Design and testing of coring bits on drilling lunar rock simulant

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ScienceDirect Advances in Space Research xxx (2016) xxx–xxx www.elsevier.com/locate/asr

Design and testing of coring bits on drilling lunar rock simulant Peng Li a,1, Shengyuan Jiang a,⇑,1, Dewei Tang a,1, Bo Xu b, Chao Ma a,1, Hui Zhang a,1, Hongwei Qin a,1, Zongquan Deng a,1 a b

Harbin Institute of Technology, Harbin 150001, China Institute of Advanced Technology, Harbin 150001, China

Received 16 March 2016; received in revised form 31 October 2016; accepted 7 November 2016

Abstract Coring bits are widely utilized in the sampling of celestial bodies, and their drilling behaviors directly affect the sampling results and drilling security. This paper introduces a lunar regolith coring bit (LRCB), which is a key component of sampling tools for lunar rock breaking during the lunar soil sampling process. We establish the interaction model between the drill bit and rock at a small cutting depth, and the two main influential parameters (forward and outward rake angles) of LRCB on drilling loads are determined. We perform the parameter screening task of LRCB with the aim to minimize the weight on bit (WOB). We verify the drilling load performances of LRCB after optimization, and the higher penetrations per revolution (PPR) are, the larger drilling loads we gained. Besides, we perform lunar soil drilling simulations to estimate the efficiency on chip conveying and sample coring of LRCB. The results of the simulation and test are basically consistent on coring efficiency, and the chip removal efficiency of LRCB is slightly lower than HIT-H bit from simulation. This work proposes a method for the design of coring bits in subsequent extraterrestrial explorations. Ó 2016 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Lunar regolith coring bit; Bit geometric optimization; Lunar rock drilling; Drilling behaviors

1. Introduction Drilling and coring have traditionally been part of a commonly employed method in geological engineering, and are employed in extraterrestrial explorations because of the capability of chip conveying without the need for additional liquid. After performing laboratory analyses of native samples returned from celestial bodies, explanations about the origin and evolution of the earth, planets, and even the solar system may be understood (Duffard et al., 2011; Zacny et al., 2011). From the 1960s, the United States and the former Soviet Union have successively landed on the moon, and have obtained approximately ⇑ Corresponding author.

E-mail addresses: [email protected] (P. Li), [email protected] (S. Jiang), [email protected] (D. Tang). 1 School of Mechatronics Engineering, China.

380 kg of lunar regolith samples (Barsukov, 1977; Taylor, 1975). Recently, China has also planned a lunar sampleand-return mission, called the Chinese Lunar Exploration Program (CE), to acquire the lunar regolith 2 m beneath the surface employing a coring bit jointed with a hollow auger (Duan et al., 2014; Tian et al., 2015). According to the lunar regolith data announced by the National Aeronautics and Space Administration (NASA), lunar regolith components having a variety of shapes are widely distributed on the lunar subsurface, and include types such as granular soil and rock block (Allton, 1989; El-Khayatt and Al-Rajhi, 2015). General failures typically experienced during the drilling process mainly include (a) choking due to the soil chips and (b) blockages due to the hard rock (Carrier et al., 1991; Tian et al., 2012). As the guiding component of the drill auger, the drilling behaviors are strongly related to the coring bit geometries. Thus, for

http://dx.doi.org/10.1016/j.asr.2016.11.012 0273-1177/Ó 2016 COSPAR. Published by Elsevier Ltd. All rights reserved.

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the CE program, a good coring bit should (1) convey lunar soil chips without the aid of lubricants or flushing fluids, (2) achieve good drill-core recovery, and (3) break through the lunar rock block with the drillability above VI (Deng et al., 2013; Shi et al., 2014). In 1976, the stair-type coring bit was utilized in the unmanned Luna-24 sampling mission launched by the former Soviet Union (Pitcher and Gao, 2015). The bit was embedded with eight columnar cutting blades, with the main task being to break through the lunar rock block. During the lunar soil drilling, the chips were gradually accumulated near the bit body, and were eventually removed by the auger spiral groove with the increasing drilling depth. Recently, the Northern Centre for Advanced Technology (NORCAT) developed a dry drill bit for NASA’s moon polar exploration program (Bar-Cohen and Zacny, 2008). The screw grooves were dug on the drill bit body to remove the polar lunar soils, and the diamond grits were impregnated on the helical surface to deal with the rock. In the field test, the drill bit penetrates the loose lunar soil simulant at a lower weight on bit (WOB), and comminutes rocks such as basalt and anorthosites. In addition, the Jet Propulsion Laboratory (JPL) introduced a rock-coring bit for the Mars Sample Return (MSR) mission in 2012 (Hudson et al., 2010; Kriechbaum et al., 2010). The bit inlaid four tungsten carbide cutting blades on the top plane for rock breaking, and the radioactive grooves that are connected to the auger were excavated along the blade rake face to contain the rock chips. Because the objects being drilled are Mars rocks and the drilling depth is only 50 mm, the drilling loads caused by chip accumulation can be omitted (Mattingly and May, 2011; Klein et al., 2012). Besides, some other sampling devices have been developed to acquire the lunar surface regolith in recent years. The typical one is the rigid-flexible link combined lunar sampler, which is mainly composed of three rigid rotational links and one flexible shrinking link (Ling et al., 2014). The difference of this sampler compared with coring method is the sampling objective which is the multi-

point loose soil on lunar surface. The sampling volume is much more than coring method, and the sampling peak power is no more than 6 W which is far less than drilling. The theory of rock-cutting load prediction can be traced to Merchant’s model, which proposed the metal-cutting theory in rock-cutting processes with properties of plastic material, and was based on the Coulomb criterion and the shear plane assumption (Che et al., 2012a). Then, Nishimatsu proposed a formula for the cutting force in rock cutting by using a wedge-shaped tool based on the Mohr criterion of failure and the specific stress distribution assumption (Che et al., 2012b). Detournay and Defourny built the cutting force models (D-D model) of the drag bit for both sharp and worn cutters, and which was based on the intrinsic specific energy and a quantity with dimension of stress. To obtain an accurate prediction of the rockdrilling response, Detournay differentiated between three successive regimes, namely the dominance of frictional contact, the cutting depth, and hole-bottom poor cleaning (Detournay and Richard, 2008; Perneder et al., 2011). In summary, the features of lunar soil convey are determined by the drill bit body, and the blade shape affects mainly the rock-drilling performance. Recently, the Research Center of Aerospace Mechanism and Control developed a helical-type drill bit body (HIT-H) for lunar soil coring. The spatial helix grooves combined with the ring-type soil coring isolated structure are employed on the HIT-H bit, which improves the performance in terms of both conveying the soil chips and drill-core recovery in lunar soil sampling (Zhao et al., 2016a). With the purpose of design a coring bit which the drilling feature includes smooth chip conveying, high drill-core recovery and low rock drilling load, the LRCB is developed based on the HIT-H bit body. In this study, we focus mainly on the parametric design of LRCB cutting blades. We assume the Coulomb-Mohr criterion and compact core, and we establish the interaction model between the lunar rock simulant and the LRCB. Meanwhile, we analyzed the variations in the drilling loads derived from the blade shape

Fig. 1. 3D view of spiral helix bit (HIT-H) and LRCB.

