- Email: [email protected]
Optimum parameter matching obtained by experiments for coring drilling into lunar simulant
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research 63 (2019) 2239–2244 www.elsevier.com/locate/asr
Optimum parameter matching obtained by experiments for coring drilling into lunar simulant Zhen Zhao a,⇑, Tao Chen a, Yong Pang b a
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China b Beijing Space Crafts, China Academy of Space Technology, Beijing 100094, China
Received 28 August 2018; received in revised form 18 December 2018; accepted 19 December 2018 Available online 31 December 2018
Abstract This paper performs a series of ground experiments (on the Earth) to obtain optimum parameter matching for a future core drill on the Moon. Three common stages, I, II, III, are recognized with respect to the cut per revolution (CPR), which is defined as the ratio between the feeding speed and the rotating speed. The optimum matching between the feeding speed and the rotating speed for drills locates at the boundary position between Stage II and Stage III, where the coring rate saturates and the weight on the bit and the driving torque are still low. Further data analysis of the ground experiments reveals that the optimum matching signifies a proportional relation between the maximum conveying rate (MCR) by the groove of the auger and its rotating speed. The kinetic analysis in an ideal condition without gravity, the friction from the auger groove and the pressure at the bit confirm a similar proportion. The correlation between the proportions needs further study to determine whether the optimum matching obtained on the ground can be directly applied to future drills on the Moon. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Auger drill; Auger groove; Cut per revolution; Auger flute; Maximum conveying rate
1. Introduction A core drill with an auger is a reliable and realistic approach to sample scientific information trapped in geologic formations at the subsurface of regolith on the Moon. Discharging redundant soil from the side of a bit with only the help of an auger in harsh dry circumstances has been recommended by most researches (Zacny et al., 2008). One of the greatest constraints of extraterrestrial drilling is power budgets (Zacny et al., 2011; Zacny and Cooper, 2006). Therefore, investigating the efficiency of a core drill with an auger is important before tasks are implemented in practice. Core samples should be brought back to Earth as ⇑ Corresponding author.
E-mail addresses: [email protected] [email protected] (T. Chen).
(Z.
Zhao),
https://doi.org/10.1016/j.asr.2018.12.025 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
many as possible, and both the weight on bit (WOB) and driving torque (DT) should be decreased to the greatest extent possible to save energy. When a core drill is working, the bit and stem occupy the space of the lunar simulant. Part of the soil simulant in situ is removed by the helical groove of the auger. The other part enters the inlet at the bottom of the bit and forms core samples in the coring tube at the center of the hollow stem. Obviously, the coring amount is closely correlated to the discharging capacity of the auger. To obtain a highly effective drilling strategy, the drilling mechanism should be fully understood. According to Mellor’s study (Mellor, 1981), the efficiency of an auger was determined by many interrelated parameters, such as pitch angle, flute width, auger diameter and rotating speed. The threshold of rotating speed required to initiate movement of the cuttings up the scroll
2240
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
was given by Zacny and Cooper (2007). Since higher penetration velocity caused the cuttings volume increasing, the auger needed higher rotational velocity to convey the soil outside the hole. The higher rotating speed implied more effective cuttings removal, but power consumption was higher and more heat was generated (Zacny et al., 2008). To achieve the goals of maximum conveying volume and minimum power consumption, different structure parameters of the auger were tested (Tian et al., 2015). The trajectory of cuttings was a spiral and its lead angle was affected by the auger’s rotating speed and feeding speed (Tan et al., 2016). By analyzing the conveyance mechanism of lunar soil chips in the auger groove, an optimization of auger parameter with high transportation efficiency was presented (Zhao et al., 2016). Coring process was also strongly affected by the drilling parameters. The experimental study (Quan et al., 2017) discovered that the coring amount decreased with an increase in the rotating speed and that the WOB decreased with a decrease in CPR. Applying a camera and an ultrasonic sensor to monitor the soil flowing characteristics of the removed cuttings and sampled core, the experiments (Tang et al., 2016, 2018) indicated that under suitable drilling parameters, the coring ratio could be high and stable. To date, no parametric optimization has been found between feeding speed and rotating speed for drills in experimental studies. As previous studies have found that the performance of a drill is strongly connected to the drilling parameters, under suitable drilling parameters, there exists an ideal drilling state in which the coring saturates, while the WOB and DT are still low. The goal of these experiments is to find optimum matching between the feeding speed and rotating speed for the ideal working state. This article is arranged as follows. Section 2 presents the experimental set up for the core drill into the lunar simulant. Section 3 presents the optimum parameter matching found in the experiments and the experimental phenomenon which indicates that the drilling process is immune to the influence of the hydrostatic pressure from the borehole wall. Section 4 analyses the experimental data and obtains a proportional relation between the maximum conveying rate (MCR) and the rotating speed. Then, the experimental phenomena are explained reasonably by the proportional relation. Section 5 gives a proportional relation between MCR and the rotating speed under ideal conditions. 2. Experimental setup The drilling and coring system studied here is shown in Fig 1. The drill tool in the system consists of a carbide (WC-Co) drill bit, a right-hand auger string, and a coring mechanism. As shown in Fig. 1e, the four inner and four outer carbide cutters are uniformly distributed around the bit in two layers. There is a 9 mm diameter hole in center of the bit, as an inlet for coring. The bit and stem have the same radius of R ¼ 15:5 mm. The pitch of the auger is
Fig. 1. Drilling and coring test-bed. (a) Drilling and coring system, (b) drill tool, (c) actual test-bed, (d) auger, (e) drill bit.
