Analysis and Optimization for a Focal Plane Mechanism of a Large Sky Area Multi-object Fiber Spectroscopic Telescope

Size: px

Start display at page:

Download "Analysis and Optimization for a Focal Plane Mechanism of a Large Sky Area Multi-object Fiber Spectroscopic Telescope"

Horatio Ethelbert Beasley
5 years ago
Views:

1 Analysis and Optimization for a Focal Plane Mechanism of a Large Sky Area Multi-object Fiber Spectroscopic Telescope Abstract Guo-min Wang, Guo-ping Li, Xiang-qun Cui, Zheng-qiu Yao National Astronomical Observatories of Chinese Academy of Sciences Nanjing Institute of Astronomical Optics & Technology The Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST), a national major scientific project in the process of construction in China, is a special reflecting Schmidt telescope with 4- meter aperture and 5 field of view. There are three sub-assemblies: the reflecting Schmidt correcting plate, the focal plane mechanism and the spherical primary mirror. The focal plane mechanism is the assembly by which the physical information of the celestial bodies can be obtained from optical spectroscopies. The static and dynamic performance of the focal plane mechanism have a significant effect on the ability of the telescope to obtain the optical spectra of various celestial bodies. So, with the help of ANSYS, the optimization of the focal plane mechanism according to the static and dynamic characteristics requested by specifications is presented in this paper, along with the analysis of truss number, deformation in different compensation positions and contribution to the total deformation of each component. The results of study show that a feasible and reliable design scheme can be achieved. Introduction This paper describes the results of a finite element analysis in investigating of the focal plane mechanism of LAMOST using the finite element software ANSYS. The static flexures of the structure has a significant effect on the ability of the structure to sustain its precise position. According to Reference [2], the maximum deflection of focal plate, namely, the center of focal plate deflecting the optical axis, is 0.2mm, and the tilt angle caused by the supporting structures is less than 10. These specifications could be met by optimizing the supporting structure, such as the number and section properties of truss, the thickness of the steel plate, and so on. Another design feature that has been investigated in this paper is the dynamic performance of the focal plane mechanism. With a high structure natural frequency (and the associated wider servo bandwidth)the possibility of the structure being dynamically coupled to vibrations generated by the vibration source, such as wind loading, is reduced. A stiff structure will allow higher servo gain and higher acceleration rates giving faster setting times which will increase the efficiency of observing. According to Reference [2],the lowest eigenfequency of the whole mechanism is above 10H Z. Focal Plane Mechanism The focal plane mechanism is shown in Figure1. It consists of five major components: the focal plate, the trusses, the rotating axis, the frame and the base. The focal plate, 2 tons in weight including the fibers and 1.75m in diameter, is supported from the rotating axis by trusses. During the observation, the focal plate will rotate to compensate the rotation of the earth, and when observing different sky area, the focal plate should tilt for a small angle. The rotating axis is supported from frame by bearings and driving rollers which drive the rotating axis to move. The frame is connected to the stiff base which defines the location of the whole mechanism.

Figure 1 - The Focal Plane Mechanism Schematically Analysis and Optimization of Focal Plane Mechanism Finite Element Analysis Model With the help of ANSYS parametric design language, the finite

2 Figure 1 - The Focal Plane Mechanism Schematically Analysis and Optimization of Focal Plane Mechanism Finite Element Analysis Model With the help of ANSYS parametric design language, the finite element model of the focal plane mechanism has been developed in terms of parameters (variables). Approximately 4486 nodes and 5433 elements are used for the model, using solid45 to simulate the focal plate,drive disc,drive rollers and bearing base, using pipe16 to simulate the trusses and using shell63 to simulate the rotating axis and frame plates, and the element model is shown in Figure 2.

3 Figure 2 - The Finite Element Model Of Local Plane Mechanism Boundary conditions: the rotating axis is supported from the frame by bearings and drive rollers, so the connecting nodes between drive disc and drive rollers are coupled in radial direction, and the connecting nodes between rotating axis and bearing bracket are coupled in axial direction and radial direction. The boundary conditions are shown in Figure 2. Just as Figure 1 shows that the whole focal plane mechanism is supported from the base by three pedals which adjust the position of the focal plane to ensure its center coincides with the optical axis. So three transition degrees of freedom of the nodes connecting to the three pedals in the bottom plate of the frame are constrained. In order to investigate the graviational deformation, a 1.0g gravity field is applied to the finite element model with the whole focal plane mechanism tilting 25 from horizontal direction. Analysis of Truss Number On the basis of the above analysis of the focal plane mechanism, it should be noted that the trusses,supporting the focal plate whose weight is about 2 tons, will tilt under the weight loading of focal plate. This tilt will affect the focal plate position, and result in the deflection and tilt of focal plate. Changing the truss number has a pronounced effect on the deflection and tilt of the focal plate. During the calculation, the focal plate is assumed to be a rigid body because the self-deformation of focal plate due to its own weight has been calculated by others. For simplification, the field rotator is separated from the mechanism and other parameters are assumed to be constants. The element model(solid45, pipe16, shell63, shown in Figure 3, was run with different truss number. The results are given in Table 1.