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parameters after performing laboratory drilling tests. Then, we performed a parametric optimization of the LRCB with the purpose of minimizing the WOB. Finally, to compare the effects on the chip-removal efficiency and drill-core recovery of LRCB before and after inlaying the sharp blades, we performed discrete-element simulations involving lunar soil simulant sampling by using EDEM software. 2. Definition of LRCB geometric parameters According to the constrains of the CE program, the mass and size of the landing platform in actual mission is approximately 1.5 ton and 3.5
3.5
5 m. Besides, the mass and power of the sampling system on the landing platform should be limited to 35 kg and 450 W or less. The rated WOB is about 800 N and the bit needs to break through the rock with the drillability above VI. The ability to break through a rock block on the LRCB can be achieved by impregnating grinding grits or inlaying cutting blades. Due to the drilling load of the grinding bit is much higher than the cutting bit at the same drilling parameters, and the load limitations of the drilling system, the cutting blades have been adopted on LRCB. Moreover, to weaken the breakage effect of the flows that convey the chips, we employed double rows of sharp cutting blades (SCBs), as shown in Fig. 1. We used the sharp point on

3

the blade to enhance the bit stabilization during the initial stage of the rock blade contact. The geometric parameters of the LRCB are illustrated in Table 1. In Table 1, the minor axis length of the ellipsoid with a helix profile hH is deduced using the helix pitch angle according to the auger parameters. Both the parameters for the cutting blade positions are fixed by the start and end points of the helix profile. The forward rake angle con is defined as the angle of SCB moving around the bit radial direction. The outward rake angle ksn is defined as the angle of the SCB as it moves in a direction normal to the plane of the inlaid blades. The sharp-point position coefficient k r is equal to the ratio between the width of the elemental blade in row I wb1 and the width of the SCB wSb . The flow diagram (as shown in Fig. 2) of the design procedure of the LRCB is summarized as follows: (1) confirm the geometric parameters of the drill bit body; (2) input the values or ranges of the cutting blade’s geometric and positional parameters; (3) divide the cutting blades into elemental blades, and calculate the geometric or kinematic parameters of each elemental blade; (4) model the resistant-force prediction of elemental blade rock cutting; (5) enforce the elemental blade-cutting tests on a lunar rock simulant, and calibrate the friction angles in the model; (6) transform the coordinates and calculate the drilling loads of the LRCB; (7) optimize the LRCB parameters with

Table 1 Geometric parameters of LRCB. Parameters

Symbols

Values

Drill bit body

Drilling hole diameter Coring diameter Minor axis length of ellipsoid of helix profile The number of helices

DH DC hH NH

32 mm 14.5 mm 15.8 mm 3

Position of cutting blade

The height differences between two blades in different rows The angle differences between two blades in different rows

Dhb Dwb

1 mm 93.08°

Shape of cutting blade

Forward rake angle Outward rake angle Sharp-point position coefficient Sharp-point height Sharp blade width

con ksn kr hs wSb

25 to 0° 0–25° 0.3–0.7 0.5–2 mm 3–7 mm

Fig. 2. Flow diagram of LRCB design procedure.

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Fig. 3. Trajectory curves of single-blade drilling.

Fig. 4. Rock-breaking areas at small cutting depth.

the aim to minimize the WOB; (8) verify the results by performing lunar rock simulant drilling experiments. The specifications of symbols in Fig. 2 are listed in Table 2. 3. Theoretical method During the drilling and sampling process on the moon, the main drilling target is the granular lunar soil. Therefore, the speed control mode of the penetration should be adopted to prevent auger choking caused by an excessive penetrating speed. The drilling strategy of LRCB can be classified as the auger speed nD and the rate of penetration vPen . The penetrations per revolution (PPR) are defined as

the ratio of the rate of penetration to the auger speed. The actual physical meaning of PPR is the penetrating displacement in the drilling direction when the bit completes one cycle. When the bit is drilling with a certain PPR value, the cutting blades are thrust into the lunar soil with the spiral movement, as shown in Fig. 3(a). After one cutting cycle around the rotary center of the drill, the penetrating displacement of the blade is equal to the value of the cutting depth multiplied by the number of blades, as shown in Eq. (1). The outspread curve of the blade trajectories is shown in Fig. 3(b). k PPR ¼

vPen ¼ N b  hPen nD

ð1Þ

where Table 2 Load and motion parameters of LRCB. Symbols

Specification

qbi

The radius vector of the elemental blade edge in the absolute coordinate system The rake face normal vector of the elemental blade The unit vector of the elemental blade edge The normal unit vector on rake face of the elemental blade edge The cutting-speed vector of the elemental blade The auger/bit rotational speed The penetrations per revolution The normal unit vector of the working reference plane The normal unit vector of the working velocity plane The normal unit vector of the working orthogonal plane The rake angle of the elemental blade The side rake angle of the elemental blade The width of the elemental blade The cutting depth of the elemental blade The cutting depth fluctuations of the elemental blade

k

gi k bi k ai k vei k nD k PPR ri k si k oi k coei k ksei k wbei k hpenei k Dhpnei k

Note: the subscript ‘i k’ represents the ith elemental blade in row k.

 hPen = cutting depth of single blade;  N b = the number of blades along the bit circumferential distribution. When rocks are encountered during the lunar soil coring process, the PPR should be maintained at a small cutting depth range (approximately 10 lm) in order to prevent the drilling loads from exceeding the drilling system restrictions. 3.1. Mechanics of lunar rock simulant cutting process by using elemental blade 3.1.1. Rock-cutting prediction in section of elemental blade In the cutting process, the rock is crushed by the compacting effect at the tip of the blade, and the compact core will be formed. When the shearing stress exceeds the shear

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strength of the lunar rock, the rock fragments fall off when the cracks appear, and the cutting loads suddenly drop. Then, with the blade cutting in the forward direction, a new compact core will be formed, and the rock cutting enters the next breaking period. During the periodic rock-breaking process, the rock crushing area could be divided into three parts: (1) Shearing area I, the shearing and tensile fracture of the rock is generated by a cutting force; (2) Compact core II, the rock chips are compacted in the core by the cutting force and penetrating force; (3) Over-cutting area III, the rock breaking area emerged near the preset cutting depth, which is affected by the cutting fluctuation, contact friction, and system stiffness; this area is caused mainly by the penetrating force. The crosssectional view of the rock-breaking process at small cutting depths is shown in Fig. 4.