h ¼ 12 mm. The helical groove has a flute with a radial width as a ¼ 0:9 mm and an axial length of b ¼ 10:5 mm. The lunar simulant is manufactured of anorthosite and basaltic pozzolana, according to the composition of lunar samples brought back by the Apollo missions. The particle size of the simulant ranges from 0.1 mm to 1 mm, and the bulk density is q ¼ 1:74 g/cm3. To control the bulk’s density and volume fraction, the simulant is vibrated for hours until the material is almost incompressible. After the operation, the packed density of the simulant increases to 2.14 g/cm3, and the fraction is 71%. The internal friction angle is 35.7°, and the cohesion is 0.9 kPa. The simulant is stored in a 2.5 m long and 0.52 m diameter barrel, and the moisture content of the simulant is maintained to below 0.5%. The drill string is driven by servo motors with a constant rotating speed and feeding speed 1-m deep into the long barrel of the simulant. Some simulant enters the inlet at the bottom of the bit, and a coring tube in the hollow stem
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
of the string is used to form the coring sample. The coring tube in the hollow stem is dragged by a fixed rigid rope while the string is drilling into the soil (Quan et al., 2017). Then, the coring tube has the same speed as the feeding speed relative to the drilling stem though the coring tube does not actually move. In the drilling process, the bit cuts and stirs the in situ simulant into a fluid state, which is redundant and should be removed quickly because the drill stem and the bit both occupy the space of the simulant. The redundant simulant either becomes the coring sample or is discharged by the helical groove of the rotating auger. Otherwise, the drilling process is likely to be clogged and cannot proceed straight forward. The target of the experiments is to seek the optimum drilling matching between the feeding speed and the rotating speed. The drilling tests are conducted under different feeding and rotating speed matching. During the tests, the WOB (Fig. 2a) and DT (Fig. 2b) are measured in real time by force sensors, and the coring amount is weighed.
2241
Fig. 3. Coring amount (a), average WOB (b) and DT (c) in the experiment varying with CPR.
Stage I, where the coring amount is zero and the WOB and DT are small. Stage II, where the coring amount increases with CPR but the WOB and DT are still small. Stage III, where the coring amount saturates and the WOB and DT rise sharply and flutter.
3. Experimental results 3.1. Optimum working parameters In the first group of the experiments, the rotating speed _ is chanis fixed as h_ ¼ 120 r/min, and the feeding speed, u, ged. We term g as the cut per revolution (CPR) of the bit, _ For each CPR (g), the measured WOB and DT _ h. so g ¼ u= in the experiment are presented in Fig. 2. Their values remain small and change slightly with an increase in drilling depth when the CPR is confined within a considerably small range (CPR< 0:5 mm/r). Otherwise, the WOB and DT increase rapidly and flutter significantly. Similar results are obtained for the other two sets of experiments, in which the rotating speed is adjusted to h_ ¼ 80 r/min and h_ ¼ 160 r/min. We average the WOB and DT with respected to g for the three groups of the experiments and plot them in Fig. 3b and c. The coring amount with respect to g is also plotted in Fig. 3a. Interestingly, three common stages, I, II and III, with respect to the CPR are clearly recognized:
According to the experimental results shown in Fig. 3, we define g1 the first boundary position between Stage I and Stage II and g2 the second boundary position between Stage II and Stage III. The optimum working parameter is of great interest to the situation at the secondary common boundary position, g2 ¼ 0:5 mm/r. The parametric matching between the feeding speed and the rotating speed just before g2 is obviously the optimum for each rotating speed because the coring is relatively saturated while the WOB and DT are still small. 3.2. MCR achieved at g2 When the auger is working, the stem and bit of the auger occupy the space that used to be that of the simulant. The helical groove conveys the simulant in situ from the side of the bit to the surface. At the same time, part of the in situ soil may enter the bottom inlet at the center of the bit to be collected as samples. The redundant simulant is removed by both the rotating helical groove and the coring tube. It is clear from Fig. 3 that the WOB and DT increase significantly if g > g2 , which indicates that the pressure at the bit increases accordingly. The pressure increases because the in situ soil cannot be conveyed out in time if the CPR exceeds g2 as g > g2 . However, the coring is already saturated at g2 . Thus, we speculated that the auger reaches its maximum conveying rate at g2 , too. The term m_ dis is the discharging mass rate of the groove, then m_ dis ðg2 Þ ¼ qc /_ max ;
Fig. 2. WOB and DT in the experiment vary with drilling depth. h_ ¼ 120 r/min.
ð1Þ
where qc is expressed as the density of the cuttings (conveyed soil) in the groove and /_ max is termed as the maximum discharging volumetric rate by the groove. We mentioned in Section 2 that the coring tube is dragged by a fixed rigid rope, so the tube moves relative
2242
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
_ Thus, to the stem at the same speed as the feeding speed, u. the maximum coring volumetric rate can be estimated as _ where r is the radius of the tube. The term m_ core is pr2 u, the coring mass rate by the tube, and it reaches saturation at g2 . Therefore, _ m_ core ðg2 Þ ¼ qpr2 g2 h;
ð2Þ
where the density of the collected sample in the coring tube, q, is usually same as that of the simulant in the barrel. 3.3. Without hydrostatic pressure Additionally, the experiments presented an interesting phenomenon. The borehole was well preserved and did not collapse after the drill string was fully extracted from the simulant (see Fig. 4). In general, the borehole may actively exert pressure on the cuttings because the outside soil is not fully solid. The pressure may increase with depth. However, the experimental phenomenon in Fig. 4 indicates that the hydrostatic pressure from the borehole wall can be ignored in our experiments. The lunar soil simulant used in the experiments is dense and cohesive. The cohesion and internal friction are strong enough to allow self-support, which means that the borehole wall provides only a ‘rigid-like’ constraint for the conveyed soil in the semiopen groove. Therefore, we ignore the hydrostatic pressure in the following analysis. 4. Analysis 4.1. A proportional relation for the optimum matching Now, we explain the experimental results, especially at g2 . According to the mass conservation law, the mass rate of the redundant soil in situ termed mtotal , is equal to the sum of the discharging mass rate by the helical groove, mdis , and the coring mass rate by the tube in the hollow stem, m_ core , namely m_ total ¼ m_ dis þ m_ core :
ð3Þ
The total rate of the redundant soil produced by the bit _ where R is the radius of can be estimated as m_ total ¼ qpR2 u, the stem and the bit.
