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On the damping effect due to bolted junctions in space structures subjected to pyro-shock
Acta Astronautica 60 (2007) 947 – 956 www.elsevier.com/locate/actaastro
On the damping effect due to bolted junctions in space structures subjected to pyro-shock M. de Benedetti∗ , G. Garofalo, M. Zumpano, R. Barboni Dipartimento di Ingegneria Aerospaziale e Astronautica, Università degli Studi “La Sapienza” Via Eudossiana, 18 Roma 00184, Italy Received 25 May 2005; received in revised form 6 November 2006; accepted 8 November 2006 Available online 7 February 2007
Abstract The damping due to bolted or riveted joints in the dynamics of assembled structures subjected to pyro-shock has been studied. A relevant effect in this phenomenon is the micro-slip between the jointed surfaces. In order to verify the feasibility and the reliability of the numerical analyses performed on structures with junctions, the numerical results obtained by the finite elements method have been compared with those obtained experimentally. Several numerical analyses, in which friction forces have been represented as nonlinear loads, have been carried out for the FE models of two application cases: an electronic unit mounted within the Radarsat-2 satellite, and the complete Cosmo-Skymed spacecraft. Considering the load type, involving a typical high frequency response spectrum between 100 and 10 000 Hz, both numerical and experimental data have been reduced to the shock response spectrum form. After the comparative evaluation, taking into account also the damping effect, the agreement between numerical results and experimental data has been evaluated. The proposed numerical approach yields an effective and less expensive instrument, able to provide indications in the design phase, to allow the prevision of the dynamic behaviour of the structure for the prevention of failures in units or systems mounted within the spacecraft or launch vehicle. With the proposed model, it is possible to determine in a simple and direct way the characteristics of the damping due to the single bolted and riveted joints, and use them in similar multiple joints in the complete structure assembling or substructuring. © 2006 Elsevier Ltd. All rights reserved.
1. Introduction Current launchers and spacecrafts often utilize pyrotechnic devices to separate structural subsystems and/or deploy appendages [1–5]. The firing of the pyrotechnic devices generates intense shock stress waves, travelling throughout the structures with various modes of propagation. The shock waves are reflected and transmitted through the interfaces and excite the structure mode shapes. Bolted and riveted joints are a
∗ Corresponding author.
E-mail address: [email protected] (M. de Benedetti). 0094-5765/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2006.11.011
primary source of energy dissipation in the dynamics of assembled structures [6–15]. Previous experimental expertise confirms that the damping effect generated by this phenomenon is more important than the one of the material properties. The junction damping effect increases with the frequency of the dynamic excitation [16–24]. Because of the high frequency spectral content, many hardware elements and small components are susceptible to pyrotechnic shock failure, while resistant to a variety of lower frequency environments, including sine and random vibrations [25]. The purpose of this study is to demonstrate that it is necessary to keep in account the damping effect due to bolted and riveted joints to analyse the dynamics of structures subjected to pyrotechnic shock, and that numerical
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analyses using the finite elements method are able to provide sufficiently accurate results even on structures subjected to these loads. A physical model able to reproduce the structural phenomena at the interface between lap surfaces has been formulated and implemented in the FEM simulation [26–31]. 2. Interface damping theoretical model The interface friction depends on the load type and direction. Considering two plates jointed by a bolt, if the load is normal to the plates (Fig. 1), there is no slip between plates, then there is no friction, then there is no damping; on the contrary, if the load is tangent to the plates (Fig. 2) there is slip, then there is friction, then there is damping. This slip occurs at a microscopic level. It is usually referred as micro-slip. The Coulomb’s friction law states that the friction force depends on the applied normal loads and on the friction coefficients. The pressure applied by the bolt gives the normal load. It has been demonstrated that this pressure decreases linearly versus radial distance from the bolt axis
(Fig. 3). The force reaches its maximum value at the bolt centre, and it becomes null at a distance of two or three times the radius of the hole. The slip occurs in a limited area, where the pressure is higher than zero, thus allowing the contact, but sufficiently low to overpass the adherence imposed by the static friction. This area has an annular shape, centred on the bolt axis, where the internal radius r2 is twice the hole radius r1 , while the external radius r3 is equal to three times the hole radius (Fig. 4). It has been assumed that the behaviour at the interface can be simulated through the combined action of the linear elastic and nonlinear dissipative element such as reported in Fig. 5. This approach has been adopted also in [7,8,14,15]. The dependence law of the damping force F versus the velocity V for this nonlinear dissipative element is reported in Fig. 6, where N is the normal load, fs is the static friction coefficient, fd is the dynamic friction coefficient. The FEM representation of the damping force is described in Fig. 7.
