PARAMETRIC STUDY OF FLANGE JOINT AND WEIGHT OPTIMIZATION FOR SAFE DESIGN AND SEALABILITY- FEA APPROACH Chavan U. S.* Dharkunde R. B. Dr. Joshi S.V.

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1 Research Article PARAMETRIC STUDY OF FLANGE JOINT AND WEIGHT OPTIMIZATION FOR SAFE DESIGN AND SEALABILITY- FEA APPROACH Chavan U. S.* Dharkunde R. B. Dr. Joshi S.V. Address for Correspondence Department of Mechanical Engineering, Vishwakarma Institute of Technology, Pune, Maharashtra, India - umeshschavan@rediffmail.com, umesh.chavan@vit.edu ABSTRACT The present work utilized finite element analysis (FEA) to investigate the mechanics of the bolted flange joint and effect of the flange thickness on working stresses of the components of the flange assembly and gasket performance. The nonstandard flange design case is considered for study purpose. The FE model is formulated using structured mesh considering gasket behavior and preloaded fasteners. The customized parametric module is developed using ANSYS Parametric Design Language (APDL) to automate the nonstandard flange analysis tasks. Optimization is done using subproblem approximation method to obtain minimum weight of flange such that all components of the flange joint are exhibiting fundamental joint characteristics i.e. safe design and sealability. KEYWORD: Flange joint, finite element analysis (FEA), APDL, Optimization, and Seal-ability. I.INTRODUCTION Flange joint are widely used in chemical plants and power plants. Flanges use on the pressure vessel to permit disassembly and removal or cleaning of internal parts. Leakages small or large from flange joints, is a continued significant safety concern in terms of human life, environmental effect, and cost. With the rapid advancement in technology for high pressure and temperature applications, trends are changing hence it is important to evaluate the integrity and sealing performance of flange joint under applied operating conditions. Available design rules (ASME, BS) for flange joints are mainly concerned with the strength of the flanges and do not sufficiently consider for their sealing [1-3]. M. Abid, K.A. Khan and J.A. Chattha [4] specified that ASME codes do not provide information regarding maximum bolt spacing, minimum flange thickness and exact flange surface profile. FEA has been used to model flange joints by many researchers to study the safe design and sealability [4, 7-8]. J. Montgomery [5] suggested the methods for modeling pretension bolted joints using the FEA. A parametric study was performed by D. H. Nash, J. Spence, A. S. Tooth, M. Abid, and D. J. Powel [6] for large diameter metal-to-metal nongasketed flanges using FEA and analytical approach from standard design codes. M. Abid and D. H. Nash Abid et al. [7] performed 3D nonlinear FEA of nongasketed flange joint to investigate two main joint characteristics Joint Strength and Sealing Capability. G. Mathan and N. Siva Prasad [8] obtained actual behavior of gasket by experimentally obtained nonlinear pressureclosure properties of gasket and FEA is performed to obtain actual sealing performance. In the present work, a customized gasketed flange joint FEA model is developed using APDL code for inputting analysis parameters, reviewing parameters, automation of preprocessing activities, solver selection, solution and post-processing activities. To obtain exact bolt preload, higher order structural element is selected for the analysis. Gasket nonlinear

2 pressure closure material property is used to simulate actual sealing behavior of gasket. Subproblem approximation method is used for optimization to obtain minimum weight under safe stress and no-leakage conditions in flange joint. II. MATERIAL PROPERTIES AND COMPONENT GEOMETRY A. Material properties of the flange, vessel, weld and bolt The material properties of all components are assumed to be homogenous, isotropic and linearly elastic The material considered for flange, vessel and weld is carbon steel A181 with Young s modulus GPa, Poisson s ratio 0.29 and allowable stress MPa at design temperature [9]. Bolts material considered is carbon steel A193-B7 with tensile strength 362 MPa, Young s modulus 200 GPa and Poisson s ratio 0.3. The allowable stress for bolts is taken as 2/3 of tensile strength (2/3*362 = MPa) [6]. B. Gasket characterization The gasket material is compressed elastomeric reinforced with asbestos fibers (CAU4). The modulus of elasticity for the bolting-up or compression (loading) stage is different from the decompression (unloading) stage of the gasket due to the internal pressure. When the gasket is decompressed, it shows strong hysteresis which is nonlinear and leads to permanent deformation usually confined to through-thickness. The FE programming code used to simulate gaskets material nonlinearity. Thus the pressure-closure behaviour can be directly applied to characterize the gasket material. A load compressive mechanical test (LCMT) [2, 3] has been used for finding the mechanical characteristics of gasket material which are in turn used in the FEA. Fig. 1 shows the experimentally obtained pressure closure material property CAU4 gasket with allowable stress MPa. C. Component geometry In the present study, an 800NB slip-on flange with M24 size bolts is considered. The dimensions of flange joint with 20 number of bolt holes are shown in fig Pressure (mm) Closure (mm) Loading Unloading1 Unloading2 Fig. 1. Pressure-closure material property CAU4 gasket.