Figure 3 - The Model for Truss Calculation Table 1 - Analysis of Truss Number truss number ρ max θ max (μm) ( ) 6 43.975 14.8453 8 32.092 9.3190 10 29.123 7.8083 12 28.108 7.174 14 28.3 6.9476 16 29.

4 Figure 3 - The Model for Truss Calculation Table 1 - Analysis of Truss Number truss number ρ max θ max (μm) ( ) ρ max deflection of focal plate θ max tilt angle of focal plate Figure 4 shows the curve of the variation of focal plate deflection ρ max and tilt angleθ max with the truss number. It is found that, at first, an increase in the truss number obviously results in a reduction in the deflection ρ max and tilt angleθ max, and then, with the increasing of the truss number, theρ max and θ max are increasing with the truss number. Here, the increasing of truss number has two effects. One is to increase the flexural stiffness of the structure. So the more truss number, the less deflection and tilt angle. On the other hand, with the increasing of truss number, the weight of the structure increases too. The increasing weight results in the increasing of deflection and tilt angle. As can be seen in Figure 4, the curves of the deflection and tilt angle versus the truss number has a minimum. The optimal number of truss is 10.

5 t r uss number Figure 4 - ρ max θ max Versus Truss Number Optimization of Structure Static and Dynamic Characteristics Design Variables (DVs) are independent quantities that are varied in order to achieve the optimum design. The design variables of the focal plane mechanism are given in Table 2 and illustrated in Figure 5. The upper and lower limits are specified to serve as "constraints" on the design variables. Table 2 - Optimization Design Variables DVs name range of variation(mm) memo t2 10~30 thickness of truss tube d2 80~120 outer diameter of truss t4 10~30 thickness of rotation axis tube l6 100~400 length of bearing base t81 10~120 thickness of top frame plate t82 40~120 thickness of lateral frame plate t83 20~120 thickness of middle frame plate t84 40~120 thickness of bottom frame plate top-l 100~800 length of square hole on top frame plate top-w 100~600 width of square hole on top frame plate mid-l 100~800 length of square hole on middle frame plate mid-w 100~1000 width of square hole on middle frame plate lat-l 100~800 length of square hole on lateral frame plate lat-w 100~1000 width of square hole on lateral frame plate

6 Figure 5 - Design Variables Illustration State Variables (SVs) are quantities that constrain the design. State variables are given in Table 3. Table 3 - Optimization State Variables SVs name max. and min. limit memo ρ max 0.02mm maximum deflection θ max 10 maximum tilt angle σ r4 240MPa maximum equivalent stress of whole structure fre1 10H Z first eigenfrequency

7 The total volume of the structure is defined as objective function. Comparing with defining the weight as objective function, defining total volume of the structure as objective function will save some computer time because the mass matrix is not calculated. The subproblem approximation method, described as an advanced zero-order method in that it requires only the values of the dependent variables, and not their derivatives, is used to optimize the parameters. At first, some feasible designs, satisfying all specified constrains on the SVs as well as constrains on the DVs, was generated using random design generation tool which performs 60 analysis loops using random design variable values for each loop, then based on the feasible designs the subproblem approximation method is used to optimize the parameters. The optimization results are given in Table 4. Besides, the initial solution is given in Table 4, too. Table 4 - Optimization Results initial solution optimized solution memo t2(mm) thickness of truss tube d2(mm) outer diameter of truss t4(mm) thickness of rotation axis tube l6(mm) length of bearing base t81(mm) thickness of top frame plate t82(mm) thickness of lateral frame plate t83(mm) thickness of middle frame plate t84(mm) thickness of bottom frame plate top-l(mm) length of square hole on top plate top-w(mm) width of square hole on top plate mid-l(mm) length of square hole on middle plate mid-w(mm) width of square hole on middle plate lat-l(mm) length of square hole on lateral plate lat-w(mm) width of square hole on lateral plate ρ max (μm) maximum deflection θ max ( ) maximum tilt angle σ r4 (MPa) maximum 4th equivalent stress fre1(h Z ) first eigenfrequency volume(m 3 ) total volume weight(t) total weight Comparing the optimized solution with the initial solution. it is clear that the initial solution can not meet all the specifications. Especially, through optimization, the dynamic performance of the structure is improved largely. The first eigenfrequency of the structure increased from 5.09H Z to 11.10H Z.

