Precision Measurement Method for Inertial Principal Axis Inclination of Aerospace Vehicles

Inclination of the inertial principal axis in high-speed rotating rotors, spin-stabilized spacecraft, and other equipment induces dynamic unbalance and attitude–inertia coupling. Traceability and calibration technologies for principal axis inclination are critical to guarantee the dynamic performance of such equipment, yet a complete metrological calibration system remains absent. Aiming at the inherent model bias of the ellipsoid simplification algorithm widely adopted in engineering, this paper derives two sets of sufficient conditions—single-plane decoupling and transverse isotropy—under which the ellipsoid method and the 3D eigenvector method produce strictly identical, error-free results. Based on first-order eigenperturbation theory, an explicit bias scaling law is established: under general orientations, the model bias grows linearly with the inherent asymmetry of the rigid body and approximately linearly with the principal axis inclination, degenerating into a cubic function of inclination only under symmetric configurations; the first-order law is verified to remain quantitatively valid over the inclination range of 0–7°. Targeting zero theoretical error, a single-plane dual-counterweight loading calibration scheme is proposed; the mass centroid of the rigid body remains unchanged after loading, and three gradient calibration points of 2.0013°, 3.7869°, and 6.7970° are generated, fully covering the 0–7° engineering range with accurately traceable reference inclination angles. Three approaches—GUM, eigenperturbation, and Monte Carlo—are combined to evaluate the measurement uncertainty, and the expanded uncertainty of inclination at the calibration points with a coverage factor of 2 reaches 0.063°, with consistency among the three methods better than 0.12%. This work improves the error theory for inertial principal axis inclination measurement, and provides comprehensive theoretical support and simulation verification for traceability and calibration of this parameter.