analysis and testing of load characteristics for rotary

Research ArticleAnalysis and Testing of Load Characteristics forRotary-Percussive Drilling of Lunar Rock Simulant witha Lunar Regolith Coring Bit

Peng Li12 Hui Zhang1 Shengyuan Jiang1 andWeiwei Zhang1

1State Key Laboratory of Robotics and System Harbin Institute of Technology (HIT) Harbin 150001 China2Mechanical Engineering College Beihua University Jilin 132022 China

Correspondence should be addressed to Peng Li lemmber163com and Shengyuan Jiang jiangshyhiteducn

Received 9 January 2017 Accepted 10 April 2017 Published 30 April 2017

Academic Editor Longjun Dong

Copyright copy 2017 Peng Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Based on an optimized lunar regolith coring bit (LRCB) configuration the load characteristics of rotary-percussive drilling of lunarrock simulant in a laboratory environment are analyzed to determine the effects of the drilling parameters (the rotational velocitythe penetration rate and the percussion frequency) on the drilling load The process of rotary drilling into lunar rock using anLRCB is modeled as an interaction between an elemental blade and the rockThe rockrsquos fracture mechanism during different stagesof the percussive mechanism is analyzed to create a load forecasting model for the cutting and percussive fracturing of rock usingan elemental blade Finally a model of the load on the LRCB is obtained from the analytic equation for the bitrsquos cutting bladedistribution experimental verification of the rotary-impact load characteristics for lunar rock simulant with different parametersis performed The results show that the penetrations per revolution (PPR) are the primary parameter influencing the drilling loadWhen the PPR are fixed increasing the percussion frequency reduces the drilling load on the rock Additionally the variationpattern of the drilling load of the bit is in agreement with that predicted by the theoretical model This provides a research basis forsubsequent optimization of the drilling procedure and online recognition of the drilling process

1 Introduction

During the sampling and exploration of extraterrestrialcelestial bodies humans normally employ rotary-percussivedrilling to improve drilling efficiency to obtain pristinesamples from a celestial body reveal the origin and evolutionof the celestial body explore the possibility of extraterrestriallife and effectively explore and properly use space resources[1 2] The former Soviet Unionrsquos ldquoLunardquo series of unmannedlunar sampling missions the United States ldquoApollordquo series ofsampling projects which included a manned moon landingand the ldquoCuriosityrdquo Mars exploration mission all employedpercussion-assisted rotary drilling to ensure reliable samplingduring exploration [3ndash6] In the near future China willcomplete an unmanned lunar surface sampling and returnmission that is the ldquoChangrsquoe projectrdquo which will involvecollecting soil samples from the lunar surface and 2m belowit using drill sampling [7 8] When the drilling process is

blocked by a large chunk of lunar rock percussion will beused to improve the bitrsquos ability to fracture rock Thereforewhen the drillrsquos configuration is determined the ability toadjust the drilling parameters to achieve the desired drillingperformance is necessary to guarantee reliable lunar surfacesampling

When the former Soviet Union conducted the Luna-24 unmanned autonomous sampling mission on the lunarsurface the experience of the Luna-1620 drillingsamplingmission was drawn upon and a percussion function wasincluded in the drilling machine During the actual lunarsurface sampling the drillrsquos alarm was triggered due to anexcessive drilling load After percussion was enabled thedrilling load decreased to a certain extent and finally alunar soil sample was collected successfully and sent to Earth[9 10] Recently many researchers have conducted extensiveresearch on rock fracture via drilling tool percussion Amongthem Jalali and Zare Naghadehi conducted an experimental

HindawiShock and VibrationVolume 2017 Article ID 3012749 15 pageshttpsdoiorg10115520173012749

2 Shock and Vibration

study of excavation and percussion of rock using a disccutter tooth in a tunnel excavating machine The resultshowed that the sample excavation efficiency of the disc cuttertooth improved significantly under the combined effect ofcutting and percussion Additionally the percussion loadeffectively improved the penetration rate of the simulatedtunnel excavating machine [11] Hashiba et al conducted anexperimental study of a single percussion rock penetrationprocess via button bits and modified the obtained load-penetration depth curve using numerical simulation [12]Based on the fracture criteria for viscoplastic rock Saksala etal conducted a simulation analysis and an experimental studyof the percussive drilling of granite via a specially designedtriple-button bit The results showed that the rock fracturedwhen the percussion velocity was ascending Additionallylateral compressive fracture occurred between adjacent but-tons [13ndash15] Furthermore based on theRayleigh-Lovemodeland a one-dimensional viscoelastic model Tian et al derivedan equation for the axial vibration of a drill string during oilexploration and verified it experimentallyThe results showedthat the length of the drill string is inversely proportional tothe damping at the bottom of the bore When the string wasshorter the effect of horizontal inertia on the dynamic rigidityof the drill string was more significant [16]

Besides acoustic emission (AE) techniques have alwaysbeen adopted in identifications of microseismic source (MS)locations Dong and Li have proposed an innovative MSAEsource location method without the need for premeasuredPS wave velocities and this method greatly weakens theinfluence of the big error derived from the change ofthe wave velocities and propagation traces [17] Then heapplies three nonlinear methodologies (such as randomforests support vector machines and naive Bayes classifier)to discriminate between 20 earthquakes and 27 nuclearexplosions And based on the leave-one-out cross-validationROC curve and test accuracy random forests method clearlyshows the best predictive power [18] Recently Dong etal investigate the typical characters of seismic parametersbetween events and blasts using the datasets of three minesin Canada and Australia and 7 parameters are extractedas discriminant indicators to establish discriminant modelsusing the logistic regression method The classified accuracyof training samples test samples and cross-validated resultshave demonstrated that the discriminant models with gooddiscriminant performance are effective and efficient methodsto identify the blasts from events in real-time [19] Thesemethodologies provide an effective way to quantify theprocess of rock fragmentation which are not easy to observein rock impacting or cutting process

