Bottom End-Closure Design Optimization of DOT-39 Non-Refillable Refrigerant Cylinders

Transcription

1 Y. Kisioglu a) Department of Mechanical Education, Kocaeli University, Izmit, Kocaeli, 41100, Turkey J. R. Brevick Industrial and Systems Engineering, The Ohio State University, Columbus, Ohio G. L. Kinzel Mechanical Engineering, The Ohio State University, Columbus, Ohio Bottom End-Closure Design Optimization of DOT-39 Non-Refillable Refrigerant Cylinders This study addresses the problem of stability (standing of cylinders upright) of DOT-39 nonrefillable refrigerant cylinders using both experimental and finite element analysis (FEA) approaches. When these cylinders are designed using traditional methods they often suffer permanent volume expansion at the bottom end closure and become unstable when they are pressure tested experimentally. In this study, experimental investigations were carried out using hydrostatic pressure tests with water. In the case of numerical investigations, FEA models were developed for three-dimensional (3D) axisymmetric quasi-static conditions. The FEA models were constructed using nonhomogenous material nonlinearity and geometrical nonuniformity conditions. The results obtained from both FEA models and experimental tests were compared. To eliminate the instability of these cylinders, a design of experiment technique was employed to optimize the bottom endclosure design using the FEA models. DOI: / Keywords: Instability Analysis, DOT-39 Refrigerant Cylinder, Nonlinear Failure Analysis, Nonuniform FEA Model, NRV Cylinders 1 Introduction DOT-39 nonrefillable refrigerant cylinders, approved by the Department of Transportation DOT, can be commercially filled and used in industrial, commercial and consumer markets, as well as in medical applications. These cylinders are generally used for refrigerant applications by refrigerant producers and packagers around the world and contain refrigerant gases such as R12, R22, etc. These refrigerant cylinders are known as NRV nonrefillablevalve or NRC nonrefillable cylinder, and have capacities ranging from 15 to 50 lbs. These cylinders are also equipped with a nonrefillable valve, which is a one-way hermetic leak-stop valve to prevent refilling 1. The nominal dimensions of these cylinders can be defined by the ratio of the internal diameter (ID) to the shell thickness t, which is in the range of 95 ID/t 475. NRV cylinders can also be specified by their design pressures, which are defined along with service, test, and burst pressures 2. The service pressure SP, specified by DOT rules, is the working operating pressure at which the cylinders are filled and used in industrial applications. The test pressure TP, defined by both DOT and ASME codes, is 1.5 times the SP. When the TP is applied and released, the permanent volume expansion must not exceed 10% of the original measured volume. Also, the cylinders must stand in an upright position on the feet, i.e., remain stable, when they are subjected to the TP. Finally, the burst pressure BP is the maximum pressure that the cylinder can hold without bursting. Typically the BP must be at least double the TP 3. The instability problems associated with failures of the endclosure with different shapes such as ellipsoidal and torispherical under internal pressure have been studied by many investigators utilizing mostly experimental, analytical, and occasionally FEA and finite difference approaches. These instabilities have been mostly related to material failures bursting of the cylinders and a Author to whom correspondence should be addressed. Telephone: Ex.1044, Fax: ykisioglu@kou.edu.tr Contributed by the Pressure Vessels and Piping Division for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the PVP Division August 18, 2003; revision received September 23, Review conducted by: B. Blyukher. end-closures. Some local buckling failures were predicted in experimental studies in Ref. 4 and numerically in Refs Elastic plastic instabilities of the end-closures were studied in Refs. 8, 9 using different materials including aluminum, mild steel, and copper. In addition, design equations for preventing buckling failure of torispherical end-closures under internal pressures have been developed in Ref. 10. The stability of the NRV cylinders, standing on 4-dimples feet in the vertical position and related design components are shown in Fig. 1. When the end-closures experience permanent deformation, the cylinder loses its stability as a result of ballooning at the bottom and all four feet no longer support it vertically. Therefore, the objective of this study was to predict the permanent ballooning deflection of the bottom end closure at the TP using both experimental and FEA modeling approaches. The results obtained from both approaches were compared. In addition, a new design for the end-closures was developed using the FEA models to prevent the ballooning formation at the bottom end of the DOT-39 nonrefillable cylinders. 