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某可见光相机主反射镜为凹非球面刚性单体镜,如图1(a)所示,口径Φ1550 mm,镜坯选用高比刚度、热稳定性好的SiC材料。反射镜绕光轴对称六等分,每六分之一内部呈镜像对称,背部采用全开放的三角形减轻槽设计,加强筋交汇处布有圆孔,可用于零件支撑或卸载,如图1(b)所示,反射镜设计质量122.7 kg,面密度仅69 kg/m2。
设反射镜等效厚度为tA,由公式(1)表示:
$$ {t}_{A}=\frac{{\rho }_{s}{S}_{A}}{\rho {S}_{A}} $$ (1) 式中:ρs为反射镜面密度;ρ为材料密度;SA为口径面积。因此,当反射镜口径及材料确定时,面密度越小,代表等效厚度越小,此时反射镜轴向刚度较低,光轴竖直状态自重作用下变形也就越大,面形对卸载力的变化也更为敏感。所研究反射镜轻量化程度高,面密度较小,为尽量避免光轴方向刚度差对面形的不利影响,采用光轴水平状态进行重力卸载,重力加速度g0方向如图1所示。
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一般情况下,卸载力分布密度越大,重力对反射镜面形的影响越小,但工程实施难度也就越大。因此,在既保证面形卸载精度又尽量简化实施的前提下,根据一定的原则(文中不予详述)将镜体在面内划分为18种规格共计192个分区,各规格以1~18依次编号,在每个分区内选定一个轻量化结构孔作为卸载力的作用位置,如图1(b)所示,卸载力大小等于分区重力,形成对反射镜的分布式多点主动支撑,不同规格分区的数量及卸载力大小见表1。
表 1 不同规格分区的数量及卸载力大小
Table 1. Quantity and unload force of different mass blocks
Block number i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Unload force Fi/N 8.69 10.76 9.40 9.17 8.48 6.19 5.54 5.39 4.22 4.01 3.89 3.70 4.27 5.38 10.44 4.44 3.98 3.36 Quantity Ni 12 6 -
各质量分区的卸载力作用于反射镜卸载孔内壁,在满足面形精度要求的前提下,支点数量应尽量少,以降低工程实施难度。将单个质量分区抽象为独立的柱体,柱体长度与分区的厚度正相关,将支撑点放置在重心位置,受力状态如图2所示,卸载力F与重力G大小相等,显然,离支撑点越远的截面,挠度及转角越大。分区厚度增加时,镜面变形加剧,当厚度超过一定界限时,单点支撑无法获得好的面形,此时应增加支撑点,减小镜面变形。
各质量分区背部的筋高度不一,根据公式(2)计算各分区的等效镜体厚度Hi:
$$ {H}_{{i}}={V}_{r{i}}/{S}_{r{i}}+h $$ (2) 式中:Vri为编号为i的质量分区立筋部分的体积;Sri为该分区筋截面沿光轴方向的投影面积;h为镜面面板厚度。根据公式(2)得到各分区等效镜体厚度Hi值,最大值H2为163 mm,最小值H14为39 mm,文中取最大值的1/2 (81.5 mm)作为划分单、双点支撑方式的厚度界限,得到表2中所示的8种双点支撑分区及10种单点支撑分区,总计产生282个卸载力支点。
表 2 不同质量分区的等效镜体厚度
Table 2. Equivalent thickness of different mass blocks
Double-point supporting blocks Block number i 1 2 3 4 5 6 7 15 Equivalent thickness Hi/mm 128 163 146 148 136 99 87 160 Single-point supporting blocks Block number i 8 9 10 11 12 13 14 16 17 18 Equivalent thickness Hi/mm 44 69 64 63 59 42 39 73 63 50 -
卸载力在光轴方向的位置直接决定了重力矩的大小进而影响镜面变形,因此将其作为重力卸载待优化参数。以卸载合力与重力轴向位置相同为原则进行初值设定,针对单点支撑分区,卸载力Fi轴向位置过重心;针对双点支撑分区,如图3所示,沿重心所在平面将分区划分为前、后两部分子区,再根据各子区的重心位置确定支撑分力Fi1、Fi2的大小及位置,且Fi1、Fi2的相对位置不再改变。
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根据第1、2节,总结出大口径反射镜光轴水平状态下,以重力对面形RMS的影响最小为目标进行重力卸载参数优化的要点:(1)反射镜各质量分区内,以与重力相等为原则确定卸载力的大小,以等效厚度值确定支点数量,以卸载合力轴向位置过重心为原则,确定支撑点位置初始值;(2)以卸载力的轴向位移为参数进行仿真优化;(3)卸载力位置变化本质上通过改变反射镜合力矩而影响面形,初步优化时可将参数降至一维,即所有位移取相同值进行迭代;(4)若仍未满足指标要求,可增加优化参数进行二次优化:将位于反射镜上、下半部的卸载力位移分取不同值,上部位移对面形影响较大,初步优化已基本达到最优取值,可仅改变下部位移进行迭代计算。
对相同口径结构相似的多个反射镜采用同样的方式进行重力卸载优化,均证明了该方法可准确、快速地确定大口径反射镜的面形检测卸载方案,且能极大地加速优化过程,适用于其他类似大口径反射镜的重力卸载。
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对某Φ1550 mm口径高轻量化SiC反射镜进行重力卸载优化设计,根据反射镜的实际尺寸和质量进行模型及卸载参数修正,再将重力卸载单元按设计的支撑位置和卸载力大小进行安装调试,应用于反射镜光轴水平背部三点静定支撑的面形检测中。
由于反射镜静定支撑结构采用弱约束设计,强度不足以支撑镜体自重,因此无法对反射镜不卸载状态进行面形检测来作出直接对比。假定反射镜原始面形为随机生成的RMS误差约为1/60λ的面形,通过有限元方法分别计算其绕光轴旋转0°、120°及240°时受重力及卸载力作用下的面形,得到如表3所示结果(表中面形均处理为同一结构方位)。可以看出,反射镜受重力作用不卸载时,面形主要呈现重力影响分量,三方位RMS误差大幅偏离原始面形,波动量0.0056λ,且误差云图出现明显方位差异,而将反射镜按文中参数进行重力卸载后,三方位面形分布及RMS误差均接近原始面形,且其间仅波动0.0002λ。因此,通过对比反射镜三个旋转对称方位的面形分布及RMS误差对卸载效果进行间接验证。
表 3 三方位重力及卸载力作用下反射镜面形图
Table 3. Surface figure of the mirror with gravity unloaded or not in 3 directions
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采用Zygo干涉仪对反射镜绕光轴三个方位(0°、120°及240°)下的面形分别进行检测,结果如图11所示。0°方位面形RMS为0.0157λ,120°方位面形RMS为0.0161λ,240°方位面形RMS为0.0159λ,差异小于0.001λ,且未出现仿真结果中重力导致的旋转大像散,说明该方法卸载后重力对反射镜面形的影响基本消除,实际卸载状态接近设计效果,保证了反射镜满足优于1/50λ的使用要求。
