Скачать 0.52 Mb.

Project Bellerophon A.5.0 Structures A.5.1 Introduction Before igniting the first engine, a launch vehicle must prove that it can withstand the basic structural forces during flight. Through iterative math models produced in MATLAB, we are able to appropriately size all components of the launch vehicles to combat buckling, bending, and shear forces. The propellant tanks, interstage skirts, intertank couplers, and nose cone are designed in this manner. Whether it results in adding internal structural members (stringers and support rings) or increasing the thickness of certain components (tanks, interstage skirts), our launch vehicle’s structural success is justified in the following sections. Prior to the final launch vehicle configuration, we had to be very flexible with our design. At a moment’s notice we were able to create launch vehicles employing different materials for different propellant types, without losing any confidence in mission success. As certain options were eliminated, our analysis became more detailed and thorough. When the final mission specifications were selected, we branched out to other investigations such as finite element analysis and the design of the gondola that carries the launch vehicle to a 30 km altitude. The design process, methods used, and research performed are presented in the subsequent pages. We anticipate that the work accomplished by this group will be useful for anyone looking to advance this design further. A.5.2 Design Methods A.5.2.1 Propellant Tanks A.5.2.1.1 Overview Our launch vehicle contains a number of propellant storage tanks, which comprise much of its inert mass. The final launch vehicle configuration has a pressurant tank and an oxidizer tank in the first stage of the rocket and a Liquid Injection Thrust Vector Control (LITVC) tank in the second stage. The tanks are subjected to pressure loading as well as axial and bending loads in flight and on the ground. In the preliminary design phase, liquid and cryogenic rocket fuels were also considered, so we also designed fuel tanks. Collectively, we refer to the fuel and oxidizer tanks as propellant tanks in this report. The tanks are considered to be pressureflight stabilized structures. This means that they are designed to be strong enough to withstand ground loads while unpressurized, but are pressurized while in flight, meaning that the launch vehicle may be transported and assembled while unpressurised, resulting in safer and less complicated (and thus cheaper) ground logistics. At the same time, treating the tanks as pressurized structures while in flight allows us to make the tanks lighter and more structurally efficient. A.5.2.1.2 Tank Material The primary materials that we are considering for our launch vehicle are aluminum, steel, titanium, and composites. Research proved that these are the most common materials employed in space flight. Our analysis involves finding different alloys of these materials and figuring out which alloys give us the best results for cost, strength, weight, and manufacturability. After compiling information on physical properties of the materials, we contacted manufacturing companies to find out the costs associated with producing a tank. The data we obtained helps us compare the materials suitably. These costs include: welding, riveting, and labor hours required for production. These cost numbers are then placed into Matlab codes to give an overall cost for the tank. We looked at several different alloys for each of the materials. The strength of each of these alloys is compiled into a database. These strengths are then compared to the costs output by the code in order to figure out the best costtostrength ratio of the material. Along with the strength, the manufacturability of the alloys is also considered. We looked at the time it would take to weld or rivet the material, as well as the formability of each material. The alloys that we analyzed were Aluminum 7075, Stainless Steel, Isotropic Carbon Fiber, and Titanium Ti5Al2.55Sn. Table A.5.2.1.2.1 through Table A.5.2.1.2.4 show the database for each of the materials considered for the tanks.
Our propellant tanks are designed with Aluminum 7075. We chose this material because it has been incorporated for many historical launch vehicle tank materials. Our analysis of strengthtoweight ratios favors aluminum. The cost also favors aluminum due to the ease of manufacturability. This material is used for all three stages on all three launch vehicle configurations. References ^{1 }Setlak, Stanley J., “Aluminum Alloys; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000. ^{2}Setlak, Stanley J., “Titanium Alloys; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000. ^{3}Setlak, Stanley J., “Stainless Steel; Cast,” Aerospace Structural Metals Handbook, Purdue University, Indiana, 2000. ^{4}Callister, W.D. Jr, Fundamentals of Materials Science and Engineering, 2^{nd} Ed., Wiley & Sons, 2005 A.5.2.1.3 Preliminary Design Preliminary design for the propellant tanks and pressurant tanks is carried out by sizing the tanks to contain the required amount of propellant and designing the tanks to withstand maximum inflight internal pressure. We use a safety factor of 1.25 to account for transient spikes in pressure and to cover other failure modes. We also add 5% additional volume to the propellant tanks to account for internal structure and dead space. We specify a minimum tank wall thickness of 0.75mm in the preliminary design algorithms for manufacturability and practicality. A.5.2.1.3.1 Tanks The propellant tanks for liquid fuel/oxidizers are designed as cylindrical tanks with hemispherical ends for the purposes of structural efficiency and ease of manufacture. The hemispherical end configuration is stronger and lighter than using elliptical ends, but takes up more space.