Thermal Stability Design of Asymmetric Support Structure for an Off-Axis Space Camera

applied sciences

Case Report Thermal Stability Design of Asymmetric Support Structure for an Off-Axis Space Camera

Weiyang Song 1,2,3, Peng Xie 1,3,*, Shuai Liu 1,3 and Yunqiang Xie 1,2,3

1 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; [email protected] (W.S.); [email protected] (S.L.); [email protected] (Y.X.) 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Key Laboratory of Space-Based Dynamic & Rapid Optical Imaging Technology, Chinese Academy of Sciences, Changchun 130033, China * Correspondence: [email protected]

Abstract: With the development of space optical remote sensing technology, especially off-axis space cameras, the thermal dimensional stability of the support structure has become increasingly demanding. However, the asymmetry of the camera structure has not been fully considered in the past design of the thermal stability of off-axis cameras. In order to solve this problem, a support structure with very low thermal deformation in the asymmetric direction is presented in this paper for an off-axis TMA camera. By means of the negative axial thermal expansion coefficient of carbon- fiber-reinforced plastics (CFRP), a composite laminate with near zero-expansion was obtained by adjusting the direction of fiber laying, and the asymmetric feature of the off-axis remote sensing camera structure was fully considered, thus enabling the support structure to have good thermal dimensional stability. We carried out a thermal load analysis and an optical analysis of the whole camera in the case of a temperature rise of 5 ◦C. The results show that the zero-expansion support Citation: Song, W.; Xie, P.; Liu, S.; Xie, Y. Thermal Stability Design of structure has good thermal stability, and the thermal deformation in the asymmetric direction of the Asymmetric Support Structure for an camera is obviously smaller than that of the isotropic laminate support structure. Compared with the Off-Axis Space Camera. Appl. Sci. isotropic support structure, the influence of thermal deformation on MTF is reduced from 10.43% to 2021, 11, 5184. https://doi.org/ 2.61%. This study innovatively incorporates the asymmetry of the structure into the thermal sta-bility 10.3390/app11115184 design of an off-axis TMA camera and provides a reference for the thermal stability design of other off-axis space cameras. Academic Editor: Theodore E. Matikas Keywords: remote sensing; thermal deformation; CFRP; asymmetric structure

Received: 30 April 2021 Accepted: 28 May 2021 Published: 3 June 2021 1. Introduction In recent years, space remote sensing technology has played an increasingly im- Publisher’s Note: MDPI stays neutral portant role in military and civil high-tech fields, and more and more precision support with regard to jurisdictional claims in published maps and institutional affil- structures are required for the new generation of space remote sensors. However, when iations. the remote sensing camera moves around the earth, due to the influence of external heat flux, such as solar radiation, the earth’s reflection of sunlight and infrared radiation, the camera experiences complex periodic temperature changes. The thermal deformation of the remote sensing camera structure reduces the position accuracy of the optical elements and causes them to deviate from the ideal position. In order to reduce the influence of Copyright: © 2021 by the authors. the thermal load on the imaging quality of the remote sensing camera, the thermal dimen- Licensee MDPI, Basel, Switzerland. sional stability of the structure should be fully considered in the design of the camera This article is an open access article distributed under the terms and support structures [1–4]. conditions of the Creative Commons Reflective space remote sensors, including coaxial and off-axis remote sensors, are Attribution (CC BY) license (https:// commonly used due to their large aperture, high resolution and lightweight design. A creativecommons.org/licenses/by/ concentric remote sensor structure is centrally symmetrical with respect to the optical 4.0/). axis. In the thermal stability design of a coaxial remote camera, only the spacing changes

Appl. Sci. 2021, 11, 5184. https://doi.org/10.3390/app11115184 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 5184 2 of 14

