1. Introduction
The network, information, services fused and reactive speed have become the key to the victory in the form of future war. A cooperative operation based on UAVs satisfies the requirements of future war [
1]. UAV cooperative operations always come with the decentration and functional decentralization of UAV [
2]. For that reason, the mass of medium and large UAVs varies [
3], thus creating high requirements for the arresting force variation range and control ability of the arresting gear of UAV carrier platforms.
There are a few hydraulic arresting systems designed for medium and large UAVs. Huang [
4] designed and studied a hydraulic arresting system for small UAVs by using dynamic simulation. This system cannot satisfy the requirement of medium and large UAVs’ arresting processes. Moreover, the hydraulic arresting system contains a necessary subsystem which consists of the arresting control valve and weight elector unit [
5]. It controls the initial arresting force and the force during the arresting process. Because of the mechanical structure of the constant runout valve, the range of force variation is limited, and the resetting interval is long, which is the reason why it cannot be used to arrest the UAVs with short take−off and landing cycle intervals and a variety of masses. Making MR dampers replace traditional hydraulic dampers as damping force generation devices will significantly expand the range of damping force variation and increase response speed of force variation.
A magnetorheological damper is an intelligent damping force generating device that uses MR fluid to change its own rheological properties under different magnetic fields. The piston is an important component of the damper. The structural parameters and coil arrangement of the piston have a great influence on the performance of the damper. Hu [
6] studied the shape of the piston and found that the damper with the flat−end piston configuration can obtain a greater damping force and a wider adjustable range of damping force. Khan [
7] studied the effects of the piston chamfer; chamfer shape; and single coil, double coil, and triple coil on the damper’s performance. The study showed that the rounded piston chamfer could increase the pressure drop of the piston. Yazid [
8] used the finite element method (FEM) magnetics software package to establish a magnetic field simulation model. Six parameters were proposed to obtain the best damper performance, and alternate polarities of coil also helped to strengthen the magnetic field in the shear and squeeze area. Current research provides guidance for the selection of parameters and coil arrangement.
Jang [
9] optimized the minimum number of coil-turns and maximum adjustable range of a single-coil MR damper based on the genetic algorithm. Dong [
10] took the damping force, adjustable range, response time and magnetic flux density as optimization objectives and optimized the geometric size of the magnetorheological damper for a bridge by utilizing the genetic algorithm. The optimization method of Dong’s study was to establish a numerical model. Then, it used the genetic algorithm to optimize the numerical model and used the finite element simulation to verify the optimization results. The processes of finite element magnetic field calculation and optimization are independent. Olivier [
11] designed and analyzed an MR damper with two permanent magnets apart from an electromagnet. The optimization process was developed to optimize the geometric parameters and generated the maximum damping force of the hybrid MR damper by using the response surface method and Box-Behnken design. The genetic algorithm has potential parallelism for multiparameter optimization and has strong convergence. It is suitable for multiparameter optimization. The accuracy of the multiparameter optimization process can be improved if the FEM calculation is incorporated into it.
Magnetorheological dampers are also used in arresting gears. Fu [
12] applied the MR damper to pulley shock absorbers for shipboard aircraft arresting system. Then, the fuzzy control rules were designed, and the buffer control for the pulley buffer of shipboard aircraft was completed in the touchdown moment based on MR technology. The pull peak of the arresting cable was reduced. However, MR dampers were not a source of resistance to stop the UAVs. Cheng [
13] verified the accuracy of the modified sigmoid model by comparing the experimental data and calculation results. Then, a basic model for the carrier-based aircraft arresting gear was built, and the force of UAV during arresting process was demonstrated. They did not involve the structural parameter determination and structural optimization of MR dampers, and they did not carry out the deeper study of the dynamic response of the multitype UAV arresting process.
In this paper, based on parametric modeling, the finite element simulation results are connected to the genetic algorithm optimization process to improve the accuracy of optimization results. The optimization results of the single-coil arrangement and double-coil arrangement are compared. Finally, the simulation results are substituted into the UAV arresting model to verify the arresting performance of the device based on the MR damper.