In 2014 the Research Center of Aerospace Mechanismand Control (RCAMC) at Harbin University of Technologysuccessfully designed a lunar regolith coring bit (LRCB)that exhibited excellent drilling performance in tasks suchas continuous chip removal without an auxiliary mediumand rock blockage breakthrough with a limited ability todrill Compared with other geological drill bits and planetarysampling bits it has advantages such as a low load per unitarea for fracturing rocks [20 21] In this paper based onan optimized LRCB configuration and the Mohr-Coulomb

criterion a model of cutting and percussive fracture forlunar rock simulant is created and expanded to the rotary-percussive drilling process to analyze the load characteristicsof rotary-percussive drilling of lunar rock simulant with acoring bit The effect of the impact load on the rockrsquos fractureload for different drilling parameters is determined thisprovides a basis for optimizing the drilling parameters forlunar surface drilling and sampling

The structure of this paper is as follows Section 2 mainlyintroduces the background of previous research that is theLRCB configuration and themodel for the load during rotarydrilling of lunar rock simulant Section 3 describes howthe interaction between the LRCB and lunar rock simulantduring rotary percussion is modeled Section 4 providesexperimental verification of the rotary-percussive drillingload for lunar rock simulant and Section 5 is the conclusion

2 LRCB Configuration andDrilling Load Analysis

21 LRCB Configuration Parameters Based on requirementsof sampling deep lunar soil the LRCB should support the fol-lowing functions (i) ensuring smooth lunar soil chip removalwithout an auxiliary chip removal medium (ii) specifyingthe coring rate of the lunar soil sample and ensuring theability to collect original information and (iii) being able tobreak lunar rock with less than grade-VI drillability withoutexceeding the drilling load limit [22]Therefore the RCAMCteam developed the LRCB shown in Figure 1 which employsinner and outer rows of sharp cutting blades (SCBs) (iedual primary cutting blades) to increase the stability of thedrilling system in the initial stage of lunar rock drillingLaboratorial tests showed that this bit excels at coring lunarsoil and removing chips and has excellent lunar rock drillingload characteristicsThe detailed configuration parameters ofthe LRCB are listed in Table 1

22 Analysis of the Drilling Load of the LRCB The LRCBrsquosconfiguration parameters are abstracted as an analytic geo-metrical model which is shown in Figure 2The relationshipsof the torque on bit (TOB) and the weight on bit (WOB) tothe cutting load of the elemental blade are shown in

119879TOB = 2sum119896=1

2sum119894=1

Δ119865119897119894_119896 sdot radic1199092119887119898119894_119896 + 1199102

119887119898119894_119896

119865WOB = 2sum119896=1

2sum119894=1

Δ119865119899119894_119896(1)

where 119909119887119898119894_119896 is coordinate of the midpoint of the 119894th ele-mental blade at the 119896th row of SCBs on the I axis 119910119887119898119894_119896 iscoordinate of the midpoint of the 119894th elemental blade at the119896th row of SCBs on theK axisΔ119865119897119894_119896 is cutting force of the 119894thelemental blade at the 119896th row of SCBs along the l axis andΔ119865119899119894_119896 is cutting pressure of the 119899th elemental blade at the 119896throw of SCBs along the n axis

In (1) Δ119865119897119894_119896 and Δ119865119899119894_119896 are the cutting loads of elementalblade in the absolute coordinate system The cutting load of

Shock and Vibration 3

Sharp cutting blade (SCB)

Forward rake angle

Outward rake angle

훾on

휆sn

wb1

wSb

h s kr = wb1wSb

ΔΨb

Δhb

(a) Three-dimensional configuration illustration

DH

DC

(b) The actual LRCB

Figure 1 Three-dimensional configuration illustration of the LRCB and the actual LRCB

휙bg

Rock oblique cutting process by elemental blade

Rock

ℎH

I

K

J

ℎo Δℎb

ΔΨb

Om2_II

훼H

l2_IIn2_II

휆sn_II훾on_II

Oe2_II

sퟐ_II

bퟐ_II

rퟐ_IIoퟐ_II

v ퟐ_II

ℎpe

n

FRg 훼

훾nΨ휆

휆s

wb Fcut

Fpen

Δℎpn

o

IIII

W Ua

V

s

bFRU

120588b2_II

FRW

e

휆shIIFFR

휙휙bgI

I

Figure 2 Curves for the LRCBrsquos dual-row sharp cutting blade and matrix ellipsoid spiral chip removal

Table 1 LRCB configuration parameters

Parameter Symbol Value

Bit matrix parameters

Borehole diameter 119863119867 32mmCoring diameter 119863119862 145mm

Short axial length of spiral ellipsoid ℎ119867 158mmNumber of bit spirals 119873119867 3

Cutting blade position parameters Cutting blade height difference Δℎ119887 1mmCutting blade angle difference Δ120595119887 9308∘

