IAC-15,E2,3-YPVF.4,9,x30874

IAC-15,E2,3-YPVF.4,9,x30874 PREDICTION AND IMPROVEMENT IN FATIGUE LIFE OF LEO 1U PICO-SATELLITE USING FEA TOOL TO MAXIMIZE THE MISSION S PREDICTED LIFE Mr. Aniket Marne College of Engineering, Pune, India, marneas11.meta@coep.ac.in Ms. Bhagyashree Prabhune *, Mr. Abhijit Rathod, Mr. AliMurtaza Kothawala, Ms. Tanvi Katke Mr. Pradip Bobade **, Ms. Saranga Kamble At the time of launch and till the satellite reaches the required orbit, it is subjected to various static and dynamic loads. Due to these variable and uncertain loading, the satellite body experiences continuous fluctuations which are nothing but random vibrations. The cyclic loading due to random vibrations will result in stresses in structure and thereby structure is highly susceptible to fatigue failure. Now a days, high launching cost, fabrication cost, low mass and compact design constraints and predicted life of satellite determine the mission feasibility and hence it is necessary to estimate fatigue life of satellites. College of Engineering, Pune (COEP) has designed SWAYAM, a Low Earth Orbit (LEO) 1U Pico-satellite, having capability of self-stabilization without the need for electric power. The three Printed Circuit Boards (PCBs), four batteries and most importantly the delicate solar cells, are crucial for the proper functioning of satellite. The paper details the method used and results obtained during prediction of fatigue life of the satellite. In order to assess and ascertain proper functioning of satellite, the structure was analysed using Finite Element Method (FEM) based robust analysis tool, ANSYS for which 3D design was done in Pro-Engineer. Modal analysis was performed for predicting parts susceptible to largest deformation at various frequencies. Also, a random analysis from 20-2000 Hz, under PSD (Power Spectral Density) with Grms of 6.7 g 2 /Hz was performed for observing the most natural response of structure under external loads. The results were a testimony to the robustness and durability of the structural system. I. INTRODUCTION During the last two decades the advancements in space science has led to a gradual increase in the launch of picosatellites. These satellites are built and launch both for commercial and educational purposes. However, there is very less literature available on the fatigue analysis of cube satellites. This paper illustrates vibration fatigue analysis of a 1U picosatellite having 100*100*113.5 mm size and 1 kg weight limit. Vibration analysis of the satellite has been carried out using finite element method. Swayam is a 1-U class picosatellite with the scientific objective of passive attitude stabilization [1]. Assembly and environmental testing of the flight model of Swayam has been completed and is soon going to be launched by the Indian Space Research Organization (ISRO). Figure I shows the internal components of the satellite. Fatigue is dynamic phenomenon which initiates small (micro) cracks in the material or component and causes them to grow into large (macro) cracks which result in catastrophic failure when material is subjected to cyclic loading. The structure should keep all its specified dimensions, alignments and tolerances, taking into account the required positioning accuracy of the attitude determination and control sensors and actuators relative to the payload during the mission lifetime after being subjecting to all handling, testing, transportation, launching and orbital loads. The structure should be strong and stiff enough to sustain various loads. Fatigue failure can occur even when the maximum stress value is less than the ultimate tensile stress limit or possibly even below the yield stress limit. Therefore, although satellite structure possesses sufficient strength to withstand the most * College of Engineering, Pune, India, prabhunebc12.mech@coep.ac.in College of Engineering, Pune, India, rathodal12.mech@coep.ac.in College of Engineering, Pune, India, kothawalaah12.civil@coep.ac.in College of Engineering, Pune, India, katketm13.mech@coep.ac.in ** College of Engineering, Pune, India, bobadeps12.mech@coep.ac.in College of Engineering, Pune, India, kamblesp12.mech@coep.ac.in IAC-15,E2,3-YPVF.4,9,x30874 Page 1 of 8