1 hPna wb C cos u   n þ 1 sin ksh sin ðu þ /c þ ksh þ kc Þ

ð5Þ

From the static analysis of the compact core in Fig. 4, the resistant force on the rake face is F R ¼ F rp 

sin ð2/c þ ksh þ kc Þ cos ð/c þ /b þ ksh  aÞ

ð6Þ

where  /b = the friction angle between the elemental blade and compact core;  a = the rake angle in the section. (2) Over-cutting area After the static analysis of the over-cutting area ACD, the resistant force on the flank face is

(1) Shearing area and compact core The shearing plane in the lunar rock simulant is assumed to be along BO, and the stress on BO can be described as
n lsh  sin ksh p ¼ p0 1  ð2Þ hPna where  p0 = the stress constant (as s = 0, p0 represents the resultant stress on point B);  lsh = distance from a random point to point B on BO;  hPna = minimum cutting depth;  ksh = shearing angle;  n = stress distribution coefficient. This is a value above 0 that is related to the stress-distribution state in the rockcutting process. After the integral to lsh along the BO, the stress equations on the shearing plane are found to be ( nþ1Þ rB ¼  hðPna sin ksh cos ð/c þ ksh þ kc ÞF rp wb ð3Þ ðnþ1Þ sB ¼ hPna wb sin ksh sin ð/c þ ksh þ kc ÞF rp In addition, rB and sB obeys Mohr-coulomb criterion sB ¼ C þ tan u  rB

F rp ¼

5

ð4Þ

where    

C = rock cohesion; u = rock’s internal friction angle; rB ; sB = compressive stress and shear stress on point B; kc = direction angle between the compact core and cutting velocity;  /c = friction angle between the compact core and rock;  wb = width of the elemental blade. The resultant force F rp on the shearing plane can be deduced as

FN ¼

rph DhPn wb cos /B sin b

ð7Þ

where  rph = rock indentation hardness;  /B = the friction angle between the elemental blade and rock;  DhPn = the cutting depth fluctuations;  b = the relief angle in the section. Depending on the static analysis of the shearing area, compact core, and over-cutting area, the cutting and penetrating force in the section of the lunar rock simulant cutting can be deduced as 

F Cutsp ¼ F R cos ð/b  aÞ þ F N sin ð/B  bÞ F Pensp ¼ F R sin ð/b þ aÞ þ F N cos ð/B  bÞ

ð8Þ

3.1.2. Model of elemental blade linear rock cutting During the cutting process of the lunar rock simulant, in addition to the effect of the rake-face parameters on the magnitude of the rock chips, the removal velocity of the rock chips is also changed by the varying rake-face parameters (Shi, 1999). It is assumed that the chip-removal vector U is generated along the rake face at the moment at which the rock is broken. The absolute velocity W (in the shearing direction) of the rock chip has been altered so that the direction of the shearing section (in Fig. 4) is no longer orthogonal to the cutting blade. The three-dimensional (3D) model of the elemental blade linear rock cutting is established in the coordinate system ½Oe : o; s; r. The convected velocity and the relative velocity of the rock chips are the blade-cutting speed V and the chip-removal velocity U, respectively, and W ¼ U þ V. The relation between the chip-removal velocity U and the cutting velocity V is defined as (Shi, 2003)

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Fig. 5. Mechanics of rock oblique cutting process by elemental blade.

U ¼ rV ðcos wk  a þ sin wk  bÞ

ð9Þ

In addition, the norm of the shearing force vector F RW is F RW ¼ F s þ F n  sin /c

where  r = removal-cutting ratio (the ratio between the removing vector and the cutting vector);  wk = chip-removal angle (the angle between the chipremoval direction and the normal line of the blade edge on the rake face);  a = the normal unit vector of the blade edge on the rake face;  b = the unit vector of the blade edge. In Eq. (9), the unit vector a and b are respectively found to be  a ¼  sin cn sin ks  o þ cos cn  s  sin cn cos ks  r ð10Þ b ¼ cos ks  o þ cos cn  s  sin ks  r

where F s and F n are respectively the rock-shearing force and the compact core-pressure force on the shearing plane in Fig. 4. The expressions are ( F s ¼ F rp  cos ð/c þ ksh þ kc Þ ð15Þ cos ðkc þ/c /b þaÞ F n ¼ F rp  cos ð/c þksh þ/b aÞ Moreover, the shearing angle ksh in the equations above is found to be sin ksh ¼

The normal vector of the rake face g is g ¼b
a

ð11Þ

To simplify the model parameters, it is assumed that the friction direction of the rock chips (shearing area and compact core) on the rake face is aligned with the chip-removal velocity. The resultant force vector F R between the rake face and the rock chips is
 U ð12Þ F R ¼ F R cos /b  g  sin /b  U The projection vector of the resultant force in the shearing direction is F RW , namely, the shearing-force vector for the breaking lunar rock simulant. It obeys
 U W ¼ F RW  F R  W ¼ F R ¼ F R cos /b  g  sin /b  U W ð13Þ

W s W

ð16Þ

Thus, the resultant force F R on the rock chips can be acquired using Eq. (17). FR ¼ 

where  co = the rake angle (measured in the orthogonal plane);  cn = the normal rake angle (tan cn ¼ tan co  cos ks );  ks = the side rake angle.

ð14Þ

F RW W  cos /b  g  sin /b  UU  W

ð17Þ

As shown in Fig. 5, the rake angle in the shearing section of the lunar rock simulant can be deduced as cos a ¼

g
ðj
W Þ j j g
ðj
W Þj

ð18Þ

Moreover, the force on the over-cutting area is expressed by Eq. (7), and the direction vector F Nvq is F Nvq ¼ cos /B  gb  sin /B  ab

ð19Þ

where  gb = the normal unit vector of the flank face;  ab = the normal unit vector of the blade edge in the flank face. and ( ab ¼ cos ða þ bÞ  a  sin ða þ bÞ  g g b ¼ ab
b

ð20Þ

Thus, the resultant force vector F N on the over-cutting area is F N ¼ F N  F Nvq

ð21Þ

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According to Eq. (9)–(21), the cutting power consumption P Cut of the elemental blade can be obtained using P Cut ¼ ðF R þ F N Þ  V   ¼ f Pcut r;wk ; co ;ks ; wb ;hPen ; b; V ; DhPn ; /b ; /B ; C; u; rph ; /c ; kc ð22Þ

In the elemental blade’s linear cutting model of the lunar rock simulant, the control parameters are the rake angle of the blade co , the side rake angle ks , the relief angle in section b, the cutting speed V, cutting depth hPen , cutting depth fluctuation DhPn , lunar rock simulant cohesion C, internal friction angle u, rock indentation hardness rph , the friction angle between the elemental blade and the compact core /b , the friction angle between the compact core and rock /c , and the direction angle between the compact core and cutting velocity kc . Besides, the state parameters are the removal-cutting ratio r and the chip-removal angle wk . Based on the minimum-energy principle, when the control parameters are set at specific values, there is a set of state parameters fr; wk g that makes the blade gain the least cutting-power consumption (Shi et al., 1999; Yusuf, 2012). The cutting force F Cut and penetrating force F Pen can be expressed as  F Cut ¼ ðF R þ F N Þ  r ð23Þ F Pen ¼ ðF R þ F N Þ  s

3.2. LRCB drilling model of lunar rock simulant The spiral profile on the drill bit body of the LRCB is also on the ellipsoid. The absolute coordinate system of the spiral profile on the ellipsoid is shown in Fig. 6. The origin of the coordinates is based on the center point O of the drill bit body’s top surface, and the +z axis is aligned with the auger axial direction. ðI; J; KÞ are the unit vectors of the three coordinate axes. Thus, the parametric equations of the spiral chip-removal groove on the LRCB can be expressed as

8 xH ¼ DH sin ðptÞ sin ð2ptÞ=2 > > < y H ¼ DH sin ðptÞ cos ð2ptÞ=2 > > : zH ¼ hH cos ðptÞ  ho

7

ð24Þ

where  hH = minor axis length of ellipsoid with a helix profile;  ho = distance between the center of the ellipsoid and origin of coordinates O. ho ¼ hH cos