Optimization method for large-aperture space mirror’s gravity unload
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摘要: 针对某Φ1550 mm口径高轻量化反射镜在轨面形误差RMS优于1/50λ (λ=632.8 nm)的高精度要求,为模拟在轨失重状态,降低反射镜光轴水平状态面形检测时重力的影响,对反射镜进行了多点主动支撑式重力卸载参数优化。首先,在反射镜分区的基础上,提出了卸载力大小、支撑点数量及轴向初始位置的确定原则;随后,建立反射镜的有限元模型,以重力与卸载力共同作用下主镜面形RMS优于0.002λ为目标,以卸载力轴向位置为参数进行仿真优化,通过对参数的影响规律分析总结出快速优化要点,实现优化过程的简化;最终使重力引起的面形误差RMS值减小至0.00145λ。将优化后参数应用于反射镜光轴水平状态的面形检测中,测得绕轴0°、120°、240°时面形RMS分别为0.0157λ、0.0161λ及0.0159λ,且面形分布较为一致,说明经卸载后重力对面形的影响被有效消除。所提出的重力卸载优化方法灵活高效,为实现大口径反射镜的高精度光学加工及在轨使用提供保障。Abstract: A Φ1550 mm aperture space mirror’s surface figure RMS was required to be superior to 1/50λ (λ=632.8 nm) under the zero-gravity orbit environment. In order to simulate the state of weightlessness and reduce the influence of gravity in the mirror’s surface figure test with horizontal optic axis, the mirror was actively supported by multiple forces to unload the gravity and the forces’ parameters were optimized. Firstly, the principle to determine the value, the number of support points and the initial axial position of each unload force was proposed based on dividing the mirror into blocks. Secondly, with the optimization goal of the mirror’s surface figure RMS be superior to 0.002λ under the function of gravity along with all unload forces, a structural FEM model was established. Taking the positions of all unload forces along the optic axis as optimal variables, influences on target were analyzed and quick optimization points were concluded to simplify the optimization. Finally, the mirror’s surface figure RMS when unloaded was found minimal of 0.00145λ. Putting the parameters of the optimization result into use of the surface figure test of the mirror with horizontal optic axis, it turned out that when the mirror revolved around the optic axis 0°, 120° and 240°, the surface figure RMS were 0.0157λ, 0.0161λ and 0.0159λ respectively and the figures were consistent, which proved that the gravity impact was eliminated effectively. The optimization method for gravity unload is flexible and efficient which guarantee the large-aperture mirror’s high-precision machining and space mission.
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Key words:
- space mirror /
- large aperture /
- gravity unload /
- surface figure optimization
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表 1 不同规格分区的数量及卸载力大小
Table 1. Quantity and unload force of different mass blocks
Block number i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Unload force Fi/N 8.69 10.76 9.40 9.17 8.48 6.19 5.54 5.39 4.22 4.01 3.89 3.70 4.27 5.38 10.44 4.44 3.98 3.36 Quantity Ni 12 6 表 2 不同质量分区的等效镜体厚度
Table 2. Equivalent thickness of different mass blocks
Double-point supporting blocks Block number i 1 2 3 4 5 6 7 15 Equivalent thickness Hi/mm 128 163 146 148 136 99 87 160 Single-point supporting blocks Block number i 8 9 10 11 12 13 14 16 17 18 Equivalent thickness Hi/mm 44 69 64 63 59 42 39 73 63 50 表 3 三方位重力及卸载力作用下反射镜面形图
Table 3. Surface figure of the mirror with gravity unloaded or not in 3 directions
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