S (MPa) severe expected loads, the parts can fail under fatigue (fluctuating loads) at much lower values of stress than their normal static failure stress. Hence it is very crucial to check the structure for fatigue failure [2],[3]. Commercially available finite element software have been used for fatigue analysis of the satellite. The life of the satellite depends on the performance life of individual components. Hence stress fluctuations are induced by thermal expansions and contractions. 4. Random vibration fatigue- It results by high frequency stress fluctuations due to vibrations excited by the launch vehicle. The deformation caused due to random vibration is critical to certain parts of the satellite. Fatigue life evaluation under a random process is highly complicated. Fatigue cracks are most frequently initiated at the sections where there is sudden change in geometry, holes, and notches. The stress concentration factor must be taken into account for the design of such components. In SWAYAM structure, in order to satisfy stringent constraints on weight and size, many components have intricate shape. This makes them prone to stress concentration effects which decrease the fatigue life of the component. Figure I: Internal Components of Swayam II. BASIC APPROACH The structure of the satellite is fail-safe meaning that the failure of a member in structure does not necessarily lead to collapse of the complete structure. However positioning and deformation some parts is important from the point of view of the effective functioning of the satellite. From this point of view, critical parts are supporting panel of solar cells substrate, PCB support plates, ABS (Acrylonitrile Butadiene Styrene) antenna guides and covers, solar cells and ACS (Attitude Control System) fixtures. Other structural components do not have severe restrictions. Fatigue damage is produced in variety of ways: 1. Fretting fatigue- It occurs due to small-scale rubbing movements and abrasion of adjacent parts which can be neglected in the structure as there is no relative motion between parts 2. Corrosion fatigue- It occurs as a result of surface corrosion of material penetrating inwards so that the material strength deteriorates. The possibility of the corrosion fatigue occurring is very less in satellite. 3. Thermal fatigue-the satellite is subjected to temperature cycles as it orbits the planet. III. FATIGUE PROPERTIES OF MATERIALS USED IN SATELLITES Fatigue strength of a material for give number of cycles of loading is the amount of stress it can withstand before fracture. Some materials like mild steel have a stress level that can be withstood for an infinite number of cycles. This stress is known as Endurance limit. But no such limit has been found for Al and its alloys, which are the materials of the most critical parts of the satellite structure. S-N curve is frequently used to represent the fatigue data. Fatigue properties of Al 6061 T6 are discussed in references [4] and [5]. 500 400 300 200 100 S-N Curve 0 1.E+01 1.E+03 1.E+05 1.E+07 1.E+09 Figure II: Fitted curve of Al 6061-T6 fatigue data N IAC-15,E2,3-YPVF.4,9,x30874 Page 2 of 8

Fatigue strength of Al 6061= 96.5 MPa for 500 X 10 6 cycles completely reversed stress. IV. FINITE ELEMENT MODEL IV.I Meshing Meshing is critical in formulation of a finite element problem. Finer mesh provides more accurate results [6]. Given the fact that the computational cost increases as the mesh size decreases, an optimum meshing technique has been implemented. By experimenting with various mesh techniques, mesh parameters which takes minimal time and provides accurate results have been calculated. Various quality parameters like aspect ratio, Jacobian ratio, warping factor, skewness have been checked beforehand so that the convergence of solution is guaranteed. Reader may refer [6], [7] for details on the meshing techniques