An Approximate Torque Model for Electromagnetic De-Tumbling of Space Debris: Finite-Element Correction and Experimental Verification

The rapid accumulation of space debris presents a serious threat to operational spacecraft, with the capture and removal of rapidly tumbling non-cooperative targets being a primary challenge. Non-contact electromagnetic de-tumbling technology is a promising solution due to its enhanced safety. This paper addresses the issue of torque modeling and validation in the electromagnetic de-tumbling process for a specific configuration involving a magnetic dipole and a spherical shell under a symmetrically distributed magnetic field. Based on the principles of electromagnetic induction, an approximate analytical expression for the electromagnetic eddy current torque on a rotating spherical shell within a dipole magnetic field is first derived. A high-fidelity finite element model is then established, which reveals a systematic discrepancy between the initial theoretical model and numerical simulation results. A distance-dependent power-law correction factor is introduced to calibrate the theoretical model, significantly improving its accuracy and reducing the average error to 1.5 percent. Finally, a ground-based experimental platform is designed and implemented. Experimental results demonstrate that the corrected approximate analytical model agrees well with the empirical data, verifying its validity and accuracy under the given conditions and providing a reliable theoretical basis for the design of future space debris de-tumbling controllers.