基于FEM的引力参考传感器自引力计算与补偿

Calculation and compensation of self-gravity for gravitational reference sensor based on finite element method

空间引力波探测太极计划将利用激光干涉的方法,测量两个检验质量之间的距离变化反演引力波信息。在0.1 mHz处,要求检验质量在敏感轴方向的总残余加速度保持在3×10^(-15)m·s^(-2)/√Hz以下。由航天器载荷静引力、热形变和质量波动引起的自引力噪声是检验质量的残余加速度噪声主要来源之一,要求检验质量在敏感轴方向的自引力加速度小于1×10^(-10)m/s^(2),引力梯度小于5×10^(-8)s^(-2)。为了计算检验质量处的自引力大小和引力梯度,针对检验质量与引力源几何形状的不规则性,基于有限元法编写程序计算了引力参考传感器中的引力源作用在检验质量上的线加速度、角加速度和引力梯度。为了缩短计算时间,提出“类自适应”网格划分方法以减小网格数量,并设计了配重以补偿自引力。计算结果显示,经过补偿后的检验质量在敏感轴方向的自引力加速度为9.2377×10^(-12)m/s^(2),引力梯度为-2.5691×10^(-8)s^(-2),满足设计要求。本研究能够为航天器和引力参考传感器的设计与引力补偿提供参考与指导。

Spaceborne gravitational wave detection Tai-ji Project is going to measure the distance change of two test mass blocks with gravitational reference sensors through laser interference to retrieve the physical information of gravitational waves.The total residual acceleration noise of the test mass should be below 3×10^(-15)m·s^(-2)/√Hz along sensitive axis at 0.1mHz.The self-gravity noise arising from spacecraft payloads attraction,thermal distortions and mass fluctuation is one of the most significant noises.The self-gravity induced acceleration at test mass location along sensitive axis should be below 1×10^(-10)m/s^(2),and the self-gravity induced gradient of the acceleration field at test mass location along sensitive axis should be below 5×10^(-8)s^(-2).In order to calculate the accelerations and gradients of the acceleration field,aiming at the geometry irregularity of test mass and attraction sources,a custom programme was coded.The linear accelerations,angular accelerations and gradients of the acceleration field were calculated.In addition,to minimize the calculation time,a“quasi adaptive”method for meshing was proposed.The balance mass was designed to compensate self-gravity.The results show that the self-gravity induced acceleration at test mass location along sensitive axis is 9.2377×10^(-12)m/s^(2),and that the self-gravity induced gradient of the acceleration field at test mass location along sensitive axis is^(-2).5691×10^(-8)s^(-2),which meet the design requirement.This research will provide reference and guidance for the design and compensation of spacecraft and gravitational reference sensors.