2 A Brief Definition of the Ballooning Problem Ballooning is defined as the permanent deformation of the bottom end-closure which occurs within a circle inscribed by the 4 dimples feet, which are located at the bottom of the cylinder as shown in Fig. 1. The purpose of these 4 dimples is to provide a stable platform for the cylinder. When the NRV cylinder is subjected to the TP and then the pressure is released, the cylinder is permanently deformed especially near the dimples at the bottom end-closure. As a result, the bottom of the cylinder extends beyond the plane of the feet and the cylinder loses its stability. Consider the horizontal plane, where the cylinder can sit on only the 4 dimples located at the bottom because of the positive clearance between points a and b shown in Fig. 2. This clearance between these two points is named Differ. Typically, the Differ is approximately in 2.52 mm as manufactured. The dimples were originally designed and located with the circumferential radius of DL dimple location of in mm at the bottom of the cylinders as seen in Fig. 2. With this 112 Õ Vol. 127, MAY 2005 Copyright 2005 by ASME Transactions of the ASME

2 Table 1 Experimental ballooning test results Experimental Test for Ballooning Deflection ID 9.5-in Ballooning Bottom test Applied Pressures psi Sample untested Number Ballooning Deflection Differ in Average Fig. 1 The DOT-39 non-refillable cylinders NRV or NRC and its components design, the rate of the ballooning instability experienced with the NRV cylinders at the TP was 20%. To avoid the ballooning deflection, the manufacturer then selected a new DL by reducing the dimension of the old DL by about 70% or 1.5 in 38.1 mm. The new DL (DL New ), can be defined as DL NEW DL L X DL 0.7 DL. Unfortunately, the DL New causes the NRV cylinder to be less stable in general because of the smaller distances between the dimples. 3 Experimental Ballooning Test The experimental ballooning investigations of the DOT-39 nonrefillable cylinders were carried out in the R&D laboratory of a major U.S. cylinder manufacturer. To test these NRV cylinders, the cylinder specimens were completely filled with water, and the pressure was controlled by means of a single acting hydraulic pump. By venting air during the filling, the water was utilized for Fig. 2 The bottom-end-closure geometry of the current NRV cylinder the tests at room temperature. The cylinder specimens were randomly selected from the manufacturing stack and carefully placed into the experiment equipment. The cylinders were placed horizontally in the equipment instead of sitting on the dimples at the bottom of the cylinders. The pressures for the ballooning experiments were applied stepby-step for the given values in the title row of Table 1. After the cylinders were subjected to each of the pressure values listed, the pressure was released after holding it at least 10 s. Each cylinder sample was subjected to the pressure values from 325 to 400 psi separately since the cylinders have caused some residual deformations after the first testing. After each test to the given pressures, it was observed that the cylinders were permanently deformed at points a and b shown in Fig. 2. This deformation is the residual deflection, and the value of Differ measured for cylinder sample 1 is given in the first row of Table 1. As can be seen in Table 1, the Differ values decrease as the applied pressures increase. When the NRV cylinders having the ratio of ID/t 297 were subjected to 400 psi 2.8 Mpa, the Differ value became negative, in 0.66 mm, thus permanent ballooning deformation took place. The average values of Differ obtained from six specimens tested in the experiments are listed in the last row of Table 1. Therefore, the Differ values for each applied pressure; 325, 350, 375, and 400 psi were obtained as , , , and in, respectively. These pressures were taken as the base loads for the computer modeling process. Figure 3 shows the ballooning deformation at the bottom of the NRV cylinders tested at TP 325 psi and at the BP 730 psi. As can be seen from the figure, the value of Differ is positive at TP 325 psi. However, the value of Differ at the BP is not only negative but also the geometry of the dimples has disappeared because of the large ballooning formation at the BP. 4 FEA Model Development for Evaluation of Ballooning The commercial finite element software, ANSYS 11, was employed to predict the permanent ballooning formation that occurs at the bottom end-closure. To create the 3D FEA model, the current design parameters including dimple geometry, drawn cylindrical shell material including weld zone properties and shell thickness variations of the NRV cylinders were investigated and considered in the modeling process. 4.1 Investigations of Material Properties and Thickness Variations. The DOT-39 refrigerant cylinders were manufactured from SAE-1008 steel sheet by using a deep drawing process. The material is low-carbon cold-rolled steel, which is a ductile material and suitable for cold forming processes. Because of strain hardening in the deep drawing process, the material properties vary along with thickness and location in cylindrical shells, especially in the weld zone. To consider the variation in material prop- Journal of Pressure Vessel Technology MAY 2005, Vol. 127 Õ 113