Fig. 1. Normal load.
Fig. 4. Friction area.
Fig. 2. Tangent load. Fig. 5. Interface model.
Fig. 3. Pressure distribution.
Fig. 6. Coulomb’s friction law.
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Fig. 7. Friction law model for numerical analyses.
Fig. 9. Shock table configuration.
Fig. 8. Normalized pulse load.
Fig. 10. Shock table plane view.
To avoid numerical integration problems, the load discontinuities close to the axes origin have been replaced by a linear function. 3. Pyroshock load To reproduce the test conditions, a shock solution analysis has been performed on the FEM model [26,27], applying a single impulse load with the characteristics illustrated in Fig. 8 on the point of the frame where the pyrotechnical device acts. 4. Experimental setup The experimental measures have been obtained with a dedicated setup, described in Figs. 9–13. The setup can be used to test different specimens, units or systems. The item to be tested is constrained onto a 1 m×2 m×0.01 m
plate, made of aluminium alloy UNI 9006/4-USAAA6082. To simulate the free-free constraint condition, a foam layer supports the plate. The pyrotechnic shocks have been simulated through impacts between metals. The shockwave is obtained through lateral or perpendicular impacts of oscillating or sliding impactors on the shock table. For the in-plane shock test simulation the impacting mass is fixed on a pendulum and it acts on the lateral anvil. For the perpendicular shock test simulation, the impacting mass falls into a vertical rail tube and it acts on the anvil positioned in the centre of the plate (Figs. 11–13). In the preliminary setup calibration, the opportune combinations of impacting mass (usually 1–4 kg) and dropping height have been found to correctly reproduce the shock vibration environment.
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Fig. 13. Impact points details.
Fig. 11. Side view of the shock table.
Fig. 14. Inside view of the unit lower module.
Fig. 12. Isometric view of the shock table.
5. Electronic unit description As a first shock test study case, an electronic unit with dimensions 0.288 m × 0.315 m × 0.140 m (Fig. 14) has been considered. The unit is composed of two modules, the upper S-Module and the lower I-Module. An internal view is in Fig. 14. In the I-Module are housed four printed circuit boards (PCBs). Each small PCB is fixed to a large one by an aluminium alloy supporting frame, as described in Fig. 15. The frame also constrains these PCBs to the housing box of the unit. The experimental data have been measured by accelerometers placed on the circuits located within the I-module.
Fig. 15. PCBs of lower module.
6. Shock test description and FEM simulation Experimental tests have been performed to evaluate the dynamic behaviour of PCBs under pyrotechnic
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Fig. 18. Electronic unit on the shock table, with accelerometers and power supply connections. Fig. 16. The electronic unit.
Fig. 19. FE model of the shock table with the electronic unit.
