Advances in Spacecraft Technologies Part 6 pot

Advances in Spacecraft Technologies 190 9.70 9.75 9.80 9.85 9.90 9.95 10.00 10.05 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 p' x'' t=177 o C t=300 o C t=500 o C t=700 o C t=1000 o C Fig. 8. Distribution of shearing stress p’ along the glue layer with different t 1 (part curve) -10-8-6-4-20246810 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 q' x'' L=4h2 L=6h2 L=10h2 L=15h2 L=20h2 Fig. 9. Distribution of shearing stress q’ along the glue layer with different length for TPS tiles 4.3 The effects of the thickness of TPS tiles on peeling stress The thickness of the tiles in TPS design was also a very important consideration. The thickness of TPS tile thermal protection system in the design is also a very important consideration. We should analyze the effect of the TPS tiles thickness on the shear and normal stress of the layer. Let the working stress of the structure P=20MPa, and E 1 =2E 2 , L=10 h 2 , t 0 =20°C, t j0 =177°C, t 1 =500°C. When h 1 /h 2 = 1/2, 1/3, 1/5, 1/8, by the above theory, we also get the distribution of shear and normal stress, as shown Figures 11 and 12 respectively. The Mechanics Analysis of Desquamation for Thermal Protection System (TPS) Tiles of Spacecraft 191 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 p' x'' L=4h2 L=6h2 L=10h2 L=15h2 L=20h2 Fig. 10. Distribution of shearing stress p’ along the glue layer with different length for TPS tiles -6-5-4-3-2-10123456 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 q' x'' h1=h2 h1=0.5h2 h1=0.1h2 h1=0.05h2 Fig. 11. Distribution of shearing stress q’ along the glue layer with different thickness for TPS tiles 4.4 The effects of the material of TPS tiles on peeling stress The selected material is different in different spacecraft TPS. For different thermal systems of spacecraft, the selection of protection tile material is also different. Here, from a mechanical point of view, we study the effects of different material on the thermal protection tiles peeling off, i.e. the adhesive layer stress, mainly considering the effect of elastic modulus. Let the working stress of the structure P=20MPa, and h 1 /h 2 =0.5, L=10 h 2 , t 0 =20=°C, t j0 =177°C, t 1 =500°C. When E 1 /E 2 =0.5, 1, 2, and 3, by the above theory, we also get the distribution of shear and normal stress, as shown Figures 13, 14 and 15 respectively. Advances in Spacecraft Technologies 192 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 p' x'' h1=h2 h1=0.56h2 h1=0.1h2 h1=0.05h2 Fig. 12. Distribution of shearing stress p’ along the glue layer with different thickness for TPS tiles -5-4-3-2-1012345 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 q' x'' E1=0.5E2 E1=E2 E1=2E2 E1=3Eh2 Fig. 13. Distribution of shearing stress q’ along the glue layer with different materials for TPS tiles The Mechanics Analysis of Desquamation for Thermal Protection System (TPS) Tiles of Spacecraft 193 -5 -4 -3 -2 -1 0 1 2 3 4 5 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 p' x'' E1=0.5E2 E1=E2 E1=2E2 E1=3E2 Fig. 14. Distribution of shearing stress p’ along the glue layer with different materials for TPS tiles 4.5 4.6 4.7 4.8 4.9 5.0 5.1 0.10 0.15 0.20 0.25 0.30 0.35 p' x'' E1=0.5E2 E1=E2 E1=2E2 E1=3E2 Fig. 16. Distribution of shearing stress p’ along the glue layer with different materials for TPS tiles (part curve) 5. Conclusions By analyzing the glue layer stress between TPS tiles and structures, and the influence of the size and material of TPS tiles, we concludes: 1. In the connection between TPS tiles and internal structure, the normal stress on the glue layer end reaches the max value with naught shear stress. Hence, it can be indicated that potential factors of the peeling off of the tiles are mainly contributed by peeling normal stress and influenced little by shear stress. Advances in Spacecraft Technologies 194 2. Glue layer stress concentrates near the edge of the tiles and almost naught in other areas. The fact that the ratios of glue layer shear stress and normal stress to working stress decreases with increasing working stress in the inner structure indicates that the increasing rate of glue layer stress is less than that of working stress. 