Abstract Static and Modal Analysis of Telescope Frame in Satellite Sun Libin Department of Mechanical Engineering Tsinghua University Feng Hui School of Material Science and Engineering University of Science and Technology, Beijing To improve precision of satellite telescope, the telescope frame must be designed scrutinizingly so that it has minimal distortion under different loads during machining, assembly and satellite shot process. A telescope frame has been simulated by ANSYS software mainly in static and modal analysis in recent months. After evaluation of results, initial design has been refined several times and a satisfactory project gained. Now the final design is being actualized. Introduction The hard X-ray telescope is an important functional part of a satellite that can be applied on different fields such as remote sensing, scientific experiment, communication etc. Its frame is main assembly that joints and fixes the body of collimations. So the frame distortion under different loads directly affects telescope precision. In order to keep telescope in good condition, frame must satisfy requirements, especially on intensity, rigidity, security and technique. Three main factors are investigated including structure, material and load: 1) In structure part three projects have been respectively analyzed that are multi-plate structure, casting structure and shell structure (Figure 1 through Figures 3). 2) To reach the best balance point of weight, intensity and rigidity, different material parameters of Al alloy, Ti alloy and composite material have been calculated for the frame. 3) During satellite shot process and working in outer space, different kinds of loads will been applied on the frame. In order to simplify FE model of real status, all loads are classified to two kinds- axial inertia and radial inertia. Figure 1 - Multi-plate structure
Figure 2 - Casting structure Figure 3 - Shell structure 3-D 20-node structural solid element solid95 is chosen because it can tolerate irregular shapes without as much loss of accuracy. If the whole frame model is meshed all together, number of elements will so big (about 100,000) that it will cost very long time for one simulation. So symmetry of frame and loads must be utilized. According the loads, we plan two symmetrical ways for static and modal analysis that quarter
symmetry is chosen for static because of easily loads applying and sixth cyclically symmetry for modal. Further transient dynamic analysis is studying yet. Procedure CAD and FE model CAD model of the telescope frame is built then exported as ACIS-neutral file-sat by using AutoCAD software (Figure 4 through Figures 6). After that the SAT file of model is imported into ANSYS by the SAT connection Kit add-on. Because the section of beams in frame is circular and conjoint parts of beams and plates have very complex topological shape, there are so many short edges near conjoint parts that meshing the frame model is very hard. In order to reduce meshing difficulty, the beams are simplified with square section that has same area as circle. Through this way and repairing the model in ANSYS, the frame is meshed successfully (Figure 7). There are totally about 25,000 solid95 elements in quarter symmetry part of the frame. Figure 4 - Quarter model without centric brace
Figure 5 - Quarter model with centric brace Figure 6 - Sixth cyclically symmetry model for modal
Figure 7 - FEM model Static analysis with and without centric brace The frame will be fixed on telescope with bolt-nut. However, the dimension of bolthole is quite small relative to the whole dimension of the frame so that the holes are neglected in FE model. Therefore, the base plane of frame is applied zero displacement constraints at X, Y and Z directions. At the same time, the symmetry boundary conditions are applied on two symmetrical planes. For considering mass factor, 20G gravitational acceleration is applied at axial or radial directions respectively. Under this constraints and boundary conditions, a static analysis has been carried into effect and the results are showed in Figure 16 through Figure 21. However the maximum stress and deformation is greater than the allowable designed value. So the structure of frame must be mended until it lower than designed value. Through research the calculated results, it can be found that centric part rigidity of frame is so small that maximal value of stress and deformation appear near it. In order to improve the centric part rigidity, a centric brace is added to the frame structure. Then a new result is gained under the same constraints and boundary conditions with centric brace (Figure 8 through Figure 14).