Cutting blade configuration parameters

Forward rake angle 120574119900119899 Row I 0∘

Row II 0∘

Outward rake angle 120582119904119899

Row I 25∘

Row II 25∘

Sharp-point position coefficient 119896119903 Row I 05Row II 03

Sharp-point height ℎ119904 Row I 2mmRow II 2mm

Sharp blade width 119908119878119887

Row I 4mmRow II 533mm


the elemental blade in the local coordinate system o s ris calculated first Next a coordinate transformation is per-formed to obtain the result An analysis of the stress onthe elemental blade in the local coordinate system o s r isshown in Figure 2The cutting and fracture region of the rockfor a shallow cutting depth (approximately 100120583m) is dividedinto the following parts [23] (i) a shear fracture region (I) inwhich the rock ismainly under the cutting force and developsa shear-tensile fracture (ii) a dense core crushing area (II)which is an area of compressed dense powder produced bythe cutting force 119865Cut and the cutting pressure 119865Pen and (iii)an overcut area (III) that is a region in which the fracturenear a predefined cutting depth is produced by fluctuationsin the cut contact friction and the systemrsquos rigidity whichprimarily affects the cutting pressure The cutting force 119865Cutand the cutting pressure 119865Pen of the elemental blade are asfollows

119865Cut = [119865119877 (cos120601119887 sdot g minus sin120601119887 sdot U119880)+ 119865119873 (cos120601119861 sdot g120573 minus sin120601119861 sdot a120573)] sdot r

119865Pen = [119865119877 (cos120601119887 sdot g minus sin120601119887 sdot U119880)+ 119865119873 (cos120601119861 sdot g120573 minus sin120601119861 sdot a120573)] sdot s

(2)

where 119865119877 is resultant force on the rock fragment due to thefront blade surface 119865119873 is resultant force on the overcut areadue to the rear blade surface 120601119887 is friction angle between thecutting blade and the dense core 120601119861 is friction angle betweenthe cutting blade and the parent rock g is normal vector ofthe front blade surface U is chip removal velocity vector g120573is unit vector normal to the rear blade surface and 120572120573 is unitvector normal to the rear surface of the inward cutting blade

In (2) the chip removal velocity vector U satisfies

U = 119903119881 (cos120595120582 sdot a + sin120595120582 sdot b) (3)

where 119903 is removal-cutting ratio (the ratio between theremoving vector and the cutting vector) 120595120582 is chip removalangle (the angle between the direction of chip removal at thefront blade surface and the direction normal to the cuttingblade) a is unit vector normal to the front surface of thecutting blade and b is unit vector parallel to the cutting blade

Based on minimum energy dissipation theory when thesystemrsquos other control parameters are constants there mustbe a group of state parameters 119903 120595120582 that minimize thepower consumed by the front surface of the cutting bladeTheobtained state parameters 119903 120595120582 are substituted into (2) toobtain the cutting load on the elemental blade For a detailedderivation of the LRCBrsquos drilling load please refer to [20]

Because the process of sampling the lunar surface isbased on controlling the drilling velocity the LRCBrsquos drillingparameters are generalized as the rotational velocity 119899119863 andthe penetration rate VPen The penetrations per revolution(PPR) are defined as the ratio of these two control parametersand its actual physical significance is the progress of bit as it

Percussive springCylindrical

cam

Percussive mass(Hammer)

Roller

Auger

Spline joint

Figure 3Three-dimensional configuration of the percussive mech-anism

penetrates vertically during each rotation When the drill bitprogresses at a constant PPR each cutting blade performs adownward spiral After the cutting blade cuts around the bitrsquoscenter of rotation for a cycle the corresponding penetrationdisplacement is the product of the number of cutting bladesand a single-bladersquos cutting depth as shown in

119896PPR = VPen119899119863 = 119873119887 sdot ℎPen (4)

where ℎPen is the real-time cutting depth of a single cuttingblade during the drilling process and 119873119887 is the number ofcutting blades deployed around the bit

3 Mechanical Model forRotary-Percussive Drilling

31 Analysis of the Rotary-Percussive Drilling Process In theprocess of lunar surface sampling applying a certain amountof impact load to the drill effectively improves its efficiencyat fracturing lunar rock simulant According to the designof the deep drillingsampling mechanism for use on thelunar surface the principle underlying the operation of thepercussive mechanism is as follows when the motor rotatesthe cylindrical cam it also drives the cyclic motion of a set ofspring-mass elements to apply an impact load to the drill asshown in Figure 3 [24 25]

In rotary-percussive drilling process the cutting bladesinteract directly with the rock When rotary-percussivedrilling of lunar rock with a coring bit is expanded along thebitrsquos circumferential direction it is equivalent to rock cuttingand percussive fracturing using an elemental blade along astraight line as shown in Figure 4

Impact-cutting and fracture of lunar rock simulant usinga single blade is divided into the following stages (as shownin Figure 4) (i) the impact-cutting coupling stage the impactload is suddenly applied to the cutting blade during forwardcutting by a hammer at the same time the cutting bladequickly changes its original track penetrates the rock alonga direction that combines the percussion velocity and thecutting velocity and creates a tiny impact fracture pit (ii)the force-control cutting stage because the effective impacttime is extremely short (far less than the time required for thecam to return) the cutting blade progresses in response to apercussive spring pretightening force to cut and fracture the


