Shape of mole nose providing minimum axial resistance
© Shen et al.; licensee Springer. 2014
Received: 17 April 2014
Accepted: 10 September 2014
Published: 26 November 2014
As a carrier of different sensors, moles can penetrate into the regolith automatically and keep investigating the subsurface environment continuously. In this section, features of several moles with different applications are introduced to explain why we choose a hammer-driven mole to study.
Mole driven by a hammer
In this section, the penetrating principle of a hammer-driven mole is illustrated and a circular arc shape for the front nose is proposed. Moreover, applying the penetrating principle, experiments of the mole with an arc-shaped nose are performed to observe the penetration phenomena in a simulated lunar regolith.
According to soil mechanics theory, regions of soil failure are divided and a mechanics model is established between soil and mole with an arc-shaped nose. The work is done to get approximate axial resistance equations which are analyzed with the defined geometric parameters caliber-radius-head.
EDEM is leading global software based on discrete element method, whose main function is to analyze and observe the movement of particles. Lunar soil simulacrum is established to simulate axial resistance. Eventually, the theoretical results are validated by simulation.
As a novel technique of in situ investigation, a mole device employs a self-penetrating mechanism, which is considered to be a promising direction for space missions to get information about the geological structure, evolution, and physical and chemical properties of the material if we want to know whether there is life on Mars or the conditions were ever suitable for humans. It is more compact, is lightweight, and has low power consumption. Once it has penetrated into a certain depth, it can acquire geological information of the medium constantly, using various sensors.
In order to conduct deep space exploration, many countries have been involved in the development of a low-speed, unmanned subsurface investigation device. Several prototypes of the mole have been designed and tested in laboratory conditions even though it started late. The mole was first developed by the Russian Federal Space Agency for the Mars-96 mission, called Mars 96 Penetrator, utilizing high speed to penetrate into the regolith, which can penetrate a deeper distance but cannot be used repeatedly and causes great damage to the detecting instruments, leading to data errors . To overcome the disadvantages above, a hammer-driven mechanism was applied to the mole, which will be described in the next sections. In 2011, Japanese researchers proposed a robotic screw explorer which can excavate into soil and transport it backward automatically ,. Inspired by animals, such as mouse and earthworm, more and more researchers focus on the bionics design, e.g., an earthworm-type robot which can make use of the reactive force caused by pushing the discharged regolith above the robot ,. As for China, apart from the development of a thermal drill which is a combination of a rotary drill and a melting probe in Hong Kong Polytechnic University , it is seldom studied so far. In addition, it is worth mentioning that all those prototypes are still in the exploratory pilot phase and none is implemented in space mission successfully, which provides a great space for China to develop the automatic penetrating device.
Although discharging soil backward has great advantage compared with squeezing soil, the hammer-driven mole penetrates better on current technology. So this paper still focuses on optimization of a mole driven by a hammer. As opposed to that of the conventional rotary drill, forward motion of the mole is done by displacement and compression of the soil. Penetration depth depends on the matching of three qualities and shape of the front nose. So it is crucial to study the shape of the front nose. Up to now, the hammer-driven mole has several types of front nose, e.g., MMUM , derived from PLUTO developed by DLR for the Beagle 2 lander on the ESA Mars Express mission with added capability of sampling at the 60° front cone that can open during further penetration ,. Another interesting device is MUPUS on the Philae lander by PAS, whose front nose was designed with sharp and elastic barbs to get anchoring property . Following the successful MUPUS development, a nonlinear conical shape (ogive-shaped tip angle starts from 45° at the base and 30° at the end) was applied to the KRET .
The remainder of this paper is organized as follows. The principle of operation of the hammer-driven mole is illustrated and an arc-shaped front nose is proposed in the ‘Methods’ section. Besides, experiment results of a convex arc-shaped nose in simulated lunar are also presented in the ‘Methods’ section. A mechanical model between the front nose and soil is built in the ‘Results and discussion’ section. What's more, EDEM simulations of the mole with different geometric parameters are given in the ‘Results and discussion’ section to further prove the relationship between axial resistance and caliber-radius-head, followed by the ‘Conclusions’ section.