of optical components along the optical axis caused by thermal deformation need to be considered due to the system’s symmetry [5,6]. The off-axis reflective optical system is widely used in space remote sensing camera because of its advantages of a larger field of view and the lack of central occlusion [7,8]. However, the off-axis remote sensing camera has an obvious asymmetrical structure, and its reflector exhibits a relative displacement in many directions when it is subjected to a temperature load. Therefore, the thermal stabil-ity design of off-axis cameras needs to reduce the thermal deformation in multiple direc-tions at the same time, which makes the design more difficult [9]. Carbon-fiber-reinforced plastics (CFRPs) have excellent mechanical properties, such as high stiffness, high strength and low coefficient of thermal expansion (CTE), and are considered to be the next generation of aerospace application materials [10–13]. In recent years, structural thermal stability has increasingly been accomplished through the use of carbon-fiber-reinforced composites. Jen Chueh Kuo made a low expansion truss support structure with carbon-fiber-reinforced materials for FORMOSAT-5 remote sensing [14]; Yuan Qian copied a prototype carbon-fiber-reinforced plastics (CFRP) panel for a 5-m Dome A Terahertz Explorer antenna using resin-rich layer technology [15]. Yoshinori Suematsu used cyanate ester carbon fiber composite to construct the supporting structure of a solar telescope [16]. In addition, researchers have paid attention to thermal character-istics in the design of carbon fiber materials. By adjusting the angle and sequence of the carbon fiber layer, the coefficient of thermal expansion of the CFRP structure can be ad-justed, even close to zero thermal expansion [17]. Shun Tanaka researched the effect of the angle error of carbon fiber ply on the coefficient of thermal expansion [18]. Zhengchun Du manufactured carbon fiber truss bars with an extremely low coefficient of axial thermal expansion through the adjustment of the carbon fiber ply angle [19]. Lin Yang quantita-tively studied the axial thermal expansion coefficient of the carbon fiber rod through the CTE function, and demonstrated passive thermal compensation for an off-axis space cam-era in the optical axis direction [20]. However, in these studies, the thermal stability design was only committed to ensuring the position accuracy of the structure along a certain main direction under the thermal load, which is scarcely sufficient to meet the thermal stability requirements of the asymmetric support structure in an off-axis remote sensing camera. In this sutdy, we solved the problem of how to use carbon-fiber-reinforced compo-sites to reduce the thermal deformation of an asymmetric structure in an off-axis remote sensing camera. By adjusting the angle of the carbon-fiber-reinforced polymer (CFRP) laminate, we were able to design a type of composite laminate with extremely low thermal expansion, which was applied to the support structure design of an off-axis space remote sensing camera, and the thermal stability of the support structure in the asymmetric di-rection was thus realized. Finally, the effectiveness of the thermal stability design for an off-axis camera was verified using finite element thermal deformation analysis and optical analysis.

2. Low Thermal Deformation Optical Mechanical Structure 2.1. The Remote Sensing Camera A typical off-axis three-mirror optical system is used in the remote sensing camera. The optical system consists of three mirrors. The primary mirror and third mirror are as-pherical mirrors, and the secondary mirror is a spherical mirror. The distance between the primary mirror and the secondary mirror is 297 mm. The optical system diagram of the space camera is shown in Figure1. Appl.Appl. Sci. Sci. 20212021, ,1111,, x 5184 FOR PEER REVIEW 3 of 14 3 of 14

Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 14

FigureFigureFigure 1. 1. TMA TMA1. TMA optical optical optical system. system. system.

ForForFor our our ourpurposes, purposes, purposes, the the basic basicthe structure basic structure structure of the of theremote remoteof thesensing sensingremote camera camerasensing system system cameracan be can system be can be simply divided into the main support structure and optical components, as shown in Fig- simplysimply divided divided into into the the main main support support structure structure and opticaland optical components, components, as shown as shown in in Fig- ureFigure 2. The2. Themain main support support structure structure is composed is composed of frames of and frames the bearing and the cylinder bearing made cylinder ure 2. The main support structure is composed of frames and the bearing cylinder made ofmade CFRP. of The CFRP. optical The component optical component comprises comprises the reflectors, the reﬂectors, metal plates metal and plates the metal and con- the metal nectorscon-nectorsof CFRP. between The between the optical plate the and platecomponent the and frame. the frame.comprises the reflectors, metal plates and the metal con- nectors between the plate and the frame.