HammerHammer

Hammer

Blade BladeBlade

Rock

Stage of impact-cutting coupling

Stage of force-control

Stage of position-control

lpos lforlcra

Cut

nPerPer

Figure 4 Fracture process for lunar rock simulant with impact-cutting coupling

0 0

P0 kP

x

wP uP

bP

mP

Fi(t)

Figure 5 Simplified mechanical model of the collision between thehammer and the drill

rock after the impact load disappears at the same time thecutting depth of the rock is determined by the pretighteningforce of the percussive spring and (iii) the position-controlcutting stage when the hammer and the roller start thenext cycle of motion the percussive spring pretighteningforce on the cutting blade disappears at the same timethe cutting blade enters the position-control cutting stagethat is it completely follows the predefined cutting depth tofracture the lunar rock simulant Now the impact load cycleis complete and the cutting blade waits for the next impact

32 Mechanical Model of the Collision between the Hammerand the Drilling Tool Assume the hammerrsquos collision withthe drill is an interaction between a single mass block anda semi-infinite polished rod via a spring damping elementwithout the additional effect of reflected waves on thepercussive stress as shown in Figure 5 [26]

According to Newtonrsquos second law and the equation forthe transmission of a one-dimensional stress wave transmis-sion the collision between the hammer and the drill shouldsatisfy the following equations and boundary conditions

119898119875119875 = minus119896119875 (119908119875 minus 119906119875) minus 119887119875 (119875 minus 119875) 119887119875119875 + 119896119875119908119875 minus (119887119875 + 119864119860119888 ) 119875 minus 119896119875119906119875 = 0

119908119875 (0) = 0119875 (0) = V1198750119906119875 (0) = 0

(5)

where 119898119875 is hammer mass 119864 is elastic modulus of the drillmaterial 119860 is contact area between the hammer and the drillduring the collision 119896119875 is contact rigidity of the hammer andthe drill during the collision and 119887119875 is equivalent dampingcoefficient of the hammer and the drill during the collision

The Laplace transform of (5) is taken variables aresubstituted and the Laplace transform is inverted to obtain

119908119875 (119905) = V11987502120578119875 1 minus 119890minus120572119875119905 cos120596119875119905 + 1205731198751119890minus120572119875119905 sin120596119875119905 119906119875 (119905) = V11987502120578119875 1 minus 119890minus120572119875119905 cos120596119875119905 minus 120573119875119890minus120572119875119905 sin120596119875119905

(6)

where

1205962119875 = 1612057821198751205962

1198750 minus (12059621198750 minus 4120585119875120578119875)2

16 (120585119875 + 120578119875)2

120572119875 = 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875)

1205731198751 = 81205782119875 minus 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

120573119875 = 12059621198750 minus 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

(7)


Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)

Figure 6 Stress analysis of the percussive fracture of lunar rocksimulant via the cutting blade

and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)

The impact force on the contact surface is

119865119894 (119905) = 119898V0radic1 + 1205732radic1205722 + 1205962119890minus120572119905 sin (120596119905 + 120593) (9)

33 Model of the Impact-Cutting Coupling Stage In a com-plete impact load cycle because the effective impact time isextremely short (several milliseconds) the horizontalmotionof the cutting blade during this cycle is ignored that is thefracture of the lunar rock simulant due to the impact-cuttingcoupling is discretized as a percussive fracture process and acutting fracture process

331 Mechanical Model of the Percussive Penetration of theElemental Blade into the Lunar Rock Simulant As with asingle impact the interaction between the cutting blade andthe rock is extremely short The load 119865Per on the rock due tothe cutting blade and the penetration depth ℎPer satisfy thefollowing relation (the variation of the rockrsquos contact rigidityduring the loadingoffloading process is ignored)

119865Per = 119870ℎPer (10)

where 119870 represents the contact rigidity of the rockAn analysis of the stress at the instant of percussive

fracture of the lunar rock simulant via the cutting blade isshown in Figure 6 Based on the fluctuation dynamics thepercussion is transmitted as a fluctuation via the cutting bladeto the rock On the contact surface between the cutting bladeand the rock the wave is transmitted and reflected Based on

force equilibrium and fluctuation dynamics the relationshipbetween the incidentreflected stress and the velocity is

119889119865Per119889119905 = 119870119889ℎPer119889119905 = 119870VPer119865Per (119905) = 2119865119894 (119905) minus 119885 sdot VPer (119905) + 119865Pen

(11)

where VPer is velocity of the cutting bladersquos percussive pene-tration into the rock 119865119894(119905) is cutting bladersquos incident impactforce on the rock 119865Pen is cutting bladersquos pressure on the rock119885 is wave damping of the drill

After substituting variables and rearranging (11) a dif-ferential equation or the percussive fracture of lunar rocksimulant by a cutting blade is as follows

119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)

When the initial condition 119865Per|119905=0 = 0 is substituted intothe incident percussion equation (9) the impact force that thecutting blade exerts to fracture the lunar rock simulant is

119865Per = 119890minus119870lowast sdot119905 sdot 119870lowast sdot 2119898V0radic1 + 1205732radic1205722 + 1205962

(119870lowast minus 120572)2 + 1205962

sdot 119890(119870lowastminus120572)sdot119905sdot [(119870lowast minus 120572) sdot sin (120596119905 + 120593) minus 120596 sdot cos (120596119905 + 120593)]minus [(119870lowast minus 120572) sdot sin120593 minus 120596 sdot cos120593] + 119865Pen (1minus 119890minus119870lowast sdot119905)

