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Bonding Effect Analysis of the Primary Mirror of an Experimental Telescope with Reverse Engineering of Finite Element Method
Yi-Kai Huang1 and Po-Hsuan Huang2
1 Research Assistant, 2 Principal Engineer, System Engineering Division,National Space Organization, National Applied Research Laboratories, 8F, 9 Prosperity 1st Road, Hsinchu Science Park, Hsinchu, Taiwan
A. AbstractIn this paper, a reverse engineering method was adopt to the finite element and wavefront error analysis of theprimary mirror of a small space telescope experimental model. The experimental space telescope with 280mmdiameter primary mirror has been assembled and aligned in 2011, but the measured system optical performanceand wavefront error did not achieve the goal.In order to find out the root causes, static structure finite element analysis (FEA) has been applied to analyze thestructure model of the primary mirror assembly. We established the corresponding model and boundarycondition setup for several assuming effects which may cause deformation of the primary mirror have beenproposed, such as gravity effect, adhesive effect, flexures bonding effect, thermal expansion effect, etc.Now a new assumption of the flexures bonding effect is proposed, and we adopt reverse engineering to verifythis effect. Besides, the numerical wavefront error and Zernike polynomials will be calculated by opto‐mechanicalanalysis software.
B. System Architecture
Types of Telescopes Ritchey‐Chrétien Cassegrain
Effective Focal Length 1400 mm
Diameter of Primary Mirror 280 mm
Materials
Mirror (M1 & M2) Zerodur®
Iso‐Static Mount (ISM) 304 Stainless Steel
Main Plate Aluminum Alloy
M2 Supporting Ring Aluminum Alloy
Struts Carbon‐Fiber‐Reinforced Polymer
Table 1. System architecture of ExM100 telescope
Figure 1. System architecture of ExM100 telescope.
System architecture of M1 Assembly:The supporting system of primary mirror during ISM bonding is illustrated in Figure 2(a). Before three ISMs werebonded to the primary mirror, the mirror was supported by three metallic hemisphere supporting structuresfrom backside as shown in Figure 2(b). Then, three metallic hemisphere supporting structures would be releasedfrom the primary mirror after finishing ISM bonding procedure.
Figure 2. Supporting system of ExM100 primary mirror during ISM bonding. (a) Supporting system architecture (b) Hemisphere supporting structure
C. Finite Element Analysis with Reverse Engineering 1. Reverse Engineering Method Process:
Figure 3. Reverse engineering method flow chart.
Figure 4. CAD model of primary mirror with adhesive, ISM and supporting system.(a) Stage 1 (b) Stage 2
Figure 5. Deformation of primary mirror with gravity effect along Z‐axis.(a) Isometric view (b) Bottom view
Figure 6. Deformation of primary mirror (a) Deformed CAD Model from FEA 1 (b) Gravity effect along ‐Y‐axis.
3. FEA 2: Gravity Effect Along ‐Y‐axis with Three ISMs Support
Figure 7. WFE map of primary mirror surface with gravity effect along ‐Y‐axis.(a) Analyzed WFE map of primary mirror (b) Measured WFE map of primary mirror
Term Aberration Name Analyzed WFE Measured WFEPV 2.11E‐01 1.55E‐00 RMS 5.05E‐02 2.86E‐01
4 Astigmatism‐x ‐1.07E‐01 5.20E‐01 6 Astigmatism‐y ‐1.00E‐05 ‐2.83E‐02 7 Trefoil‐x ‐1.00E‐05 2.10E‐02 8 Coma‐x ‐1.00E‐05 1.09E‐01 9 Coma‐y ‐1.06E‐02 ‐7.51E‐02 10 Trefoil‐y 1.00E‐05 3.19E‐01 11 Tetrafoil‐x ‐3.00E‐03 ‐4.08E‐0212 Astigmatism‐x ‐1.48E‐02 1.23E‐01
Unit: λ (λ=632.8 nm)
Table 1. Zernike polynomials of primary mirror surface with gravity effect along ‐Y‐axis.
D. Optical Analsys of WFE map of primary mirrorFigure 7(a) shows the analyzed WFE map of primary mirror which was caused by the superposition of gravityeffect along Z‐axis and ‐Y‐axis. Figure 7(b) shows the measured WFE map of primary mirror. The measured WFEPVis 1.55 λ and the WFERMS is 0.29 λ (λ=632.8 nm), respectively.
Supporting Pad Supporting Pad
Adhesive Adhesive
(a) (b)
ISM
2. FEA 1: Gravity Effect Along Z‐axis with Three Points Support
(a) (b)
(a) (b)
E. ConclusionAccording to the Zernike polynomials value of Table 1, both of the analyzed and measured result obtain primaryaberration such as Astigmatism‐x, Coma‐y, and Tetrafoil‐x. However, the analyzed result of reverse engineeringmethod presents quite different pattern from the measured WFE map because of term 10 trefoil‐y. Which means,there could be other reasons cause the trefoil‐y aberration.In conclusion, the new assumption of the flexures bonding effect is reasonable according to the similaritybetween measured WFE and analyzed WFE. Despite this, in order to improve the simulation accuracy, theshrinkage of structural adhesive should be considered. Therefore, the method of structural adhesive analysisshould be refined in our future work.
M1
M2
Mainplate
ISM
Adhesive
ISM