Fig. 4. An integrated borehole preserved after the drill string is fully extracted from the soil in the experiment.
At g2 , we put Eqs. (1) and (2) into Eq. (3) to obtain the proportional relation between the MCR and the rotating speed as q _ /_ max ¼ pðR2 r2 Þg2 h_ ¼ C h: qc
ð4Þ
where we define C ¼ qqc pðR2 r2 Þg2 . Based on the experimental results above, g2 is a constant that is unrelated to rotating speed, and the lunar simulant used in the tests is dense and uniform. Then, C can be taken as a constant. 4.2. Explanation of the experiments Once the proportional relation in Eq. (4) is revealed, the three stages of the experiment in Fig. 3 are easy to under_ a MCR, / , is stand. For a proper rotating speed h, max determined. When the CPR is small, all the redundant simulant in situ that is stirred by the bit can be removed by the auger, m_ total ¼ m_ dis 6 qc /_ max , and nearly no soil enters the coring tube. This is Stage I, as g < g1 . With an increase in CPR, part of the in situ simulant begins to enter the coring inlet to form a sample, and the drilling process enters Stage II. Although the total generation rate of the redundant simulant may exceed the MCR, namely m_ total > qc /_ max , and the auger may reach its discharging ability, MCR, the sum rate of discharging and coring are not yet saturated, m_ total ¼ m_ dis þ m_ core < qc pr2 u_ þ q/_ max if g < g2 . All of the in situ soil can still be removed easily. The WOB and DT are still at low levels because the coring does not influence them, and the increased moment and force (see Fig. 3b and c) are almost attributed to the increased cut rate of the bit. The discharging groove of the auger and coring tube are both saturated at g ¼ g2 , when m_ total ¼ qc pr2 u_ þ q/_ max . In the former two stages, the loads do not go up with the drill depth. Actually, the loads contain the part from the bit and the part from the auger stem. The loads on the bit generated by cutting the in situ soil, is correlated to the pressure at the bit. Since the soil is dense and cohesive, the cohesion and internal friction make the pressure in the soil keep constant with the increasing depth. As the auger can remove the new generated cuttings in time, the pressure at the bit does not increase without accumulation of excess cuttings. So, the pressure at the bit does not increase with an increase of drill depth, until the generating rate of cuttings exceeds the conveying capacity of the auger. Therefore, the loads on the bit become constant, as the drill depth increases. Meanwhile, the loads on the auger stem come from the friction of soil pressing against the surface of the auger stem and the horizontal component of the normal force on the flute. This part increases with the increment of cuttings volume on the flute. However, the flute is narrow and the coefficient of friction between the soil and the surface of the stem is small. Compared with the
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
part on the bit, this part could be negligible. So, the increase is not obvious, unless the auger becomes clogged. As the CPR continues to increase, the drilling process enters Stage III. At CPR of 0.833 (Fig. 2), both the discharging rate of the auger and the coring rate of the coring tube have saturated. The sum of the MCR and the maximum coring rate cannot satisfy all the in situ soil stirred by the bit, namely m_ total > qc pr2 u_ þ q/_ max . The auger become clogged with excess cuttings, due to the high value of CPR. The accumulation of excess cuttings causes a significant increase in the pressure at the bottom (and in turn WOB and DT). Once the pressure exceeds the resistance of the coring tube or the conveying channel, the cuttings move up and leave room for new cuttings to enter into it, which also causes a drop in the WOB and DT. The cycles of these two process make the WOB and DT fluctuate (Zacny and Cooper, 2007). Thus, the three stages in the experiment show that. in Stage I, namely 0 < g 6 g1 ; qqc pR2 u_ 6 /_ max . _ in Stage II, namely g < g 6 g ; /_ max P q pðR2 r2 Þu. 1
2
qc
_ in Stage III, namely g2 < g; /_ max < qqc pðR2 r2 Þu. The secondary boundary position g2 is completely clear when the coring rate and the auger’s discharging rate are both saturated. The first boundary position, g1 , marks where the coring begins. This process is ambiguous without understanding the complicated flows that originate from the complicated structure at the bit, which we will study in subsequent studies. 5. Discussion Although the optimum working matching for drilling is obtained, whether the optimum matching between the feeding and rotating speed can be applied to future drilling on the Moon, is vague. The gravity on the moon is entirely different from that on the Earth, so further studies should answer the following question:
2243
tance from the friction of the groove and gravity. Further, we neglect both the gravity and the resistance friction from the groove and study the relation between the MCR and the rotating speed under ideal conditions. A stable conveyance of the soil by the auger results in a non-zero centripetal acceleration but zero tangential and binormal accelerations for each element of the conveying layer. Then, in the ideal condition, we obtain a balancing relationship between the pushing force, Fb , and the dragging friction, Fd , in the binormal direction of the groove (see Fig. 5), namely Fb ¼ Fd . The dragging force can be estimated by the Coulomb friction law from the pressure of the borehole, namely F d ¼ ls F n , where ls ¼ tan u and u is the frictional angle of the soil. The dragging friction, Fd , may trigger vortex flows in the transverse cross section of the conveying layer (see Fig. 5), which we will study in a future paper. According to the Coulomb frictional law, the direction of the absolute velocity of element va is opposite to the dragging friction Fd . The kinetic analysis indicates that va ¼ vr þ ve , where ve ¼ Rh_ and R represent the radius of the location of the groove axis. We then determine that vr ¼
R2 _ h; A
ð5Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where A ¼ R2 þ ðh=ð2pÞÞ and h are the thread pitch of the auger helix. In the kinetic analysis in Eq. (5), we neglect the feeding velocity due to its comparative smallness. The relative velocity vr actually represents the discharging velocity varying only with the rotating speed and without the aspect of the conveying layer. Thus, the auger discharge rate can be expressed as / ¼ Cvr , where C is the transverse cross-section area of the conveying layer in the groove. The MCR is then expressed as /_ max ¼ Cmax vr when C reaches a maximum Cmax (Fig. 5). Thus, the MCR is also proportional to the rotating speed: 2
R _ /_ max ¼ Cmax h_ / h: A
ð6Þ
D1: What leads to the proportional relation in Eq. (4)? 5.1. Proportional relation in an ideal condition We present here the proportional relationship between the MCR of the auger and the rotating speed under ideal conditions. We study the drilling in a stable working condition if g 6 g2 . The stirred in situ soil by the bit can be fully conveyed by the auger groove and the coring tube. There is no obvious pressure at the entrance of the conveying channel near the bit. The interaction between any two elements (segments) of the conveying layer can be neglected. Thus, the cuttings are fully transported by the pushing force from the bottom flute of the groove and the dragging friction from the borehole against the resis-
Fig. 5. Elementary analysis under ideal conditions at the conveying layer in the groove.