5. Optimization Results and Analysis
We set the evolution group members to 10 and the evolution steps to 100. With the increase in the number of iterations, most parameters basically become stable after 600 iterations, while the coil depth became stable after 900 iterations. The final optimization results are shown in
Table 2.
After optimization, the piston volume of the single-coil MR damper is 0.324 m3, and the double-coil piston volume is 0.333 m3. The double-coil piston volume is 28% larger than the single-coil piston volume. When the piston velocity is 1.8 m/s, the damping force variation range of the single-coil piston is 1,769,801 N, and that of the double-coil piston is 1,950,654 N, which is a 10.2% increase over the single-coil one.
The parameters of AMESim simulation model are set to the optimized parameters. The mass of the UAV is set as 4000 kg, 6000 kg, 8000 kg and 10,000 kg respectively. The initial speed of the UAV is 40 m/s, and the ideal acceleration of the control system is 20 m/s
2. The adaptability of the MR damper and arresting system is verified by changing the mass of the UAV. The peaks of the UAV acceleration before and after structural optimization are shown in
Table 3. The value of the parameters before optimization is the value that maximizes the damping force.
It can be seen that the structural optimization significantly reduces the peak accelerations of UAVs. For the single-coil damper, when the UAV mass increases from 4000 kg to 10,000 kg, the reduction in the peak acceleration is increased from 19.8% to 25.4%. For the double-coil damper, the reduction in peak acceleration is increased from 22.2% to 25.7%. The optimization of the damper structure not only reduces the peak load of the UAV during arresting but also expands the damping force variation range of the damper and improves the arresting efficiency of the damper.
Furthermore, the effects of different coil arrangements on the performance of the MR damper are compared, and the simulation results are shown in
Figure 10,
Figure 11,
Figure 12 and
Figure 13.
As shown in
Figure 10a and
Figure 11a, the coil arrangement has no significant impact on the arresting process of small- and medium-mass UAVs. For a 4000 kg UAV, the acceleration of the UAV rapidly increases from 0 m/s
2 to 32.5 m/s
2 in the early stage of the arresting process, decreases to 15 m/s
2 within 0.8 s and then maintains a slow rise until the UAV is stopped. For a 6000 kg UAV, the peak arresting acceleration decreases to 24.8 m/s
2, and then it drops to 19 m/s
2 and remains at this value until the UAV is stopped. As can be seen from
Figure 10b and
Figure 11b it takes 1.9 s for the arresting gear to stop the UAV of 4000 kg and 2.0 s for the UAV of 6000 kg. As shown in
Figure 10c and
Figure 11c, the arresting gear stops the 4000 kg UAV at 35.1 m, and the 6000 kg UAV needs 41.9 m to stop. Therefore, different coil arrangements have no significant impact.
As shown in
Figure 12 and
Figure 13, the coil arrangement has a great influence on the arresting performance of the high−mass UAV. Under the condition of 8000 kg UAV, the arresting performance appears to have an obvious difference after 1.8 s, and the single-coil damper appears to have an obvious inflection point at 1.8 s. After 0.4 s, it decreases from 20 m/s
2 to 15.0 m/s
2. The double-coil damper has no obvious inflection point, and there is a small but not obvious decline after 2.1 s. The single-coil arresting gear takes 2.2 s to stop the UAV within 45.5 m. The double-coil arresting gear’s stopping time is 2.1 s, 4.5% lower than that of the single-coil one, and the arresting distance is 44.5 m, which is 2.2% shorter. When the UAV mass is 10,000 kg, the single-coil inflection point appears at 1.4 s, and the double-coil inflection point appears at 1.7 s, i.e., 21% delayed. It takes 2.4 s for the single-coil arresting gear to stop the UAV at 45.5 m. I confirm. The double-coil arresting gear takes 46.5 m to stop the UAV, so the distance is shortened by 2.2% compared with that of the single-coil arresting gear. The arresting time is 2.2 s, making it 9.1% shortened.
