3-D Finite Element Analysis of Bolted Flange Joint of Pressure Vessel

Transcription

1 ISSN No MIT Publications 35 3-D Finite Element Analysis of Bolted Flange Joint of Pressure Vessel Nomesh Kumar, P.V.G. Brahamanandam and B.V. Papa Rao Advanced Systems Laboratory, Defence Research and Development Organisation, Ministry of Defence, Hyderabad, Andhra Pradesh, India Abstract- The objective of this work is to find out the stresses in the bolts of the bolted flange joint of the pressure vessel so that bolts/studs should not be failed during proof pressure test. Bolted flange joints perform a very important structural role in the closure of flanges in a pressure vessel. It has two important functions: (a). to maintain the structural integrity of the joint itself, and (b). to prevent the leakage through the gasket preloaded by bolts. One flange is having a groove for the gasket, and other flange is flat connected by a number of bolts/studs. The preload on the bolts is extremely important for the successful performance of the joint. The preload must be sufficiently large to seat the gasket and at the same time not excessive enough to crush it. The flange stiffness in conjunction with the bolt preload provides the necessary surface and the compressive force to prevent the leakage of the gases contained in the pressure vessel. The gas pressure tends to reduce the bolt preload, which reduces gasket compression and tends to separate the flange faces. Due to flange opening, bending has been noticed in the bolt. Hence the bolts/studs should be designed to withstand against preload, internal pressure load and bending moment. Due to existence of Preload, internal pressure and bending moment at a time, the bolt behavior is nonlinear which cannot not be evaluated by simple mathematical formulas. 3-Dimensional finite element analysis approach is only the technique which shows some satisfactory result. Nomenclature Fi = Initial Pretension T in = Torque Applied on each stud D = Diameter of the bolt/stud K = Nut factor F e = Total external load on all studs/ bolt F p = external load due to pressure on each bolt/stud P= Proof Pressure in bar n = number of studs/ bolts Ft = Total load on each stud/bolt Fb = Prying force Φ = Joint factor based on stiffness, dimensionless quantity I. INTRODUCTION Generally one dimensional analytical formulae are used to design bolts and flanges of the bolted flange joint in which the contact surfaces, which include the area between the flanges and the gasket are assumed to be constant and without friction between the flanges. The non-linear forcedeflection behavior of the bolted flange joint was presented in Brickford [1]. In the paper of Zahavi[10] the numerical analysis based on finite element method is presented and non-linear stiffness characteristics of the bolt joint is considered. In this paper, 3-dimensional finite element analysis of the bolted flange joint of the pressure vessel has been presented with the assumption of friction exist between the flanges. BOOSTER motor is a major propulsion system for surface to surface missile. It has bolted flange joint between motor and nozzle. The bolted flange joint consist 44 numbers of M14 x 1.5 studs of class 10.9 at the PCD of 590 mm. The detail of joint is shown in figure-1and figure-2.. The motor is having M14 x 1.5 tapped holes with 21.0 mm threaded length and 24.0 mm drilling depth. Convergent is having free holes of 14.5 mm. The maximum expected operating pressure (MEOP) of the motor is 70 Ksc and proof pressure (PP) is 77 Ksc (1.1 times of MEOP). The motor casing material is Maragin steel and a fastener is of 15-5-PH steel. Booster motor act as a pressure vessel and named as PC vessel. The main objective of this work is to find out the strength of the bolted flange joint so that bolt should not be failed during proof pressure test. II. STRESSES IN THE BOLT Tightening the bolt on a flange sets up stress and strain in both the bolt and flange members. The bolt is placed in tension while the joint members are in compression, at least in the vicinity of the bolt. To load the joint by applying the torque in criss-cross pattern, so stress is equally distributed in the flange. Short-form torque preload equation is used to evaluate the initial preload created in a bolt. Nut factor value ranges from 0.1 to 0.2. In this case, 0.2 is assumed for worst condition.