2244
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
Although Eq. (6) provides a proportional relationship between the MCR and the feeding speed, it is obtained under an ideal situation, so further investigation is needed to clarify the influences of gravity, friction and bit pressure on the discharging rate, i.e., D2: What correlation exists between the proportional relations Eqs. (4) and (6)? If the two proportional relations are essentially the same, the MCR depends only on the rotating speed and is independent of gravity. Then, we can apply the optimum matching obtained by the ground experiments in future drilling on the Moon. Otherwise, the expensive ground results may be useless. In a subsequent paper, we will carry out such studies.
The common optimum matching between the feeding and rotating speeds signifies a proportional relation between the MCR and the rotating speed. A proportional relation between them is confirmed by a kinematic analysis for the conveying layer in the helical groove of the working auger under ideal conditions without considering gravity, the friction from the groove or the pressure at the bit. Whether the optimum matching can be directly applied to future drilling on the Moon needs to distinguish the correlation between the two proportional relations, which will be presented in a future paper. Acknowledgements This work was supported by the National Nature Science Foundation of China (Grant Nos. 11572017 and 11502277).
5.2. Estimation of Cmax References If we further hypothesize that Eqs. (6) and (4) are essentially the same, we can obtain a new expression for the maximum cross-sectional area of the conveying layer, Cmax , as a function of the experimental parameters g2 : r 2 q Cmax ¼ Ap 1 ð7Þ g2 : q1 R The parameter Cmax is worth identifying because a lunar simulant with a different particle distribution may have a different thickness of the conveying layer when it is drilled. 6. Conclusion A series of ground experiments (on the Earth) have been conducted for future core drilling on the Moon with different constant feeding and rotating speeds. Three common stages were recognized with respect to the CPR, which is defined as the ratio between the feeding speed and rotating speed. The coring is zero in Stage I, although the WOB and DT are small. On the contrary, the coring is saturated in Stage III, and the WOB and DT increase sharply and flutter. Only Stage II is the working stage, in which the coring is not zero and the WOB and DT are small. The optimum matching between the feeding speed and the rotating speed occurs at the boundary position between Stage II and Stage III, where the coring almost saturates the sample and the WOB and DT are still low.
Mellor, M., 1981. Mechanics of cutting and boring. Part 7: dynamics and energetics of axial rotation machines. Cold Regions Research and Engineering Laboratory, Hanover, NH. Quan, Q., Chen, C., Deng, Z., Tang, J., Jiang, S., 2017. Recovery rate prediction in lunar regolith simulant drilling. Acta Astronaut. 133, 121–127. Tan, S., Duan, L., Guo, Z., Gao, H., 2016. Theoretical derivation of the cuttings transportation trajectory for lunar sampling auger drilling. Int. J. Rock Mech. Min. 86, 204–209. Tang, J., Quan, Q., Jiang, S., Chen, C., Yuan, F., Deng, Z., 2016. A soil flowing characteristics monitoring method in planetary drilling and coring verification experiments. Adv. Space Res. 59 (5), 1341–1352. Tang, J., Quan, Q., Jiang, S., Li, H., Bai, D., Tang, D., Deng, Z., 2018. Experimental investigation on flowing characteristics of flexible tube coring in lunar sampling missions. Powder Technol. 326, 16–24. Tian, Y., Tang, D., Deng, Z., Jiang, S., Quan, Q., 2015. Drilling power consumption and soil conveying volume performances of lunar sampling auger. Chin. J. Mech. Eng. 28 (3), 451–459. Zacny, K., Barcohen, Y., Brennan, M., Briggs, G., Cooper, G., Davis, K., Dolgin, B., Glaser, D., Glass, B., Gorevan, S., 2008. Drilling systems for extraterrestrial subsurface exploration. Astrobiology 8 (3), 665– 706. Zacny, K., Cooper, G., 2006. Considerations, constraints and strategies for drilling on mars. Planet. Space Sci. 54 (4), 345–356. Zacny, K., Cooper, G., 2007. Methods for cuttings removal from holes drilled on mars. MARS 3, 42–56, 12. Zacny, K., Paulsen, G., Szczesiak, M., 2011. Challenges and methods of drilling on the moon and mars. IEEE Aerosp. Conf., 1–9 Zhao, D., Tang, D., Hou, X., Jiang, S., Deng, Z., 2016. Soil chip convey of lunar subsurface auger drill. Adv. Space Res. 57 (10), 2196–2203.