used. Summary of the meshing parameters on which simulations were based are summarized in Table I. frequencies occurring at the same time, the structural resonances of different components can be excited simultaneously, thus increasing the potential damage of random vibrations [8]. The random vibration can be characterized using a mean, the standard deviation and a probability distribution. Individual vibration amplitudes are not determined. Rather, the amplitudes are averaged over a large number of cycles and the cumulative effect determined for this time period. This provides a more practical process for characterizing random vibrations than analysing an unimaginably large set of time history data for many different vibration profiles. Particular Value No of Elements 103281 No of Nodes 365163 Aspect ratio 4 Jacobian Ratio 1.49 Warping Factor 4.5 x10-2 Skewness 0.4 Table I: Meshing parameters used Figure IV: Representation of Random vibrations as overlapping sinusoidal curves Figure III: Meshed model of Swayam satellite V. RANDOM VIBRATION CHARACTERIZATION The complex nature of random vibrations is demonstrated with Fourier analysis of the random time history shown in Figure IV, revealing that the random motion can be represented as a series of many overlapping sine waves, with each curve cycling at its own frequency and amplitude. With these multiple Most random processes follow a Gaussian probability distribution. This distribution can be seen in a frequency-of-occurrence histogram (probability density function). The severity of damage for random vibration is in terms of its power spectral density (PSD) [8]. V.I STRESSES INDUCED IN SATELLITE DUE TO RANDOM VIBRTION Modal analysis of the structure using commercially available software giving appropriate boundary conditions. The structure qualified the stiffness requirements given by VSSC (Vikram Sarabhai Space IAC-15,E2,3-YPVF.4,9,x30874 Page 3 of 8

Centre). The vibration testing of the structure was also performed at ARAI (Automotive Research Association of India) and VSSC. There was close match between predicted modal frequencies by simulation and the values obtained by actual testing. For detailed analysis of results refer [9]. Random vibration test was also carried out practically as well as using FEA simulation in ANSYS. As random vibration is of more concern regarding fatigue analysis, here is the overlook on the results obtained for random vibration simulation. Random Vibration test levels specified by VSSC are shown in Table II. Frequency (Hz) Qualification PSD (g 2 / Hz) 20 0.002 110 0.002 250 0.034 1,000 0.034 2,000 0.009 g RMS 6.7 Duration 2 min/axis Table II: Random vibration test specification Figure V: Deformation contour during random vibration along lateral axis Maximum Equivalent stress (3σ) was found to be 92.3 MPa in same conditions. Location is shown in figure VI. Axis definition used during simulation is summarized in table III. Axes X axis Y Axis Z Axis Table III: Axes definition Direction Ejection axis Lateral axis Longitudinal axis V.I.I RESULTS After simulating the entire meshed model for obtaining maximum deformation and stress value we got following results. Lateral Axis: Figure VI: Location with maximum stress during Random vibration along lateral axis Response Power Spectral Density (PSD) on Y- panel is shown below. Grms value obtained from this graph is 2g. Axes Deformation (micron) Part with maximum deformation X axis 25 Solar panel Y Axis 393.7 Communication PCB Z Axis 89.7 Battery box flange Table IV: 3 σ values of directional deformation during random vibrations along Y direction Figure VII: Response Power Spectral Density (PSD) on Y- panel IAC-15,E2,3-YPVF.4,9,x30874 Page 4 of 8