Figure 2. Support structure for the off-axis TMA camera. Figure 2. Support structure for the off-axis TMA camera. In the working process of the remote sensing camera in orbit, the periodic change of temperatureIn the working inevitably process of causes the remote serious sensing deformation camera ofin orbit, the mirror. the periodic The deformation change of not temperature inevitably causes serious deformation of the mirror. The deformation not only comes from the expansion deformation caused by the thermal load, but also from the only comes from the expansion deformation caused by the thermal load, but also from the thermalFigure stress2. Support between structure the support for the structure off-axis TMA and the camera. body of the mirrors. Therefore, the thermal stress between the support structure and the body of the mirrors. Therefore, the final thermal deformation control of the mirror should be realized in two aspects: final thermal deformation control of the mirror should be realized in two aspects: • TheIn surfacethe working deformation process of reflectorsof the remote caused sensing by thermal camera stress: in Thermalorbit, the stress periodic will change of  The surface deformation of reflectors caused by thermal stress: Thermal stress will temperatureinevitablyinevitably occur occurinevitably when when different differentcauses materials serious materials are deformation arejoined joined together, together, of whichthe whichmirror. ultimately ultimately The re- deformation re- not onlyducesduces comes the the accuracy from accuracy the of ofexpansionthe the mirror mirror surface. deformation surface. In this In thiscase, caused case, it is itbyimportant is the important thermal to ensure to load, ensure that but that also from the thermalthethe reflector reflector stress body bodybetween matches matches the the support the thermal thermal expansionstructure expansion coefficient and coefficient the bodyof the of ofmounted the the mounted mirrors. back- back- Therefore, the finalplate.plate. thermal Studies Studies deformation have have shown shown that control that the the combination combinationof the mirror of a ofZerodure should a Zerodure reflector be realized reflector and an andin Invar two an Invaraspects: backplatebackplate is iseffective, effective, enabling enabling remote remote sensing sensing cameras cameras to maintain to maintain good surface good ac- surface  curacyac-curacyThe in surface periodically in periodically deformation changing changing temperatures of reflectors temperatures [21–23]. caused [21 –23 by]. thermal stress: Thermal stress will • RigidRigidinevitably body body displacement displacement occur when of ofthe different the reflectors: reflectors: materials This This means means are that joined thatappropriate appropriate together, technology technologywhich ultimately re- shouldshouldduces be be usedthe used accuracy to tominimize minimize of the the the thermal mirror thermal expansion surface. expansion of In the ofthis support the case, support structure. it is structure. important There- There- to ensure that fore,fore,the the the reflector components components body with with matches zero zero or ornear-zero the near-zero thermal CTE CTE are expansion preferable, are preferable, coefficient in order in order to achieve of to the achieve mounted back- lowlow thermal thermal deformation, deformation, for for example, example, in the in thesupporting supporting frame frame and central and central bearing bearing plate. Studies have shown that the combination of a Zerodure reflector and an Invar cylinder.cylinder. It Itis isdifficult difficult to toreduce reduce the theactual actual thermal thermal deformation deformation to zero to in zero every in everydi- di- rection,rection,backplate and and the the is thermal effective, thermal expansion expansion enabling deformation deformation remote is sensing smaller is smaller in cameras the in direction the directionto maintain with good with good good surface ac- symmetry,symmetry,curacy soin so weperiodically we need need to tostrictly strictly changing control control thetemperatures thethermal thermal deformation deformation [21–23]. in the in asymmetric the asymmetric  direction.Rigid body This methoddisplacement can reduce of the the actualreflectors: rigid This body means displacement that appropriate of the optical technology should be used to minimize the thermal expansion of the support structure. There- fore, the components with zero or near-zero CTE are preferable, in order to achieve low thermal deformation, for example, in the supporting frame and central bearing cylinder. It is difficult to reduce the actual thermal deformation to zero in every direction, and the thermal expansion deformation is smaller in the direction with good symmetry, so we need to strictly control the thermal deformation in the asymmetric Appl. Sci. 2021, 11, 5184 4 of 14

module and obtain the optimal thermal stability of the structure in the periodic temperature environment. In the following sections, we will discuss how to use CFRP materials to design a support structure with low CTE, so as to realize the extremely low thermal deformation of the optomechanical structure for the off-axis remote sensing camera.

2.2. Design Theory of Zero-Thermal-Expansion Material The support structure of a remote sensing camera is traditionally made of aluminum alloy or titanium alloy. However, the requirements in this field are to significantly reduce the weight of the camera, improve its stiffness and enhance its environmental adaptability. The technology of using carbon-fiber-reinforced plastics (CFRP) has been developed and successfully applied in various remote sensing camera structures, because it has excellent specific stiffness, specific strength and low CTE. We choose CFRP to construct a support structure with near zero thermal expansion, so as to realize the low thermal expansion support structure design of the remote sensing camera. The basic design theory of the single- and multi-layer thermal expansion of various composite components is introduced in [24]. For the single-layer composite, the stress–strain relationship caused by temperature is as follows: {σ} = [Q]({ε} − {α}∆t) (1) where {σ} is temperature-induced stress, [Q] is the stiffness matrix describing the relationship between stress and strain, {ε} is the strain of the composite, {α} is the coefficient of thermal expansion and ∆t is the temperature change. According to the classical theory of composite laminates, the stress–strain relation-ship can be expressed as: N AB ε Nt = − (2) M BD κ Mt where [A], [B] and [D] are the tension compression stiffness matrix, coupling stiffness matrix and bending stiffness matrix, respectively and {Nt} and {Mt} are the internal stress matrix and internal bending moment matrix caused by temperature load, respectively. In engineering applications, laminated composites are usually designed with symmetrical folding to avoid torsion due to temperature changes [25]. For multi-layer composite structures with symmetrical layers, the coupling stiffness matrix is zero, and the ma-terial thermal deformation can be expressed as:

n Z Z t k {N } = ∑ [Qk]{αk}∆tdz (3) k=1 Zk−1

For multilayer symmetrical laminates, the coefﬁcient of thermal expansion along the center layer can be expressed as:

− n ! 1 n ! −1 {αc} = ∑ [Q]k ∑ [T]k {[Q][α]} (4) k=1 k=1

Carbon-fiber-reinforced plastics (CFRP) not only have a very low linear thermal expansion coefficient, but also have a negative axial linear thermal expansion coefficient. Therefore, composites with a thermal expansion coefficient of zero can be obtained by utilizing these characteristics.