 DH þ wSbI  cos ksnI 1 arctan 2 2 wSbI  sin ksnI

ð25Þ

The curves of the double-row SCB of the LRCB are shown in Fig. 6. The SCB in row I, which is connected to the chip-removal screw profile, is located on the top surface of the drill bit body. The SCB in row II is located at the junction of the auger and bit along the screw profile. The partial enlarged view of the SCB is illustrated on the upper right corner. The SCB could be considered as a combination of two elemental blades. The five geometric parameters in the row kðk 2 fI; IIgÞ can be defined as the sharp blade width wSb k , sharp-point height hs k , sharp-point position coefficient k r k ðwb1 k =wSb k Þ, forward rake angle con k , and outward rake angle ksn k . The standard SCB is defined as the sharp cutting blade with both a zero forward rake angle and outward rake angle. The parametric equations of the standard SCB are as follows: 8 0 0 > < xb1 k ¼ k r k  wSb k  t y 0b1 k ¼ 0 t0 2 ½0; 1 > : 0 zb1 k ¼ hs k  t0 8 0 0 > < xb2 k ¼ ð2k r k  1ÞwSb k þ ð1  k r k ÞwSb k  t y 0b2 k ¼ 0 t0 2 ð1; 2 > : 0 zb2 k ¼ 2hs k  hs k  t0 ð26Þ Because the forward rake angle and outward rake angle are both inlaid posture angles, the parametric equations of the random SCB can be acquired by the vector of the standard SCB post multiplied by the geometric transformation matrixes. Thus, according to the arrangement of the blades in the LRCB, we can obtain the parametric coordinate vector bvi I and bvi II of the elemental blade edges in the SCB, which is in rows I and II, respectively. ( T bvi I ¼ bv0i I  M con I  M ksn I ð27Þ T bvi II ¼ bv0i II  M con II  M ksn II  M wb

Fig. 6. Curves of double-row SCB and spiral profile on the ellipsoid.

where T  bv0i k = the ith parametric coordinate vector of the elemental blade edge in the standard SCB in row k, T and bv0i k ¼ ðx0bi k ; y 0bi k ; z0bi k ; 1Þ; i 2 f1; 2g; k 2 fI; IIg;

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 bvi k = the ith parametric coordinate vector of the elemental blade edge in the SCB in row k, and bvTi k ¼ ðxbi k ; y bi k ; zbi k ; 1Þ;  M con k = the transformation matrix that rotates the SCB in row k in the bit radial direction;  M ksn k = the transformation matrix that rotates (or translates) the SCB in row k around (or along) the mounting-plane normal direction;  M wb = the transformation matrix that rotates the SCB in row II around the bit axial direction. In Eq. (27), xbi k ; y bi k and zbi k is the absolute coordinates of the elemental blade edge after posture transformation. The transformation matrix M con k ; M ksn k and M wb are respectively denoted as 8 2 3 1 0 0 0 > > > > 6 7 > > 6 0 cos con k sin con k 0 7 > > 6 7 > M con k ¼ 6 > 7 > > 4 0  sin con k cos con k 0 5 > > > > > 0 0 0 1 > > > 2 3 > > sin ksn k 0 0 cos ksn k > > > > 6 7 < 6  sin ksn k cos ksn k 0 0 7 7 ð28Þ M ksn k ¼ 6 6 7 > 0 0 1 0 > 4 5 > > > > > rdk 0 0 1 > > 2 3 > > > sin Dwb 0 0 cos Dwb > > > 6 7 > > 6  sin Dwb cos Dwb > 0 07 > 6 7 > M ¼ > wb 6 7 > > 0 0 1 0 > 4 5 > > : 0 0 Dhb 1 where  Dwb = the angle differences between two blades in different rows;  rdk = the initial location radius of the SCB in row k, and k 2 fI; IIg; rdII ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðwSbI  cos ksnI þ rdI Þ2 þ ðwSbI  sin ksnI Þ2 ; rdI ¼ DC =2.

According to the parametric coordinate vector in Eq. (27), we can deduce the unit vector bi k of the ith elemental blade edge in row k in the absolute coordinate system. Besides, the midpoint coordinates ðxbmi k ; y bmi k ; zbmi k Þ of the elemental blade edge have been employed as the radius vector qbi k in the absolute coordinate system, as shown in Eq. (29) (Shi, 2003). qbi

k

¼ xbmi k  i þ y bmi k  j þ zbmi k  k

ð29Þ

The cutting-speed vector vei k of the elemental blade can be expressed by the radius vector. vei

k

¼

2pnD k
qbi 60

k

þ

nD  k PPR k 60

ð30Þ

Actually, the analysis of the elemental blade mentioned above is executed in the local coordinate system. The expression of the local coordinate system in the absolute coordinate system should be inferred. Because the local coordinate system and the cutting-speed vector vei k are

related to the unit vector of the elemental blade edge bi k , the normal unit vector of the working reference plane ri k , working velocity plane si k , and the working orthogonal plane oi k can be respectively deduced as 8 r ¼ vei k ¼ rxi k  I þ ryi k  J þ rzi k  K > < i k jvei k j i k ð31Þ si k ¼ jvveiei kk
b ¼ sxi k  I þ syi k  J þ szi k  K
bi k j > : oi k ¼ si k
ri k ¼ oxi k  I þ oyi k  J þ ozi k  K Based on Eq. (31), the working side rake angle ksei k and working rake angle coei k of the elemental blade are found to be ( sin ksei k ¼ bi k  ri k ð32Þ g i k ;ri k ;bo k Þ tan coei k ¼ ðg ð
o i k Þðri k
oi k Þ i k

where g i k is the normal unit vector of the SCB in row kðg 1 k ¼ g2 k ¼ gk Þ, and it obeys 8 2 k gi k ¼ jbb11 kk
b ¼ gxi k  I þ gyi k  J þ gzi k  K >
b2 k j > > > >   > >  gxi k gyi k gzi k  > > >   > >   > >  < ðg ; ri k ; oi k Þ ¼  rxi k ryi k rzi k  i k     > >  oxi k oyi k ozi k  > > > > >   > >  oi k  oi k g i k  oi k  > >   > >  > : ðgi k
oi k Þ  ðri k
oi k Þ ¼  r i k  oi k g i k  r i k  ð33Þ Thus, the cutting width wbei k , cutting depth hPenei k , and the cutting depth fluctuations DhPnei k of the elemental blades in SCB can be expressed as 8 wbei k ¼ jxbi k ðiÞ  xbi k ði  1Þ y bi k ðiÞ > > > > > > < y bi k ði  1Þ zbi k ðiÞ  zbi k ði  1Þj > > hPenei k ¼ k PPR sin ½arccos ðbi k  K Þ > > > > : DhPnei k ¼ DhPn sin ½arccos ðbi k  K Þ ð34Þ After substituting the control parameters of the SCB, the removal-cutting ratio r and the chip-removal angle wk may be acquired based on the minimum-energy principle. The cutting loads of the elemental blade in the local coordinate system ½Oei k : oi k ; si k ; ri k  can be deduced. To obtain the drilling loads of the LRCB, the coordinate transformation, which transforms the cutting loads of the elemental blade to the integral coordinate system, should be carried out, and the vector calculation should be executed. As shown in Fig. 6, the coordinate axes of the integral coordinate system ½Omi k : l i k ; mi k ; ni k  are in the tangential, radial, and axial directions, respectively, of the SCB. The expression of the integral coordinate system ½Omi k : l i k ; mi k ; ni k  in the absolute coordinate system ½O : I; J; K can be deduced as

