Deformation field reconstruction technology for star tracker bracket system based on strain measurements

Star sensor bracket systems are composed of star sensor mounting plates and star sensor brackets. The bracket system connects the star sensor with the satellite body. Because such sensors must maintain high operational accuracy during operation, their structural characteristics considerably impact the deformation field distribution. In addition, existing deformation reconstruction techniques have high computational complexity and long calculation times. For instance, B-spline interpolation and inverse finite element deformation reconstruction methods have large computational loads when processing large-scale data, and their accuracy is determined by the mesh conditions and initial conditions such as constraint and loading method. To address these issues, a deformation field reconstruction technology based on strain measurements was proposed for the star sensor bracket system.

For the reconstruction and analysis of deformation fields, the system deformation was decomposed into mounting plate and bracket deformations, as well as the bracket displacement caused by the mounting plate deformation. The strain field was determined by reconstructing the discrete point strain measurement data for the large deflection deformation of the mounting plate using the inverse distance weighting method. The relationship between bending, tensile, and compressive strains, as well as the deformation field in the microelements, was determined, and a discrete digital integration method was used to derive the deformation curves of N parallel lines. These N curves were then fitted to obtain the surface deformation diagram of the mounting plate. The star sensor bracket was simplified as a beam structure, with its deformation mainly manifesting as a small deflection. Bending stress produced the strain that induced the deformation in the structure, with a mid-surface strain of 0. When a beam structure undergoes small bending deformation, it will generate a rotation angle. Multiplying the rotation angle by the radius of curvature gives the chord length. The difference in curvature radius between the upper surface and the neutral plane is known. Therefore, the chord length of the upper surface and the neutral plane is obtained, which leading to the beam surface strain. Based on these findings, the discrete curvature and distance between discrete points were used as inputs for calculation, and the coordinate positions of each point on the curve were determined via point-by-point iterative operation. These positions were fit to obtain the corresponding curve for calculating the deformation. Finally, the geometric relationship of the deformation of the sensor bracket and mounting plate was established, and the displacement expression of the bracket mounted on the deformed mounting plate was derived.

As a result, the deformations of the mounting plate and bracket were superposed. An experimental deformation measurement platform was also developed for the star sensor bracket system. By applying weighted loads, the deformation of the sensor bracket and mounting plate was measured using the FBG strain monitoring system. The reconstruction results were compared with the displacement sensor measurement data, which revealed that the bracket reconstruction error did not exceed 3.84%. The proposed deformation field reconstruction method realized the rapid and accurate reconstruction of the deformation fields based on discrete point strain monitoring data. It thus provided a basis for studies on the deformation field reconstruction of assemblies under complex constraint conditions.