2.3. Design of Zero-Expansion Laminated Plates The support structure consists of frames and a bearing cylinder, and its basic structure is a CFRP laminated plane. Therefore, the thermal stability of the support structure Appl. Sci. 2021, 11, 5184 5 of 14 is closely related to the CTE of the CFRP laminates. The CFRP laminates are made of carbon fiber and adhesive resin in a certain proportion. The CTE of CFRP laminates is deter- mined by the properties and proportions of the carbon fiber and adhesive resin [13]. Cy- anatecar-bon esters fiber are andwidely adhesive used in resin CFRP in design a certain due proportion. to their low The coefficient CTE of CFRP of thermal laminates expan- is siondeter-mined [26]. In this by paper, the properties M40/cyanate and proportions ester unidirectional of the carbon prepreg fiber is and used adhesive as the resinbasic [ma-13]. terialCy-anate of the support esters are structure, widely used and inthe CFRP basic designproperties due of to the their material low coefficient are shown of thermalin Table 1. expan-sion [26]. In this paper, M40/cyanate ester unidirectional prepreg is used as the basic ma-terial of the support structure, and the basic properties of the material are shown Tablein Table 1. Mechanical1. parameters of M40/cyanate.

Table 1. MechanicalBasic Properties parameters of M40/Cyanate of M40/cyanate. Parameter Values Coefficient of thermal expansion in 0° direction −0.17 × 10−6/°C Basic Properties of M40/Cyanate Parameter Values Coefficient of thermal expansion in 90° direction 28.5 × 10−6/°C Coefficient of thermal expansion in 0◦ direction −0.17 × 10−6/◦C CoefficientElastic of thermal Module expansion in 0° direction in 90◦ direction 28.5 ×20010− 6GPa/◦C ElasticElastic Module in in 0 ◦90°direction direction 200 GPa7 GPa Elastic ModulePoisson in 90 ratio◦ direction 7 GPa 0.3 Poisson ratio 0.3 Considering the formability of the material and the design principle of composite laminates,Considering three layering the formability methods are of thechosen material for this and kind the of design material principle in order of compositeto achieve zerolaminates, expansion: three layering methods are chosen for this kind of material in order to achieve 1. zero±θ/0°/90°; expansion: ◦ ◦ 2. 1. ±θ/0°/±θ/0∓θ;/90 ; ◦ 3. 2. ±θ/90°/±θ/0∓θ./ ∓θ; 3. ±θ/90◦/∓θ. The definition of the fold angle for the laminated plate is shown in Figure 3. The definition of the fold angle for the laminated plate is shown in Figure3.

Figure 3. Plying angle definition of the plane. Figure 3. Plying angle definition of the plane. For the three different types of laying angles presented above, the relationship be- tweenFor the three thermal different expansion types coefficient of laying and angles the layingpresented angle above, can be the calculated. relationship When be- tweenus-ing the± thermalθ/0◦/90 expansion◦ in the laying coefficient scheme, and the the relationship laying angle between can be the calculated. thermal expansion When us- ingcoef-ficient ±θ/0°/90° in and the the laying folding scheme, angle ofthe multi-layer relationship composites between the was thermal calculated. expansion The calcula- coef- ficienttion resultsand the are folding shown angle in Figure of multi-layer4a. Similarly, composites the thermal was expansion calculated. coefficients The calculation of the resultscom-posite are shown laminates in Figure at the 4a. other Similarly, two folding the thermal angles expansion were calculated, coefficients and are of shown the com- in Figure4b,c. posite laminates at the other two folding angles were calculated, and are shown in Figure◦ 4b,c. It can be easily observed in Figure4 and Table2 that the theoretical CTE in the 0 direction is 0.383 × 10−6/◦C when the laying angle is ±20◦/0◦/90◦. When the laying angle is ±50◦/0◦/∓50◦, the theoretical CTE in the 0◦ direction is 0.168 × 10−6/◦C. Both of the two plies can meet the requirements of low thermal expansion coefficients. Appl. Sci. 2021, 11, 5184 6 of 14 Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 14

(a)

(b)

(c)

FigureFigure 4. 4.The The relationship relationship between between the the CTE CTE and and ply ply angel angel of of M40 M40 composite composite material material with with respect respect to ∓ ∓ theto plyingthe plying style: style: (a) ±(aθ) /0±θ/0°/90°,◦/90◦,( b(b) )± ±θ/0°/θ/0◦/∓θ,θ (,(c)c ±θ/90°/) ±θ/90θ.◦/ ∓θ. Appl. Sci. 2021, 11, 5184 7 of 14

Table 2. Coefﬁcient of thermal expansion with respect to different plying angle under 3 kinds of plying styles (×10−6/◦C).