ScienceDirect Advances in Space Research 63 (2019) 2239–2244 www.elsevier.com/locate/asr
Optimum parameter matching obtained by experiments for coring drilling into lunar simulant Zhen Zhao a,⇑, Tao Chen a, Yong Pang b a
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China b Beijing Space Crafts, China Academy of Space Technology, Beijing 100094, China
Received 28 August 2018; received in revised form 18 December 2018; accepted 19 December 2018 Available online 31 December 2018
Abstract This paper performs a series of ground experiments (on the Earth) to obtain optimum parameter matching for a future core drill on the Moon. Three common stages, I, II, III, are recognized with respect to the cut per revolution (CPR), which is defined as the ratio between the feeding speed and the rotating speed. The optimum matching between the feeding speed and the rotating speed for drills locates at the boundary position between Stage II and Stage III, where the coring rate saturates and the weight on the bit and the driving torque are still low. Further data analysis of the ground experiments reveals that the optimum matching signifies a proportional relation between the maximum conveying rate (MCR) by the groove of the auger and its rotating speed. The kinetic analysis in an ideal condition without gravity, the friction from the auger groove and the pressure at the bit confirm a similar proportion. The correlation between the proportions needs further study to determine whether the optimum matching obtained on the ground can be directly applied to future drills on the Moon. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Auger drill; Auger groove; Cut per revolution; Auger flute; Maximum conveying rate
1. Introduction A core drill with an auger is a reliable and realistic approach to sample scientific information trapped in geologic formations at the subsurface of regolith on the Moon. Discharging redundant soil from the side of a bit with only the help of an auger in harsh dry circumstances has been recommended by most researches (Zacny et al., 2008). One of the greatest constraints of extraterrestrial drilling is power budgets (Zacny et al., 2011; Zacny and Cooper, 2006). Therefore, investigating the efficiency of a core drill with an auger is important before tasks are implemented in practice. Core samples should be brought back to Earth as ⇑ Corresponding author.
E-mail addresses: [email protected] [email protected] (T. Chen).
(Z.
Zhao),
https://doi.org/10.1016/j.asr.2018.12.025 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
many as possible, and both the weight on bit (WOB) and driving torque (DT) should be decreased to the greatest extent possible to save energy. When a core drill is working, the bit and stem occupy the space of the lunar simulant. Part of the soil simulant in situ is removed by the helical groove of the auger. The other part enters the inlet at the bottom of the bit and forms core samples in the coring tube at the center of the hollow stem. Obviously, the coring amount is closely correlated to the discharging capacity of the auger. To obtain a highly effective drilling strategy, the drilling mechanism should be fully understood. According to Mellor’s study (Mellor, 1981), the efficiency of an auger was determined by many interrelated parameters, such as pitch angle, flute width, auger diameter and rotating speed. The threshold of rotating speed required to initiate movement of the cuttings up the scroll
2240
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
was given by Zacny and Cooper (2007). Since higher penetration velocity caused the cuttings volume increasing, the auger needed higher rotational velocity to convey the soil outside the hole. The higher rotating speed implied more effective cuttings removal, but power consumption was higher and more heat was generated (Zacny et al., 2008). To achieve the goals of maximum conveying volume and minimum power consumption, different structure parameters of the auger were tested (Tian et al., 2015). The trajectory of cuttings was a spiral and its lead angle was affected by the auger’s rotating speed and feeding speed (Tan et al., 2016). By analyzing the conveyance mechanism of lunar soil chips in the auger groove, an optimization of auger parameter with high transportation efficiency was presented (Zhao et al., 2016). Coring process was also strongly affected by the drilling parameters. The experimental study (Quan et al., 2017) discovered that the coring amount decreased with an increase in the rotating speed and that the WOB decreased with a decrease in CPR. Applying a camera and an ultrasonic sensor to monitor the soil flowing characteristics of the removed cuttings and sampled core, the experiments (Tang et al., 2016, 2018) indicated that under suitable drilling parameters, the coring ratio could be high and stable. To date, no parametric optimization has been found between feeding speed and rotating speed for drills in experimental studies. As previous studies have found that the performance of a drill is strongly connected to the drilling parameters, under suitable drilling parameters, there exists an ideal drilling state in which the coring saturates, while the WOB and DT are still low. The goal of these experiments is to find optimum matching between the feeding speed and rotating speed for the ideal working state. This article is arranged as follows. Section 2 presents the experimental set up for the core drill into the lunar simulant. Section 3 presents the optimum parameter matching found in the experiments and the experimental phenomenon which indicates that the drilling process is immune to the influence of the hydrostatic pressure from the borehole wall. Section 4 analyses the experimental data and obtains a proportional relation between the maximum conveying rate (MCR) and the rotating speed. Then, the experimental phenomena are explained reasonably by the proportional relation. Section 5 gives a proportional relation between MCR and the rotating speed under ideal conditions. 2. Experimental setup The drilling and coring system studied here is shown in Fig 1. The drill tool in the system consists of a carbide (WC-Co) drill bit, a right-hand auger string, and a coring mechanism. As shown in Fig. 1e, the four inner and four outer carbide cutters are uniformly distributed around the bit in two layers. There is a 9 mm diameter hole in center of the bit, as an inlet for coring. The bit and stem have the same radius of R ¼ 15:5 mm. The pitch of the auger is
Fig. 1. Drilling and coring test-bed. (a) Drilling and coring system, (b) drill tool, (c) actual test-bed, (d) auger, (e) drill bit.