Fig. 17. Unit position on the shock table.
shock and to evaluate the damping effect of the bolted junctions between the electronic unit and the shock plate. For these reasons, an in-plane shock test simulation has been performed, using the pendulum impacting mass. The electronic unit (Fig. 16) has been fixed on the shock table in the position represented in Figs. 17 and 18. The finite elements model (Fig. 19), of the shock table has been realized with 2-D planar finite elements, while the electronic unit has been modelled with 1-D line elements, 2-D triangular or quadrangular planar elements, and 3-D brick or parallelepiped solid elements (Fig. 20). The pyrotechnic shock has been simulated by the pulse load introduced in Fig. 8, applied on the centre of the side of the shock table. The simulation of the micro-slip damping has been introduced with four nonlinear damping forces, located on each fixing bolt, at the interface between the unit and the shock table. The
Fig. 20. Internal view of the electronic unit FE model.
output of two accelerometers placed on PCB I3 and PCB I4 (the two small PCBs of the I-module) has been measured.
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Fig. 21. Results PCB I-3 Y-direction. Fig. 24. Results PCB I-4 Y-direction.
Fig. 22. Results PCB I-3 Z-direction. Fig. 25. Results PCB I-4 Z-direction.
As a consequence of an accelerometer failure, the experimental output for the I3 PCB along the X-axis direction has not been considered reliable, and is not shown here. Considering the achieved results, the same approach has been extended to an entire spacecraft. 7. FEM simulation on the Cosmo-Skymed satellite
Fig. 23. Results PCB I-4 X-direction.
In Figs. 21–25 the results of the experimental test, the numerical simulation with damping forces and the numerical simulation without damping forces are compared.
The Cosmo-Skymed spacecraft is subjected to the mechanical shock occurring at the separation of the satellite from the launch vehicle. This event is commanded by the firing of a pyrotechnic band. The FEM model of the satellite in its stowed configuration is reported in Fig. 26. The pyrotechnic device acts on the marman clampband placed at the base of the satellite. The junction in which the friction has been considered is located between the propellant tank and the external cone frame;
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Fig. 27. Cross-section of the FEM model.
Fig. 26. Cosmo-Skymed spacecraft FEM model.
this particular can be seen in the FEM cross-section reported in Fig. 27. In Fig. 28, a more detailed section of propellant tank end cone frame can be seen. It is possible to compare the numerical results with the experimental data obtained from the test performed on the satellite during the simulation of its separation from the launch vehicle. Two cases have been considered. In the first one the effect of the junctions damping is present. In the second one, this effect has been neglected. The purpose of this comparison is to determine if FEM is suitable for the simulation of complex systems such as an entire satellite. If validated, this approach can be used whether during the project phase or during the performance compliance check. It is possible to calculate the acceleration maximum values, as a function of the frequency, reducing or avoiding expensive experimental simulations campaigns. The results obtained are reported in the figures in the form of SRS [32–34]. The three diagrams (Figs. 29–31) show the experimental and calculated shock response spectrum (SRS) responses based on accelerometer placement
Fig. 28. FEM model of the main supporting cone and tank.
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Fig. 29. Results SRS along the X-axis on the spacecraft cone.
Fig. 30. Results SRS along the Y-axis on the spacecraft cone.
Fig. 32. Results SRS along the X-axis on the spacecraft tank.
Fig. 33. Results SRS along the Y-axis on the spacecraft tank.
before the junction on the spacecraft structure main supporting cone. The SRS diagrams (Figs. 32–34) are referred to the accelerometer placed after the junction on the tank. The last three SRS (Fig. 35) are based on the accelerometer located on the cone in a 90◦ position from the others. In the last diagram (Fig. 36) the numerical SRS of two points placed before and after the junction have been compared. As described in the previous paragraphs, the effect of damping at high frequencies is evident. 8. Conclusions
Fig. 31. Results SRS along the Z-axis on the spacecraft cone.
It can be noted that the numerical and experimental results in several cases reach a sufficiently good
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Fig. 34. Results SRS along the Z-axis on the spacecraft tank.