Ejection Axis Axes Deformation (micron) Part with maximum deformation X axis 137.1 Solar panel Y Axis 187.8 Power PCB Z Axis 202 Solar panel Table V: 3 σ values of directional deformation during random vibrations along X direction Figure X: Deformation contour during random vibration along longitudinal axis Equivalent stress (3σ) in this condition about 89 MPa. Figure VIII: Deformation contour during random vibration along ejection axis Equivalent stress (3σ) on solar panel in ejection axis was found to be maximum and its value was 94.66 MPa. Response PSD on X- panel is shown in Figure IX from which we got Grms value about 15.19 g. Figure XI: Location with maximum stress during Random vibration along longitudinal axis Figure IX: Response Power Spectral Density (PSD) on X- panel Response PSD on Z- panel is shown in following Figure XII. Longitudinal Axis Axes Deformation (micron) Part with maximum deformation X axis 129.3 Solar panel Y Axis 153.6 Power PCB Z Axis 173.31 Solar panel Table VI: 3 σ values of directional deformation during random vibrations along Z direction IAC-15,E2,3-YPVF.4,9,x30874 Page 5 of 8

Due to adhesive bonding the loads get distributed over the surface instead of locally at fasteners. This results in lesser stress concentration areas leading to more fatigue life [7]. Figure XII: Response Power Spectral Density (PSD) on Z- panel From above PSD we got the frequencies at which maximum stress was occurred. They are listed in Table VII. Axes Frequency X axis 290 Y Axis 300 Z Axis 326 Table VII: Frequencies along each axis when maximum stress observed. VI. METHODS TO IMPROVE FATIGUE LIFE Considering the vibrations encountered by the structure during transportation, handling, installation, quasi-static loads, launch vibrations and appendage deployment shock, there is room for improvement of predicted fatigue life in order to ensure complete robustness. Following methods were employed to improve fatigue life of the structure. 1. Surface engineering- The surface finish was improved to increase the fatigue life as surface scratches and machine marks are the sources of fatigue crack initiation. 2. Fillets are provided at necessary sections to avoid stress concentrations due to sharp corners. 3. In machined parts, the material thickness was increased around the bolt holes. Avoiding asymmetry can reduce stresses due to bending. 4. Using Adhesives- Adhesive bonding was widely used in joining various parts of the structure especially the ones0 made of ABS using rapid-prototyping technique. It was also used to isolate solar cells from the other structural parts. It was also used to join two dissimilar metals to avoid galvanic corrosion. VII. METHODOLOGY TO DETERMINE RANDOM VIBRATION FATIGUE LIFE Determining the fatigue life of parts under periodic, sinusoidal vibration is a process in which damage content is calculated by multiplying the stress amplitude of each cycle from harmonic analysis with the number of cycles that the parts experience in the field. Damage content = Stress amplitude X No. of cycles [1] The amplitude of the alternating stress varies and is random in nature. Therefore, the S-N curve does not apply directly and alternative means of predicting failure is required. Miner s Rule Miner s cumulative fatigue damage ratio is based on the idea that every stress cycle uses up part of the fatigue life of a structure. Miner s cumulative damage theory suggests that the failure will occur when n 1 + n 2 + + n r = 1 [2] N 1 N 2 N r Where n 1, n 2,, n r are the number of applications of stresses σ 1, σ 2,, σ r and N 1, N 2,, N r are the number of cycles to failure of stresses σ1, σ2,, σr. Fatigue estimation method: Calculations for fatigue life estimation are given below. 3σ stress= 92.3 MPa N 1 = N 2 ( S 2 S 1 ) b [3] N 2 = 1000 (S1000 reference point) S 2 = 198.91 MPa (stress to fail at S1000reference point) S e = 48.99 MPa (Refer Figure II) S 1 = 30.76 MPa (1σ RMS stress) b = 8.2 (slope of fatigue line with stress concentration K = 1) Number of cycles required to produce fatigue for corresponding stress values are: IAC-15,E2,3-YPVF.4,9,x30874 Page 6 of 8