3 Fig. 3 Experimental ballooning test 2 erties, a drawn shell component of the cylinder is divided into four regions between points a and b shown in Fig. 4. These named regions are; shell by weld between the points a and c, shell by knuckle between the points c and d, crown by knuckle between the points d and e, and finally crown between the points e and b. For each region, tensile test specimens were cut out in both the circumferential and longitudinal directions as shown in Fig. 4, and the corresponding engineering stress strain data ESSD were obtained using tensile tests. The material properties of these regions are represented by their true stress-strain curves converted from corresponding ESSD as shown in Fig. 5. The thickness variation of the drawn cylindrical shell was measured and is given as a function of shell regions in Fig. 6. As shown in Fig. 6, the wall thickness in the cylindrical drawn shell region varies more than that of the crown region. It is also observed that the maximum thickness decreases about 18% at point d in the shell by knuckle region, and the minimum thickness decreases about 1% at point b in the crown region Selection of Finite Shell Element and Boundary Conditions. The FEA modeling requirements include a thin-shell structure, material nonlinearity, large strain analysis, and geometrical nonuniformity. The finite element, SHELL181, is a suitable shell element for analyzing the thin-shell structure of the NRV cylinders. The SHELL181 element is specified with 4 nodes and 6 degrees of freedom DOF at each node 11. In terms of boundary conditions BCs, a model was chosen which is axisymmetric with respect to the geometrical and loading conditions. In the case of the loading conditions, the FEA models were subjected to an incremental uniform internal pressure until the TP. Fig. 4 Drawn shell regions where the material properties were measured 4.3 Development of Nonlinear Axisymmetric FEA Model In the processes of FEA modeling, the cylinder geometry was specified in 3D quarter-symmetry form by using the mid-surface of the cylindrical shell thickness as shown in Fig. 7. This geo- Fig. 5 True stress-strain curves of drawn cylindrical shell regions 114 Õ Vol. 127, MAY 2005 Transactions of the ASME

4 Fig. 6 Thickness variation of the drawn cylindrical shell 3 Fig. 7 The 3D geometrical model metrical model of the NRV cylinders was divided into different areas to develop an appropriate FE mesh generation. Using the material non-linearity see Fig. 4, geometrical nonuniformity see Fig. 6, the BCs and the SHELL181 specifications, the FEA model was developed to simulate the NRV cylinder shown in Fig. 8. The material nonlinearities were applied for nonhomogeneous conditions in the modeling. To do this, the isotropic hardening option involving the Von Mises yield criterion with an isotropic work hardening assumption was applied. In addition, the geometrical nonuniformity requires shell thickness variations as well as the weld zone thickness variation generated in the modeling processes by using a geometrical step function 2. At the initiation of the axisymmetric FEA modeling development, some assumptions were made. First, it was assumed that the effects of the weld zones at the valve-and-tubing area including the nozzle zone, where the tube is placed see Fig. 1, were not important for these models. Second, the thickness variation and material property of the dimples see Fig. 6 were assumed to be constant after the dimpling process and to be the same as in the crown region. Finally, it was assumed that there were no residual stresses due to the deep drawing and welding processes. 4.4 Predictions of Ballooning Using the FEA Model. In the simulations, the FEA model was subjected to the internal pressure by incrementally increasing it linearly with 10 psi 0.7 Mpa steps from the beginning until the TP. This incremental pressurization was performed during loading as well as unloading. Since the material properties of the cylinder remain in the range of the elastic plastic state, the loading conditions were sustained linearly until the TP was reached. In the FEA applications, convergence criteria on both forces and moments were applied with the Newton Raphson method ANSYS Manual, To conduct the ballooning tests based on the TP values 325, 350, 375, and 400 psi given in Table 2, four different ballooningtest trials were conducted in both the analytical and experimental tests. In the first trial, the cylinder models were subjected to an Fig. 8 Residual deflections of the end-closure after releasing the pressure Journal of Pressure Vessel Technology MAY 2005, Vol. 127 Õ 115

