Fabricating_a_pressure_vessel___Michael_Ashby__Materials_Selection_in_Mechanical_ pdf

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8.3 Fabricating a pressure vessel 223 Pressure vessel Circular prismatic Non-circular prismatic Flat sheet Dished sheet 3-D solid 3-D hollow Sand casting Die casting Optical Investment casting table Metal shaping Low pressure casting Forging Extrusion Sheet forming Powder methods Ceramic shaping Electro-machining Conventional machining Injection molding Blow molding Polymer Compression molding shaping Rotational molding Thermo-forming Polymer casting Resin-transfer molding Composite shaping Filament winding Lay-up methods Vacuum bag Nylon fan Figure 8.3 The process shape compatibility matrix, showing the requirements of the three case studies. A summary of the material compatibility appears at the left. The intersection of this selection stage and the last narrows the choice. Postscript. There are (as always) other considerations. There are the questions of capital investment, local skills, overhead rate and so forth. The charts cannot answer these. But the procedure has been helpful in narrowing the choice, suggesting alternatives, and providing a background against which a final selection can be made. Related case 6.6 Materials for flywheels studies 8.3 Fabricating a pressure vessel A pressure vessel is required for a hot-isostatic press or HIP. Materials for pressure vessels were the subject of an earlier case study (Section 6.11); tough steels are the best choice.224 Chapter 8 Process selection case studies Optical table Sand casting Die casting Metal shaping Investment casting Low pressure casting Forging Extrusion Sheet forming Powder methods Ceramic shaping Electro-machining Conventional machining Injection molding Blow molding Polymer shaping Compression molding Rotational molding Thermo-forming Pressure Polymer casting Resin-transfer molding vessel Composite shaping Filament winding Nylon Lay-up methods Vacuum bag fan 10⁻² 0.1 1 10 10² 10³ 10⁴ Mass (kg) Adhesives Joining Welding, metals Welding, polymers Fasteners Figure 8.4 The process mass range chart, showing the requirements of the three case studies. The inclusion of joining processes allows the possibility of fabrication of large structures to be explored. The design requirements. The design asks for a cylindrical pressure vessel with an inside radius R of 0.4 m and a height h of 2 m, with removable end-caps (Figure 8.9). It must safely contain a pressure p of 50 MPa. A steel with a yield strength of 500 MPa has been selected. The necessary wall thickness t is given approximately by equating the hoop stress in the wall, roughly pR/t, to the yield strength of the material of which it is made, divided by a safety factor that we will take to be 2. Solving for t gives: (8.1) The outer radius R₀ is, therefore, 0.38 m. The volume V of steel in the cylinder is approximately 0.34 m³. Lest that sounds small, consider the weight. The density of steel is just under 8000 kg/m³. The cylinder weighs 2.7 tonnes.8.3 Fabricating a pressure vessel 225 Optical Sand casting table Die casting Investment casting Metal shaping Low pressure casting Forging Extrusion Sheet forming Powder methods Ceramic shaping Electro-machining Conventional machining Injection molding Blow molding Polymer Compression molding shaping Rotational molding Pressure Thermo-forming vessel Polymer casting Resin-transfer molding Composite shaping Filament winding Lay-up methods Nylon Vacuum bag fan 0.1 1 10 100 1000 Section thickness (mm) Figure 8.5 The process section thickness chart, showing the requirements of the three case studies. A range of presses is envisaged, centered on this one, but with inner radii and pressures that range by a factor of 2 on either side. (A constant pressure implies a constant "aspect ratio", R/t.) Neither the precision nor the surface roughness of the vessel are important in selecting the primary forming opera- tion because the end faces and internal threads will be machined, regardless of how it is made. The order is for 10 cylinders. What processes are available to shape them? The selection. Table 8.3 summarizes the requirements. They are plotted on the charts, Figures 8.2-8.5 and 8.8. The discriminating requirements, this time, are mass and batch size. They single out the four possibilities listed in Table 8.4: the vessel can be machined from the solid, forged, cast, or fabricated (by welding plates together, for instance). Material constraints are worth checking (Figure 8.2), but they do not add any further restrictions. Tolerance and roughness do not matter except on the end faces and threads (where the end-caps must mate) and any ports in the sides these require a precision of ±0.1 mm. The answer here (Figure 8.6, lower part) is to add a second process: an additional machining or grinding step can achieve it.226 Chapter 8 Process selection case studies Sand casting Die casting Metal shaping Investment casting Low pressure casting Forging Optical Extrusion table Sheet forming Powder methods Ceramic shaping Electro-machining Conventional machining Injection molding Blow molding Polymer shaping Compression molding Rotational molding Nylon Thermo-forming fan Polymer casting Resin-transfer molding Composite shaping Filament winding Lay-up methods Vacuum bag Optical 0.01 0.1 1 10 table Tolerance (mm) Precision machining Finishing Grinding Pressure Lapping Polishing vessel Figure 8.6 The process tolerance chart, showing the requirements of the three case studies. The inclusion of joining and finishing processes allows the possibility of fabrication of large structures to be explored. Tolerance and surface roughness are specified as an upper limit only, so the selection boxes are open-ended to the left. Postscript. A "systematic" procedure is one that allows a conclusion to be reached without prior specialised knowledge. This case study is an example. We can get so far (Table 8.4) systematically, and it is a considerable help. But we can get no further without adding some expertise. A cast pressure-vessel is not impossible, but it would be viewed with sus- picion by an expert because of the risk of casting defects; safety might then require proof testing or elaborate non-destructive inspection. The only way to make very large pressure vessels is to weld them, and here we encounter the same problem: welds are defect-prone and can only be accepted after elaborate inspection. Forging, or machining from a previously-forged billet are the best because the large compressive deformation heals defects and aligns oxides and other muck in a harmless, strung-out way. That is only the start of the expertise. You will have to go to an expert for the rest.8.4 An optical table 227 Sand casting Die casting Metal shaping Investment casting Low pressure casting Forging Extrusion Sheet forming Powder methods Ceramic shaping Electro-machining Conventional machining Injection molding Blow molding Polymer shaping Compression molding Rotational molding Nylon Thermo-forming fan Polymer casting Resin-transfer molding Composite shaping Filament winding Lay-up methods Vacuum bag 0.01 0.1 1 10 100 Roughness (µm) Precision machining Finishing Grinding Lapping Polishing Figure 8.7 The process surface roughness chart. Only one case study that of the fan imposed restrictions on this. Related case 6.11 Safe pressure vessels studies 8.4 An optical table An optical table is a flat plate mounted in a way that minimizes vibration pick- up, on which optical systems can be positioned with an accuracy comparable with the wavelength of light. They used to be made of polished granite or cast iron; more recently stainless steel or aluminum is used. The key feature of the table is its flatness: a good one is flat to within 0.01 mm over its entire surface. The design requirements. A design for such a table is sketched in Figure 8.10. The table is a plate 350 mm square and 16 mm thick, weighing 10kg, with edge grooves and threaded fixing points, but these features can be added later by simple machining and need not concern us here. It is to be