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Fig. 36. Results SRS before and after the junction, damping effect.
experimental results, allowing one to conclude that the proposed numerical analysis can be considered a reliable, fast and economic method to obtain realistic predictions of the behaviour of the assembled structures. Acknowledgements The authors would like to thank Dr. E. Sciandra of TÜV Italia S.r.l., Div. PS-TEC, Via Montalenghe n. 12, 10010, Scarmagno, Torino, Italy, for the experimental data collection, and Mr. L. Collini of Alcatel Alenia S.p.A., Roma, for his important contribution and help. Fig. 35. Results SRS along the Z-axis on the spacecraft cone, at 90◦ from the others.
agreement. The accuracy of the numerical results is enhanced if the damping force is taken into account. Even when the damping forces have not been considered, the damping property of the material has been taken into account. In the SRS responses, two types of effects due to the damping forces can be observed: a variation on the acceleration response maximum values and the frequencies at which these values are reached. Taking into account the damping forces, the acceleration maximum values and the frequencies at which they have been reached in numerical simulation are more close to the experimental simulation. It can be assessed that by taking into account the damping effect due to bolted joints the numerical analysis of assembled structures can provide results with a sufficiently good agreement with
References [1] L.J. Bement, H.A. Multhaup, Determining functional reliability of pyrotechnic mechanical devices, AIAA Journal 37 (3) (1999). [2] L.J. Bement, Pyrotechnic system failures: causes and prevention, NASA TM 100633, 1998. [3] L.J. Bement, M.L. Schimmel, A manual for pyrotechnic design, development and qualification, NASA TM 110172, June 1999. [4] R.W. Clough, J. Penzien, Dynamics of Structures, McGrawHill, New York, 1975. [5] C.J. Moening, Views of the world of pyrotechnic shock, Shock and Vibration Bulletin 56 (3) (1986) 3–28. [6] L. Gaul, U. Nackenhorst, K. Willner, J. Lenz, Nonlinear vibration damping of structures with bolted joints, Proceedings of the 12th International Modal Analysis Conference, vol. 1, 1994, Honolulu, Hawaii. [7] L. Gaul, J. Lenz, Nonlinear dynamics of structures assembled by bolted joints, ACTA Mechanica 125 (1997) 169–181. [8] L. Gaul, S. Bohlen, Identification of nonlinear structural joint models and implementation in discretized structure models, Presented at 1987 the ASME Design Technology
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M. de Benedetti et al. / Acta Astronautica 60 (2007) 947 – 956 Conference-11th Biennial Conference on Mechanical Vibration and Noise, Septemper 1987, Boston, MA. S. Vitelleschi, L.C. Schmidt, Damping in friction-grip bolted joints, Journal of the Structural Division, ASCE Proceedings, 103, N◦ ST7 J. K.K. Padmanabhan, A.S.R. Murty, Damping in structural joints subjected to tangential loads, Journal of the Structural Division, Proceedings of Institution of Mechanical Engineers 205 (1991) 121–129. D.L. Gregory, D.O. Smallwood, R.G. Coleman, M.A. Nusser, Damping investigation of simplified frictional shear joint, Proceedings of the 71st Shock and Vibration Symposium, November 2000, Alexandria, VA. F. Spann, Pyro-shock attenuation techniques, IES Pyro-Shock Tutorial Session 31st Annual Technical Meeting, Institute of Environmental Sciences, May 1985. E.E. Ungar, The status of engineering knowledge concerning the damping of built-up structures, Journal of Sound and Vibration 26/1 (1973) 141–154. T.H.H. Pian, Structural damping of a simple built-up beam with riveted joints in bending, Journal of Applied Mechanics (1957) 35–38. L.E. Goodman, A review of progress in analysis of interfacial slip damping, in: Ruzicka (Ed.), Structural Damping, ASME, New York, 1959, pp. 35–48. D.O. Smallwood, D.L. Gregory, R.G. Coleman, Experimental studies to investigate damping in frictional shear joints, Proceeding of 70th Shock and Vibration Symposium, 1999. Anon., Pyroshock test criteria, NASA STD 7003, May 1999. H. Himelblau, D.L. Kern, A.G. Piersol, Proposed pyroshock test criteria, Standard for NASA STD XXXX-96. N.T. Davie, V.I. Bateman, Pyroshock testing, in: C.M. Harris (Ed.), Shock and Vibration Handbook, fourth ed., McGraw-Hill, New York, 1996 (Chapter 26). A.G. Piersol, Tutorial on design of equipment for pyroshock environments. A.G. Piersol, Recommendations of the acquisition and analysis of pyroshock data, Journal of Sound and Vibration 26 (4) (1992) 18–21.
