Simulations and Tests of a KRET Aerospace Penetrator

: This manuscript presents the simulation tests of an aerospace penetrator conducted to check the device’s validity and functionality. For this work, the numerical model was created on the basis of engineering data, the laboratory model of the tube reluctance actuator was created on the basis of the numerical model, and a set of simulations were executed on the basis of both presented. Moreover, the mathematical model was supplemented by precise boundary conditions. The main goal was the analysis of the introduced device’s properties by comparing them to experimental values. Three di ﬀ erent variants were taken into account to check the construction functionality and to study the most important parameters, e.g., the hammer displacement, hammer velocity, eddy currents and overall electromagnetic properties of the penetrator’s hammer displacement. The high-end values of the applied components were derived on the basis of the results and are presented in the summary of the concluded work. An overall method for checking the validity of the penetrator was proposed, which is cost and time e ﬀ ective. The model used was not limited in the representation of physical phenomena.


Introduction
Soil penetrators are research instruments used in space missions for scientific and technical purposes. The examined space entities can be either small bodies-asteroids, comets, and larger objects; planets; or moons. Penetrators are used to conduct scientific research and carry out the following technical tasks: • Soil mechanics analysis; • Chemical and mineralogical analysis; • Thermal tests (e.g., measurement of the temperature under the body surface, thermal conductivity); • Electrical and magnetic research; • Soil sampling for further analysis or delivery on a return mission to Earth; • Transporting and placing other components in a given soil; • Anchoring objects.
In general, penetrators can be divided into impactors (kinetic penetrators), which are characterized by having a very high initial speed while breaking under the surface. The second types are stationary penetrators, which are used after landing on a given body.
Impactors are used in missions where landing is not provided. Their advantages include the high kinetic energy of the impact and thus great opportunities to sink under the surface. The disadvantage of this type of solution is the huge overloads that can damage sensors or other research components. An example of a mission in which the impactor was used is the NASA Deep Impact mission [1]. Stationary penetrators are characterized by a relatively low driving speed. Two methods of insertion are distinguished-drilling and driving. The first method is used to sink or take samples from hard materials. This device of this type was used on the European Space Agency (ESA) rover during the ExoMars 2018 mission [1]. Drilling seems to be the most obvious way to break below the surface. However, in the case of space missions, it has several major disadvantages, such as high forces affecting the lander/platform or relatively high energy consumption.
In the case of hammering, two methods of soil penetration can be distinguished: penetration during one short continuous process or discreet penetration by repeating the hammer action. An example of a continuous hammering penetrator is the PHILAE harpoon of the Rosetta mission [2][3][4][5] presented in Figure 1. The drive used in this case was a compressed gas cartridge. These harpoons were used to anchor the lander immediately after contact with the comet and enable it to further carry out its mission. However, the devices did not work properly, which was one of the main reasons for Rosetta's mission goals not being fully realized. Generally, a big problem with this type of penetrator (moving in fast motion) is the cable unrolling (especially at low temperatures) and the inability to control the thrust and one-off operation. The last of the currently used devices in space missions to penetrate the surface of celestial bodies are penetrators characterized by low-velocity penetration. The main executive element in this type of solution is the so-called hammer. The component is accelerated and then hits the housing, resulting in the breaking of the surface (usually a few millimeters). A very important feature of this type of construction is the energy accumulator, which is-depending on the design-a capacitor (electrical energy) or a spring (mechanical energy). One of the institutions in the world where low-speed penetrator technologies are being developed is the Space Research Center (CBK) of the Polish Academy of Sciences. Examples of penetrators with a battery in the form of a capacitor are MUPUS [6] and CHOMIK [7]-a penetrator developed for the Phobos Grunt mission. The driving unit of both penetrators is an electromagnet with a movable dive (hammer), shown in Figure 2. The pulling of the dive inside is caused by the creation of a ponderomotive force seeking to reduce the gap. The return of the dive (hammer) to the starting position is ensured by two small return springs with low pressure. A hammer hitting the foot causes the test rod (MUPUS) or soil sample container (CHOMIK) to sink. The penetrators are shown in Figure 3. For both penetrators described above, the maximum driving depth is limited by the drive section. It means that those penetrators can sink to a maximum of about 30-40 cm, i.e., as much as the length of the test rod will allow. Mole-type penetrators do not have such a restriction. These devices are characterized by a compact construction with a small diameter, enabling the sinking of the entire penetrator into the hammered object. The only limiters of the penetration for this type of construction are the mechanical properties of the soil and the length of the power cable. The energy accumulator in this case is a spring compressed by an electric actuator. When the shortening is achieved, the spring-retaining clip is released, which releases the energy that drives the hammer. The penetration of the penetrator is induced by the hitting of the hammer against the casing tip. An example of this type of penetrator is KRET, shown in Figure 4. The KRET penetrator belongs to the group of self-piercing space penetrators. The task of the device is to provide small detectors (such as thermal sensors) under the surface of the body for scientific research. The depth of the penetration of the soil for Mars or the Moon is estimated at about 7 m. The instrument was developed to be placed on board lunar landers as part of the International Lunar Network initiative. Work is currently underway to integrate KRET with the Lunar Geophysical Investigation Package as part of the NASA project. Thanks to measurements carried out with the help of this device, it will be possible to determine, among other things, the value of the heat flux that reaches the surface of the Moon from its interior.
The KRET penetrator tube reluctance actuator construction and basic components are shown in  The ability to operate in a vacuum. This paper's main objective is the analysis of simulations involving the design parameters that had an impact on the operational characteristics of the tube reluctance actuator for impulse operation in the KRET penetrator. That was achieved by using the mathematical model, field-circumferential model, directly coupled field-circuit numerical model and Finite Element Method model in the ANSYS environment [15][16][17].