1σ N 1 = (1000)( 198.91 1X30.76 )8.2 = 4.55 x10 9 2σ N 1 = (1000)( 198.91 2X30.76 )8.2 = 1.53 x10 7 3σ N 1 = (1000)( 198.91 3X30.76 )8.2 = 5.47 x10 5 The actual number of fatigue cycles (n) accumulated during four hours of vibration testing can be obtained from the percent of time exposure for the 1σ, 2σ and 3σ values. n 1 = (number of cycles) (probability of occurrence of the stress) [4] 1σ n 1 =24588 cycles 2σ n 2 =9756 cycles 3σ n 3 =1559 cycles Using Miner s equation, it comes out that 2 min of test consumes about 0.35% of the fatigue life. Similar calculations were done for the other axes as well. Obtained results are summarized in Table VIII. No. of cycles X- axis Y-axis Z-axis possible 1σ N 1 3.72x109 4.55x109 6.16x109 2σ N 2 1.25x107 1.53x107 2.07x107 3σ N 3 2.94x106 5.47x105 7.4x105 % fatigue life consumed 0.41 0.35 0.28 Table VIII: Fatigue life calculations from the random vibration data. 1σ RMS stress level is in effect for about 68.3% of total time. But as the stress value is low, it does very little damage. As we go towards the 3σ level, the damage done becomes more evident even though it is in effect for very little time (4.33 % of total time).the above fatigue cycle ratio shows that about 0.347 percent of the life of the structure is used up by the 2min vibration test. This means that 99.65 percent of the life remains, with the expected life of the structure obtained from the following calculation: Used life + remaining life = 576 minutes. VIII. EFFECT OF STRESS CONCENTRATION FACTOR The stress concentration factor of the critical components on which maximum stress occurs is shown in the Table IX. k b 3 σ N1 Expected Life (min) 1 8.22 5.47 x105 573 1.5 6.37 1.33 x105 115 2.5 4.97 4.52 x104 30.5 3 4.61 3.43 x104 21 Table IX: Effect of stress concentration factor on expected fatigue life Appropriate fillet radius and r/d ratio in order to reduce the stress concentration factor has to be find. However, Specimens of aluminium alloy 6061-T6 sheet were not notch sensitive [10]. Therefore we have used here k=1. IX. CONCLUSION Random vibration analysis performed on the satellite gave us the results as discussed in the paper. The fatigue life predictions were made by extracting results from the same test. The discussed results attest the assertion that Swayam Satellite is robust enough to take the dynamic loads it shall face during launch and shall deliver satisfactorily its intended purpose. X. ACKNOWLEDGEMENT The authors wish to sincerely thank Dr. Anil D. Sahasrabudhe, former Director of College of Engineering, Pune, Dr. B. B. Ahuja, Hon. Director of College of Engineering, Pune and Dr. M. Y. Khaladkar, Applied Science Department, College of Engineering, Pune for supporting the COEP Student Satellite Program throughout. They also extend their gratitude towards the COEP Fab-Lab. They would also like to thank Dr. D.W. Pande for his constant guidance and timely reviews. XI. REFERENCES [1] Kulkarni, Rahul et al., SWAYAM-Passively Stabilized Communication Satellite, 64th International Astronautical Congress, Beijing, 2013 [2] Kumar Santhosh M., Analyzing Random Vibration Fatigue Powerful ANSYS Workbench tools help calculate the damage of vibrations that lack straightforward cyclic repetition, 2008 [3] V. B. Bhandari, Design of Machine Elements, Third Edition, 2015 [4] Yahr GT. Fatigue Design Curves for 6061-T6 Aluminum, ASME. J. Pressure Vessel Technol. 1997;119(2):211-215. doi:10.1115/1.2842286 [5] ASM Metals Datasheet, ASM Aerospace Specifications Metals Inc., http://asm.matweb.com/search/specificmaterial.a sp?bassnum=ma6061t6 IAC-15,E2,3-YPVF.4,9,x30874 Page 7 of 8

[6] Hutton David, Fundamental of Finite Element Analysis, McGraw-Hill, 2004 [7] Abdelal, G F. et al., Finite Element Analysis for Satellite Structures: Applications to their Design, Manufacture and Testing, 2013 [8] S. S. Rao, Mechanical Vibrations, Addison- Wesley Longman, Incorporated, 1986 [9] Marne, Aniket et.al. Design and Optimization of the Structure of A 1U Picosatellite, 28 th Space Simulation Conference, Maryland, USA, 2014 [10] S.E. Mahmoud, Failure by Blowout of Aluminum Alloy 6061-T6 Connector Tubes From a Water-Cooling System, Failures of Cold Formed Parts, Failure Analysis and Prevention, Vol 11, ASM Handbook, ASM International, 1986, p 307 313 IAC-15,E2,3-YPVF.4,9,x30874 Page 8 of 8