[22] E. Filippi, F. Cambier, C. Conti, Development of the Alcatel ETCA pyroshock test facility, ESA SP-428, 1999. [23] G. Schweickert, Explanation on shock loads for Analysis and test. [24] Anon., Pyrotechnic shock testing, NASA Practice No. PT-TE1408A, 1996. [25] E. Filippi, J. Morandi, J.P. Semerie, T.H. Youssefi, P. Zemlianoy, Pyrotechnically initiated shocks—effects on electronic equipment—test implementation, ESA WPP-066, 1993. [26] R. Barboni, G. Galluccio, L. Collini, M. de Benedetti, On the use of FEM for pyro-shock propagation in space structures, Proceeding of 53rd International Astronautical Congress, The World Space Congress, IAC-I.2.07, Houston, TX, 10–19 October 2002. [27] R. Barboni, G. Galluccio, E. Sciandra, M. de Benedetti, On the experimental validation of FEM for pyro-shock propagation in space structures, AIDAA XVII Congresso Nazionale, 15–16 September 2003, Roma. [28] H.A. Gaberson, R.H. Chalmers, Modal velocity as a criterion of shock severity, Shock and Vibration Bulletin 40 (2) (1969) 31–49. [29] D.O. Smallwood, A.R. Nord, (Sandia Laboratories), Matching shock spectra with sums of decaying sinusoids compensated for shaker velocity and displacement limitations. [30] D.B. Nelson, P.H. Prasthofer, (Sandia Laboratories), A case of damped oscillatory excitation as a natural pyrotechnic shock simulation. [31] R.S. Ayre, Transient response to step and pulse function, in: C.M. Harris (Ed.), Shock and Vibration Handbook, third ed., McGraw-Hill, New York, 1988(Chapter 8). [32] H. Himelblau, A.G. Piersol, J.H. Wise, M.R. Grundvig, Handbook for Dynamic Data Acquisition and Analysis, Institute of Environmental Sciences, DTE 012.1, 1994. [33] S. Rubin, Concepts in Shock Data Analysis, in: C.M. Harris (Ed.), Shock and Vibration Handbook, third ed., McGraw-Hill, New York, 1988(Chapter 23). [34] T. Irvine, An Introduction to the Shock Response Spectrum http://www.dynamiclabs.com/tutorials, 24 May, 2002.
On the damping effect due to bolted junctions in space structures subjected to pyro-shock M. de Benedetti∗ , G. Garofalo, M. Zumpano, R. Barboni Dipartimento di Ingegneria Aerospaziale e Astronautica, Università degli Studi “La Sapienza” Via Eudossiana, 18 Roma 00184, Italy Received 25 May 2005; received in revised form 6 November 2006; accepted 8 November 2006 Available online 7 February 2007
Abstract The damping due to bolted or riveted joints in the dynamics of assembled structures subjected to pyro-shock has been studied. A relevant effect in this phenomenon is the micro-slip between the jointed surfaces. In order to verify the feasibility and the reliability of the numerical analyses performed on structures with junctions, the numerical results obtained by the finite elements method have been compared with those obtained experimentally. Several numerical analyses, in which friction forces have been represented as nonlinear loads, have been carried out for the FE models of two application cases: an electronic unit mounted within the Radarsat-2 satellite, and the complete Cosmo-Skymed spacecraft. Considering the load type, involving a typical high frequency response spectrum between 100 and 10 000 Hz, both numerical and experimental data have been reduced to the shock response spectrum form. After the comparative evaluation, taking into account also the damping effect, the agreement between numerical results and experimental data has been evaluated. The proposed numerical approach yields an effective and less expensive instrument, able to provide indications in the design phase, to allow the prevision of the dynamic behaviour of the structure for the prevention of failures in units or systems mounted within the spacecraft or launch vehicle. With the proposed model, it is possible to determine in a simple and direct way the characteristics of the damping due to the single bolted and riveted joints, and use them in similar multiple joints in the complete structure assembling or substructuring. © 2006 Elsevier Ltd. All rights reserved.