Numerical Model of the Tube Reluctance Actuator for Multiphysics Purposes
The main research problem of this work is the analysis of the impact of design parameters on the operational characteristics of a tube reluctance actuator for impulse operation via the procurement of proper simulations. The method to solve this problem is a directly coupled field-circuit numerical model. The purpose of the numerical analysis is to determine the design parameters that ensure the highest possible energy conversion efficiency-from the electricity stored in the coil to the kinetic energy of the hammer (runner). In other words, from the point of view of the usability of the device, the most important factor is the generation of the greatest possible energy of the hammer impact, which will ensure penetration into the given soil [18,19].
The tool used to solve the research problem is the Finite Element Method implemented in the ANSYS software. The reasons for choosing this software are its capabilities, which include [20][21][22][23]: • Analyzing several different physical phenomena in one model (so-called Multiphysics analyses). With this option, it is possible to directly analyze the interaction between individual phenomena.

•
The APDL script language-it allows the creation of parametric models simplifying the modification of the model significantly. This is a particularly important advantage, taking into account the need to analyze the impact of many different construction parameters, which entails the need to modify the model multiple times.
The numerical model described in this chapter was developed from scratch using the APDL language. This requires a greater effort at the model creation stage; however, thanks to this approach, the process of making changes in the construction parameters is not a problem. The most arduous processes in creating FEM models (such as creating geometry and division into finite elements) have been properly implemented and parameterized while creating the basic model, which allows their automatic execution. The methods of executing the numerical methods are shown in Figure 7, and the individual steps to create a model are shown in Figure 8 below [24][25][26][27].
The numerical model directly takes into account the dynamic interactions between the three physical phenomena needed to simulate the operation of the device: electricity, magnetism, and dynamics. The figure shows, schematically, the components that have been included in the numerical model. Due to the construction of the device, the field submodel was simulated with a two-dimensional geometry, taking into account axial symmetry. The peripheral submodel is directly coupled to the field submodel by coupling the properties and degrees of freedom of the coils ( Figure 9). As already mentioned, the model combines three different physical phenomena and finds a solution in the time domain (transient analysis) [28][29][30].   In order to simplify the model and reduce the number of finite elements, only two sections (coils) of the linear actuator are modeled (pre-estimated six sections on the entire device motors). Depending on the configuration of the construction parameters, after discretization, the model contains from 10 to 40 thousand finite elements. The model's mesh is compacted in critical areas (places of magnetic field density) in order to increase the accuracy of the obtained solution ( Figure 10). A single time step has been estimated at 0.00005 s, which provides a solution of about 80 steps to simulate a single device working action (depending on the configuration of the construction parameters). For each time step, the relative position between the core (counterweight) and the runner (hammer) is updated and included in the next time step. The displacement is carried out by moving elements simulating the runner along the contact elements. The model operation method is shown in Figure 11. In addition, the graphic presents a diagram showing the method of driving the device.