Figure 8 - Isometric view of mises stress of the frame with centric brace Figure 9 - Top view of mises stress of the frame with centric brace
Figure 10 - Front view of mises stress of the frame with centric brace Figure 11 - X translation of the frame with centric brace
Figure 12 - Y translation of the frame with centric brace Figure 13 - Z translation of the frame with centric brace
Figure 14 - Total translation of the frame with centric brace Figure 15 - Isometric view of mises stress of the frame without centric brace
Figure 16 - Top view of mises stress of the frame without centric brace Figure 17 - Front view of mises stress of the frame without centric brace
Figure 18 - X translation of the frame without centric brace Figure 19 - Y translation of the frame without centric brace
Figure 20 - Z translation of the frame without centric brace Figure 21 - Total translation of the frame without centric brace
Modal analysis It is imposed that frame is a typical undamped modal analysis; solved equation is the classical eigenvalue problem: Where [ K ] = stiffness matrix. ] [M = 2 ω i = 2 ([ K] ω [ M ]){ u} = { 0} mass matrix. Because frame is linear structure, [ M ] and [ K ] are both constant. root( eigenvalue) of the equation above. {} u i = mode shape vector (eigenvector) of mode i. Undamped equation: u=u 0 cos(ωt) To get natural frequencies and mode shapes of frame, modal analysis is executed which can also be a base for further dynamic analysis. Normally, the whole model should be mesh and simulated in modal because the non-symmetry of mode shapes. However element number of whole frame model is so large that calculation will cost too long CPU time and the symmetry boundary conditions cannot be applied on two symmetrical planes in quarter symmetry model. So the sixth cyclic symmetry is chosen in modal analysis because frame is a sixth cyclic symmetry structure. There are 7 steps for cyclic symmetry modal analysis: 1) Define a basic sector model that is sixth cyclically symmetric of frame; 2) Select the nodes on the edge with the lowest angle (zero degree) and define a component. 3) Copy the basic sector by the CYCGEN macro. 4) Define all applicable boundary conditions on both sectors. 5) Define modal analysis and its options. The Block Lanczos method is chosen for it suits big scale analysis and faster. 6) Solute by running the CYCSOL macro and define the nodal diameter range (from 0 to 4) and the sector angle. (60 degree) 7) Get the analysis results and expand the model for display. Then all 32 natural frequencies and mode shapes of frame are gained. Analysis Results and Discussion Besides Al alloy, other materials are also researched for the frame such as Ti alloy and Composite material. Part of analysis results is listed below (See Static analysis results in different conditions). Static analysis results in different conditions
Conditions Maximum von mises stress Maximum translation Al alloy frame without centric brace 58.8 Mpa 21.0 um Al alloy frame with centric brace 41.3 Mpa 12.0 um Composite material frame without centric brace 32.6 Mpa 9.5 um The structure with centric brace is increased a fixed part between frame and body of telescope so that it is more rigid and deforms less than the structure without centric brace. At same time it is very useful method to reduce stress and translation by choosing high performance material, for example composite material. In this case ANSYS can simulate and gain the corresponding results for different conditions, which is effective for redesign the initial plan. Natural frequencies of frame modal analysis Substep Load Step = 0 Load Step = 1 Load Step = 2 Load Step = 3 Natural frequencies Substep Natural frequencies Substep Natural frequencies Substep Natural frequencies 1 50.0 1 77.0 1 77.0 1 56.0 2 54.0 2 86.0 2 86.0 2 57.0 3 57.0 3 89.0 3 89.0 3 59.0 4 58.0 4 98.0 4 98.0 4 62.0 5 63.0 5 99.0 5 99.0 5 68.0 6 66.0 6 108.0 6 108.0 6 72.0 7 70.0 7 111.0 7 111.0 7 73.0 8 72.0 8 114.0 8 114.0 8 77.0 From the list above, several pair of natural frequencies has same value. However their load steps (nodal diameter) are different, so they have definitely different mode shapes. The modal analysis results are useful to further dynamic analysis, such as a transient dynamic analysis, a harmonic response analysis, or a spectrum analysis. All of them are being studied yet. Conclusion In the effort, the static and modal characteristics of telescope frame are systematically researched including three factors: structure, material and load are studied respectively. By improved structure and chosen high performance material, frame of telescope meets the request on intensity, rigidity, security and technique. ANSYS software plays a key role in simulating and redesigning different plans. References 1) ANSYS, Inc. Theory Release 5.7, 2001 2) Aleksey E. Bolotnikov, Walter R. Cook, Steven E. Boggs, Fiona A. Harrison,Stephen M. Schindler, Development of high spectral resolution CdZnTe pixeldetectors for astronomical hard X-ray telescopes, Nuclear Instruments and Methods in Physics Research A 458 (2001) 585-592 3) Finn E. Christensen, William W. Craig, David L. Windt,Mario A. Jimenez-Garate, Charles J. Hailey, Fiona A. Harrison, Peter H. Mao,James M. Chakan, Eric Ziegler, Veijo Honkimaki, Measured reflectance of graded multilayer mirrors designed for astronomical hard X-ray telescopes, Nuclear Instruments and Methods in Physics Research A 451 (2000) 572-581