^{1} Due to the small size of the launch vehicle, the space savings from using an ellipticalend tank are negligible, so we incorporate the hemispherical end configuration instead. Should a spherical tank be small enough to fit into the stage, we choose a spherical tank instead of a cylindrical tank for structural efficiency. For cylindrical tanks, a maximum length to diameter (L/D) ratio of 6.0 is chosen in preliminary design as a tradeoff between drag and structural efficiency/dynamic stability. This value is later refined to 3.0 in final design based on scaling from existing launch vehicle designs; provided more time to analyze the interaction between size and drag/controllability, a more optimal aspect ratio range could have been determined via simulation runs. However, since the final designs do not reach anywhere near the maximum L/D ratio, we regard this exercise as not crucial to our current design and do not pursue it any further. Propellant tanks for solid propellants (and the solid components of hybrid rockets) are designed as an openended cylinder with an elliptical cap. The same maximum L/D ratio is applied as with the liquid propellant tank design. Spherical tanks are not appropriate for solid rocket fuel, so the tanks were kept cylindrical. The pressurant tank is designed as a spherical tank, as it is rated to a much higher internal pressure (12 MPa) compared to the propellant tanks (typically ~ 2.0 MPa for liquid propellant tanks and ~ 6.0 MPa for solid propellant tanks). The spherical tank configuration provides the highest structural efficiency for a pressure vessel^{1} and is the ideal layout for a small, highpressure tank. A.5.2.1.3.2 Intertank Couplers The intertank couplers connect the pressurant tank to the oxidizer tank, and the oxidizer tank to the fuel tank. They are designed as cylindrical skin sections with longitudinal and hoop stiffeners, and are designed to carry axial and shear load at maximum flight gloading. A.5.2.1.4 Stress Analysis A.5.2.1.4.1 Tanks For the purpose of our analysis, we assume that the tanks carry only axial and bending loads, and that the intertank couplers and interstage skirts carry only axial and shear loads. Tanks are analyzed as thinwalled structures. We consider these assumptions to be a conservative and reasonable approximation of the actual loads seen in the vehicle. The oxidizer tank is manufactured from Aluminum 7075 spun in two halves, with a fullthickness circumferential weld at the butt. This provides the optimal weld conditions for strength, as the hoop stress in a cylindrical pressure vessel is twice the axial stress (Eqs.(A.5.2.1.4.1) and (A.5.2.1.4.2)). Assuming a weld strength factor of 0.85^{1} for a spotexamined joint, this ensures that the tank wall thickness is designed entirely by the hoop stress due to pressure, as the reserve factor for axial loading will consequently always be greater than for hoop loading. As mentioned above, the propellant tank is designed to the hoop stress seen due to pressure loading due to internal pressure and hydrostatic pressure at maximum flight gloading.
where _{ox_hoop} is the hoop stress in the oxidizer tank (Pa), _{ox_axia}_{l} is the axial stress in the oxidizer tank (Pa), P_{ox} is the internal pressure in the oxidizer tank (Pa), g_{max} is the maximum inflight acceleration (m/s^{2}), h is the height of the fluid level (m), t_{tank_ox} is the thickness of the tank wall (m) and D_{ox}.is the diameter of the oxidizer tank (m). We then subject the model to further failure mode analyses, buckling and bending, and either add structure or increase the wall thickness as needed to meet our strength requirements. Tank buckling strength is calculated by using Baker’s buckling criteria^{3} (Eqs. A.5.2.1.4.3) for unpressurized tanks, and using experimental data from Bruhn Figure C8.11^{4} for pressurized cylinders to determine the proportional increase in strength due to pressurization.
where P_{cr} is the critical buckling stress of the structure (Pa), k_{s} is the buckling coefficient, E is the Young’s Modulus of the material (Pa), is the Poisson’s Ratio of the material, t is the thickness of the intertank coupler (m), L is the length of the intertank coupler (m), D is diameter of the tank (m), P_{cr} is the nondimensionalized increase in critical buckling strength (see Section A.5.2.1.6.2) and P_{cr_press} is the critical buckling stress of a pressurized tank, (Pa). Tank bending strength is assessed using test data from Bruhn Figure C8.13a^{4} for unpressurized cylinders and deriving the increase in tank bending allowable due to pressurization from Bruhn Figure C8.14^{4} for pressurized vessels. Similar to the oxidizer tank, the pressurant tank is manufactured from spun Aluminum 7075 in two hemispheres and joined together with a full thickness weld. Due to the higher criticality of the tank, the weld of the pressurant is to be fully radiographically tested after manufacture. Fortunately, as the pressurant feed tank is smaller than the oxidizer tank, this is easily achieved. The pressurant tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.4).
where _{press} is the stress in the pressurant tank (Pa), P_{press} is the internal pressure in the pressurant tank (Pa), g_{max} is the maximum inflight acceleration in (m/s^{2}), h is the height of the fluid level (m), t_{tank_press} is the thickness of the tank wall (m), and D_{press.}is the diameter of the pressurant tank (m). The LITVC tank is found in the second stage of the rocket, and is designed as a spherical tank to similar principles as the pressurant tank. We place the tank near the nozzle throat. If the need arises, the LITVC tank could be redesigned as a toroidal tank, but this will require additional work not covered in this report. The LITVC tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.5).
where _{LITVC} is the stress in the LITVC tank (Pa), P_{LITVC} is the internal pressure in the LITVC tank (Pa), g_{max} is the maximum inflight acceleration (m/s^{2}), h is the height of the fluid level (m), t_{tank_LITVC} is the thickness of the tank wall (m) and D_{LITVC} is the diameter of the LITVC tank (m). A.5.2.1.4.2 Intertank Couplers The intertank couplers are designed to carry axial and shear load at maximum flight gloading. 1.1527 m 1.1264 m 