1. AAE450 Spring 2009 Primary structure for Orbital Transfer Vehicle (OTV) Tim Rebold STRC [Tim Rebold] [STRC]

2. AAE450 Spring 2009  Dnepr User’s Guide –Requirements Volume & mass Center of gravity (CG) offset Limit Loads Stiffness Requirements  Primary Structure –Transfer loads throughout structure –Handle loads greater than that created by their own weight –Secondary structure will support and mount equipment [Tim Rebold] [STRC] Payload Center of Gravity Limit Loads (g's) Acceleration AxialLateral 1 st stage burn: Maximum lateral acceleration 3.0±0.50.5±0.5 2 nd stage burn: Maximum longitudinal acceleration 7.8±0.50.2 cg OTV Table based from Dnepr User’s Guide

3. AAE450 Spring 2009 Primary Structure  Assumptions –Symmetry: no lateral displacement of cg –Loads uniformly distributed –Contribution of thin sheets to bending & compression is negligible –Worst case scenario: CG maximum distance axially [Tim Rebold] [STRC] L t D Rings Stiffeners  Conclusions  Mass: 166 kg  Cost: $ 1500  M inert budget: <70 kg f inert = 0.4 Thin wall shear panels Floor supports (beams)

4. AAE450 Spring 2009 References [Tim Rebold] [STRC]  Delta II Payload Planners Guide http://snebulos.mit.edu/projects/reference/launch_vehicles/Delta/DELTA_I I_User_Guide_Update_0103.pdf  Skullney, W.E. Fundamentals of Space Systems. 2 nd Edition. Ch. 8, pp.465-564 Oxford University Press, 2005.  “Properties of Materials.” 2009. Purdue University. http://www.lib.purdue.edu/eresources/wts/result.html?WTSAppName=Lib _edupackk http://www.lib.purdue.edu/eresources/wts/result.html?WTSAppName=Lib _edupackk  Sun, C.T. Mechanics of Aircraft Structures. New York: John Wiley and Sons, 2006.  Dnepr User’s Guide http://snebulos.mit.edu/projects/reference/launch_vehicles/DNEPR/Dnepr_ User_Guide.pdf http://snebulos.mit.edu/projects/reference/launch_vehicles/DNEPR/Dnepr_ User_Guide.pdf

5. AAE450 Spring 2009 Future Work  Mass breakdown sheet in Excel –Include mass, cg, operating temperature range, and inertia matrix of all subsystems and components that make up the OTV and its payload (lander & rover)  Matlab script –Read data from Excel to calculate entire OTV (with payload) cg, and inertia matrix (about cg coordinates) in stowed (launch) and deployed (trans-lunar) stages  FEM analysis –Obtain better approximation of cg and inertia values –Perform modal analysis to see if OTV meets stiffness requirements placed on Delta II payload [Tim Rebold] [STRC]

6. AAE450 Spring 2009 Dnepr Payload Requirements [Tim Rebold] [STRC] Payload Center of Gravity Limit Loads (g's) Acceleration AxialLateral 1 st stage burn: Maximum lateral acceleration 3.0±0.50.5±0.5 2 nd stage burn: Maximum longitudinal acceleration 7.8±0.50.2 Notes: 1.Lateral accelerations may act in any direction, simultaneously with longitudinal ones 2. Dynamic accelerations are preceded by “±” symbol Spacecraft System Stiffness Requirements Thrust (Hz)Lateral (Hz) 2010 Tables based from Dnepr User’s Guide

7. AAE450 Spring 2009 Limit Loads [Tim Rebold] [STRC] D = 2.7 m L = 2.7 m cg 2.0 m +8.3 g axial limit load 0.2 g lateral limit load m OTV = 1000 kg L and D determined from mission volume needs & fairing restrictions Worst case: limit loads applied at CG

8. AAE450 Spring 2009 Primary Structure [Tim Rebold] [STRC] L t D Rings Stiffeners Thin wall shear panels Carry compressive and bending loads Provide stability by increasing buckling critical loads Carry shear loads Floor supports (beams) Aluminum 7075-T6 Material selected for all structural elements