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8 > li > > <

k

(

k Iþxbmi k J ¼ ypbmiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

xbmi

þy bmi k

k

ð35Þ

k Iy bmi k J mi k ¼ xpbmiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > x2bmi k þy 2bmi k > > : ni k ¼ K

In the coordinate system ½Oei k : oi k ; si k ; ri k  and ½Omi k : l i k ; mi k ; ni k , the ith cutting loads of the elemental blade in row k can be expressed as DF lci

k

¼ DF oi k  oi

DF ici

k

¼ DF li k  l i

k

¼ M tran  DF ici

þ DF si k  si

k k

þ DF mi k  mi

k

þ DF ri k  ri k

ð36Þ

k

þ DF ni k  ni

k

ð37Þ

and DF lci

ð38Þ

k

where M tran = the transformation matrix between the local coordinate system and the integral coordinate system, and 0 1 l i k  oi k l i k  si k l i k  ri k B C ð39Þ M tran ¼ @ mi k  oi k mi k  si k mi k  ri k A ni k  oi k ni k  s i k ni k  r i k The cutting torque and penetrating force of the elemental blade in the absolute coordinate system are ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DT Di k ¼ DF li k  x2bmi k þ y 2bmi k ð40Þ DF Peni k ¼ DF ni k Finally, the torque on bit (TOB) and WOB of the LRCB can be acquired after the summation of the cutting loads of each elemental blade.

T TOB ¼ F WOB ¼

9

P2 P2 k¼1

i¼1 DT Di k

k¼1

i¼1 DF Peni k

ð41Þ

P2 P2

4. Test, verification, and optimization The test and verification of the LRCB drilling loads can be divided into three parts. First, the four factor tests of rock cutting have been performed using elemental blades on the blade-cutting load test-bed to calibrate the frictional factors of the elemental blade rock-cutting model. Then, the rock drilling tests of the detachable bits assembled with two SCB were implemented on the drilling and coring testbed to verify the influences on the drilling loads of the SCB parameters. Finally, the parameter optimization and verification of the LRCB blades aimed to minimize the WOB. The marble with the VI drillability class was chosen as the lunar rock simulant. 4.1. Test and verification of elemental blade rock-cutting model The parameter ranges for the elemental blade test could be determined by the SCB geometric parameters of the LRCB in Table 1. Owing to the previous test results (Ding, 2015), the relief angle in the section of the elemental blade affects mainly the frictional loads between the rock and blade. The frictional loads in the rock-cutting process are not obvious when the relief angle exceeds a certain value. Thus, the three factors (rake angle, side rake angle, and blade width) that remain in Eq. (22) are chosen in

Table 3 Distribution of factor levels in elemental blade-cutting test. No.

Rake angle co =

Side rake angle ks =

Blade width wb /mm

Cutting depth hPen /mm

1 2 3 4 5 6

35 24 13 0 13 24

0 5 15 25 35 –

2 3 4 5 6 –

0.033 0.05 0.075 0.1 0.15 0.2

Mobile Plate

Penetrating Mechanism

Servo Electric Cylinder

Magnescale

Cutting Blade Rock Holder and Sixaxis Sensor Assembly

Lunar Rock Stimulant (marble)

Fig. 7. Scene of blade-cutting load test-bed.

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Table 4 Characteristic parameters of lunar rock simulant in rock-cutting model. Item

Symbol

Values

Unit

Cohesion Internal friction angle Indentation strength Frictional angle between the compact core and rock Direction angle between the compact core and cutting velocity

C u rph /c kc

24.2 41.8 1080 32.2 60

MPa ° MPa ° °

Fig. 8. The reduced cutting loads as the rake and side rake angle increases.

mobile plate that connects the ball screws. Meanwhile, the horizontal movement of the blade is driven by a servo electric cylinder. There is a magnescale stick to the left side of the mobile plate, and this serves to monitor the vertical displacement and cutting depth fluctuation of the blade in real time. The rock holder is fixed on the six-axis sensor that connects the supporting structure of the test-bed. In the test, the cutting speed is set as 26 mm/s. The mean value of the vertical displacement of the blade during one cutting period is confirmed as the calibration value of the cutting depth fluctuation DhPn . When the rake angle and the side rake angle change, the fluctuation in the cutting depth varies according to the resistant force. The fitting function of the cutting depth fluctuation can be obtained as shown in Eq. (42) after the quadric surface fitting. Fig. 9. The shortened rock-shearing length as the rake and side rake angle increases.

the rock-cutting tests, and the relief angle in section (in Eq. (7)) is selected as the certain value of 8 . The ranges of the rake angle, side rake angle, and blade width can be respectively determined from 34:75 to 23:35 ; 0 to 34:7 , and 1.03 mm to 5.3 mm. The levels of the four factors mentioned above can be dispersed, as shown in Table 3. The lowest level of the blade width is limited to 2 mm, considering the strength of the blade during rock cutting. The blade-cutting load test-bed is illustrated in Fig. 7. To realize the vertical motion, the blade is placed on the

 DhPn ¼ 4022  4:147co  66:73ks  0:1442c2o þ 0:042co  ð42Þ ks þ 0:7555k2s
106

After substituting Eq. (42) into the elemental-blade rock-cutting model, the unknown parameters in Eq. (23) remain the friction angle /b and /B . We can assume that the two friction angles altered in the range from 0°to 60°. Then, we substitute the two values into Eq. (23) with different rake angles and side rake angles, and compare the calculation results with the load results from the rock cutting test. By using enumeration method, the values of two friction angles which make theoretical result and experimental

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value the closest would be gained. And the function of the friction angle /b and /B with different rake angles and side rake angles in the cutting process could be fitted as 

/b ¼ 21:55 þ 0:2704co  0:05609ks  0:008246c2o  0:002717co  ks /B ¼ 33:5 þ 0:2693co  0:3163ks ð43Þ

Other characteristic parameters in the model are shown in Table 4. Thereinto, the first four parameters are acquired by performing a rock mechanics characteristic test. The direction angle between the compact core and cutting velocity could be obtained from rock-cutting simulation by using the discrete-element method. For a given blade width and cutting depth of the elemental blade at certain values (wb ¼ 4 mm and hPen ¼ 0:1 mm in Fig. 8), the cutting loads F Cut and F Pen will

11

increase with the reduction of the rake angle and side rake angle. As the rake angle increases from 35 to 0 , the cutting and penetration force decrease markedly, and the trend begins to reduce when the rake angle exceeds 0 . This phenomenon can be explained as follows: a larger rake angle leads to a larger shearing angle and a shorter rockshearing length. When the side rake angle is a certain value, we can assume that the rock is broken according to the cross-section shown in Fig. 4. With the rake angle increasing, the rock breaking plane BO will rotate along clockwise direction and shearing angle becomes larger automatically. Due to the cutting depth is not changed, the rock breaking plane BO becomes shorter (as shown in Fig. 9, which could be deduced by the shearing angle, as shown in Eq. (16)). This will cause a decreasing trend in the cutting loads, and the reduced shearing-length quantities obtained with

Fig. 10. The rising cutting loads with the enlargement of blade width and cutting depth.