3. Glue layer shear stress and normal stress both increases with temperature increasing, however, the increasing magnitude is not very large compared to influence of working stress’s increasing on peeling stress, which also illustrates that the more aerodynamic heating is, the larger peeling stress of tiles is, quickening the desquamation of tiles. 4. Glue layer shear stress and normal stress concentrates much more near the end of tiles and their extremum get larger as the length of TPS tilse increases; furthermore, the shear stress varies much more. This fact indicates that larger size of TPS tiles leads to peeling stress of glue larger and the influence of the length of the TPS tiles on the extremum of glue layer stress is obvious. 5. However, glue layer stress does not decrease (or increase) as the thickness of TPS tiles decreases (or increases). The thickness of TPS tiles does not influence the extremum of glue layer shear stress obviously, but much glue layer normal stress. 6. The influence of material Elastic modulus on peeling stress of glue layer is not strong, however, as a whole, the larger material Elastic modulus (i.e. Stiffness) is, the larger peeling stress of glue layer is. 6. References XING Yu-zhe., 2003. The final investigation report of columbia disaster[J].Spece Exploration, pp. 12:18-19. Kuhn P., 1956. Stress in Aircraft and Structures[M].McCraw-HIHLL BOOK COMPANY, ZANG Qing-lai, ZHANG Xing, WU Guo-xun. (2006). New model and new method of stress analysis about glued joints[J]. Chinese Journal of Aeronautics, pp.6:1051-1057. Timoshenko S., 1958. Strength of Materials[M].Van Nostrand Reinhold Company. HU Hai-chang., 1980. Variational Principle and Application in Theory of Elasticity[M]. Beijing:Science Press. ZHANG Xing (editor in chief)., 1995. Advanced Theory of Elas-ticity [M]. Beijing:Beijing University of Aeronautics and Astronautics Press. QIAN Wei-chang., 1980. Variational Method and finite Element[M].Beijing:Sci-enee Press. The editorial department of Mechanical dic-tionary., 1990. Mechanical Dietinary [M]. Beijing:Encyclopedia of China Publishing House, pp.197-597. Davis J,Green, translsted by Gong Jiang-hong., 2003. The Mechanical Properties Introduction of Ceramic Materials [M].Beijing:Tsinghua University Press, pp.21-35.] Part 2 Cutting Edge State Estimation Techniques 10 Unscented Kalman Filtering for Hybrid Estimation of Spacecraft Attitude Dynamics and Rate Sensor Alignment Hyun-Sam Myung 1 , Ki-Kyuk Yong 2 and Hyochoong Bang 1 1 Korea Advanced Institute of Science and Technology, 2 Korea Aerospace Research Institute, Republic of Korea 1. Introduction Requirements of highly precise pointing performance have been imposed on recently developed spacecrafts for a variety of missions. The stringent requirements have called on on-orbit estimation of spacecraft dynamics parameters and calibration of on-board sensors as indispensible practices. Consequently, on-orbit estimation of the mass moment of inertia of spacecraft has been a major issue mostly due to the changes by solar panel deployment and a large portion of fuel consumption (Creamer et al., 1996; Ahmed et al., 1998; Bordany et al., 2000; VanDyke et al., 2004; Myung et al., 2007; Myung & Bang, 2008; Sekhavat et al., 2009). As for measurement sensors, on-board calibration of alignment and bias errors of attitude and rate sensors is one of the main concerns of attitude sensor calibration researches (Pittelkau, 2001 & 2002, Lai et al., 2003). Pittelkau (2002) proposed an attitude estimator based on the Kalman filter (Kalman, 1960), in which spacecraft attitude quaternion, rate sensor misalignment and bias, and star tracker misalignments are taken