9. AAE450 Spring 2009 Margin of Safety [Tim Rebold] [STRC] allowable experienced x FS MS = - 1 FS : Factor of Safety (FS=1.6 in these calculations) “allowbable” can be yield tress or critical buckling load “experienced” can be actual stress or applied load

10. AAE450 Spring 2009 Matlab scripts [Tim Rebold] [STRC] % AAE 450 STRC code % Author: Tim Rebold % Given the volume dimensions (circular cylinder) and acceleration loads % (g's), this script will calculate the basic structural component % characteristics (weight,numer,size) for the primary structure of the OTV % Note: This script is intended to be used in SI units. % Inputs: % L=length of OTV in units of meters D=diameter of OTV in units of meters % m=Launch Vehicle payload mass (OTV) % limit_loads=vector [axial g's, lateral g's]; maximum flight loads function [stiff_num,ring,t,Mass,Cost]=primary_structure(L,D,limit_loads); clc; g=9.80665; %gravity [m/s^2] r_o=D/2; %outer radius %[m]

11. AAE450 Spring 2009 [Tim Rebold] [STRC] %Material Properties for Al 7075-T6 (reference 4) Fy=480*10^6; %Yield stress [Pa] Fu=550*10^6; %Ultimate stress [Pa] E=72*10^9; %tensile modulus of elasticity [Pa] v=0.33; %Poisson's ratio rho=2768; %density [kg/m^3] cost=25000; %~US dollars per cubed meter %Mass Estimate of OTV on Launch Vehicle (LV) ratio=0.3; %payload to total mass ratio mpay=300; %[kg] payload estimate (lander+rover+10kg) m=mpay/ratio; %[kg] axial=g*m.*limit_loads(1); %axial load on payload [N] lat=g*m.*limit_loads(2); %lateral load on payload [N] %Center of Gravity (CG) Requirements for 6915 PAF interface cg=2.0; %[m] %Material Factor of Safety %Fs2=1.6; %(2) p.491 needs no static qualification Fs2=1.3; %(3) p.54 Matlab scripts (continued)

12. AAE450 Spring 2009 [Tim Rebold] [STRC] % ASSUMPTIONS made in Structural Analysis % Stiffeners take all the compressive and bending stresses % Shear Panels (Thin walled cylinder) take shear loads; no analysis % done in this script, wall thickness assumed to be 2 mm (standard?) % Loads are uniformly distributed % CG has no lateral offset % Mass is uniformly distributed throughout length of OTV to yield given %%%% % Stiffeners % %%%% % Bending Stress Analysis % Assumption: % Stiffeners bear all bending and compressive stresses (1) p. 124 % Stiffeners placed in such away that Iyz=0; My=lat*cg; %Circular hollow cross-section assumed with thickness of 2mm & diameter 2cm d=0.02; t=0.002; r=r_o-0.002-d/2; %radius out to center of stiffener A=pi*(d^2/4-(d-2*t)^2/4); %individual stiffener area Matlab scripts (continued)

13. AAE450 Spring 2009 [Tim Rebold] [STRC] %Global Bending Analysis (1) p. 125 stiff_num=0; for k=1:1:10; theta=0; Iy=0; Iz=0; Iyz=0; for stiff=1:1:k; %moment of inertia for entire OTV cross-section (stiffeners only %contribute) Iy=Iy+A*(sin(theta*pi/180)*r_o)^2; Iz=Iz+A*(cos(theta*pi/180)*r_o)^2; Iyz=Iyz+A*(sin(theta*pi/180)*r_o)*(cos(theta*pi/180)*r_o); theta=theta+360/k; end stress_b=axial/(k*A)+My*r/Iz; %bending stress MS(k)=Fy/(stress_b*Fs2)-1; %margin of safety if MS(k)>0 & stiff_num==0; stiff_num=k; else end plot([1:10],MS,'b',[1:10],zeros(1,10),'k') title('Stiffener Bending Analysis');xlabel('Number of Stiffeners'); ylabel('Margin of Safety (MS)');legend('MS','Zero Margin'); Matlab scripts (continued)

