- Research
- Open Access

# Shape of mole nose providing minimum axial resistance

- Yi Shen
^{1}, - Xuyan Hou
^{1}Email author, - Yiwei Qin
^{1}, - Shengyuan Jiang
^{1}and - Zongquan Deng
^{1}

**1**:10

https://doi.org/10.1186/s40638-014-0010-7

© Shen et al.; licensee Springer. 2014

**Received:**17 April 2014**Accepted:**10 September 2014**Published:**26 November 2014

## Abstract

### Introduction

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.

### Mechanics analysis

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 simulations

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.

## Keywords

- Mole
- Circular arc shape
- EDEM

## Background

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 [1]. 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 [2],[3]. 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 [4],[5]. 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 [6], 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 [7], 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 [8],[9]. 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 [10]. 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 [11].

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.

## Methods

### Principle of penetration

- (a)
Accumulation of energy in the driving spring by the movement of the hammer upward relatively to the casing via the servo driving unit.

- (b)
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. - (c)
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.

- (d)
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*/2*R*, where *R* is the radius of the casing. The length of the front nose is *l*.

### Penetrating experiments

## Results and discussion

### Theory of mechanics analysis

#### Soil failure

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 [12]. 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.

*P*, the mole penetrates into the geological layer and soil moves to region III initially. When positive pressure reaches a certain value, soil in region III reaches the limited state. And soil starts to fail if the pressure continues to increase. Region II has two sets of slip lines. One set is two rays, AC from point A and BE from point B. The other set is logarithmic spiral curves CG and EF, expressed as

where *φ* is the internal friction angle [13].

*δ*=

*π*/4 −

*φ*/2. After the mole with a convex arc shape penetrates into soil, the initial length of the logarithmic spiral curves is:

*γ*is the bulk density of soil.

*H*is given by

*σ*

_{ z }is the minimum principal stress

*σ*

_{3}and horizontal stress

*σ*

_{ x }is the maximum main stress

*σ*

_{1}. So we can get:

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
}.

*p*

_{ F }, namely Rankine's active earth pressure. Taking point B as centroid, according to the condition of the static equilibrium of block BEFK, we have:

*p*

_{ r }to point B is zero and the rest of the moment to point B are:

*N*_{
q
} and *N*_{
c
} are the bearing capacity coefficients of soil, which are functions of internal friction angle *φ*.

*s*is the increment of the arc length on the surface of the nose and

*p*′ is the radial stress acting on the cambered surface BO. Take the coefficient of friction to be

*μ*and

*τ*

_{0}and ${\tau}_{F}^{\prime}$ can be expressed as:

#### Axial resistance

where *x* = *S* sin *θ* − (*S* − *R*).

*β*=

*π*/2 into Equation 20, we can get the axial resistance ${F}_{1}^{\prime}$ on the total convex arc-shaped front nose. What's more, the lateral surface of the mole also contacts soil, whose mechanical analysis is shown in Figure 9. Regarding the lateral surface as a retaining wall, according to Rankine's earth pressure theory, passive earth pressure

*p*

_{P 1}has the following expression:

where *K*_{
P
} is the passive earth pressure coefficients and *K*_{
P
} = *tg*^{2}(45*°* + *φ*/2).

*y*=

*l*and (

*D*−

*l*) to give the net positive force

*N*:

*H*is the distance from the ground to surfaces AJ and BI, which can be expressed as:

*F*from

*θ*=

*β*

_{0}and

*θ*=

*π*/2. So axial resistance on the front nose has the following expression:

*F*

_{ c }=

*μN*, integrate Equation 22 between

*y*=

*l*and

*y*=

*l*+

*L*to get the net resistance on the lateral surface:

#### Axial resistance vs caliber-radius-head

**Physical parameters of the mole and soil**

Parameters | ||||||
---|---|---|---|---|---|---|

R(mm) | L(mm) | c | φ(°) | γ(kN/m | μ | |

Value | 15 | 200 | 0 | 30 | 18 | 0.3 |

*ψ*are drawn (shown in Figure 11). As can be seen from Figure 11, the curve of axial resistance is similar to a parabola changing with penetration depth. Moreover, axial resistance decreases with the increase of

*ψ*. However, the advantage is not obvious when

*ψ*increases to 3 and a very large value of

*ψ*causes an increase in total length of the front nose which is not advisable.

### EDEM simulation

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.

**Material parameters**

Material | Poisson's ratio | Shear modulus (Pa) | Density (kg/m |
---|---|---|---|

Particle | 0.3 | 2 × 10 | 1,750 |

Mole | 0.3 | 2 × 10 | 7,850 |

**Interaction parameters**

Interaction | Particle-particle | Particle-mole |
---|---|---|

Coefficient of restitution | 0.1 | 0.2 |

Coefficient of static friction | 0.574 | 0.3 |

Coefficient of rolling friction | 0.01 | 0.01 |

*ψ*from 1 to 4 and all simulations are shown in Figure 13.

*ψ*. But the variation is not obvious when

*ψ*increases from 3 to 4, which can explain the relationship between axial resistance and

*ψ*in the certain conditions. Exporting the EDEM simulation data, curves of axial resistance vs penetration depth for various values of

*ψ*are shown in Figure 14, which is consistent with theoretical analysis.

## Conclusions

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.

## Declarations

### Acknowledgements

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).

## Authors’ Affiliations

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.