into consideration as states, whereas the body rate is dealt as a synthesized signal by the estimates. Lai at al. (2003) derived a method for alignment estimation of attitude and rate sensors based on the unscented Kalman filter (UKF) (Julier and Uhlmann, 1997). Ma and Jiang (2005) presented spacecraft attitude estimation and calibration based only magnetometer measurements using an UKF. An interesting point is that we need predesigned 3-axis excitation manoeuvres of spacecraft for both dynamics parameter estimation and sensor calibration. Therefore, this study is motivated to merge above estimation and calibration processes into a single filtering problem. It is noteworthy that poor information of moments of inertia is to be treated as a system uncertainty while the rate sensor model errors are to be incorporated into the measurement process. As a filtering algorithm, this study employs a UKF. Extended Kalman filters (EKFs) have been successfully applied to the nonlinear attitude estimation problem (Crassidis et al., 2007). Hybrid estimation using the EKF has been reported by Myung at al. (2007). However, the EKF estimates using the first order linearization, which may lead to instability of the filter (ValDyke et al., 2004). The UKF approximates the nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear Advances in Spacecraft Technologies 198 transformation of sigma points produces the posterior mean and covariance. Despite the computational burden of the UKF, extension of convergence region and numerical stability greatly outperform the EKF. Parameter estimation by a dual UKF was proposed by VanDyke et al. (2004). Since UKF has more computational burden compared to EKF, a numerically efficient UKF was also developed for state and parameter estimation (van der Merwe & Wan, 2001). In this paper, the UKF is applied to simultaneous spacecraft dynamics estimation and rate sensor alignment calibration using star tracker measurements. The spacecraft attitude and the body angular velocity are the state vectors. Estimation parameters are the six components of moment of inertia, and the bias, scale factor errors and misalignments of a rate sensor. Numerical simulations compare the results to those using the EKF. 2. Equation of motion of spacecraft 2.1 Attitude representation Spacecraft attitude parameter is the unit quaternion defined by [] [] T T T 1234 T 13 4 q= sin cos 22 =q q q q =q q ⎡ ⎤φφ ⎛⎞ ⎛⎞ ⎜⎟ ⎜⎟ ⎢ ⎥ ⎝⎠ ⎝⎠ ⎣ ⎦ n (1) where n is the Euler axis and φ is the Euler angle. q 13 is the vector part and q 4 is the scalar part in quaternion representation. Quaternion multiplication represents successive rotation (Wertz, 1978) 43 211 34 12 2 2 1433 1234 4 q=q q qq-qq q -q q q q q = q-qqq q -q -q -q q q ′ ′′ ⊗ ′′′′ ⎡⎤ ⎡ ⎤ ⎢⎥ ⎢ ⎥ ′′ ′′ ⎢⎥ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ′′′′ ⎢⎥ ⎢ ⎥ ′′′′ ⎣ ⎦ ⎣⎦ (2) And inverse of quaternion [] T -1 1234 q = -q -q -q q (3) implies the opposite rotation of q. By combining Eq. (2) and (3) residual rotation of q” with respect to q’, or error quaternion δq, is obtained such as () -1 q=q q δ ′ ′′ ⊗ (4) 2.2 Spacecraft attitude equation of motion The equation of motion of spacecraft is given as Jω + ω ×Jω =u  (5) [...]... (82.4) 1.17 (32.0) λ2 (1σ) 56. 3 (205 .6) 61 .8 (138.0) λ3 (1σ) 13.7 (117.0) 18.8 (55.3) Table 2 Rate sensor scale factor error estimation results of EKF and UKF by Monte-Carlo Simulation 2 06 Advances in Spacecraft Technologies units δ21 δ23 δ31 δ32 (1σ) (1σ) (1σ) (1σ) (1σ) % error 91.2 121.9 72.0 103.8 59 .6 14.0 % (87.1) (47 .6) (75.0) (72.9) (85.0) (64 .1) % error 28.3 6. 81 13.5 7.74 6. 51 10.9 % UKF δ13 (1σ)... % error 28.3 6. 81 13.5 7.74 6. 51 10.9 % UKF δ13 (1σ) EKF δ12 (49.3) (18.3) (32.9) (34.3) ( 46. 2) ( 26. 9) Table 3 Rate sensor misalignment estimation results of EKF and UKF by Monte-Carlo Simulation units EKF UKF % error % % error % b2 (1σ) 166 .1 (47 .6) 11 .6 ( 16. 0) b1 (1σ) 267 .1 (29 .6) 2. 