Principle of penetration
Accumulation of energy in the driving spring by the movement of the hammer upward relatively to the casing via the servo driving unit.
Escapement mechanism separates suddenly when the hammer reaches a certain distance and the driven hammer accelerates and hits the bottom of the casing, thus contributing the displacement x 1 by overcoming the restraint of the soil around.
At the instant of the release of the hammer, the servo driving unit moves backward compared with the hammer, and then the buffer spring is compressed to avoid reverse movement of the mole.
Under the effect of the buffer spring and its own gravity, the servo driving unit hits the casing, thus forcing the mole to move down at x 2. The movement of the mole repeats just like that, which is suitable for the regolith that can be compressed for making space. After the mole penetrates to a certain depth, a hole with a higher density appears at the back.
An arc-shaped front nose
The shape is arc of a circle with radius S that is tangent to the casing of the mole. Caliber-radius-head is defined as ψ = S/2R, where R is the radius of the casing. The length of the front nose is l.
Results and discussion
Theory of mechanics analysis
As mentioned previously, there is a great deal of complexity about the regolith of space bodies. Currently, it is accepted that the surface and subsurface materials of space bodies consist of granulated matter with grain size in a range from several micrometers to several millimeters, like terrestrial sand . In addition, the mole device is driven by a hammer, which means that it is capable of working in the regolith in the dynamic range. Thus, the mechanical properties and failure model of the regolith are crucial to correctly calculate resistance force. Based on the study of soil on the earth, we assume the mole penetrates a semi-infinite shield.
where φ is the internal friction angle .
where c is cohesion.
Stresses on surface EF are cohesion of the soil c (distribution uniform), normal stress p n , and friction force p n tanφ (distribution non-uniform). p r is the joint stress of p n and p n tanφ, and it has an included angle of φ with p n . According to the characters of the logarithmic spiral curve, point B should be on the force line of p r .
N q and N c are the bearing capacity coefficients of soil, which are functions of internal friction angle φ.
where x = S sin θ − (S − R).
where K P is the passive earth pressure coefficients and K P = tg2(45° + φ/2).
Axial resistance vs caliber-radius-head
Physical parameters of the mole and soil
Generally, granular matter behaves like a compressible non-Newtonian complex fluid including fluid solid transition and can be simulated using EDEM simulation. An obvious advantage of EDEM simulation is that it provides the possibility of obtaining movement, forces, and other dynamical properties of the system at any time.
Shear modulus (Pa)
2 × 107
2 × 1010
Coefficient of restitution
Coefficient of static friction
Coefficient of rolling friction
In this paper, we focus on the front nose of a hammer-driven mole. Distinguishing with the conical one, an arc-shaped front nose has been proposed, which is tested in laboratory conditions. The contributions of this paper are the establishment of a mechanics model, derivation of axial resistance based on soil mechanics, and application of the discrete element method to observe the flow of the lunar soil. Through theoretical analysis, it is found that the axial resistance of the mole shows a negative correlation with the shape parameter ψ. Besides, parameters like penetration depth D, friction coefficient μ, internal friction angle φ, and cohesion c also affect the axial resistance to some extent. Such theoretical approach can be used to optimize the geometric design of the front nose. What's more, a series of EDEM simulations show excellent accordance with the result. However, the length of the front nose increases with a large value of ψ, which decreases the stiffness of the front nose seriously. Therefore, we compromise to balance the two factors to get an appropriate value depending on demand. The study of optimization of the front nose is still ongoing. Other parameters and other shapes will be taken into consideration in order that the mole can penetrate into a deeper subsurface. Besides, several noses have already been tested and more experiments will be carried out in the future.
The project is financially supported by the National Nature Science Foundation of China (Grant No. 51105092) and College Discipline Innovation Wisdom Plan of China (111 Project, Grant No. B07018).
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