1. Introduction Current launchers and spacecrafts often utilize pyrotechnic devices to separate structural subsystems and/or deploy appendages [1–5]. The firing of the pyrotechnic devices generates intense shock stress waves, travelling throughout the structures with various modes of propagation. The shock waves are reflected and transmitted through the interfaces and excite the structure mode shapes. Bolted and riveted joints are a
∗ Corresponding author.
E-mail address: [email protected] (M. de Benedetti). 0094-5765/$ - see front matter © 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2006.11.011
primary source of energy dissipation in the dynamics of assembled structures [6–15]. Previous experimental expertise confirms that the damping effect generated by this phenomenon is more important than the one of the material properties. The junction damping effect increases with the frequency of the dynamic excitation [16–24]. Because of the high frequency spectral content, many hardware elements and small components are susceptible to pyrotechnic shock failure, while resistant to a variety of lower frequency environments, including sine and random vibrations [25]. The purpose of this study is to demonstrate that it is necessary to keep in account the damping effect due to bolted and riveted joints to analyse the dynamics of structures subjected to pyrotechnic shock, and that numerical
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analyses using the finite elements method are able to provide sufficiently accurate results even on structures subjected to these loads. A physical model able to reproduce the structural phenomena at the interface between lap surfaces has been formulated and implemented in the FEM simulation [26–31]. 2. Interface damping theoretical model The interface friction depends on the load type and direction. Considering two plates jointed by a bolt, if the load is normal to the plates (Fig. 1), there is no slip between plates, then there is no friction, then there is no damping; on the contrary, if the load is tangent to the plates (Fig. 2) there is slip, then there is friction, then there is damping. This slip occurs at a microscopic level. It is usually referred as micro-slip. The Coulomb’s friction law states that the friction force depends on the applied normal loads and on the friction coefficients. The pressure applied by the bolt gives the normal load. It has been demonstrated that this pressure decreases linearly versus radial distance from the bolt axis
(Fig. 3). The force reaches its maximum value at the bolt centre, and it becomes null at a distance of two or three times the radius of the hole. The slip occurs in a limited area, where the pressure is higher than zero, thus allowing the contact, but sufficiently low to overpass the adherence imposed by the static friction. This area has an annular shape, centred on the bolt axis, where the internal radius r2 is twice the hole radius r1 , while the external radius r3 is equal to three times the hole radius (Fig. 4). It has been assumed that the behaviour at the interface can be simulated through the combined action of the linear elastic and nonlinear dissipative element such as reported in Fig. 5. This approach has been adopted also in [7,8,14,15]. The dependence law of the damping force F versus the velocity V for this nonlinear dissipative element is reported in Fig. 6, where N is the normal load, fs is the static friction coefficient, fd is the dynamic friction coefficient. The FEM representation of the damping force is described in Fig. 7.
Fig. 1. Normal load.
Fig. 4. Friction area.
Fig. 2. Tangent load. Fig. 5. Interface model.
Fig. 3. Pressure distribution.
Fig. 6. Coulomb’s friction law.
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Fig. 7. Friction law model for numerical analyses.
Fig. 9. Shock table configuration.