±θ/0◦/90◦ ±θ/0◦/∓θ ±θ/90◦/∓θ Ply Angle θ 0◦ 90◦ 0◦ 90◦ 0◦ 90◦ 0◦ 0.417 2.804 −0.170 28.500 0.586 1.965 5◦ 0.413 2.786 −0.299 28.299 0.588 1.944 10◦ 0.401 2.729 −0.670 27.568 0.595 1.879 15◦ 0.388 2.630 −1.215 25.967 0.620 1.767 20◦ 0.383 2.482 −1.782 23.116 0.679 1.600 25◦ 0.402 2.279 −2.143 18.980 0.808 1.371 30◦ 0.465 2.021 −2.120 14.182 1.065 1.065 35◦ 0.591 1.716 −1.717 9.709 1.547 0.668 40◦ 0.792 1.386 −1.096 6.236 2.407 0.168 45◦ 1.065 1.065 −0.433 3.875 3.875 −0.433 50◦ 1.386 0.792 0.168 2.407 6.235 −1.096 55◦ 1.716 0.591 0.668 1.547 9.709 −1.717 60◦ 2.021 0.465 1.065 1.065 14.182 −2.120 65◦ 2.280 0.402 1.371 0.808 18.980 −2.143 70◦ 2.482 0.383 1.601 0.679 23.116 −1.782 75◦ 2.630 0.388 1.767 0.620 25.967 −1.215 80◦ 2.730 0.401 1.879 0.595 27.568 −0.670 85◦ 2.786 0.413 1.944 0.588 28.299 −0.299 90◦ 2.804 0.417 1.965 0.586 28.500 −0.17

In the practical application of the off-axis remote sensor considered in this paper, the elastic modulus is also an important parameter, which must be carefully considered in the practical application of composite materials. The elastic moduli corresponding to the above two plies are shown in Table3. Considering the elastic modulus requirements, we chose ±20◦/0◦/90◦ as the best practical winding angle for the CFRP plane structure. In this case, the maximum stiffness of the laminate can be obtained while meeting the CTE re-quirements.

Table 3. The elastic modulus of the plane in two main directions.

Equivalent Elastic Modulus Equivalent Elastic Modulus Ply in 0◦ Direction (GPa) in 90◦ Direction (GPa) ±20◦/0◦/90◦ 128.79 56.01 ±50◦/0◦/∓50◦ 74.58 41.37

3. Design of Support Structure with Low Expansion Coefﬁcient CFRP is widely used in the design of space camera structure because of its good per-formance, such as its light weight, high rigidity and low thermal expansion [13,18,22]. Based on the above calculations and discussion, a support structure made of M40 carbon ﬁber composite for the remote sensing camera was designed and developed. The supporting structure consists of front frame, rear frame and central bearing cylinder, as shown in Figure5. The camera support structure needs to have high stiffness, strength and low weight to ensure that the remote sensing camera has good mechanical properties. By optimizing the mechanical properties of the whole structure of the camera, the optimal size of the supporting structure of each part can be obtained. After optimization, the thickness of front and rear frames is 4 mm and the thickness of center bearing cylinder is 1.5 mm. For this kind of structure, the common design method is to use isotropic ply to ensure the consistency of the structure in all directions. However, the thermal stability of the sup-port structure of the remote sensor is not considered in the isotropic stacking mode, and the thermal deformation in the direction of structural asymmetry will especially affect Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 14

supporting structure of each part can be obtained. After optimization, the thickness of front and rear frames is 4 mm and the thickness of center bearing cylinder is 1.5 mm. Appl. Sci. 2021, 11, x FOR PEER REVIEW For this kind of structure, the common design method is to use isotropic ply 8 ofto 14ensure

the consistency of the structure in all directions. However, the thermal stability of the support structure of the remote sensor is not considered in the isotropic stacking mode, and thesupporting thermal deformationstructure of each in the part direction can be ofobtained. structural After asymmetry optimization, will the especially thickness affect of the imagingfront and quality. rear frames According is 4 mm to and the the existing thickness optical of center element bearing layout cylinder and form is 1.5 ofmm. the support structure,For this the kind remote of structure, sensor structure the common has design good methodsymmetry is to in use the isotropic X direction, ply to ensureso we need tothe strictly consistency control of the the thermal structure expansion in all directions. deformation However, of thethe thermal structure stability in the of Y theand sup- Z asym- Appl. Sci. 2021, 11, 5184 8 of 14 metricport structure directions. of the remote sensor is not considered in the isotropic stacking mode, and the thermal deformation in the direction of structural asymmetry will especially affect the imaging quality. According to the existing optical element layout and form of the support thestructure, imaging the quality. remote According sensor structure to the existing has good optical symmetry element layout in the and X direction, form of the so we need supportto strictly structure, control the the remote thermal sensor expansion structure hasdeformation good symmetry of the in structure the X direction, in the so Ywe and Z asym- need to strictly control the thermal expansion deformation of the structure in the Y and Z metric directions. asym-metric directions.

Figure 5. Support structure made of carbon-fiber-reinforced plastic.

