liua, & Bing-Sheng Zhan, Limit pressure and design criterion of cylindrical pressure vessels with nozzle, International Journal of Pressure Vessels and Piping 81 (2004) 619 624 [8] Yashar Javadi and Hamed Salimi Pirzaman, Ultrasonic stress evaluation through thickness of a stainless steel pressure vessel, International Journal of Pressure Vessels and Piping xxx (2014) 1-10 [9] Prabir K. Sen and Hojjat Adeli, A new steel expansion joint for industrial plants: Bubble joint, International Journal of Pressure Vessels and Piping 83 (2006) 447 463 [10] Kaishu Guan and Xinghua Zhang, Failure of 304 stainless bellows expansion joint, Engineering Failure Analysis 12 (2005) 387 399