Design of de-tumbling device for improving the de-tumbling performance of uncooperative space target

 In a research article recently published in Space: Science & Technology, scholars from Beijing Institute of Technology and University of Technology Sydney together focusing on uncooperative targets present a design of an optimal coil structure for 2 de-tumbling devices based on electromagnetic eddy current method, which can de-tumble over 1 million targets of various sizes, demonstrating universality.

First, basics including design process, mechanism analysis, and magnetic field modeling are illustrated.

The schematic diagram of the de-tumbling system is shown in Fig. 1, which mainly consists of the de-tumbling robots, de-tumbling devices composed of an ironless stator and coils, and the uncooperative space target. To improve the de-tumbling performance, a comprehensive framework is constructed to guide the optimization of the de-tumbling robot, ensuring that the magnetic field acting on the target is maximum. The specific flow of the proposed optimization scheme is shown in Fig. 2. First, optimal structure parameters of the coils at different distances between the target and coils are found based on magnetic field analytical model. Then, the above accuracy is validated using FEM. At last, de-tumbling torque is calculated by the improved Maxwell’s stress tensor method and compared with the traditional Maxwell’s stress tensor.

The mechanism of de-tumbling force is as followed. The magnetic flux density B induces eddy currents J within the rotating conducting target, which in turn interacts with B to produce a force F_t (i.e., de-tumbling force). Meanwhile, the rotational speed n_t of the target will be reduced under the action of F_t, and the de-tumbling process can be realized. B generated by an energized coil with current I will affect the magnitude of the de-tumbling torque T due to T ∝ B² ∝ I², and B will vary with the change of the structure parameters a and d of the coils when I is constant.

The analytical model of magnetic field is established in Fig. 4, where the excitation coils carried by the 2 de-tumbling robots are assumed to be C_i (i = 1, 2). B_li (i = 1, 2) is the magnitude of magnetic field Bli generated by l_i of C_i at point Q. θ_li (i = 1, 2) is the inclined angle between central axis O_c1Q or QO_c2 and the direction of Bli. B_li,x = B_li cosθ_li (i = 1, 2) is the magnitude of Bli lying on the central axis generated by l_i of C_i at point Q. Similar to the above method, B_Li, θ_Li, and B_Li,x can be obtained. For two coils, according to the symmetry, the magnitude of synthetic magnetic field generated by C_i (i = 1, 2) carrying I at any point in the x-axis direction can be calculated as: B_x^C1,2 = Σ²_i=1[2(B_li,x + B_Li,x)].

Then, an optimization process is conducted including the analysis of the optimal structure parameters and the influence of current direction on the magnetic field.

The expression of the magnetic field B_x at x_t is only related to the structure parameters L and l of the coils. Therefore, the problem of improving the de-tumbling performance is transformed into a parameter optimization. Thus, the nonlinear optimization model is built as follows:

max B_x

Subject to: √(L²+l²) < D_fairing ,

where D_fairing is the diameter of the launcher. Subsequently, optimal structure parameters are analyzed by traversing step length for L and l. For convenience, the step length of 0.5 m is used for calculation. Given the constraint, the optimal coil structure parameters are always (L, l) = (2.5, 3) m and remain unchanged when d > 1 m. The optimal coil structure parameters decrease with the decrease of d and are no longer constrained when d < 1 m. The larger L and l do not imply the larger B_x. So, it can be concluded that the optimal structure parameters of the rectangular coil are (L, l) = (2.5, 3) m.

The influence of current direction in C_i (i = 1, 2) on de-tumbling efficiency is shown in Fig. 7. The optimal model to de-tumble the target is to have I for C_i (i = 1, 2) flowing in the same direction, producing the maximum magnetic field, as shown in Fig. 7 A. In addition, the values of B¹_S,x, B²_S,x, B¹_O,x, or B²_O,x at the center of mass of the target (i.e., x_t = 0) are equal to 1.141 × 10⁻³ T, which matches the values for (L, l) = (2.5, 2.5) in the previous analysis, further confirming the accuracy of the established model.

Finally, the proposed improved Maxwell’s stress tensor method is applied to calculate the de-tumbling torque on the target through FEM, based on the optimal model obtained above. B_r, B_θ, and B_r·B_θ are calculated by FEM and the detailed characteristics of the magnetic field B_r·B_θ are shown in Fig. 9. It can be seen that the magnitude of B_r·B_θ along the axial direction (i.e., L_t) is different and is symmetric about the O_t–x_ty_t plane. As it moves away from O_t–x_ty_t plane, its value increases. By substituting B_r·B_θ calculated by FEM shown above into the improved de-tumbling torque calculation method, the de-tumbling torque acting on the target can be obtained. The de-tumbling torque of different numbers of segments when r = 0.1 m is analyzed through FEM computations, as shown in Fig. 11. It can be seen that de-tumbling torque increases with the increase of N_seg, and as N_seg reaches 40, the computed de-tumbling torque converges more closely to the true value under the summation limit. Furthermore, compared to the de-tumbling torque calculated using the traditional Maxwell’s tensor method, the accuracy of the de-tumbling torque calculated using the proposed improved Maxwell’s stress tensor method in this paper has been improved by 26.64%. This improvement also validates the advantage of the proposed method.