(13)

where 119870lowast the impact coefficient of the cutting blade on therock is equal to 119870119885

Because the percussive fracture region of the rock ismuchsmaller than the width of the cutting blade the impact forceof the cutting blade on the rock calculated in the previoussection is treated as a linear load For a linear load 119865Per119908119887the internal stress state of the rock (a semi-infinite plane asshown in Figure 6) is

120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)

where 119903119901 is polar radius of pole 119874 in a polar coordinatesystem 120579119901 is polar angle of pole 119874 in a polar coordinatesystem 120590119903 is normal stress on a microelement of the rockalong the polar radius 120590120579 is normal stress on a microelementof the rock along the polar angle and 120591119903120579 is shear stress on amicroelement of the rock along the polar radiusangle

As shown in Figure 6 the shear stress 120591119903120579 = 0 therefore120590119903 and 120590120579 are main stresses on the microelement of the lunarrock simulant Under a linear load shear cracks in rock


normally spread along tracks that maintain constant angleswith respect to the maximum principle stress For a linearload these tracks constitute two logarithmic spirals as shownin

119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)

where 1199031199010 is the distance between the intersection point ofthe two logarithmic spirals and pole 119874 and 120582119891 is the anglebetween the tangent at any point along the shear crackrsquos trackand the maximum principle stress at that point

Next based on equation of state for the stress on anymicroelement in an object under external load and (14) and(15) the shear stress 120591119901 and the normal stress120590119901 at any pointon the logarithmic spiral are

120591119901 = 119865Per sin 21205821198911205871199031199010119908119887

119890plusmn120579119901 cot120582119891 cos (plusmn120579119901)

120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887

119890plusmn120579119901 cot120582119891 cos (plusmn120579119901) (16)

Additionally rock fracture satisfies the Mohr-Coulomb yieldtheorem that is 120591119901 = 120590119901 sdot tan120593 + 119862 Equation (16) issubstituted and (17) is obtained after rearrangement

1199031199010 = 2119865Per (sin 120582119891)2 (cot 120582119891 minus tan120593) cos (plusmn120579119901)120587119908119887119862119890plusmn120579119901 cot120582119891 (17)

Equation (17) suggests that when the rock surface is undera certain load both sides of the load develop two shearcracks as shown in Figure 6These cracks satisfy relationshipgiven by (15) The distance between the intersection of thetwo cracks and pole 119874 is 1199031199010 This area is defined as thecompressive dense area formed after the impact load isapplied to rock After 1199031199010 is obtained a complete profile ofthe impact fracture pit on the lunar rock simulant is obtainedvia (15)

332 Analysis of the Cut Fracture Characteristics of LunarRock Simulant during Impact After an impact two impactfracture pits are formed before and after the load is appliedto the lunar rock simulant While the cutting blade continuescutting forward the lunar rock simulant continues to fracturealong the shear fracture previously formed by the impactload To simplify the stress analysis the shear fracture surfaceof the rock during cutting is treated as a plane whose startingand end points are where the profile of the impact fracturepit (a logarithmic spiral) intersects the cut and uncut surfacesof the lunar rock simulant When the impact and cutting arecoupled three regions are formed in front of the cutting blade(as shown in Figure 7) that is OAGF is the compact fractureregion formed by the impact ABCD is the percussive fracturefragment formed by the impact and BEC is the shear fracture

Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra

Figure 7 Stress analysis for lunar rock simulant fracture via anelemental blade by means of coupled impact and cutting

region formed by cutting The equilibrium equations are asfollows

119865119877 cos (120601119887 minus 120572119909) = 119865120590119901 cos(120582119888 + 120601119888 minus 1205872 ) + 119865119899119909119865119877 sin (120601119887 minus 120572119909) = 119865120590119901 sin(120582119888 + 120601119888 minus 1205872 ) + 119865119899119910

(18)

where 119865119877 is resultant force on the cutting blade 119865119899119909 ishorizontal component of the resultant reaction force exertedby the parent rock on a rock fragment in the fracture regionand 119865119899119910 is vertical component of the resultant reaction forceexerted by the parent rock on a rock fragment in the fractureregion

In (19) 119865120590119901 satisfies following relationship119865120590119901 = 1119899 + 1 sdot ℎ119875119899119886119908119887

sin 120582shsdot 119862 cos120593sin (120593 + 120601119888 + 120582sh + 120582119888) (19)

where 119899 is stress distribution coefficient ℎ119875119899119886 is actual cutdepth 119908119887 is cutting blade width 120582sh is shear fracture angle119862 s cohesion of the rock 120593 is inner friction angle of therock 120582119888 is angle between the percussive fracture fragmentand the cutting direction and 120601119888 is friction angle between thepercussive fracture fragment and the parent rock

For the other parameters and variables in Figure 7 and(19) please refer to the stress analysis for the cutting andfracturing of lunar rock simulant using an elemental blade[17] Before the resultant force on the cutting blade 119865119877 iscalculated the resultant force exerted by the parent rock ona rock fragment in fracture region 119865119899 should be calculatedAssume uniformly distributed force 119902 in logarithmic spiralAB satisfies the following condition

119902 = 1199020 sdot sin 120579 (20)

where 1199020 is the stress constantThe polar function in (15) is converted to rectangular

coordinates as follows

119909 (120579) = 119903 sdot sin 120579 = 1199030119890120579 cot120582119891 sdot sin 120579119910 (120579) = 119903 sdot cos 120579 = minus1199030119890120579 cot120582119891 sdot cos 120579 (21)