In summary, after optimization via the genetic algorithm, the arresting performance of the double-coil damper was better than that of the single-coil damper. Combined with
Table 2, it can be seen that, under the conditions of a similar viscous damping force, the Coulomb damping force of the double-coil damper is greater than that of the single-coil damper. Under the condition of the same total coil length, the coil depth of the double-coil damper is shallower than that of the single-coil damper, indicating that the magnetic field generation efficiency of the double-coil damper is better than that of the single-coil one. From the UAV acceleration curve, it can be seen that the performance differences of the different coil arrangements of the dampers are mainly reflected in the arresting process of the large-mass UAV. Under the condition of the UAV with a high mass and low speed, the acceleration maintenance time of the double coil is longer than that of the single coil, the arresting efficiency is higher and the performance is better.
Because the hydraulic arresting gear designed for medium and large UAVs is rare, this paper refers to the force line of MK7-I, and the hydraulic arresting gear is reproduced. On this basis, the hydraulic arresting gear is adjusted so that the hydraulic arresting device can be adapted to the medium and large UAVs. Taking the force line of 10,000 kg UAV as an example, the comparison with MK7-I [
17] is shown in
Figure 14.
It can be seen from
Figure 14 that the result of the hydraulic arresting gear simulation model is reliable. The acceleration simulation results according to the change in the mass of the UAV are shown in
Figure 15.
According to the
Figure 15, the MRAG (MR arresting gear) has a much faster response time than the HAG (hydraulic arresting gear). Since the best arresting performance of HAG is designed for 10,000 kg UAV, with the mass decreases from 10,000 kg to 4000 kg, the peak load of the UAV becomes higher. The damping force control performance of the runout valve becomes poorer and poorer when the UAV mass deviates from the design point. Moreover, the runout valve is a passive control unit, meaning that it cannot control the damping force according to the state of the arresting object during the arresting process like the MRAG can.
The arresting displacement difference between 4000 kg UAV and 10,000 kg UAV is 11.4 m for the MRAG and 18.3 m for the HAG, as seen in
Table 4. It shows that the stopping points of the MRAG are more concentrated than those of the HAG. The same phenomenon also appears during the arresting time, meaning that there is better predictability and controllability. As for acceleration, the peak acceleration of the MRAG is 13.1% lower than that of HAG for 4000 kg UAV, 14.5% for 6000 kg UAV, 14.9% for 8000 kg UAV and 4.3% for 10,000 kg UAV.
6. Conclusions
In this paper, the structural parameter optimization model of the MR damper is established based on the genetic algorithm, and the structural parameters of dampers with different coil arrangements are optimized. The dynamics simulation model of the UAV arresting process is established, and the following conclusions are obtained:
(1) Maxwell and Python were used to establish the structural parameter optimization model of the MR damper based on the genetic algorithm and finite element magnetic field simulation. Under the same constraints, the structural parameter optimization results of the single-coil MR damper and the double-coil MR damper were calculated, respectively. It is found that, under the approximate volume and structure, the variation range of the damping force of the double-coil damper is increased by 10.2% compared with that of the single-coil damper; thus, performance of the single-coil damper is inferior to that of the double-coil damper.
(2) The model of the UAV arresting gear based on magnetorheological technology was established by AMESim. When the UAV mass increases from 4000 kg to 10,000 kg, the reduction in the peak acceleration is increased from 19.8% to 25.4%.
(3) By substituting the optimized parameters into the simulation model, based on the obtained UAV dynamic response, the adaptability of the arresting gear to a variety of mass UAVs was studied. Under the action of the control system, there is an obvious damping-force regulation process.
(4) Compared with the hydraulic arresting gear, the response of MR arresting gear is faster. The UAV’s stopping points are more concentrated. The peak acceleration of the UAV is reduced by between 4.3% and 14.9%. It illustrates the adaptability of the arresting gear based on the MR damper to multitype and multi-mass UAVs.