3 Fig. 2. Dimensions of the flange joint used in the FEA: (a) Flange and (b) flange joint components. III.FINITE ELEMENT MODELING characterized by a pressure-versus-closure A three-dimensional FE model has been developed for bolted flange connections with gaskets using ANSYS to obtain exact bolt preload. Higher order structural solid elements (SOLID95) [10] are used to model the geometry of the flange. Customized module is used throughout the study, so that the time involved in building scaled geometry models of different geometries could be minimized and utilized for optimization. A. Modeling of the gasket The gasket is modeled with interface elements (INTER195) [10]. These elements are based on the relative deformation of the top and bottom surfaces and offer a direct means to quantify the through-thickness deformation of the gasket joints. The complete gasket behavior (throughthickness (relative displacement of top and bottom gasket surfaces) relationship. B. Pretension in the bolts Pretension elements (PRETS179) [10] shown in fig. 3 are used to model the load in a bolted joint due to tightening at the time of assembly. All pretension elements have a common pretension node (K). This node is the third node for the pretension element whereas nodes I and J are on the sectioned mid-surface of the bolt. Sides A and B on the pretension section are connected by one or more pretension elements, one for each coincident node pair. A pretension node (K) is used to control and monitor the total tension loads. In the first stage (bolting-up), load was applied to the pretension node as a force. The force locks on the second stage deformation of the gasket) is (pressurized), allowing additional loads the

4 effect of the initial load is preserved as a displacement after it is locked. The bolt and nut threads are modeled as part of an unthreaded shank with the minor diameter of the bolts, and the bolt head and nut are assumed cylindrical to avoid meshing difficulties. C. Loading and boundary conditions 1) Boundary Conditions: Symmetry boundary conditions reduce the convergence, computational errors and time require for the analysis. An angular portion (18 0 rotation of main profile or 1/20 part) of flange is modeled with a single bolt hole and symmetry is applied by restricting circumferential displacements. Second flange is replaced by a symmetry plate so symmetry boundary conditions are applied along gasket mid-plane and mid-section of the bolt. The cross sectional area and resulted flange joint meshed model is shown in fig. 4. 2) Bolt preload and pressure loading condition: Pretension/clamping force ( N) is applied on pretension element section through the pretension node of bolt which is obtained by ASME design rule. Pressure of internal fluid ( MPa) is applied on internal areas of the vessel, weld and inside of the gasket. Hydrostatic end thrust pressure due to internal pressure ( MPa) is applied on annular area segment of vessel. 3) Development of Customized Module: Customized module is scripting language use to automate common tasks or build model in terms of parameters (variables) such that its parameters can be varied with least human interaction. The customized module is developed using APDL coding for inputting analysis parameters, loading parameter, material properties, solver selection and solution and post-processing activities. Fig. 8 shows generated user prompt window to enter independent geometric parameters of the components of the flange assembly. (a) Fig.3. PRETS179 element: (a) before adjustment and (b) after adjustment. [10]. (b)