Table 5 The masses of the sampling system’s key components on DCTB. Item

Auger

LRCB

Slipway

Motors and reducers

Sensing and control system

Other components

Mass/kg

3.4

0.062

4.4

11.1

5.8

17.2

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a negative rake angle are more apparent than the status with the rake angle above zero. Besides, when the side rake angle varies from 0 to 35 , the cross-section perpendicular to the rake face of blade begin to deflect, as shown in Fig. 5. A larger space will be formed for the chips breaking away from rocks. This also leads to a larger shearing angle and a shorter rock-shearing length. Thus, the cutting loads will decrease by increasing the side rake angle. Fig. 10 shows the load curves with different blade widths and cutting depths. The cutting and penetration force both have a linear positive correlation with the blade width and cutting depth, and the experiment results are consistent with the theoretical values. 4.2. Test on drilling loads with varied SCB parameters Depending on the SCB parameter ranges for the LRCB shown in Table 1, the geometric parameters are respectively dispersed as the forward rake angle con 2 f0; 5;  10; 15; 20; 25g , outward rake angle ksn 2 f0; 5; 10; 15; 20;  25g , sharp-point position coefficient k r 2 f0:3; 0:4; 0:5;

Fig. 11. Images of drilling and coring test-bed (DCTB) and detachable bits.

0:6; 0:7g, sharp-point height hs 2 f0:5; 0:75; 1; 1:25; 1:5; 1:75; 2g mm, and sharp blade width wSb 2 f3; 4; 5; 6g mm. The drilling and coring test-bed is shown in Fig. 11. The drill bit is placed on the drilling mechanism through a 1-m length auger. There are two guiding rails beside the drilling mechanism, which connects the penetrating mechanism by dragging chains, to realize the rotating and penetration motions of the drill bit. During the drilling process, the TOB and WOB can be respectively monitored by the torque sensor and the load cell. Additionally, magnescale sticks between the drilling mechanism and guiding rails were employed to estimate the drilling depth (Shi et al., 2013). The masses of the sampling system’s key components on DCTB is shown in Table 5. In order to reduce the number of test bits that are manufactured, detachable bits assembled with the SCB have been introduced in the drilling tests instead of nonremovable bits, as shown in Fig. 11. The drilling strategy of the bit is set as follows: auger speed nD ¼ 100 rpm and rate of penetration vPen ¼ 10 mm/min. The variation in the drilling loads (TOB and WOB) with different forward and outward rake angles are shown in Fig. 12. Other parameters of SCB are set to specific values, including k r ¼ 0:5; hs ¼ 1 mm, and wSb ¼ 4 mm. The increase in the forward rake angle will prompt the enlargement of two working rake angles and one working side rake angle of two elemental blades. Accordingly, the TOB and WOB will decrease by increasing the forward rake angle. Furthermore, the increase of the outward rake angle will cause the amplification of one working rake angle and two working side rake angles which could be deduced by Eq. (32), and we obtain a negative correlation between the drilling loads and the outward rake angle. Because the drill radius is on a small scale, the amplitude of the variation of the TOB is smaller than that of the WOB with the same resistant force on the SCB. Curves of drilling loads with various sharp-point position coefficients, sharp-point heights, and sharp blade width are illustrated in Fig. 13. As the sharp-point position coefficient increases, the variations of the drilling loads are

Fig. 12. The decreased drilling loads with the larger forward and outward rake angles.

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13

Fig. 13. Curves of drilling loads with different sharp-point position coefficient, sharp-point height, and sharp blade width.

inconspicuous. The reason for this is that the sharp-point position coefficient changes only the distribution proportion of the cutting forces and the penetrating forces on the two different elemental blades, yet the resultant forces of the SCB are not clearly altered. As the sharp-point height increases, the load distributed in the bit-axial direction of the flank face will be smaller. The total WOB exhibits a reduction trend in Fig. 13(d). The TOB is stable as the forward rake angle of 0 remains

fixed. However, the friction angle between the elemental blade and the rock increased slightly with the forward rake angle of 25 , and this caused the increase in the bit torque raise. Besides, there is no significant discrepancy in the bitdrilling loads when regulating the sharp blade width. In the above-mentioned tests, we employed detachable bits assembled with two sharp cutting blades in different rows in the drilling load test with different shape blade widths. Further, other tests adopt the bit with the blade

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Table 6 Optimization results of lunar regolith coring bit. Items

Forward rake angle con = Row I

Opt. result Ran. value

0 25

Items

Sharp-point height hs /mm

Sharp blade width wSb /mm

Theoretical values of drilling loads

Row I

Row II

Row I

Row II

TOB/N m

WOB/N

2 1

2 0.5

4 4

5.33 4.75

3.77 4.53

478.5 668.6

Opt. result Ran. value

Contrastive Version

Outward rake angle ksn =

Sharp-point position coefficient k r

Row II

Row I

Row II

Row I

Row II

0 25

25 0

25 0

0.5 0.5

0.3 0.5

Optimal Version

Fig. 14. Scenes of the contrastive and optimal version of LRCB.

in a single row. Because of the limited repeat at each test point, only the qualitative trends of the drilling loads could be obtained with different geometric parameters of blades. More iterations are necessary to acquire the quantitative results. 4.3. Optimization of LRCB and drilling-load verification Before the drilling load tests of the LRCB, the SCB geometric parameters are screened with the purpose of minimizing the WOB. We adopted the enumeration method in the optimization. The optimal result and the random value (for contrast) are shown in Table 6.

The optimal version and contrastive version (with the random value in Table 6) of LRCB are shown in Fig. 14. The drilling load curves of the two versions are shown in Fig. 15, with an auger speed nD ¼ 100 rpm and rate of penetration vPen ¼ 10 mm/min. As the drilling depth increases, the drilling loads increase rapidly at first, and then gradually becomes stable. The TOB and WOB of the optimal version of the LRCB are stable at approximately 3.65 N m and 485.9 N, respectively. In contrast, the TOB and WOB of the contrastive version are stable at approximately 4.72 N m and 682.5 N, respectively. The test values are consistent with the theoretical values presented in Table 6. As the geometric parameters of the LRCB are fixed, the cutting depth fluctuations have a positive correlation with the PPR. According to the values of the drilling mechanism displacement along the depth direction in one penetration period, the fitting function between the cutting depth fluctuation and PPR could be obtained as   DhPn ¼ 1904  k 2PPR  122:7  k PPR þ 69:84
104 ð44Þ Fig. 16 shows curves of the drilling loads with different auger speeds, rate of penetration, and PPR. When the rate of penetration is a specific value, we can obtain the negative correlation between the drilling loads and auger speed. Meanwhile, we can obtain a positive correlation between

Fig. 15. Curves of drilling loads of optimal version and contrastive version of LRCB as the drilling depth increases.

