micro-newton thrust stand, analytical model, flexure hinge, bending stiffness, uncertainty, Materials of engineering and construction. Mechanics of materials, TA401-492, Production of electric energy or power. Powerplants. Central stations, TK1001-1841

Micro-newton thrust stands are widely used in thruster ground calibration procedures for a variety of space missions. The conventional analytical model does not consider the gravity-induced extension effect and systematic error in displacement for thrust stands consisting of hanging pendulums based on flexure hinge structures. This paper proposes an improved analytical model of a hanging pendulum for thrust measurement, where an elliptical notched flexure hinge is the key component. A parametric model of the bending stiffness of the flexure hinge is developed. Equally, both the bending stiffness shift under the gravity-induced extension effect and the systematic error in displacement due to the assumed rotational center offset of the hinge are investigated. The presented stiffness equations for elliptical notched hinges can be degenerated into stiffness equations for circular notched as well as leaf-type hinges. The improved model aims to evaluate and highlight the influence of the two considered factors for use in thrust stand parameter design and thrust analysis. A finite element modeling solution is proposed to validate the proposed analytical model. The results show that the proposed model can quantify the hinge bending stiffness shift, which also demonstrates that even a small bending stiffness shift may introduce great uncertainty into the thrust analysis.