5 Fig.4. Flange joint meshed model Fig. 5. Multi prompt window for flange geometry

6 Fig.6. Deformed shape of the assembly IV.FEA RESULTS AND PARAMETRIC STUDY A. Mechanics and behavior of flange assembly in operation During preliminary studies, FEA and analytical results (Lames theory) are compared and are found in good agreement, providing FEA model verification. The maximum deformation is found out to be mm (Fig.6) of the flange. It can be interpreted from the results that tilting of flange takes place about gasket mean diameter due to combined effect of clamping forces (i.e. assembly bolt load) and hydrostatic end thrust. The stress concentration can be observed in the region of bolting as bolt exerts force on flange which is combined effect of pretension force and force to resist hydrostatic end thrust. The Fig.7. Stress intensity distribution in flange maximum value of stress is observed at outer region of raised face underneath the bolting these stresses are localized in nature. The maximum value is found out to be MPa (Fig.7).Fig 8 shows the stress of compressive stress distribution of the gasket and there is gradual change in stress from inner to outer face. The fibers in the outer region are exposed to higher stress (compressive) due to flange rotation. Maximum stress value along the path is MPa. Fig. 9 shows the stress distribution from inside to outside face of gasket (gasket width), the separation of the gasket and flange takes place up to mean diameter of the gasket and compressive pressure acts only on half gasket width. Fig. 8. Compressive stress in gasket Fig. 9. Stress distribution across gasket width

7 B. Results of parametric study Parametric study is carried out by varying flange thickness to study the effect of flange thickness on working stresses on different components of the assembly. A range of different values of flange thickness is considered for flange joint from 41.8 mm to 57.8 mm. 1) Effect of flange thickness on maximum flange stress: With reduction in thickness, the overall stiffness of the flange and resistance to the bending decreases due to bolt load. The application of internal pressure and axial pressure further enhance the stresses in flange. Therefore, as the flange thickness reduces consequently maximum flange stresses increases (Fig. 10(a)). 2) Effect of flange thickness on maximum vessel stress: Maximum shell stresses remains almost constant with further reduction in flange thickness. Maximum shell stresses slightly increase due to reduction in overall stiffness of flange joint (Fig. 10(b)). 3) Effect of flange thickness on maximum gasket stress: The maximum compressive stresses on gasket increases with reduction in flange thickness (Fig. 10(c)) due to increase in tilting action of the flange which exerts more loads at outer face region of the gasket. As the flange thickness is reduced, due to reduction in overall stiffness of flange less strain energy is absorbed by flange and remaining is transferred to the gasket; this in turn increases the slope of the stress distribution curve. The increase in slope reduces the sealability of flange joint. 4) Effect of flange thickness on maximum bolt stress: The increase in flange deflection with reduction of flange thickness causes increase in bending of bolts, which causes slight increase in stresses in bolts (Fig. 10(d)). (a) (b) (c) (d) Fig.10. Effect of flange thickness on flange joint component stresses: (a) Flange, (b) Vessel, (c) Gasket and (d) bolts

8 V. WEIGHT OPTIMIZATION OF FLANGE JOINT A. Subproblem approximation method This method of optimization can be described as an advanced, zero-order method which requires only values of the dependent variables (objective function and state variables) and not their derivatives. The dependent variables are first replaced with approximations by means of least squares fitting, and the constrained minimization problem is converted to an unconstrained problem using penalty functions. Minimization is then performed for every iteration on the approximated, penalized function (called subproblem) until convergence is achieved or termination is indicated. B. Flange joint design variable, state variable and objective function: In order to obtain safe design [7], the stresses in flange, vessel and bolts are within allowable stress limits of the material. The load bearing capacity and sealability is determined by the compressive stresses in gasket. For the case of load bearing capacity [2] the compressive stresses in gasket should be less than MPa. In order to obtain the sealing capability [1] of flange joint the compressive stresses at gasket reaction diameter should be more than product of gasket factor (m) and internal pressure i.e MPa (=2*0.495) and the maximum compressive limit at this diameter should be less than crushing limit of gasket (51.43 MPa). In the current case, in order to reduce the stress taper is chosen for the flange geometry as a design variable along with flange thickness (Fig. 11). The objective function is considered as weight of flange. Customized FEA module of flange joint is used for optimization. Fig. 11. Position and Dimension of Taper in Flange Joint