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15

Fig. 16. Curves of drilling loads with varying drilling strategy for the optimal version of LRCB.

the drilling loads and the rate of penetration when the auger speed is fixed. This is due to the fact that the auger speed is inversely proportional to PPR, and the rate of penetration is directly proportional to PPR (according to Eq. (1)). Moreover, PPR is positively correlated with the cutting depth of single blade, which directly determines the drilling loads. Therefore, compared to the auger speed

and the rate of penetration, the drilling parameters which directly affect the drilling loads is PPR. And the trends of the drilling loads with different PPR values in the tests are consistent with the theoretical predictions. Besides, in order to observe the influence of the lunar soil on rock drilling load, a group of drilling test with the mixed drilling objects (lunar soil simulant and lunar rock

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P. Li et al. / Advances in Space Research xxx (2016) xxx–xxx

simulant) is implemented. Two blocks of rock are buried in the lunar soil simulant along the depth direction. The auger speed is set as 100 rpm, and the ROP is respectively adopted as 100 mm/min for granular soils and 10 mm/ min for rocks. The total drilling loads are shown in Fig. 17. It could be demonstrated that the drilling load of lunar soil simulant is far less than the rocks, and it has little influence on the rock drilling load. 5. Simulations of lunar soil simulant sampling by EDEM The features of soil chips that are conveyed and cored need to be verified, in addition to the capability of breaking through the rock. Because of the observable liquidity of lunar soil particles in the drilling process, we employed the EDEM simulation of the discrete-element method to verify the conveying of the soil chips and drill-core recovery. By comparing the drilling and coring process of LRCB before and after inlaying the blades, we obtained the discrepancies in the efficacy of the soil-chip removal and drill-core recovery considering the bit of the LRCB and HIT-H.

Table 7 Microparameters of lunar soil simulant in EDEM. Microparameters

Range

Final values

Unit

Density of single particle Poisson’s ratio Shear modulus Particle radius Coefficient of restitution

– 0.1–.3 50–150 – –

2500 0.25 100 0.48 0.5

kg/m3 – MPa mm –

Coefficient Particle to Particle to Particle to

of static friction particle bit/plate boundary

0.1–0.8 0.2–0.6 0.1–0.8

0.3 0.4 0.5

– – –

Coefficient Particle to Particle to Particle to

of rolling friction particle bit/plate boundary

0.01–0.08 0.01–0.05 0.04–0.08

0.01 0.01 0.05

– – –

confining pressures by using the final values of microparameters, the Mole stress circles could be drawn in Fig. 18(a). And the internal frication angle and cohesion strength deriving from simulation could be calculated as 50.1° and 51.4 kPa, which are close to the experimental values (54° and 41 kPa).

5.1. Discrete-element model of lunar soil simulant

5.2. Discrete-element simulation analysis and experimental verification

The approach to obtain the microparameters of lunar soil simulant in EDEM is referred to the method of Yoon (2007). We employ the Hertz-Mindin contact model in the simulation (Moysey and Thompson, 2008). And the microparameters matching objectives are the internal frication angle and cohesion strength of the lunar soil simulant, which could be obtained by triaxial compression test. The factors in experimental designs are listed in the first column of Table 7. After Plackett-Burman (PB) design, central composite design (CCD) and factor screening successively, the set of values which representing the lunar soil simulant are listed in the second column of Table 7. After EDEM simulation of the triaxial compression test with three

The discrete-element simulations of drilling and coring of LRCB and HIT-H at the end time are shown in Fig. 19. The bucket diameter and height of the lunar soil simulant are 66 mm and 75 mm, respectively. The drilling parameters are nD ¼ 100 rpm and vPen ¼ 100 mm/min. Meanwhile, to verify the accuracy of the simulation model, the sampling tests are also carried out. In both simulation and test, the drill-core recovery is usually calculated by particle volumes. As is observed in Fig. 18(b), the percentage of coring volumes from simulation is nearly 79.2% with LRCB and 82.3% with HIT-H. The percentage of coring volumes from experiment is nearly 80.8% with LRCB and 85.4% with HIT-H. It notes that the two bits’

Fig. 17. The drilling load test with the mixed drilling objects (lunar soil/rock simulant).

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Simulated

Drill-core recovery / %

Shear Stress / kPa

100 50.1°

80

17

Experimental

79.2% 80.8%

82.3% 85.4%

LRCB

HIT-H

60 40

51.4

20

100 300

1043 Normal Stress / kPa (a)

2562

0

Coring bit (b)

Fig. 18. Simulated strength envelope chart (a) and drill-core recovery (b) of lunar soil simulant.

Corin

g zone

Di st urb are aance

50mm

Ac cu mul a rea ati on

Removal area

Fig. 19. Comparison of LRCB and HIT-H in drilling simulation by using EDEM.

drill-core recovery derived from simulation and test are basically consistent, and the variation in the drill-core recovery after inlaying sharp cutting blades is therefore not significant. In Fig. 19, the red particles are the particles in the coring zone, and are located at the end of the simulation. The number of red particles in the LRCB is slightly less than that of HIT-H. The cutting blades of the LRCB contact the particles anterior to the ring-type structure. The particle disturbance areas ahead of the LRCB have been provoked, and the particles in the removal area intruded into the coring hole. Meanwhile, some particles in the coring zone are conveyed out of the coring hole. Thus, the leaked particles out of the LRCB exceed those in the HIT-H. In the simulation, the particles in the removal area have been conveyed by the helix grooves in the drilling bit and auger, and they accumulated on the top surface of the removal area. According to the statistical results of the number of particles in the accumulation area, the number of particles removed using the drilling bit increased gradually with the penetration. The number of particles conveyed by the LRCB is 82.2 per seconds, which is 13.9 fewer than HIT-H (see Fig. 20). The mainly reason for this

leading to a decreasing conveyance efficiency is that the particle disturbance areas ahead of the bit are widened, and some particles enter into the original area of lunar soil. Due to the lunar soil is assumed as spherical particles in the simulation, it can not fully represent the actual shape of the lunar regolith particles. If you want to further estimate the lunar soil’s highly irregular shape, the compound particles formed of fused spheres should be used. 6. Discussion In order to analyze the advantages and disadvantages, the comparisons with other existing coring bits and sampling devices are conducted in this section. Six kinds of coring bits (Luna-24, HIT-H, LRCB, JPL, impregnated diamond coring bit (IDCB), and polycrystalline diamond compact (PDC) coring bit) and one kind of sampling device (rigid-flexible link combined lunar sampler (RFLCLS)) are compared (Ling et al., 2014). And the comparisons are carried out in accordance with the following aspects. (a) Sampling methods and devices. In the celestial sampling procedure, the sampling methods and devices are

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P. Li et al. / Advances in Space Research xxx (2016) xxx–xxx 2885 HIT-H LRCB

Number of Particles

2466 2000 1500 1000 500 0 0

5

10

15

20 25 30 Drilling depth / mm

35

40

45

50

Fig. 20. Curves showing the number of particles conveyed by the bit as the drilling depth increases.