Limitations of the Numerical Model
The numerical model used did not accurately reflect reality. Some phenomena were omitted due to their negligible impacts on the results of the calculations. The chosen modeling method also did not allow for the incorporation of some engine design features. The chapter explains the most important simplifications [31,32].
The first simplification concerned the aerodynamic drag. During the runner's working motion, aerodynamic drag occurred in the air. The value of the aerodynamic force depends mainly on the speed and drag coefficient, which is dimensionless, depending on the shape and orientation of the moving body. For the geometry of the runner, the resistance coefficient takes a relatively low value. Besides, the achieved speeds are also not low in terms of aerodynamic drag. Therefore, bypassing this phenomenon would not significantly affect the accuracy of the results [33][34][35].
The second simplification concerned the rolling friction. The developed model did not include rolling resistance in the linear bearing used in the mechanism construction. The rolling friction force is directly proportional to the clamping force. It should be noted that in the case of the mechanism under consideration, the engine generates a thrust that is perpendicular to the contact force of the bearing balls. The main role of linear bearings is to ensure axiality between the core and the runner. Therefore, rolling frictional resistance has been omitted in the numerical analysis.
The third simplification concerned the geometry. Since the developed model is an axially symmetrical two-dimensional model, it presents an idealized system geometry (e.g., ideal engine axis). It also did not take into account an important design feature-undercuts in the motor core introduced to minimize the phenomenon of eddy current induction [36][37][38].

Laboratory Model of the Tube Reluctance Actuator
In order to check the validity of the penetrator concept and verify the calculations, a laboratory model of the actuator was developed and then produced. It should be noted that this model was designed on the basis of preliminary calculations. The laboratory model contains all the relevant components from the point of view of penetrator functionality and is built of the following elements: • Hammer (runner); Counter-mass return spring; • Linear ball raceway.
The construction of the device is shown in Figure 12 below. The main components of the hammer are ferromagnetic rings and a titanium tip-an element hitting the anvil. In addition, the hammer includes separators that are making a gap between two ferromagnetic rings and bearing raceways. All the components are connected by an external housing made of carbon fibers. Details regarding the construction of the hammer are shown in Figure 13. The main counter-mass component is the core made of ferromagnetic material (the same as for hammer rings-ARMCO iron) with two coils wound. At both ends of the core, there are bearing raceways on which balls move, enabling the linear movement of the hammer. An element maintaining the initial distance between the hammer and the anvil-a stop-has been attached to one of the treadmills. On the opposite side, a guide rod is attached, which moves along the linear guide. An additional mass was placed at the end of the rod to ensure the correct mass ratio between the hammer and the counter-mass. The counter-mass module is shown in Figure 14 below. Functional tests were performed in a vertical configuration ( Figure 15). The control parameter examined during the functional tests was the displacement of the hammer vs. time (velocity). The measurements were made using a camera for fast video recording.

Laboratory Model Tests and Simulation Validity Check
The numerical model verification was based on the laboratory model. The parameter values recorded during the functional tests are the most important data concerning the penetrator's performance-the hammer velocity-and thus the kinetic energy impacting on the housing. It should be mentioned that the presented test results are averages of the measurements taken. In addition, the measurement results obtained are subjected to a rather significant error (estimated at even 10%). This is due to the method of data processing. The image recorded with the camera for the fast movement was analyzed "frame by frame", determining the displacement of the hammer between the individual frames of the video. Based on the frequency at which the pictures were taken (0.12 ms), the speed characteristics were determined. The moment of the termination of the simulation and the tests carried out was assumed to be the moment of the alignment of the ferromagnetic rings.   The developed laboratory model contains a basic construction error-the coil windings were wound in the same direction, which causes a significant reduction in the motor efficiency (adjacent poles are unlike). This error was detected after performing numerical analyses with correctly modeled coil windings. Nevertheless, for the verification of the numerical model, the simulation results are presented taking into account the incorrect return of the coil winding (and hence the return of the current flow).
The comparison of the hammer speed characteristics provided shows good compatibility of the simulation with the real object. Despite its complexity lying mainly in the direct coupling of the field and peripheral models, the direct modeling of the hammer displacement in the field model, and the taking into account of the phenomenon of eddy currents, the model consists of some simplifications. The most important simplification is the presentation of the actuator core model as having a plane geometry with axial symmetry. In fact, the core contains radial incisions to reduce the phenomenon of eddy current induction. Despite the omission of this design feature, the results of the tests and simulations carried out show very good compliance.
The authors are aware of a certain disadvantage of the model verification carried out in this way-the only checked parameters are the runner velocity of the model and electromagnetic phenomena that occur while the hammer is displaced. In order to verify the model more accurately, it would be necessary to carry out measurements of other physical quantities such as the discharge characteristics of the capacitor or current and voltage coil waveforms. However, at the project planning stage, it was decided to perform only the hammer velocity and displacement measurements, as those are the most important parameters for the device structure. The value of the velocity depends on the results of the electromagnetic analysis. The electrical energy accumulated in the capacitor is converted into magnetic field energy, which generates ponderomotive force and, finally, the displacement of the hammer. Given the above, it can be concluded that if the velocity results for the tests and simulations match, the entire energy conversion process occurs correctly. The results presented are therefore a sufficient basis for further simulations to determine the design parameters to ensure more efficient actuator operation.