9 C. Results and comparison of flange joint optimization Set numbers are values of design variables obtained by initial analysis or parametric value of design variables defined by subproblem approximation method for the corresponding iteration. The flange thickness converges after set number 8, where the flange thickness obtained is mm. The variation of design variables with different set numbers is shown in fig. 12. The variation of state variables with respect to set number is shown in fig. 13. The maximum stress in flange converges after set number 7 where the maximum Von mises stress obtained is MPa. Fig. 13 (c) shows variation of compressive stress in gasket with respect to set number where the converged value retrieved is MPa at set number 8. Fig. 14 shows variation of objective function i.e. weight of flange with respect to set number. The optimization iterations of flange joint is converged at set number 9 where the weight of flange is obtained as kg. The obtained modified flange geometry is exhibiting the minimum weight criteria and all the stresses in the various components of flange joint are within allowable stress limit. The comparison of results obtained using FEA of modified design and existing design are given in table I. The minimum weight of flange joint under current operating condition is obtained as Kg with % less compared with existing dimension of flange joint. (a) (b) Fig. 12. Design variables vs set number: (a) Flange thickness and (b) Horizontal and vertical projected taper distance.

10 (a) (b) Fig. 13. State variables vs set number: (a) Max. flange Von-mises stress, (b) Stress at gasket reaction diameter Fig. 14. Objective function (weight of flange) vs set number Table I: Results of Fea and optimization for existing and Modified Design Parameter Allowable Existing Modified limit Design Design % Difference Flange thickness mm 51.8 mm mm 10.3 Reduction Horizontal projected taper mm 0 mm mm distance Increment Vertical projected taper distance 0-4 mm 0 mm 0.09 mm 2.23 Increment Max flange stresses MPa MPa MPa Reduction Max shell stresses MPa MPa MPa 1.34 Increment Max compressive gasket stresses MPa MPa MPa 6.86 Increment Max bolt stresses MPa MPa MPa 1.26 Increment Weight of flange kg kg Reduction

11 IV.CONCLUSION With the help of the customized module the overall human interactive time and workstation time for the analysis of flange joint is reduced from 48 hours to 2 hours. Customized module provides reusability of available data which save time required for problem formulation, preprocessing & post processing in parametric study and optimization. Maximum stress in flange is obtained at inside face of flange near gasket seating step and it is always increases with increase in flange thickness. Maximum compressive stress in gasket is obtained at outer gasket face. The flange gets detached from gasket at inner gasket face. The gasket performance decreases with decrease in flange thickness, due to this flange joint become prone to leakage of joint. Flange thickness has considerable effect on flange strength and gasket performance. The flange thickness must be chosen carefully to satisfy the tradeoff between strength/material requirements and gasket performance. Using Sub problem approximation optimization method the weight is optimized from Kg to Kg with % reduction under consideration of safe design and sealability. The stress in flange is decrease from MPa to MPa with % reduction. ACKNOWLEDGMENT The authors wish to acknowledge the contributions made to this work by Mr. Manish Pandye - CAE head and Dr. P. Vasudevan - technical director, FEAST Software Pvt. Ltd - IIT Bombay for funding and providing technical support. REFERENCES [1] ASME Boiler and pressure vessel code, section VIII, Division I, American Society of Mechanical Engineers, New York, [2] J. H. Bickford, Gaskets and gasketed joints. New York: Marcel Dekker Inc., [3] J. H. Bickford, An introduction to the design and behaviour of bolted joints. 2 nd ed., New York: Marcel Dekker Inc., [4] Muhammad Abid, K.A. Khan and J.A. Chattha, Performance of a flange joint using different gaskets under combined internal pressure and thermal loading, Advanced Design and Mfg. to Gain a Competitive Edge-Springer, pp , [5] J. Montgomery, Methods for modeling bolts in the bolted joint, Siemens Westinghouse Power Corporation, FL, pp 1-15, [6] D. H. Nash, J. Spence, A. S. Tooth, M. Abid and D. J. Powel, A parametric study of metal to metal full face taper hub flanges, Int. J. of Pressure Vessels Piping, vol. 77, pp , [7] M. Abid and D. H. Nash, A parametric study of metal-to-metal contact flanges with optimized geometry for safe stress and no-leak conditions, Int. J. of. Pressure Vessels Piping, vol. 81, pp , [8] G. Mathan and N. Siva Prasad, A study on the sealing performance of flange joints with gaskets under external bending, Proc. Inst. Mech. Engg. part E, vol. 222, pp , [9] ASME Boiler and Pressure Vessel Code, section II, Part D, American Society of Mechanical Engineering, New York, [10] ANSYS User s manual, theory reference. Canonsburg, USA: ANSYS Inc., 2003.