always determined by the sampling objectives. According to the surveying results of the human celestial explorations, sampling objective could be roughly divided into: (i) rock pieces, (ii) surface soil, (iii) deep regolith, and (iv) rock core. The first two objectives could be obtained by using a pincer-like sampling head. The two pincers are actually two scoops. The sampling head could dig and shovel surface soils with only one scoop, and two scoops need to work cooperatively if we want to clamp a rock piece. Besides, the sampling head is usually equipped on a manipulator arm or a couple flexible shrinking rods to realize multi-point sampling and meet the needs of sample diversity. Due to the loose soil on the planet surface, the sampler needs much less driving power than drilling. Sampling deep regolith or rock core is always utilized a coring bit to thrust and a coring drill to remove chips. Due to the compact regolith and the hard rocks, the WOB of the coring bit may up to 700 N, and a heavy landing platform is obviously needed to prevent overturning by a large WOB. For some arm-equipped drilling sampler, additional anchoring system is need to balance the WOB in deep drilling, or exerting aided percussive force on bit to reduce the drilling load in rock coring. The sampling system of LRCB in CE program is a heavy landing platform whose weight more than 1.5 ton and rated WOB nearly 800 N. Additionally, the percussive mechanism is also equipped on the drilling system. Once the drilling load exceeds limit value, the impact action will be started to decrease the WOB. (b) Chip conveying and drill-core recovery. The chipconvey efficiency could be calculated by the simulation of lunar soil simulant sampling in Section 5. The simulations are carried out only by three kinds of bits (Luna-24, HITH, LRCB), and the number of conveyed particles per seconds by using these three coring bits are respectively 52.3, 96.1 and 82.2 per seconds, as shown in Table 8. Besides, to acquire the drill-core recovery of different bits with the actual drilling depth in CE program, the 2-meter lunar soil simulant drilling and coring tests are carried out by using the platform mentioned in the reference of Zhao et al. (2016b). The lunar soil simulant is obtained by using the preparation method referred to Chen et al.

(2016). Four bits are employed in the coring tests, respectively Luna-24 bit, HIT-H bit, LRCB, and JPL bit. The percentages of coring volumes by using these four bits are listed in Table 8. The drilling parameters in this test are all set as 100 rpm of the auger speed and 100 mm/ min of the rate of penetration. (c) Rock drilling loads. The bit drilling loads are influenced by many variables, e.g. bit dimension, drilling parameters and rock properties. Therefore, the ratio of loading stress (RLS) is introduced to evaluate the rock drilling load features of the coring bit, as shown in Eq. (45). The RLS is a function of many variables, such as the drilling loads (TOB and WOB), the dimension of the coring bit (DH and DC ), the drilling parameters (PPR), and the rock properties (unconfined compressive strength (UCS)). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 F 2WOB þ ½2T TOB =ðDH þ DC Þ ð45Þ RLS ¼ ðDH  DC Þ  k PPR  UCS The five kinds of coring bits in Table 8 are shown in Fig. 21. The HIT-H bit is electroformed the material of cubic boron nitride (CBN) to break rocks. The bit of Luna-24 and JPL are the dummy bits manufactured in previous tests to obtain the results in Table 8. IDCB and PDC bit are the coring bits commonly used in the geological explorations. And the correlation data are reported by reference of Karakus and Perez (2014) and Hirokazu et al. (2016). As shown in Table 8, HIT-H bit has obvious advantages in terms of chip-convey efficiency and coring efficiency. LRCB is close to HIT-H bit in these two aspects. The coring efficiency of Lunar-24 bit and JPL bit is relatively low. This could be attributed to the helical-type bit body and ring-type soil coring isolated structure designed in both HIT-H bit and LRCB. But in lunar soil drilling process, the SCB on LRCB contacts the soil particles prior to spiral groove and ring-type structure, this will widen the soil disturbance area ahead of the bit. The soil particles staying in the coring area are reduced Zhao et al. (2016a). Besides, on rock drilling load performance, the value of RLS slightly decreased with the increase of PPR. This is

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Table 8 Comparison of LRCB and other existing coring bit or sampling device. Items

RFLCLS

Sampling objectives Target sampling depth Sampling system Chip-convey efficiency

Surface lunar soil 100 mm Rigid-flexible link –

Coring efficiency Drilling test objective UCS/ MPa DH =DC /mm Weight/g PPR/mm

– – – – 400 –

TOB/N m

–

WOB/N

–

RLS

–

(a) Luna-24 bit

Luna-24 bit 2m 52.3 p/s 85% 112 32/14 75 0.02 0.2 1.25 24.8 260 1218 8.1 13.2

HIT-H bit

LRCB

JPL bit

Deep lunar regolith 2m 2m Lunar lander 96.1 82.2 p/s p/s 96% 92% Lunar rock simulant 112 112 32/14.5 32/14.5 54 62 0.021 0.04 0.05 0.2 0.98 2.98 2.36 6.4 400 396 942 767 19.3 4.2 19.5 10.6

(b) HIT-H bit

(c) JPL bit

Martian rocks 50 mm Mars robotic arm – 81% 112 34/14.2 72 0.033 0.2 2.78 6.68 363 838 4.4 11.5

(d) IDCB

IDCB – –

PDC bit Geological rock – Drilling rig –

– Sori granite 219 36/21.7 158 0.025 0.14 5 25 1000 4200 14.3 18.9

– American black 300 66/44.8 451 0.7 150 17,000 10.6

(e) PDC bit

Fig. 21. The coring bit compared to LRCB.

due to the fact that the proportion of friction load is increased with a lower PPR (Detournay and Richard, 2008). In Table 8, the RLS of LRCB and JPL bit are very close, and are obviously lower than other bits. It means that the required load of LRCB to crush rock on unit area is higher than the coring bit such as Luna-24 bit, HIT-H bit, IDCB and PDC bit. Due to the power consumption in the lunar rock simulant drilling test are no more than 100 W, this is much lower than the power constraints of the drilling system in actual sampling mission (mentioned in Section 2). When the PPR is set to 0.2 mm/r, WOB is very close to the rated value. In actual mission, two tension sensors are connected between the drilling rig and the traction rope. The difference in tension between the two sensors is the WOB. The WOB required for drilling lunar soils and lunar rocks differs greatly (about one order of magnitude) at the same drilling parameters. If both of the value of WOB and its rate of change is respectively more than 400 N, the present drilling strategy will be switched to recognition strategy to identify the medium drillability. Then, a lower PPR from drilling strategy parameters database which is matched with drillability of present medium will be implemented in the following drilling to avoid the excessive WOB causes the platform to overturn.

7. Conclusion In this paper, we designed a new type of lunar regolith coring bit (LRCB) which has a good performance on chip continuous conveying, sample protection and rock breaking in lunar regolith sampling compared with other existing coring bits. Besides, the higher forward and outward rake angles decrease weight-on-bit. This provides the theoretical basis for the selection of posture angle of SCB on coring bit. The results of our study show that the geometric parameters and drilling strategy of LRCB affect the drilling loads, including mainly the forward rake angle, outward rake angle, sharp-point height, number of penetrations per revolution, and cutting depth fluctuation. Increasing the forward and outward rake angles will contribute to a smaller drilling load when the penetrations per revolution is at a certain value. Raising the sharp-point height could lower the WOB, while the effects on the drilling loads of the sharp blade width and sharp-point position coefficient are not clear. Meanwhile, by enhancing the PPR, we will realize a deeper cutting depth of the equivalent blade, and we can obtain a positive correlation between the drilling loads and the PPR when the geometric parameters of the LRCB are at specific values. Moreover, according to the lunar soil drilling simulation of EDEM, because the

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Please cite this article in press as: Li, P., et al. Design and testing of coring bits on drilling lunar rock simulant. Adv. Space Res. (2016), http://dx. doi.org/10.1016/j.asr.2016.11.012