3.1. Design of The Support Frames Figure 5. Support structure made of carbon-fiber-reinforced plastic. FigureThe 5. frontSupport and structure rear framesmade of carbon-fiber-reinforcedin the support structure plastic. are directly in contact with the reflector3.1. Design assembly. of The Support According Frames to the layout of the optical elements and the supporting structure,3.1. DesignThe front the of andthermalThe rearSupport frames expansion Frames in the of support the frame structure structure are directly has ina decisive contact with effect the on the thermal reflectorThe assembly. front and According rear frames to the in layout the support of the optical structure elements are anddirectly the supporting in contact with the displacementstructure, the thermal of the expansion mirror assembly of the frame in structure the Y hasdirection. a decisive Therefore, effect on the we thermal need to design the plydisplacementreflector angle toassembly. minimize of the mirror According the assembly thermal to in the theexpansion layout Y direction. of coefficient the Therefore, optical of weelements the need front to designand and the therear supporting frames in the Yply structure,direction. angle to the minimize thermal the expansion thermal expansion of the frame coefficient structure of the fronthas a and decisive rear frames effect in on the the thermal Ydisplacement direction.In Section of 2.3, the we mirror have assembly already in obtained the Y direction. the zero-expansion Therefore, we pavingneed to designscheme. the Based ply angleIn Section to minimize 2.3, we have the already thermal obtained expansion the zero-expansion coefficient of paving the front scheme. and Based rear frames on in the on the calculation in Table 2, we selected◦ ◦ ◦ ±20°/0°/90° laying method, winding the front theY direction. calculation in Table2, we selected ±20 /0 /90 laying method, winding the front and and rear frames, where◦ 0° is in the same direction as that of +Y, as shown in Figure 6. rear frames,In Section where 2.3, 0 iswe in have the same already direction obtained as that ofthe +Y, zero-expansion as shown in Figure paving6. scheme. Based on the calculation in Table 2, we selected ±20°/0°/90° laying method, winding the front and rear frames, where 0° is in the same direction as that of +Y, as shown in Figure 6.

FigureFigure 6. DeﬁnitionDefinition of plyof ply angle angle in support in support frames. frames. Figure 6. Definition of ply angle in support frames. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 14

Appl. Sci. 2021, 11, 5184 9 of 14 3.2. Design of Bearing Cylinder As the structure connecting the front and rear frames, the composite bearing cylinder has3.2. a Design great of influence Bearing Cylinder on the distance change of the optical elements in the Z direction. Therefore,As the it structure is necessary connecting to minimize the front and the rear thermal frames, theexpansion composite coefficient bearing cylinder of the bearing cyl- has a great inﬂuence on the distance change of the optical elements in the Z direction. inderTherefore, in the it isZ necessarydirection to through minimize the the design thermal of expansion the ply coefﬁcientangle. of the bearing cyl-inderWe chose in the Zthe direction ±20°/0°/90° through laying the design method of the in ply the angle. winding of the bearing cylinder, where the 0°We direction chose the is± 20the◦/0 same◦/90◦ layingas that method of +Z, in as the shown winding in of theFigure bearing 7. The cylinder, designed bearing ◦ cylinderwhere the can 0 direction reduce is the the samechange as that in ofthe +Z, distance as shown inbetween Figure7. Thethe designed secondary bearing mirror and other cylinder can reduce the change in the distance between the secondary mirror and other mirrorsmirrors whenwhen the the temperature temperature changes. changes.

Figure 7. Deﬁnition of ply angle in the load-bearing cylinder. Figure 7. Definition of ply angle in the load-bearing cylinder. So far, we have completed the thermal stability design of the off-axis camera support structureSo far, through we have the selection completed of composite the thermal layers. stability The obtained design support of the structure off-axis has camera support structurevery low CTEthrough in the Ythe and selection Z directions. of composite layers. The obtained support structure has very4. Finite low Element CTE in Analysis the Y and of the Z directions. Support Structure We obtained the low-CTE design of the off-axis remote sensing camera structure in 4.the Finite asymmetric Element direction Analysis by adjusting of the the Support CFRP ply Structure angle. In order to verify the thermal stability of the designed support structure, we take the whole space remote sensing cam-era as theWe analysis obtained object the to calculate low-CTE the thermaldesign deformationof the off-axis of the remote support structure.sensing camera structure in the asymmetric direction by adjusting the CFRP ply angle. In order to verify the thermal stability4.1. The Establishment of the designed of Finite support Element Model structure, we take the whole space remote sensing camera asWe the established analysis theobject ﬁnite to element calculate model the ofthermal the camera deformation as shown in of Figure the support8. In structure. order to reduce the joint stress between different materials caused by thermal load, the optical components of the camera in this model were composed of Zerodure mirrors and 4.1.Invar The backplanes. Establishment of Finite Element Model We established the finite element model of the camera as shown in Figure 8. In order to reduce the joint stress between different materials caused by thermal load, the optical components of the camera in this model were composed of Zerodure mirrors and Invar backplanes. Appl.Appl. Sci. Sci.20212021, 11, ,11 x, FOR 5184 PEER REVIEW 10 of 14 10 of 14

Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 14

FigureFigureFigure 8.8.Finite Finite 8. Finite element element element model model model of the ofof off-axisthe off-axis off-axis remote remote remote sensing sensing sensing camera. camera. camera.