8 Analysis of Different compensating position Due to the rotation of the earth, the pointing and tracking of the telescope should be done by the rotation in altitude and azimuth of the Schmidt corrector, at the same time the focal plane should be rotated for certain angle to compensate the rotation of the field of view. So the deflection and tilt angle of focal plate are different with the focal plate in different positions. 360range is taken into account and from the position shown in Fig.2 every counter clockwise 27is a calculation position. The finite element model is shown in Fig. 2 and the calculation results are given in Table 5. Figure 6 and Figure7 respectively show the variation of deflection ρ max and tilt angleθ max with the different compensation positions. Table 5 - Deflection And Tilt Angle With Different Compensation Position ρ max (μm) θ max ( ) ρ max (μm) θ max ( ) Table 5 shows that the variation in deflection ρ max and titl angleθ max are little when the focal plate is in different compensation position. Good results are achieved; 0.856μm for deflection and for tilt angle. Figure 6 - Deflection Versus Different Compensation Position

9 Figure 7 - Tilt Angle Versus Different Compensation Position Contribution to Total Deformation from Components The focal plane mechanism mainly consists of focal plate, trusses, rotating axis, bearing base and frame. The role each part played to the total deformation is different. The focal plate is assumed to be a rigid plate, so it has no effect on the total deformation. The deflection and tilt angle arose from each components are investigated and the results are given in Table 6. Table 6 - Contribution To Total Deformation From Substruction substruction name deflection (μm) contribution (%) tilt angle ( ) contribution (%) truss rotating axis bearing base frame total The results in Table 6 show that the role of each part played in the whole deformation are different. The truss, rotating axis and bearing base make the focal plate deflect down and tilt clockwise, while the frame makes the focal plate uplift and tilt count clockwise. So some of the deformation caused by the truss and rotating axis are offset by the deformation caused by the frame. The frame plays an important role in the focal plane mechanism deformation. Investigation of the Mechanism Eigenfrequency The 1st~10th eigenfrequency of the focal plane mechanism are calculated with the design parameters optimized above and the results are given in Table 7. The first four eigenmodes are shown in Figure 8.

Table 7 - First 10 Eigenfrequency Of Mechanism 1 2 3 4 5 eigenfrequency(h Z ) 11.065 16.473 22.477 32.163 36.643 6 7 8 9 10 eigenfrequency(h Z ) 44.

10 Table 7 - First 10 Eigenfrequency Of Mechanism eigenfrequency(h Z ) eigenfrequency(h Z ) Lateral mode H Z Fore-aft mode H Z Torsion mode H Z Lateral mode H Z Figure 8 - First Four Eigenmodes

11 Conclusions The work described here has shown the following: Through optimization, a feasible and reliable design set, meeting all specified static and dynamic characteristics, can be achieved. The lowest eigenfrequencies of local plane mechanism are: (a) the lateral mode of the local plane mechanism, H Z. (b) the fore-aft mode of the local plane mechanism, H Z. (c) the torsional mode of the local plane mechanism, H Z. Because the gravity-deformation of focal plate is calculated respectively by others, the total deformation should be the sum of the deformation calculated in this paper and the focal plate gravity-deformation. The variation in deflection ρ max and titl angleθ max are small when the focal plate is in different compensation position during a full circle. The variation in deflection is 0.856μm and the variation in tilt angle is only The contributions of each component of the mechanism to the total deflection and tilt angle are different. The contribution of truss, rotating axis, bearing base and frame to the total deformation are about 24%, 18%, 3% and 55% respectively. The contribution of truss, rotating axis, bearing base and frame to the total tilt angle are about 17%, 21%, 2% and 60% respectively. That is to say, the frame plays an important role in the focal plane mechanism deformation. References [1]Shou-guan Wang, Ding-qiang Su, Yao-quan Chu, Xiang-qun Cui and Ya-nan Wang, Special configuration of a very large Schmidt telescope for extensive astronomical spectroscopic observation, Applied Optics, Vol. 35, No.25, , 1996 [ 2 ] Guo-ping Li, Focal plane structure, focus control and image plane rotation and compensatory system, LAMOST Technology Report, [3]SAS IP, Inc., ANSYS User's manual for Revision 5.0 Volume Ⅲ Procedures, 1992 [4]SAS IP, Inc., ANSYS Theory Reference, Seventh Edition. [5]K. Raybould, Finite Element Analysis of the UKLT Structure, Oxford Project Team, 11 April 90 [6]Keith Raybould, Paul Gillett, Peter Hatton, Gordon Pentland, Mike Sheehan, Mark Warner, Gemini Telescope Structure Design, 376/SPIE Vol.2199 [7]Xin-he Zhen, Mechanical Optimization Design, Southeast University, [8]Zheng-qiu Yao, Guo-ping Li, The Tracking System of LAMOST Telescope, SPIE, 1998

Wind Vibration Analysis Giant Magellan Telescope

Wind Vibration Analysis Giant Magellan Telescope prepared for Carnegie Observatories 813 Santa Barbara Street Pasadena, CA 91101 prepared by Simpson Gumpertz & Heger Inc. 41 Seyon Street, Building 1, Suite