h ¼ 12 mm. The helical groove has a flute with a radial width as a ¼ 0:9 mm and an axial length of b ¼ 10:5 mm. The lunar simulant is manufactured of anorthosite and basaltic pozzolana, according to the composition of lunar samples brought back by the Apollo missions. The particle size of the simulant ranges from 0.1 mm to 1 mm, and the bulk density is q ¼ 1:74 g/cm3. To control the bulk’s density and volume fraction, the simulant is vibrated for hours until the material is almost incompressible. After the operation, the packed density of the simulant increases to 2.14 g/cm3, and the fraction is 71%. The internal friction angle is 35.7°, and the cohesion is 0.9 kPa. The simulant is stored in a 2.5 m long and 0.52 m diameter barrel, and the moisture content of the simulant is maintained to below 0.5%. The drill string is driven by servo motors with a constant rotating speed and feeding speed 1-m deep into the long barrel of the simulant. Some simulant enters the inlet at the bottom of the bit, and a coring tube in the hollow stem
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
of the string is used to form the coring sample. The coring tube in the hollow stem is dragged by a fixed rigid rope while the string is drilling into the soil (Quan et al., 2017). Then, the coring tube has the same speed as the feeding speed relative to the drilling stem though the coring tube does not actually move. In the drilling process, the bit cuts and stirs the in situ simulant into a fluid state, which is redundant and should be removed quickly because the drill stem and the bit both occupy the space of the simulant. The redundant simulant either becomes the coring sample or is discharged by the helical groove of the rotating auger. Otherwise, the drilling process is likely to be clogged and cannot proceed straight forward. The target of the experiments is to seek the optimum drilling matching between the feeding speed and the rotating speed. The drilling tests are conducted under different feeding and rotating speed matching. During the tests, the WOB (Fig. 2a) and DT (Fig. 2b) are measured in real time by force sensors, and the coring amount is weighed.
2241
Fig. 3. Coring amount (a), average WOB (b) and DT (c) in the experiment varying with CPR.
Stage I, where the coring amount is zero and the WOB and DT are small. Stage II, where the coring amount increases with CPR but the WOB and DT are still small. Stage III, where the coring amount saturates and the WOB and DT rise sharply and flutter.
3. Experimental results 3.1. Optimum working parameters In the first group of the experiments, the rotating speed _ is chanis fixed as h_ ¼ 120 r/min, and the feeding speed, u, ged. We term g as the cut per revolution (CPR) of the bit, _ For each CPR (g), the measured WOB and DT _ h. so g ¼ u= in the experiment are presented in Fig. 2. Their values remain small and change slightly with an increase in drilling depth when the CPR is confined within a considerably small range (CPR< 0:5 mm/r). Otherwise, the WOB and DT increase rapidly and flutter significantly. Similar results are obtained for the other two sets of experiments, in which the rotating speed is adjusted to h_ ¼ 80 r/min and h_ ¼ 160 r/min. We average the WOB and DT with respected to g for the three groups of the experiments and plot them in Fig. 3b and c. The coring amount with respect to g is also plotted in Fig. 3a. Interestingly, three common stages, I, II and III, with respect to the CPR are clearly recognized:
According to the experimental results shown in Fig. 3, we define g1 the first boundary position between Stage I and Stage II and g2 the second boundary position between Stage II and Stage III. The optimum working parameter is of great interest to the situation at the secondary common boundary position, g2 ¼ 0:5 mm/r. The parametric matching between the feeding speed and the rotating speed just before g2 is obviously the optimum for each rotating speed because the coring is relatively saturated while the WOB and DT are still small. 3.2. MCR achieved at g2 When the auger is working, the stem and bit of the auger occupy the space that used to be that of the simulant. The helical groove conveys the simulant in situ from the side of the bit to the surface. At the same time, part of the in situ soil may enter the bottom inlet at the center of the bit to be collected as samples. The redundant simulant is removed by both the rotating helical groove and the coring tube. It is clear from Fig. 3 that the WOB and DT increase significantly if g > g2 , which indicates that the pressure at the bit increases accordingly. The pressure increases because the in situ soil cannot be conveyed out in time if the CPR exceeds g2 as g > g2 . However, the coring is already saturated at g2 . Thus, we speculated that the auger reaches its maximum conveying rate at g2 , too. The term m_ dis is the discharging mass rate of the groove, then m_ dis ðg2 Þ ¼ qc /_ max ;
Fig. 2. WOB and DT in the experiment vary with drilling depth. h_ ¼ 120 r/min.
ð1Þ
where qc is expressed as the density of the cuttings (conveyed soil) in the groove and /_ max is termed as the maximum discharging volumetric rate by the groove. We mentioned in Section 2 that the coring tube is dragged by a fixed rigid rope, so the tube moves relative
2242
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
_ Thus, to the stem at the same speed as the feeding speed, u. the maximum coring volumetric rate can be estimated as _ where r is the radius of the tube. The term m_ core is pr2 u, the coring mass rate by the tube, and it reaches saturation at g2 . Therefore, _ m_ core ðg2 Þ ¼ qpr2 g2 h;
ð2Þ
where the density of the collected sample in the coring tube, q, is usually same as that of the simulant in the barrel. 3.3. Without hydrostatic pressure Additionally, the experiments presented an interesting phenomenon. The borehole was well preserved and did not collapse after the drill string was fully extracted from the simulant (see Fig. 4). In general, the borehole may actively exert pressure on the cuttings because the outside soil is not fully solid. The pressure may increase with depth. However, the experimental phenomenon in Fig. 4 indicates that the hydrostatic pressure from the borehole wall can be ignored in our experiments. The lunar soil simulant used in the experiments is dense and cohesive. The cohesion and internal friction are strong enough to allow self-support, which means that the borehole wall provides only a ‘rigid-like’ constraint for the conveyed soil in the semiopen groove. Therefore, we ignore the hydrostatic pressure in the following analysis. 4. Analysis 4.1. A proportional relation for the optimum matching Now, we explain the experimental results, especially at g2 . According to the mass conservation law, the mass rate of the redundant soil in situ termed mtotal , is equal to the sum of the discharging mass rate by the helical groove, mdis , and the coring mass rate by the tube in the hollow stem, m_ core , namely m_ total ¼ m_ dis þ m_ core :
ð3Þ
The total rate of the redundant soil produced by the bit _ where R is the radius of can be estimated as m_ total ¼ qpR2 u, the stem and the bit.