Analysis of Simulation Results
This section presents the results of an actuator FEM simulation with design parameters for a laboratory model. The purpose of the result analysis is to find weak points in the structure and identify parameters that can improve actuator performance. The results are presented for three model variants: Deriving results for the above three scenarios will allow a more in-depth assessment of the structure. Figure 19 shows the results for the hammer velocity during the working stroke. Figure 20 presents the axial component of the ponderomotive force acting on the ferromagnetic rings located in the hammer as well as the current in the coil as a function of the hammer's displacement.  The FEM magnetic field simulation results are presented in Figures 21-23 below. The simulation results in Figure 19 confirm the calculations beforehand and are in line with the theory of electromagnetism. It is obvious that for Variant I, even if the parasitic effects of eddy currents are taken into consideration, due to the incorrect winding of the coils, the velocity of the hammer is still at the lowest value. Maintaining the principle of push-wound coils for this case allows a significant increase in the final velocity. This is clearly shown in the course for Variant III. Unfortunately, in Variant III, there is the fault of the result related to the measurement of eddy current losses. The purpose of selecting such configured variants was to determine the percentage impact of model simplifications and thus the influence of eddy currents. The error of Variant II-which the authors indicate as the target, i.e., coils wound in opposite directions-considering the eddy currents is less than 10% in comparison to Variant III. The natural conclusion, referring to previous observations (Figure 19), is the simulation results from Figure 22. The results are related to the value of the ponderomotive force and current in the coil as a function of the position of the hammer with the position of the ferromagnetic rings. Despite the simplification, which is the presentation of the actuator core model as having a plane geometry with axial symmetry, the results of the tests and simulations carried out show very good compliance. This applies to both the value for the hammer velocity and the duration of the movement. Of course, this was possible due to the eddy current phenomenon as a boundary condition. Figures 21-23 show the magnetic induction field distribution for the three variants presented. Only for Variant II do the magnetic induction lines close through the core, hammer and air gap. It is worth noting that the correctness of the line closing is analogous for each hammer displacement (1 mm, 2.5 mm and 4 mm). A small part of the energy stored in the capacitors is dissipated. The value of this dispersion has a direct impact on the velocity of the hammer.    Figure 24 includes the simplified geometry of the device (without cuttings to reduce eddy current induction). It affects the eddy current FEM analysis. Even if such a phenomenon caused by the shape of the structure has not been taken into account, the boundary conditions should be properly selected. The magnetic induction values differ markedly in both cases. A result was obtained that confirmed previously acquired data (Figures 21 and 22).

Conclusions
This manuscript presents a set of simulations for use in aerospace engineering involving important construction parameters such as eddy current impact, hammer displacement, and velocity. The overall electromagnetic analysis for different variants is also presented. Simulations may be treated as a method that allows the cost-effective design of such devices. The aerospace penetrator's construction principles were introduced, as was its overall functionality. A validated laboratory model and FEM simulations were presented for three different variants. The experimental and simulation results were juxtaposed and compared. Those were made in order to conclude the presented work. The effectiveness of the procedures was confirmed. The introduced procedure allows the shortening of the production time for the final product, as well as reducing costs. The model used was not limited in the representation of physical phenomena. For the multi-variant calculations of the tube reluctance actuator, the numerical model was described in Section 2. The purpose of the calculations was to determine the structural parameters ensuring the most efficient operation of the device. The specific use of the actuator implies the presentation of high-end values of these device parameters based on the derived results. Those are presented in Table 1 below. The best simulation results were acquired from Variant II, which consisted of the following boundary conditions: reversed coils and the inclusion of eddy currents. This scenario reflects the most frequent real conditions and provides valuable data for optimizing the functionality of the penetrator. It was noticed that not considering the eddy currents simplifies the model too much. Even if such a phenomenon caused by shape is not taken into account by the model construction, the boundary conditions must be selected accordingly. The induction values in both cases clearly differed. The results confirm the previous results received, as clearly shown in Figures 21 and 22. Table 1. High-end parameters of the tube reluctance actuator derived after the laboratory model tests and simulation results.

Parameter Value
Max. length of the actuator 127 (mm) The outer diameter of the actuator (H) 22.7 (mm) The total weight of the hammer 120 (g) Total counter-mass weight 720 (g) Energy stored in the capacitor 21 (J)