14. AAE450 Spring 2009 [Tim Rebold] [STRC]

15. AAE450 Spring 2009 [Tim Rebold] [STRC] %%%%%%%% % Stiffener Buckling Analysis % %%%%%%%% % Assumptions: Load uniformly distributed among each individual stiffener % Stiffener Boundary Conditions treated as fixed-free (1) p.231 I=pi*((d/2)^4-((d-2*t)/2)^4)/4; %moment of inertia for indiviudal stiffener %Indiviual Loads / Stiffener stiff_load=1/stiff_num; %Mass Distribution z=1; %[m] distance from payload bay / OTV interface to payload CG m1=m*cg/L-2*(1+z-cg/2)*mpay; m2=m-m1-mpay; % Above cg: Below cg: am=m1/(L-cg); bm=m2/cg; %run down from top to bottom of stiffener, applying force created from mass %above to stiffener. mass is uniformly distributed so that the CG is placed %at the location specified i=1; length=0; %increment & initializations Matlab scripts (continued)

16. AAE450 Spring 2009 [Tim Rebold] [STRC] while length<=L; le=0; while le==0 & length<=L if length<(L-cg) ms=(mpay+length*am)*stiff_load; %mass above supporting stiffener else ms=(mpay+m1+(length-(L-cg))*bm)*stiff_load; end Nx=ms.*limit_loads(1).*g; %applied load above supporting stiffener Pcr=pi^2*E*I/(4*(L-length)^2); %critical buckling load MS=Pcr/(Nx*Fs2)-1; if MS<0; le=sqrt((pi^2*E*I)/(Nx*4)); %effective length ring(i)=(L-length-le); i=i+1; add=le; else add=0.01; end length=length+add; end Matlab scripts (continued)

17. AAE450 Spring 2009 [Tim Rebold] [STRC] %plotting [row,lr]=size(ring); figure(2) for inc=1:lr; plot([0,D],[ring(inc),ring(inc)],'b'); hold on end title('Stiffener Buckling Analysis');xlabel('OTV Floor [m]'); ylabel('Ring Positions [m]'); %%%%% % Floor Supports % %%%%% %Analysis of Beam supports at floor % Assumptions: Load uniformly distributed among each individual support % 4 Rectangular hollow beams assumed % of dimensions (height x width)= 10 cm x 5 cm b=0.04; h=0.08; Matlab scripts (continued)

18. AAE450 Spring 2009 [Tim Rebold] [STRC]

19. AAE450 Spring 2009 [Tim Rebold] [STRC] %Worst Case Scenario dPAF=2; %diameter of PAF [m] arm=(D/2-dPAF/2) %length of beam [m] Mc=arm*axial/4 %compressive load creates bending moment %at base of beam [Nm] Mlat=lat*cg/4 %moment created from lateral accelerations [Nm] %find thickness of beams to support these loads t=0; for T=0.0005:0.0001:0.10; I=b*h^3/12-(b-2*T)*(h-2*T)^3/12 stress_b=(Mc+Mlat)*(h/2)/I; MS=Fy/(Fs2*stress_b)-1 if MS>0 & t==0; t=T; else end Matlab scripts (continued) %%%%%% % Cost and Weight % %%%%%% %Weight %PAF ring interface (5cm thickness) Vpaf=pi*((dPAF/2)^2-((dPAF-0.1)/2)^2)*h %Floor beams (4) Vbeams=arm*(b*h-(b-2*t)*(h-2*t))*4 %Stiffeners Vstiff=A*stiff_num*L %Shear Panels (1.5mm thickness assumed) Vshear=pi*D*L*0.0015+0.0015*pi*D*sqrt((D/2)^2+1.9^2)/2 %Total volume Vol=Vshear+Vstiff+Vbeams+Vpaf %Cost (without manufacturing costs) Cost=Vol*cost; Mass=Vol*rho;

20. AAE450 Spring 2009 [Tim Rebold] [STRC] %%%% % Future Work % %%%% %Shear panel thickness %Bi-directional bending of stiffeners %Torsion of floor beam members %Von Mises Stress Failure Criteria %Ring Weight & Size %%%% % References % %%%% %(1) Meachanics of Aircraft Structure, CT. Sun %(2) Fundamentals of Space Systems, V.L. Pisacane %(3) NASA SP-8007 %(4) Statics and Mechanics of Materials %(5) Dnepr User's Guide %(6) Delta II Payload Planners Guide return Matlab scripts (continued)