Fig. 4. An integrated borehole preserved after the drill string is fully extracted from the soil in the experiment.
At g2 , we put Eqs. (1) and (2) into Eq. (3) to obtain the proportional relation between the MCR and the rotating speed as q _ /_ max ¼ pðR2 r2 Þg2 h_ ¼ C h: qc
ð4Þ
where we define C ¼ qqc pðR2 r2 Þg2 . Based on the experimental results above, g2 is a constant that is unrelated to rotating speed, and the lunar simulant used in the tests is dense and uniform. Then, C can be taken as a constant. 4.2. Explanation of the experiments Once the proportional relation in Eq. (4) is revealed, the three stages of the experiment in Fig. 3 are easy to under_ a MCR, / , is stand. For a proper rotating speed h, max determined. When the CPR is small, all the redundant simulant in situ that is stirred by the bit can be removed by the auger, m_ total ¼ m_ dis 6 qc /_ max , and nearly no soil enters the coring tube. This is Stage I, as g < g1 . With an increase in CPR, part of the in situ simulant begins to enter the coring inlet to form a sample, and the drilling process enters Stage II. Although the total generation rate of the redundant simulant may exceed the MCR, namely m_ total > qc /_ max , and the auger may reach its discharging ability, MCR, the sum rate of discharging and coring are not yet saturated, m_ total ¼ m_ dis þ m_ core < qc pr2 u_ þ q/_ max if g < g2 . All of the in situ soil can still be removed easily. The WOB and DT are still at low levels because the coring does not influence them, and the increased moment and force (see Fig. 3b and c) are almost attributed to the increased cut rate of the bit. The discharging groove of the auger and coring tube are both saturated at g ¼ g2 , when m_ total ¼ qc pr2 u_ þ q/_ max . In the former two stages, the loads do not go up with the drill depth. Actually, the loads contain the part from the bit and the part from the auger stem. The loads on the bit generated by cutting the in situ soil, is correlated to the pressure at the bit. Since the soil is dense and cohesive, the cohesion and internal friction make the pressure in the soil keep constant with the increasing depth. As the auger can remove the new generated cuttings in time, the pressure at the bit does not increase without accumulation of excess cuttings. So, the pressure at the bit does not increase with an increase of drill depth, until the generating rate of cuttings exceeds the conveying capacity of the auger. Therefore, the loads on the bit become constant, as the drill depth increases. Meanwhile, the loads on the auger stem come from the friction of soil pressing against the surface of the auger stem and the horizontal component of the normal force on the flute. This part increases with the increment of cuttings volume on the flute. However, the flute is narrow and the coefficient of friction between the soil and the surface of the stem is small. Compared with the
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
part on the bit, this part could be negligible. So, the increase is not obvious, unless the auger becomes clogged. As the CPR continues to increase, the drilling process enters Stage III. At CPR of 0.833 (Fig. 2), both the discharging rate of the auger and the coring rate of the coring tube have saturated. The sum of the MCR and the maximum coring rate cannot satisfy all the in situ soil stirred by the bit, namely m_ total > qc pr2 u_ þ q/_ max . The auger become clogged with excess cuttings, due to the high value of CPR. The accumulation of excess cuttings causes a significant increase in the pressure at the bottom (and in turn WOB and DT). Once the pressure exceeds the resistance of the coring tube or the conveying channel, the cuttings move up and leave room for new cuttings to enter into it, which also causes a drop in the WOB and DT. The cycles of these two process make the WOB and DT fluctuate (Zacny and Cooper, 2007). Thus, the three stages in the experiment show that. in Stage I, namely 0 < g 6 g1 ; qqc pR2 u_ 6 /_ max . _ in Stage II, namely g < g 6 g ; /_ max P q pðR2 r2 Þu. 1
2
qc
_ in Stage III, namely g2 < g; /_ max < qqc pðR2 r2 Þu. The secondary boundary position g2 is completely clear when the coring rate and the auger’s discharging rate are both saturated. The first boundary position, g1 , marks where the coring begins. This process is ambiguous without understanding the complicated flows that originate from the complicated structure at the bit, which we will study in subsequent studies. 5. Discussion Although the optimum working matching for drilling is obtained, whether the optimum matching between the feeding and rotating speed can be applied to future drilling on the Moon, is vague. The gravity on the moon is entirely different from that on the Earth, so further studies should answer the following question:
2243
tance from the friction of the groove and gravity. Further, we neglect both the gravity and the resistance friction from the groove and study the relation between the MCR and the rotating speed under ideal conditions. A stable conveyance of the soil by the auger results in a non-zero centripetal acceleration but zero tangential and binormal accelerations for each element of the conveying layer. Then, in the ideal condition, we obtain a balancing relationship between the pushing force, Fb , and the dragging friction, Fd , in the binormal direction of the groove (see Fig. 5), namely Fb ¼ Fd . The dragging force can be estimated by the Coulomb friction law from the pressure of the borehole, namely F d ¼ ls F n , where ls ¼ tan u and u is the frictional angle of the soil. The dragging friction, Fd , may trigger vortex flows in the transverse cross section of the conveying layer (see Fig. 5), which we will study in a future paper. According to the Coulomb frictional law, the direction of the absolute velocity of element va is opposite to the dragging friction Fd . The kinetic analysis indicates that va ¼ vr þ ve , where ve ¼ Rh_ and R represent the radius of the location of the groove axis. We then determine that vr ¼
R2 _ h; A
ð5Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 where A ¼ R2 þ ðh=ð2pÞÞ and h are the thread pitch of the auger helix. In the kinetic analysis in Eq. (5), we neglect the feeding velocity due to its comparative smallness. The relative velocity vr actually represents the discharging velocity varying only with the rotating speed and without the aspect of the conveying layer. Thus, the auger discharge rate can be expressed as / ¼ Cvr , where C is the transverse cross-section area of the conveying layer in the groove. The MCR is then expressed as /_ max ¼ Cmax vr when C reaches a maximum Cmax (Fig. 5). Thus, the MCR is also proportional to the rotating speed: 2
R _ /_ max ¼ Cmax h_ / h: A
ð6Þ
D1: What leads to the proportional relation in Eq. (4)? 5.1. Proportional relation in an ideal condition We present here the proportional relationship between the MCR of the auger and the rotating speed under ideal conditions. We study the drilling in a stable working condition if g 6 g2 . The stirred in situ soil by the bit can be fully conveyed by the auger groove and the coring tube. There is no obvious pressure at the entrance of the conveying channel near the bit. The interaction between any two elements (segments) of the conveying layer can be neglected. Thus, the cuttings are fully transported by the pushing force from the bottom flute of the groove and the dragging friction from the borehole against the resis-
Fig. 5. Elementary analysis under ideal conditions at the conveying layer in the groove.