The arc length 119897119898119894 between any two polar angles 120579119894 and120579119894+1 in the logarithmic spiral in the impact fracture pit is

119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)

The resultant force along any arc is

119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894

= 11990201199030radic(cot 120582119891)2 + 1cot 120582119891 sin 120579119898119894 sdot 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)

where 120579119898119894 is the polar angle corresponding to the midpointof the arc between adjacent polar angles 120579119894 and 120579119894+1 120579119898119894 asymp(120579119894 + 120579119894+1)2

The horizontal and vertical components of the resultantreaction force exerted by the parent rock on a rock fragmentin fracture region are

119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)

where 120593119899119894 is the angle between the normal vectorreactionforce at the midpoint of arc microelement 119897119904119894 and the hori-zontal direction

tan120593119899119894 = cot 120582119891 sin 120579119898119894 + cos 120579119898119894cot 120582119891 cos 120579119898119894 minus sin 120579119898119894 (25)

Equations (23) and (25) are substituted into (24) to obtainthe horizontal and vertical components of the resultantreaction force exerted by the parent rock on a rock fragmentin the fracture region

119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1

( sin 120579119898119894 sdot 119890120579 cot120582119891 10038161003816100381610038161003816120579119894+1120579119894) sdot cos120593119899119894

119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1

( sin 120579119898119894 sdot 119890120579 cot120582119891 10038161003816100381610038161003816120579119894+1120579119894) sdot sin120593119899119894

(26)

Equation (26) is substituted into (18) to obtain

119865119877= cos (120582119888 + 120601119888 minus 1205872) sdot 119870119865119899119910 minus sin (120582119888 + 120601119888 minus 1205872) sdot 119870119865119899119909

cos (120601119887 minus 120572119909) sdot 119870119865119899119910 minus sin (120601119887 minus 120572119909) sdot 119870119865119899119909

sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)

When impact and cutting are coupled the cutting forceand cutting pressure required by a single cutting blade tofracture lunar rock simulant are as follows

119865Cut_cra = 119865119877 sdot cos (120601119887 minus 120572) 119865Pen_cra = 119865119877 sdot sin (120601119887 minus 120572) (29)

34 Fracture Load Analysis for Lunar Rock Simulant in theForce- and Position-Control Cutting Stages The depth of acut in lunar rock simulant during the force-control cuttingstage is determined by the percussive spring pretighteningforce If the percussive spring pretightening force exceeds thecutting pressure required to cut and fracture rock the actualcut depth exceeds the initial predefined cut depth Otherwisethe cutting blade fractures the lunar rock simulant accordingto predefined cut depth Moreover the cutting load in theforce-control cutting stage is affected by both the percussivespring pretightening force and the impact load In the impact-cutting coupling stage the lunar rock simulant develops animpact fracture pit during the impactWhile the cutting bladecontinues cutting forward the rock fractures along the trail ofthe impact fracture pitTherefore part of the load in the force-control cutting stage is due to the impact pit in the fracturedlunar rock Additionally when the cutting velocity is fixedhorizontal cut displacement in the force-control cutting stageis primarily affected by the percussion frequency A higherpercussion frequency leads to a smaller cut displacementthat is a higher percussion frequency leads to a smallerdisplacement in the force-control cutting stage It takes moretime for the cutting blade to cross an impact fracture pit andthe load required to fracture lunar rock simulant increaseswhen there is an impact pit The average load required tofracture lunar rock simulant in the force-control cutting stageis

119865119865Cut_ave = 119865Cut_cra sdot 119870cra + 119865Cut_pre sdot 119870pre119865119865Pen_ave = 119865Pen_cra sdot 119870cra + 119865Pen_pre sdot 119870pre (30)

where 119865Cut_cra is cutting force required to complete the firstcutting cycle after the impact fracture pit is formed 119865Pen_cra iscutting pressure required to complete first cutting cycle afterthe impact fracture pit is formed119870cra is weight coefficient of


Lunar rock stimulant (marble)

Cutting blade

Penetratingmechanism

Servo electric cylinder

Magnescale

Rock holder and six-axis sensor assembly

Mobile plate

Percussive mechanism

(a)

Penetrating mechanism

Rotary-percussive drilling mechanism

(RPDM)

Core-drill(Hollow auger)

Rock holder

Load cell

Torque sensor

Magnescale

(b)

Figure 8 Single-blade linear cutting load test platform (a) and comprehensive drill characteristics test platform (b)

the required cutting load to complete the first cutting cycleafter the impact fracture pit is formed 119865Cut_pre is cuttingforce required to cut the rock with a percussive springpretightening force 119865Pen_pre is cutting pressure required tocut the rock with a percussive spring pretightening force119870preis weight coefficient of the cutting load for the pretighteningforce

In (30) the weight coefficient satisfies the followingcondition

119870cra = 119905cra119905for = 2120587 sdot 119897cra sdot 119891119901VCut sdot 1205731198881 sdot 119899cb

119870pre = 1 minus 119870cra(31)

where 119905cra is time required for the cutting blade to cross theimpact fracture pit 119905for is time required for the cutting bladeto complete the force-control cutting stage 119897cra is horizontaldisplacement of the impact fracture pit 119891119901 is percussionfrequency VCut is horizontal velocity of the cutting blade 1205731198881is idle movement angle of the cam in percussive mode and119899cb is number of bulges in the cam in percussive mode