5 Applied Pressures TP psi Mpa Table 2 The ballooning test results 2 Experiment Ballooning Test Results Differ Udy Uy FEA Model incremental pressure loading from zero pressure to 325 psi and then the pressure was released. Similarly, the second, third, and fourth trials for the ballooning test modeling process were performed for the testing pressure values of 350, 375, and 400 psi, respectively. When the internal loading reached the TP along with the convergence norms, the pressure was released in the simulation processes to the pressure-free state. Also, releasing the pressure was performed incrementally with a 10 psi 0.7 Mpa per increment from the TP to zero pressure. After releasing the applied pressure, the residual deflections were evaluated between the points N32 and N798 seen in Fig. 8. The maximum residual deflection occurs in the crown region. To evaluate the prediction of the ballooning deformation, the magnitude of the permanent displacements of both the N32 and N798 nodes were compared with each other on the horizontal plane. In this evaluation, the magnitudes of the residual nodal-displacements of these two nodes were considered in the y direction only. As expected, the displacements of these two nodes are nonlinear functions of the incremental loading shown in Fig. 9. These nodal displacements also represent both loading and unloading conditions in the simulation processes. At the beginning of the incremental loading cycle of the simulation, the position of N32 is lower than that for N798 as shown in Fig. 8. However, the nodal displacement of N32 increases faster than that of N798 at point a in Fig. 9 as the pressure increases. Therefore, the position of N32 in the positive y direction eventually becomes higher than that of N798, in such a way that the ballooning deformation occurs permanently. This is shown in Fig. 10, using both an untested model and a tested FEA model subjected to the TP. The results obtained from the simulations are compared with corresponding experimental results in Table 2. The first column of this table lists the pressure values, and the second and third columns give the residual deflection results obtained from both experiment and FEA modeling approaches, respectively. To find the magnitudes of Differ listed in Table 2, the displacement amount of the N32 in the y-direction was subtracted from that of N798. That is, Differ U dy U c, where U dy and U c represent the displacements of nodes N798 and N32, respectively, in the y-direction. The magnitudes of the Differ obtained at the TP of the NRV cylinders (ID/t 297) were negative, in 0.59 mm and in 0.61 mm see Table 2, from both experimental and FEA modeling approaches, respectively. 5 Elimination of Ballooning Problem Instability The purpose of this study was to develop a new design to eliminate the ballooning problem of the NRV cylinders. At the start of the redesigning processes, the design parameters of the current end-closure geometry shown in Fig. 11 were evaluated using the FEA model. It was realized that the dimple location (DL), knuckle radius (R k ), dimple radius (R d ), center location of the dimple (R L ) and crown radius (R c ) shown in Fig. 11 are the source of the ballooning problem. From the cost of the tooling and manufacturing processes standpoint, it was decided that the R d, R k, R L, and R c should remain constant with the initial shape of the current model; therefore, DL was the focus of the redesigning effort. A design of experiment method was employed to optimize the design of the bottom end closure. The design of experimental method is an optimization technique defined primarily as how to plan and analyze an experiment to address the problem to be solved 12. The goal of this study was to examine how changing the value of DL affects the response variable Differ. The DL was varied between points o or d and e on the horizontal plane as shown in Fig. 11. The distance between these two points, d and e, in Fig. 11 was designated as L x, which has one maximum value located at Fig. 9 The nodal displacement behavior of the crown N32 and dimple N Õ Vol. 127, MAY 2005 Transactions of the ASME