2 ISSN No MIT Publications 36 drastically increase the amount of tensile and bending stress produced in the bolt for a given external force as shown in figure-3. To estimate the magnitude of bolt forces produced due to prying, finite-element analysis has been carried out. Prying always bends the bolt, increasing stress on one side more than the other as shown in figure-3. The prying force is given as F b = F b ( 1+ ) a Hence total tensile load on each bolt is given by Ft. p F t =F i + Φ x F b Fig. 1. Joint Detail. Fig. 3. Free body diagram for prying force. The tension in the bolt which has been caused by the external load and magnified by the prying action, and the bending stresses created in the bolt as the joint members are pried apart. III. FINITE ELEMENT MODEL Fig dimensional joint detail. F i = Tin KxD Apart from this, internal pressure (proof pressure) of 77 bar is acting. This pressure load enhance the total load on the bolt. This is called a prying load, such a load can Modeling of bolt in 3- dimensional finite element application is still complicated. The analysis has been carried out using ANSYS As per cyclic symmetry, One sector of 8.18 (360/44) has been analysed. SOLID95 (the element is having 20 nodes with three degrees of freedom per node i.e. translations in the nodal x, y, and z directions. This element has plasticity, creep, stress stiffening, large deflection, and large strain capabilities.) has been used for meshing. The flange interface and Nut-Flange interface has been modeled with contact elements CONTA174 & TARGE170 elements. The bolt is modeled with solid elements. Cyclic symmetry boundary conditions are applied at the edges of the model. Input parameters are shown in table-1. A cyclic symmetry analysis is required to represent one part of a pattern that, if repeated N times in cylindrical coordinate space, yields the complete model. The angle θ (in degrees) spanned by the sector should be such that nθ = 360, where n is an integer. In this case n is 44. The sector is constrained by symmetric boundary condition on the corresponding surfaces. The cyclic sector of is shown if fig. 3. Here half of the sector is

3 ISSN No MIT Publications 37 considered for the analysis as shown in fig. 4 and Finite element model in fig. 5. The Preloads (initial tension) in bolts have significant effect on deflections and stresses. The pretension load is used to model a pre-assembly load in a joint fastener. The pretension section has been created in the shank portion and pre-tightening force is simulated with PREST179 Elements. Pretension section, across which the pretension load is applied, must be defined inside the fastener. The pretension load direction is along the bolt axis i.e. the body that contains Bolt Pretension has been meshed to partition along the axial direction. The meshed pretension section is flat with coincident nodes on the two sides (A and B) of the pretension section as shown in figure-6. The side A and B on the pretension section are connected by one pretension elements for each coincident node pair. The type of elements and material properties use are mentioned in Table-I and Table-II respectively. TABLE 1 ELEMENT HISTORY Component's name Element's Type No. 1. Flange and shell SOLID95 2. Bolt and Nut SOLID95 3. Contact Element CONTA174 and TARGE Pretension PREST179 Fig. 4. Half sectorial detail of the flange joint. No TABLE II MATERIAL PROPERTIES Component's Parameters Units Value name 1. Flange 2. Bolt and Nut Modulus of elasticity Kg/mm Poisson's Ratio Modulus of Kg/mm elasticity Poisson's Ratio TABLE III INPUT PARAMETERS Parameters Units Value No. 1. Bolt pre-tightening torque Kg-m Bolt pre-tightening force with torque Kg 5000 coefficient of Bolt stress area mm Thread shear area at pitch line (Length mm of engagement = 11.6 mm) 5. Bolt pre-tightening stress Kg/mm Bolt material class Yield Strength of Bolt material Kg/mm Ultimate tensile strength of motor Kg/mm material (Maragin steel-250) 9. YS of motor material Kg/mm Coefficient of friction between the flanges Fig. 5. Finite element model of half sectorial bolted flange joint.