The cutting load characteristics of lunar rock simulantunder force-control cutting conditions are essentially thesame as those with a predefined cut depth Therefore thecalculation of the cutting load of lunar rock simulant underforce-control cutting conditions given in (30) is based on (2)

When the percussive cam changes from being idle totraveling the hammermoves upward along the convex profileand compresses the percussive spring to accumulate energyfor next impact load At the same time the hammer is nolonger pressed to the top of cutting bladersquos post and thecutting blade is temporarily free As the cut continues thecutting blade is quickly lifted by the uncut surface of the lunarrock simulant and clings to the upper boundary of the toolpost At the same time the lunar rock simulant is cut andfractured according to the predefined cut depth

4 Experimental Verification

Theexperimental verification of the characteristics of the loadfor rotary-percussive drilling with an LRCB is divided into

two stages First the impact-cutting load characteristics aretested using a single-blade linear cutting load test platformto verify the characteristics of the load on the cutting bladein different stages Next a rotary-percussive drilling test ofthe lunar rock simulant is performed via a comprehensivetest platform for the characteristics of the drill to comparethe variation trends of the drilling load before and afterthe impact load is applied and to analyze and verify thecharacteristics of the LRCB drilling load for different drillingparameters Based on the specifications in the Changrsquoe planfor experimental verification of the LRCBrsquos ground function-ality marble of grade-VI drillability is selected to simulatelunar rock

41 Test Environment Overview The single-blade linear cut-ting load test platform is shown in Figure 8(a) The cuttingblade installed in themobile plate is driven by a servo actuatorto make a horizontal cut The front panel of the mobileplate is connected to the penetrating mechanism to make thecutting blade penetrate vertically Additionally the percussivemechanism (which is driven according to the theory shownin Figure 3) is attached to the top of the cutting bladersquos post toapply an impact to the cutting blade A magnescale sensoris installed on the left side of the front panel to monitorthe cutting bladersquos penetration displacement and fluctuationsin the cut in real-time A rock holder is installed on theplatform rack by means of a six-axis force sensor to measurethe cutting and impact loads on the rock in real-time duringthe cuttingpercussion process [27]

The comprehensive drillingsampling characteristics testplatform is shown in Figure 8(b) The bit is installed in arotary-percussive drill via a 1m hollow auger Guide rails areinstalled on both sides of the drill box and connected to thepenetration mechanism via the drive chain The drill andthe penetration mechanism drive the LRCB during rotary-percussive drilling Tension and torque sensors are installedin the drive chain and along the axis of the auger respectivelyto measure the drilling pressure and the torque on the coringbit in real-time A magnescale sensor is installed betweenthe drill box and the guide rails to measure the penetrationdisplacement [28]


0

TheoreticalExperimental

FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)

Figure 9 Maximum impact load on the lunar rock simulant withthe percussion energy increase

42 Experimental Verification of the Cutting Impact LoadCharacteristics for Lunar Rock Simulant According to thetheoretical model described in the previous sections theimpact load on the lunar rock simulant is related to thecollision contact rigidities of the hammer and cutting bladersquospost and between the cutting blade and the lunar rocksimulantThe lunar rock simulantrsquos impact load transmissioncharacteristics are tested to obtain these two contact rigiditycoefficients The pattern in the lunar rock simulantrsquos varia-tions when it is impacted with different percussion energies istested to calibrate the two contact rigidities during collision inthemodelThe variation pattern of themaximum impact loadas a function of the percussion energy exerted by the cuttingblade on the lunar rock simulant is shown in Figure 9 Inthe test the percussive spring pretightening force is adjustedto vary the percussion energy As the percussion energyincreases from 00138 J to 08027 J the maximum impactload on the lunar rock simulant increases from 6232N to3598N Using the method of undetermined coefficientsthe collision contact rigidities between the hammer and thecutting bladersquos post and between the cutting blade and thelunar rock simulant are obtained they are listed in Table 2The other parameters of the model are obtained from a test ofthe rockrsquos mechanical characteristics and a discrete elementsimulation of the single-blade linear cutting process

Because the effect of the cut configuration on the trans-mission loss of the impact load is insignificant a 4mm widecutting blade with a minus13∘ front rake angle and a 0∘ blade rakeangle is used for the percussive cutting and fracture of lunarrock simulant via a single blade in the load characteristicstest When the cut depth is 0033mm the cutting velocityis 261mms the percussion energy is 028 J the percussionfrequency is 4Hz and the cutting pressure load as a functionof time for the lunar rock simulant in a single impact cycleis as shown in Figure 10(a) The solid blue line representsthe test load After one cycle of impact loading the cuttingpressure on the lunar rock simulant peaks instantaneously

Table 2 Characteristic parameters in the rotary-percussive drillingload prediction model for lunar rock simulant

Rock material MarbleCohesion 242MPaInner friction angle 418∘

Indentation hardness 1080MPaFriction angle between rock fragments and parentrock 322∘

Angle between dense core and cut fracture 60∘

Contact rigidity between hammer and tool post 20 kNmmContact rigidity between cutting blade and rock 21 kNmm

falls rapidly enters the force-control cutting stage (the lightyellow area) and stabilizes at approximately 151N (whichis commensurate with the percussive spring pretighteningforce)When the percussive cam begins to push it the cuttingblade enters the position-control cutting stage (the light greyarea) When the pretightening force on the tool post isinstantaneously released the cutting blade is lifted rapidlyby the cutting area of the rock and progresses according tothe predefined cut depth The cutting pressure stabilizes atapproximately 231 N Because there are assembly gaps andelastic deformation between the rack and the tool post therigidity of the system and the overcut depth Δℎ119875119899 varyduring the cutting process Figure 10(b) shows the variationtrend of the impact load on the lunar rock simulant versustime It shows that the theoretical variation curve for theimpact load essentially matches the experimental one