46 (9 .63 ) b3 (1σ) 37.7 (67 .9) 1.93 (23.8) Table 4 Rate sensor bias estimation results of EKF and UKF by Monte-Carlo... filtering for spacecraft attitude state and parameter estimation, Advances in the Astronautical Sciences, Vol 118, No 1, pp 217-228 212 Advances in Spacecraft Technologies Wan, E A & van der Merwe, R (2000) The unscented Kalman filter for nonlinear estimation, Proceedings of IEEE Symposium 2000 (AS-SPCC), Lake Louise, Alberta, Canada, October 2000 Wertz, J R (Ed.) (1978) Spacecraft Attitude Determination... attitude sensor are considered: (i) the fault in the gyroscope, and (ii) the fault in the star tracker The fault detection index is defined as summarized in Table 1 Note that the fault detection index is 0 when all sensors are normal The fault detection index 1 indicates the fault of the gyroscope, the index 2 indicates the fault of the star tracker A, and the index 3 indicates the fault of the star tracker... filter algorithm, Proceedings of IFAC World Congress, Seoul, Korea, July 2008 Pittelkau, M E (2001) Kalman filtering for spacecraft system alignment calibration, Journal of Guidance, Control and Dynamics, Vol 24, No 6, pp 1187-1195 Pittelkau, M E (2002), Everything is relative in spacecraft system alignment calibration, Journal of Spacecraft and Rockets, Vol 39, No 3, pp 460 - 466 Sekhavat, P ; Karpenko,... Nonlinear predictive control of spacecraft, Journal of Guidance, Control and Dynamics, Vol 20, No 6, pp 10 96- 1103 Crassidis, J L.; Markley, F L & Cheng, Y (2007) Survey of nonlinear attitude estimation methods, Journal of Guidance, Control and Dynamics, Vol 30, No 1, pp 12-28 Creamer, G.; DeLaHunt, P., Gates, S & Leyenson, M (19 96) Attitude determination and control of Clementine during lunar mapping,... nonlinear systems, Proceedings of the SPIE AeroSense International Symposium on Aerospace/Defence Sensing, Simulation and Controls, Orlando, Florida, USA, April 1997 Kalman, R E (1 960 ) A new approach to linear filtering and prediction problems, Transactions of the ASME-Journal of Basic Engineering, D, Vol 82, pp 35-45 Kraft, E (2003) A quaternion-based uscented Kalman filter for orientation tracking,... Proceedings of IEEE 6th Coference of Information Fusion, pp 47-54 Lai, K L.; Crassidis, J L & Harman, R R (2003) In- space spacecraft alignment calibration using the unscented filter, Proceedings of AIAA Guidance, Navigation, and Control Conference Exhibit, Austin, Texas, USA, August 2003 Ma, G -F & Jiang, X -Y (2005) Unscented Kalman filter for spacecraft attitude estimation and calibration using magnetometer... / s ⎣ ⎦ 204 Advances in Spacecraft Technologies Quaternion reference trajectory 1 q1 q2 0.8 q3 q4 0 .6 0.4 Quaternion 0.2 0 -0.2 -0.4 -0 .6 -0.8 -1 0 5 10 15 Time (min) Fig 1 Quaternion reference trajectory Body rate reference trajectory 4 ω1 ω2 3 ω3 2 deg/s 1 0 -1 -2 -3 -4 0 5 10 Time (min) Fig 2 Body angular rate reference trajectory 15 Unscented Kalman Filtering for Hybrid Estimation of Spacecraft. .. 0 -0.5 0 5 10 15 0 5 10 15 0 5 10 15 ω3 (deg/s) 0.5 0 -0.5 ω3 0.5 0 -0.5 Time (min) Fig 4 Angular velocity estimation error with 3σ bounds Moment of inertia error 80 ΔJ 11 ΔJ 22 60 ΔJ 33 40 ΔJ 12 20 ΔJ 23 ΔJ 13 0 -20 -40 -60 -80 100 0 5 10 Time (min) Fig 5 Moment of inertia estimation error 15 208 Advances in Spacecraft Technologies 10 10 J 22 20 J 11 20 0 -10 -20 0 -10 0 5 10 -20 15 10 15 0 5 10 15 . nonlinear model to the second order by spreading points 1 sigma apart from the a priori mean. Performing nonlinear Advances in Spacecraft Technologies 198 transformation of sigma points. -1000, -2000 ppm δ = 64 8, 12 96, 972, 64 8, -64 8, 12 96 arcs b = 5, 3, 2 10 rad /s Advances in Spacecraft Technologies 204 0 5 10 15 -1 -0.8 -0 .6 -0.4 -0.2 0 0.2 0.4 0 .6 0.8 1 Quaternion reference. can be indicated that potential factors of the peeling off of the tiles are mainly contributed by peeling normal stress and influenced little by shear stress. Advances in Spacecraft Technologies