4.2.4.2. Thermal4.2. Thermal Deformation Deformation Deformation Analysis Analysis Analysis The temperature conditions of the camera during on-rail operation are 20 ◦C ± 5 ◦C, The Thetemperature temperature conditions conditions ofof the the camera camera during during on-rail on-rail operation operation are 20 °C are ± 5 20°C, °C ± 5 °C, so weso analyzed we analyzed the thermalthe thermal deformation deformation of theof the camera camera when when the the temperature temperature increased increased ◦ soby we 5 byC. analyzed 5In °C. addition, In addition, the wethermal we also also analyzed analyzeddeformation aa support of thestructure structure camera composed composed when ofthe M40 of temperature M40 material material with increased bywith 5 °C. isotropic In addition, ply ply as as a acontrast. we contrast. also Figure analyzed Figure 9 shows9 shows a support the thermal the thermal structure deformation deformation composed clouds cloudsof of the M40 isotropic of thematerial with isotropicisotropiclaminated laminated ply as support a supportcontrast. structure structure Figure and and 9the shows theasymmetric asymmetric the thermal zero-expansion zero-expansion deformation support support clouds structure, structure, of there- isotropic laminatedre-spectively.spectively. support The The inﬂuence influence structure ofof temperaturetemperature and the asymmetric load load on on the the rigid zero-expansion rigid body body displacement displacement support of the of mir-structure, the respectively.mir-rorsrors is is shown shownThe influence inin TableTable4 4.. of temperature load on the rigid body displacement of the mirrors is shown in Table 4.

(a) (b)

Figure 9.FigureComparison 9. Comparison and analysis and analysis of thermal of thermal deformation deformation of support of support structure; structure; (a) ( supporta) support structure structure with with isotropic isotropic layers; layers; (b) support(b) support Structure Structure with zero-expansion with zero-expansion layer. layer.

Table 4. Reflector position deviation with a temperature rise of 5 °C. (aTable) 4. Reﬂector position deviation with a temperature rise of 5 ◦C. (b) Displacement by Isotropic Layers Struc- Displacement by Zero-Expansion Struc- Displacement by Isotropic Layers Structure Displacement by Zero-Expansion Structure Figure 9. Comparison and analysisMirrors ofMirrors thermal deformation of turesupport structure; (a) support structureture with isotropic layers; X/mm Y/mm Z/mm X/mm Y/mm Z/mm (b) support Structure with zero-expansion layer.X/mm Y/mm Z/mm X/mm Y/mm Z/mm M1M1 DatumDatum DatumDatum DatumDatum DatumDatum DatumDatum Datum M2 −1.63 × 10−7 2.20 × 10−5 −1.25 × 10−3 −2.91 × 10−6 −2.35 × 10−5 −1.90 × 10−4 TableM3 4. ReflectorM2 −1.15 position−1× 10.63− 6× 10 −7−deviation 7.592.20× 10 −×4 10 with−5 −1.95 −1a ×temperature.2510 ×− 410−3 3.01−2×.91 rise10 ×− 610 of−6 5− °C.2.72−2.35 × 10× 10−4 −5 −−11.15.90× ×10 10−5−4 M3 −1.15 × 10−6 −7.59 × 10−4 −1.95 × 10−4 3.01 × 10−6 −2.72 × 10−4 −1.15 × 10−5 Displacement by Isotropic Layers Struc- Displacement by Zero-Expansion Struc- MirrorsConsidering the particularityture of the off-axis TMA space camera structure,ture when the structure is thermallyX/mm deformed,Y/mm the thermalZ/mm deformation X/mmcan be offset dueY/mm to the sym- Z/mm M1 Datum Datum Datum Datum Datum Datum M2 −1.63 × 10−7 2.20 × 10−5 −1.25 × 10−3 −2.91 × 10−6 −2.35 × 10−5 −1.90 × 10−4 M3 −1.15 × 10−6 −7.59 × 10−4 −1.95 × 10−4 3.01 × 10−6 −2.72 × 10−4 −1.15 × 10−5

Considering the particularity of the off-axis TMA space camera structure, when the structure is thermally deformed, the thermal deformation can be offset due to the sym- Appl. Sci. 2021, 11, 5184 11 of 14