2244
Z. Zhao et al. / Advances in Space Research 63 (2019) 2239–2244
Although Eq. (6) provides a proportional relationship between the MCR and the feeding speed, it is obtained under an ideal situation, so further investigation is needed to clarify the influences of gravity, friction and bit pressure on the discharging rate, i.e., D2: What correlation exists between the proportional relations Eqs. (4) and (6)? If the two proportional relations are essentially the same, the MCR depends only on the rotating speed and is independent of gravity. Then, we can apply the optimum matching obtained by the ground experiments in future drilling on the Moon. Otherwise, the expensive ground results may be useless. In a subsequent paper, we will carry out such studies.
The common optimum matching between the feeding and rotating speeds signifies a proportional relation between the MCR and the rotating speed. A proportional relation between them is confirmed by a kinematic analysis for the conveying layer in the helical groove of the working auger under ideal conditions without considering gravity, the friction from the groove or the pressure at the bit. Whether the optimum matching can be directly applied to future drilling on the Moon needs to distinguish the correlation between the two proportional relations, which will be presented in a future paper. Acknowledgements This work was supported by the National Nature Science Foundation of China (Grant Nos. 11572017 and 11502277).
5.2. Estimation of Cmax References If we further hypothesize that Eqs. (6) and (4) are essentially the same, we can obtain a new expression for the maximum cross-sectional area of the conveying layer, Cmax , as a function of the experimental parameters g2 : r 2 q Cmax ¼ Ap 1 ð7Þ g2 : q1 R The parameter Cmax is worth identifying because a lunar simulant with a different particle distribution may have a different thickness of the conveying layer when it is drilled. 6. Conclusion A series of ground experiments (on the Earth) have been conducted for future core drilling on the Moon with different constant feeding and rotating speeds. Three common stages were recognized with respect to the CPR, which is defined as the ratio between the feeding speed and rotating speed. The coring is zero in Stage I, although the WOB and DT are small. On the contrary, the coring is saturated in Stage III, and the WOB and DT increase sharply and flutter. Only Stage II is the working stage, in which the coring is not zero and the WOB and DT are small. The optimum matching between the feeding speed and the rotating speed occurs at the boundary position between Stage II and Stage III, where the coring almost saturates the sample and the WOB and DT are still low.
Mellor, M., 1981. Mechanics of cutting and boring. Part 7: dynamics and energetics of axial rotation machines. Cold Regions Research and Engineering Laboratory, Hanover, NH. Quan, Q., Chen, C., Deng, Z., Tang, J., Jiang, S., 2017. Recovery rate prediction in lunar regolith simulant drilling. Acta Astronaut. 133, 121–127. Tan, S., Duan, L., Guo, Z., Gao, H., 2016. Theoretical derivation of the cuttings transportation trajectory for lunar sampling auger drilling. Int. J. Rock Mech. Min. 86, 204–209. Tang, J., Quan, Q., Jiang, S., Chen, C., Yuan, F., Deng, Z., 2016. A soil flowing characteristics monitoring method in planetary drilling and coring verification experiments. Adv. Space Res. 59 (5), 1341–1352. Tang, J., Quan, Q., Jiang, S., Li, H., Bai, D., Tang, D., Deng, Z., 2018. Experimental investigation on flowing characteristics of flexible tube coring in lunar sampling missions. Powder Technol. 326, 16–24. Tian, Y., Tang, D., Deng, Z., Jiang, S., Quan, Q., 2015. Drilling power consumption and soil conveying volume performances of lunar sampling auger. Chin. J. Mech. Eng. 28 (3), 451–459. Zacny, K., Barcohen, Y., Brennan, M., Briggs, G., Cooper, G., Davis, K., Dolgin, B., Glaser, D., Glass, B., Gorevan, S., 2008. Drilling systems for extraterrestrial subsurface exploration. Astrobiology 8 (3), 665– 706. Zacny, K., Cooper, G., 2006. Considerations, constraints and strategies for drilling on mars. Planet. Space Sci. 54 (4), 345–356. Zacny, K., Cooper, G., 2007. Methods for cuttings removal from holes drilled on mars. MARS 3, 42–56, 12. Zacny, K., Paulsen, G., Szczesiak, M., 2011. Challenges and methods of drilling on the moon and mars. IEEE Aerosp. Conf., 1–9 Zhao, D., Tang, D., Hou, X., Jiang, S., Deng, Z., 2016. Soil chip convey of lunar subsurface auger drill. Adv. Space Res. 57 (10), 2196–2203.