4 ISSN No MIT Publications 38 No TABLE V RESULTED STRESS VALUES Axial Axial Bendi stress due stress due ng to to internal stress pretension pressure (Kg/ (Kg/mm 2 ) (Kg/mm 2 ) mm 2 ) Pressure Load (bar) Total stress (Kg/m m 2 ) Shear stress on nut (Kg/m m 2 ) Fig. 6. Pretension sector in the shank portion of the stud. IV. RESULTS The 3-dimensional cyclic analysis has given the value of axial forces and stress induced due to these axial forces as shown in table-4 and table-5. It also has given the value of bending moment on each bolt/stud. This bending moment divided by the sectional modulus of the stud to obtain bending stresses in the bolt/stud. The contour plot of stresses is sector shown in figure 7. The total stresses in each bolt/ stud is the sum of axial stress and bending stress. The deflection of stud due to internal pressure is shown in figure-8. The total stresses and bending stresses in the bolt/stud is shown in figure-9 and 10 respectively. The axial stress in the bolt/stud due to pretension is shown in figure- 11. The contact gap and stresses in flange are shown in table-6 and in graph no 1,2,3 and 4 respectively. The cyclic expansion of the sector is shown in fig. 12. TABLE VI RESULT OF CONTACT ELEMENTS Parameters Units values No. 1. Contact gap between flanges just mm 0.36 below o-ring (in intermediate zone between two bolt) 2. Contact gap between flanges below o-ring (just below the bolt) mm Maximum Principal stresses in Kg/mm flange (in intermediate zone between two bolt) 4. Maximum Von-misses stresses in flange (in intermediate zone between two bolt) Kg/mm Maximum Principal stresses in Kg/mm flange (just below the bolt) 6. Maximum Von-misses stresses in flange (just below the bolt) Kg/mm TABLE IV TABULATED LOAD RESULT No. Parameters Units values 1. Pretension load Kg Fig. 7. Distribution of Longitudinal stress in sector. 2. Axial load due to external load with prying action Kg Bending moment Kg-mm

5 ISSN No MIT Publications 39 Fig. 8. Distribution of deflection due to bending of the stud. Fig. 11. Distribution of axial stresses due to preloading. Graph 1: Distribution of contact gap (between two bolts). Fig. 9. Distribution of total stresses in the stud. Graph 2: Distribution of contact gap (just below the bolt)). Fig. 10. Distribution of bending stresses in the stud

6 ISSN No MIT Publications 40 Graph 3: Distribution of contact gap (between two bolts). been busted at bars. The joint withstand upto bars without any leakage/signal of failure. Hence the stresses shown by the FEM analysis are for the reference only. The actual stresses are less than 3D Finite Element analysis result. The Finite Element analysis is very conservative and shows no factor of safety on fasteners on Proof Pressure. But experiment results have been shown sufficient factor of safety is available on the bolt. Also stresses in the stud/bolt depend upon the friction exist between the flanges. As the coefficient of friction increases, stresses in the bolt/stud decreases. To predict actual stresses in the bolt/stud, measured the actual coefficient of friction between flanges and same will be used in the analysis. REFERENCES Graph 4: Distribution of contact gap (just below the bolt). [1] John H. bricford, Introduction to the design and behavior of bolted joint," fouth edition", ; CRC press, taylor & francis group", pp [2] BaroLomieg Zylinsky and Ryszard Buczkowski, Analysis of Bolt Joint using the Finite Element Method," The Archieve of Mechanical Engineering",Volume LVII, [3] NanBu, Naohiro, Ueno and Osamu Fukuda, Finite element Analysis of Contact stress in a full metallic pipe for hydrogen pipeline, "AISI, Japan", pp [4] Kathryn J. Belisle, Experimental and Finite Element Analysis of a Simplified Aircraft wheel bolted Joint model," The Ohino state University,2009. [5] Yasumasa Shoji and Santoshi Nagata, analysis of Gasket Flanges with Ordinary Elements using APDL Control," Toyo Engineering Corporation, chiba, Japan,2002. [6] JCharles S. Hseih, Steven R. Massey and Dennis H. Martens, Design of flanged joint subjected to pressure and external loads, PVP, ASME, New York, [7] ASME code, Pressure vessel Design,"chapter nine", pp [8] Robert D. Cook Finite element modeling For Stress Analysis", "John Wiley & Sons,Inc,2001", pp [9] Zahavi E., A finite Element Analysis of flange connections, Journal of Pressure Vessel Technology, ASME, , pp [10] Joseph E. Shigley, Machine Design," second edition", ; Mcgraw-hill ", pp [11] Jerome Montgomery, Method for modelling bolt in bolted joint, Siemens Westinghouse Power Corporation, Orlando, FL". Fig. 12. Contour plot of stresses in cyclic expansion. V. CONCLUSION 20 numbers of PC vessel have been proof tested successfully. The experimental result of proof pressure shows that the stresses predicted by 3-dimensional FEM analysis are more than realistic stresses. The PC vessel has