Considering the particularity of the off-axis TMA space camera structure, when the Appl. Sci. 2021, 11, x FOR PEER REVIEWstructure is thermally deformed, the thermal deformation can be offset due to 11 the of 14 symmetry of the structure in the X direction, so the displacement of the optical elements in the X direction is small in the macro view; however, in the Y and Z directions with significant asymmetry,metry of the the structure thermal in displacementthe X direction, of so the the optical displacement elements of the is obviousoptical elements [18,27]. in the X directionIt can be is small seen fromin the themacro thermal view; however, deformation in the clouds Y and Z that directions the thermal with significant deformation ofasymmetry, the camera the support thermal structure displacement is obvious of the optical when theelements support is obvious structure [18,27]. is designed with iso-tropicIt can layers. be seen The from maximum the thermal thermal deformation deformation clouds occurs that the in thermal the front deformation frame. However, of thethe thermal camera support deformation structure of theis obvious whole when structure the support tends to structure be uniform is designed when with the support iso- struc-turetropic layers. is designed The maximum with an thermal asymmetric deformation zero-expansion occurs in the layer. front frame. However, the thermalBased deformation on the actual of the displacement whole structure of the tends reflectors to be uniform under thewhen two the support support structures, struc- theture reflector is designed displacement with an asymmetric caused by zero-expansion the thermal layer. load is not obvious due to the good struc-turalBased symmetryon the actual in displacement the X direction. of the However, reflectors in under the Y the and two Z support directions, structures, where the struc-turalthe reflector asymmetry displacement is obvious,caused bythe the displacementthermal load is ofnot the obvious mirror due in to the the zero-expansion good struc- designtural symmetry is obviously in the smaller X direction. than However, that of the inisotropic the Y and laminate, Z directions, which where proves the struc- that the zero-expan-siontural asymmetry design is obvious, in the the asymmetric displacement direction of the mirror in the in off-axis the zero-expansion remote sensing design camera hasis obviously an ob-vious smaller effect than on reducingthat of the the isotropic rigid body laminate, displacement which proves of the that thermal the zero-expan- deformation ofsion the design camera in reflectors. the asymmetric direction in the off-axis remote sensing camera has an ob- viousIn effect order on to reducing further determinethe rigid body the effectdisplacement of the zero-expansionof the thermal deformation support structure of the in improvingcamera reflectors. the thermal stability of the camera, we input the displacement data of the mir-rorsIn order in Table to further3 into Zmaxdetermine to analyzethe effect the of influencethe zero-expansion of the thermal support deformation structure in of theimproving struc-ture the on thermal the optical stability transfer of the camera, function. we Theinput results the displacement of this analysis data of are the shown mir- in Figurerors in 10 Table. 3 into Zmax to analyze the influence of the thermal deformation of the structure on the optical transfer function. The results of this analysis are shown in Figure 10.

(a)

Figure 10. Cont. Appl. Sci. 2021, 11, 5184 12 of 14 Appl. Sci. 2021, 11, x FOR PEER REVIEW 12 of 14

(b)

(c)

FigureFigure 10. 10.Comparison Comparison of MTF MTF reduction reduction of of an an optical optical system system with with two two kinds kinds of structures. of structures. (a) The- (a) The- oreticaloretical MTF MTF ofof thethe opticaloptical system; (b (b) )MTF MTF with with the the thermal thermal deformation deformation in an in isotropic an isotropic structure; structure; (c) MTF with the thermal deformation in a zero-expansion structure. (c) MTF with the thermal deformation in a zero-expansion structure. The analysis shows that when isotropic layers are used in the support structure, the The analysis shows that when isotropic layers are used in the support structure, the MTF of the optical system decreases from 0.422 to 0.378 at a rise of 5 °C, and the decrease MTF of the optical system decreases from 0.422 to 0.378 at a rise of 5 ◦C, and the decrease percentage is 10.43%. When the zero-expansion layers are used in the support structure, percentage is 10.43%. When the zero-expansion layers are used in the support structure, the MTF of the optical system decreases from 0.422 to 0.411 at a rise of 5 °C, and◦ the de- thecrease MTF percentage of the optical is 2.61%. system The influence decreases of from the thermal 0.422 to deformation 0.411 at a on rise the of MTF 5 C, of and the the de-creaseoptical transmission percentage is is greatly 2.61%. reduced. The inﬂuence These ofresults the thermalprove that deformation the application on the of MTFthe of the optical transmission is greatly reduced. These results prove that the application of the zero-expansion design in the support structure of the off-axis remote sensing camera can improve the imaging performance stability under the conditions of periodic temperature Appl. Sci. 2021, 11, 5184 13 of 14

changes. It has a signiﬁcant effect on the thermal stability design of the support structure of a space off-axis remote sensing camera.

5. Conclusions In this paper, a thermal stability design method based on CFRP is proposed for the asymmetric support structure of an off-axis TMA space camera. A complete example of thermal stability design is presented in the detailed design of the CFRP support structure for the camera. The relationship between CTE and the ply angle of multi-layer composites is demonstrated through the theoretical analysis of the composites. By adjusting the laying angle of the carbon ﬁber composite, the expansion of the camera support structure can be re-duced almost to zero in the asymmetric direction. Finite element thermal analysis and optical analysis show that the proposed support structure with low CTE greatly reduces the displacement of the optical elements under temperature load conditions compared with a support structure with isotropic layers, and the inﬂuence of a temperature rise of 5 ◦C on the MTF of the optical system decreases from 10.41% to 2.67%. This proves that it is necessary to fully consider the thermal stability design method in relation to structural asymmetry, a method which has great potential in the thermal stability design of off-axis space cameras and will attract more attention with the improve-ment of the precision of off-axis space cameras.

Author Contributions: Conceptualization, W.S. and P.X.; methodology, W.S. and P.X.; software, W.S., S.L. and Y.X.; validation, W.S. and P.X.; writing—original draft preparation, W.S.; writing—review and editing, W.S. and P.X.; supervision, W.S.; project administration, P.X.; funding acquisition, P.X. All authors have read and agreed to the published version of the manuscript. Funding: This paper was supported by the National Key Research and Development Program of China (Grant No. 2016YFB0501200). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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