6 Fig. 10 Prediction of ballooning deflection at the end-closure point o where the dimple is located and one minimum value placed at point e, which is the location of DL NEW explained earlier. The experimental design in the FEA modeling process was performed in two phases. First, the DL was varied between the maximum and minimum levels, 1.5 in 38.1 mm and in mm, ofthel x as shown in Fig. 11 and Table 3. In the first phase, the L x was divided into 7 equal increments. The FEA analysis was performed for each level starting from the maximum level of the factor, which is the initial location of the design variable that causes ballooning. A negative value of Differ represents the existence of ballooning. The experiment was stopped when the positive value of the Differ was obtained at the level of the DL 1.7 in. It should be noted that to eliminate the ballooning problem at the bottom of the NRV cylinders, the best DLs would be considered as DL 1.8 in 45.7 mm. To approximate the optimum value of DL better, the experimental design was performed a second time for DL divided into five small divisions of the interval as shown on Table 3. Similarly, the second phase was also performed starting from the maximum through minimum levels of the factor until finding a positive value of Differ, which was obtained at the level of DL in. Therefore, the optimum value of the DL lies in the range of in DL 1.75 in. The procedure may be applied again within this small interval. However, from manufacturing and tooling costs points of view, the degree of precision obtained from the second phase was adequate. 6 Conclusions Using FEA, DOT-39 nonrefillable refrigerant cylinders were analyzed using an incremental internal pressure to evaluate ballooning in the bottom end-closure. Based on the results, the following conclusions can be made: a. Good agreement was found between the experiment and the corresponding FEA modeling process to predict the ballooning instability as listed in Table 2; b. to eliminate the ballooning problem of the DOT-39 nonrefillable refrigerant cylinders, an experimental optimization technique, was employed successfully. Based on the optimization results, a new DL for the NRV cylinders within the ratio of ID/t 297 was determined. As a result, the new DL was found to be significantly better than DL NEW estimated by the manufacturer; c. a 3D nonuniform geometrical model see Fig. 7 was developed successfully to generate a suitable axisymmetric nonlinear FEA model see Fig. 8 involving the variable DL and the dimple geometry. The results from the FEA simulations compare well with experimental results. Table 3 The optimization results for the new DL Fig. 11 Design variables of the end-closures 2 Optimization Results Design Variable DL Levels of Factors Response Variable Differ Udy Uc max mm First Experiment N/A min N/A max Second Experiment min Journal of Pressure Vessel Technology MAY 2005, Vol. 127 Õ 117

7 References 1 49 CFR Code of Federal Regulation, Part 178 Subpart C, Office of Federal Registrar, National Archives and Records Administration, US Government Printing Office, Washington, DC. October, Kisioglu, Y., 2000, A New Design Approach and FEA Modeling for Imperfect End-Closures of DOT Specification Cylinders, Ph.D. Dissertation, The Ohio State University. 3 Kisioglu, Y., Brevick, J. R., and Kinzel, G. L., 2001, Determination of Burst Pressure and Location of the DOT-39 Refrigerant Cylinders, ASME J. Pressure Vessel Technol., 123, pp Kirk, A., and Gill, S. S., 1975, The Failure if Torispherical Ends of Pressure Vessels Due to Instability and Plastic Deformation-an Experimental Investigation, Int. J. Mech. Sci., 17, pp Galletly, G. D., and Blachut, J., 1985, Torispherical Shells Under Internal Pressure-Failure Due to Asymmetric Plastic Buckling or Axisymmetric Yielding, Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 199 C3, pp Brown, K. W., and Kraus, H., 1976, Stability of Internally Pressurized Vessels With Ellipsoidal Heads, ASME J. Pressure Vessel Technol., pp Tafreshi, A., 1997, Numerical Analysis of Thin Torispherical End Closures, Int. J. Pressure Vessels Piping, 71, Issue: 1, pp Soric, J., and Zahlten, W., 1995, Elastic Plastic Analysis of Internally Pressurized Torispherical Shells, Thin-Walled Struct., 22, pp Bushnell, D., and Galletly, G. D., 1977, Stress and Buckling of Internally Pressurized, Elastic-Plastic Pressure Torispherical Vessels Heads-Comparisons of Test and Theory, ASME J. Pressure Vessel Technol., pp Galletly, G. D., 1986, Design Equations for Preventing Buckling in Fabricated Torispherical Shells Subjected to Internal Pressure, Proc. Inst. Mech. Eng., Part C: Mech. Eng. Sci., 200, No. A2, pp ANSYS User Manual, Swanson Analysis System, V. 6.3, Weber, D. C., and Skillings, J. H., 2000, A First Course in the Design of Experiments: A Linear Models Approach, CRC Press LLC, New York. 118 Õ Vol. 127, MAY 2005 Transactions of the ASME