Fig. 8. Normalized pulse load.
Fig. 10. Shock table plane view.
To avoid numerical integration problems, the load discontinuities close to the axes origin have been replaced by a linear function. 3. Pyroshock load To reproduce the test conditions, a shock solution analysis has been performed on the FEM model [26,27], applying a single impulse load with the characteristics illustrated in Fig. 8 on the point of the frame where the pyrotechnical device acts. 4. Experimental setup The experimental measures have been obtained with a dedicated setup, described in Figs. 9–13. The setup can be used to test different specimens, units or systems. The item to be tested is constrained onto a 1 m×2 m×0.01 m
plate, made of aluminium alloy UNI 9006/4-USAAA6082. To simulate the free-free constraint condition, a foam layer supports the plate. The pyrotechnic shocks have been simulated through impacts between metals. The shockwave is obtained through lateral or perpendicular impacts of oscillating or sliding impactors on the shock table. For the in-plane shock test simulation the impacting mass is fixed on a pendulum and it acts on the lateral anvil. For the perpendicular shock test simulation, the impacting mass falls into a vertical rail tube and it acts on the anvil positioned in the centre of the plate (Figs. 11–13). In the preliminary setup calibration, the opportune combinations of impacting mass (usually 1–4 kg) and dropping height have been found to correctly reproduce the shock vibration environment.
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Fig. 13. Impact points details.
Fig. 11. Side view of the shock table.
Fig. 14. Inside view of the unit lower module.
Fig. 12. Isometric view of the shock table.
5. Electronic unit description As a first shock test study case, an electronic unit with dimensions 0.288 m × 0.315 m × 0.140 m (Fig. 14) has been considered. The unit is composed of two modules, the upper S-Module and the lower I-Module. An internal view is in Fig. 14. In the I-Module are housed four printed circuit boards (PCBs). Each small PCB is fixed to a large one by an aluminium alloy supporting frame, as described in Fig. 15. The frame also constrains these PCBs to the housing box of the unit. The experimental data have been measured by accelerometers placed on the circuits located within the I-module.
Fig. 15. PCBs of lower module.
6. Shock test description and FEM simulation Experimental tests have been performed to evaluate the dynamic behaviour of PCBs under pyrotechnic
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Fig. 18. Electronic unit on the shock table, with accelerometers and power supply connections. Fig. 16. The electronic unit.
Fig. 19. FE model of the shock table with the electronic unit.
Fig. 17. Unit position on the shock table.
shock and to evaluate the damping effect of the bolted junctions between the electronic unit and the shock plate. For these reasons, an in-plane shock test simulation has been performed, using the pendulum impacting mass. The electronic unit (Fig. 16) has been fixed on the shock table in the position represented in Figs. 17 and 18. The finite elements model (Fig. 19), of the shock table has been realized with 2-D planar finite elements, while the electronic unit has been modelled with 1-D line elements, 2-D triangular or quadrangular planar elements, and 3-D brick or parallelepiped solid elements (Fig. 20). The pyrotechnic shock has been simulated by the pulse load introduced in Fig. 8, applied on the centre of the side of the shock table. The simulation of the micro-slip damping has been introduced with four nonlinear damping forces, located on each fixing bolt, at the interface between the unit and the shock table. The
Fig. 20. Internal view of the electronic unit FE model.
output of two accelerometers placed on PCB I3 and PCB I4 (the two small PCBs of the I-module) has been measured.
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Fig. 21. Results PCB I-3 Y-direction. Fig. 24. Results PCB I-4 Y-direction.
Fig. 22. Results PCB I-3 Z-direction. Fig. 25. Results PCB I-4 Z-direction.
As a consequence of an accelerometer failure, the experimental output for the I3 PCB along the X-axis direction has not been considered reliable, and is not shown here. Considering the achieved results, the same approach has been extended to an entire spacecraft. 7. FEM simulation on the Cosmo-Skymed satellite
Fig. 23. Results PCB I-4 X-direction.
In Figs. 21–25 the results of the experimental test, the numerical simulation with damping forces and the numerical simulation without damping forces are compared.
The Cosmo-Skymed spacecraft is subjected to the mechanical shock occurring at the separation of the satellite from the launch vehicle. This event is commanded by the firing of a pyrotechnic band. The FEM model of the satellite in its stowed configuration is reported in Fig. 26. The pyrotechnic device acts on the marman clampband placed at the base of the satellite. The junction in which the friction has been considered is located between the propellant tank and the external cone frame;
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Fig. 27. Cross-section of the FEM model.
Fig. 26. Cosmo-Skymed spacecraft FEM model.
this particular can be seen in the FEM cross-section reported in Fig. 27. In Fig. 28, a more detailed section of propellant tank end cone frame can be seen. It is possible to compare the numerical results with the experimental data obtained from the test performed on the satellite during the simulation of its separation from the launch vehicle. Two cases have been considered. In the first one the effect of the junctions damping is present. In the second one, this effect has been neglected. The purpose of this comparison is to determine if FEM is suitable for the simulation of complex systems such as an entire satellite. If validated, this approach can be used whether during the project phase or during the performance compliance check. It is possible to calculate the acceleration maximum values, as a function of the frequency, reducing or avoiding expensive experimental simulations campaigns. The results obtained are reported in the figures in the form of SRS [32–34]. The three diagrams (Figs. 29–31) show the experimental and calculated shock response spectrum (SRS) responses based on accelerometer placement
Fig. 28. FEM model of the main supporting cone and tank.
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Fig. 29. Results SRS along the X-axis on the spacecraft cone.
Fig. 30. Results SRS along the Y-axis on the spacecraft cone.
Fig. 32. Results SRS along the X-axis on the spacecraft tank.
Fig. 33. Results SRS along the Y-axis on the spacecraft tank.
before the junction on the spacecraft structure main supporting cone. The SRS diagrams (Figs. 32–34) are referred to the accelerometer placed after the junction on the tank. The last three SRS (Fig. 35) are based on the accelerometer located on the cone in a 90◦ position from the others. In the last diagram (Fig. 36) the numerical SRS of two points placed before and after the junction have been compared. As described in the previous paragraphs, the effect of damping at high frequencies is evident. 8. Conclusions
Fig. 31. Results SRS along the Z-axis on the spacecraft cone.
It can be noted that the numerical and experimental results in several cases reach a sufficiently good
M. de Benedetti et al. / Acta Astronautica 60 (2007) 947 – 956
Fig. 34. Results SRS along the Z-axis on the spacecraft tank.
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Fig. 36. Results SRS before and after the junction, damping effect.
experimental results, allowing one to conclude that the proposed numerical analysis can be considered a reliable, fast and economic method to obtain realistic predictions of the behaviour of the assembled structures. Acknowledgements The authors would like to thank Dr. E. Sciandra of TÜV Italia S.r.l., Div. PS-TEC, Via Montalenghe n. 12, 10010, Scarmagno, Torino, Italy, for the experimental data collection, and Mr. L. Collini of Alcatel Alenia S.p.A., Roma, for his important contribution and help. Fig. 35. Results SRS along the Z-axis on the spacecraft cone, at 90◦ from the others.
agreement. The accuracy of the numerical results is enhanced if the damping force is taken into account. Even when the damping forces have not been considered, the damping property of the material has been taken into account. In the SRS responses, two types of effects due to the damping forces can be observed: a variation on the acceleration response maximum values and the frequencies at which these values are reached. Taking into account the damping forces, the acceleration maximum values and the frequencies at which they have been reached in numerical simulation are more close to the experimental simulation. It can be assessed that by taking into account the damping effect due to bolted joints the numerical analysis of assembled structures can provide results with a sufficiently good agreement with
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