The average penetration distance is defined as the cali-bration value of the fluctuation in the cut depth Δℎ119875119899 Thefluctuations in the cut depth as a function of the cut depthand the percussion frequency during the force- and position-control cutting stages are obtained via fitting as follows

Δℎ119875119899_for = (39450 sdot ℎ2Pen + 22290 sdot ℎPen + 6883)times 10minus6

Δℎ119875119899_pos = (minus2111 + 7648ℎPen + 1315119891119875minus 5924ℎ2Pen + 1119ℎPen sdot 119891119875 + 20210ℎ3Penminus 4171ℎ2Pen sdot 119891119875) times 10minus4

(32)

For different cut depths and percussion frequencies theaverage cutting impact load on the lunar rock simulant isshown in Figure 11 Figures 11(a) and 11(b) show curved sur-faces representing the variation of the load on the lunar rocksimulant during the force-control cutting stage In this stagethe cutting load is inversely proportional to the percussionfrequencyThis ismainly because as the percussion frequencyincreases the proportion of the fracture load to which theimpact-cutting coupling condition applies increases and asmaller shear fracture angle becomes sufficient to completethe fracture in the lunar rock simulant under the impact-cutting coupling conditionTherefore the average load grad-ually decreases Moreover with the increase in the cut depth


0

400

800

1200

1600

1989 Stage of position-control

1510231


005 01 015 02 0250time (s)

Theoretical ExperimentalNo percussive

FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000

Theoretical Experimental

FPe

r(N

)

(b)

Figure 10 Variation trend of the resistant force on the lunar rock simulant in a single impact cycle

the cutting load becomes clearly divided into two stagesWhen the cut depth is less than 01mm no variation offracture load on the lunar rock simulant is apparent Thisis because when there is a percussive spring pretighteningforce a cut with a depth of 01mm is made on the lunar rocksimulant for comparison when cut depth exceeds 01mmthe fracture load increases significantly with the cut depthand the percussive spring pretightening force never plays adominant role Figures 11(c) and 11(d) show curved surfacesthat represent the variation in the load on the lunar rocksimulant in the position-control cutting stage When the cutis relatively shallow (less than 01mm deep) the fracture loadon the rock increases with the percussion frequency as thecut depth increases the effect of the percussion frequency onthe fracture load on the rock decreases Figures 11(e) and 11(f)show the variation trend of the average impact-cutting loadon the lunar rock simulant as a function of the percussionfrequency and the cut depth In general the fracture loadon the lunar rock simulant increases significantly with thecut depth and decreases slightly as the percussion frequencyincreases The variation trend of the test results matches thatof the theoretical calculation

43 Analysis and Experimental Verification of the LoadCharacteristics of Rotary-Percussive Drilling with an LRCBThe load characteristics of rotary-percussive drilling with anLRCB for lunar rock simulant are investigated using a com-prehensive drill characteristics test platform The variationtrends of the load on the drill bit before and after percussionis applied are compared to analyze the auxiliary effect of

the impact load on the fracture of lunar rock simulant Inthe test the LRCBrsquos percussion energy input is set to 26 JBased on the LRCBrsquos configuration the percussion energiesgained by the different elemental blades in a percussion cycleare 0196 J 0196 J 0182 J and 0294 J When the coring bitrotates at 30 rpm the penetration rate is 3mmmin and thepercussion frequency is 20Hz the variations in the LRCBdrilling load before and after percussion is applied are asshown in Figure 12

In the initial drilling stage the LRCB penetrates at PPRof 01mmr and the percussive mechanism is not activated(light yellow area) During this time the drilling load gradu-ally increases with the drilling depth and the rotary torqueand the drilling pressure stabilize at 371 Nm and 4823Nrespectively When the drilling depth reaches 30mm thepercussive mechanism is activated (light grey area) Thisshows that under an impact load the rotary torque anddrilling pressure on the LRCB both decrease and eventuallystabilize at 308Nm and 3486N respectively which showsthat the percussivemechanism effectively reduces the drillingload required to penetrate lunar rock simulant

Figure 13 shows variation trend of the average drillingload of the LRCB for different PPR as the percussionfrequency increases from 0Hz to 20Hz The bitrsquos rota-tional velocity is set to 50 rpm the PPR during drilling(004ndash02mmr) is controlled by adjusting the penetrationrate (2ndash10mmmin) When the coring bitrsquos configurationparameters are fixed the fluctuation in the cut depth isproportional to the PPR Based on the fluctuation in thepenetration displacement of the drilling machine detected by


0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)

(b) Cutting pressure

05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

(d) Cutting pressure

05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)

(f) Cutting pressure

Figure 11 Trends of the average impact-cutting load on the lunar rock simulant versus the percussion frequency and the cut depth


Drilling depth (mm)0 10 20 30 40 50

0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)

(a) Torque on bit versus drilling depth


Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)

(b) Weight on bit versus drilling depth

Figure 12 Comparison of the LRCB drilling load before and after percussion applied

05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB

Figure 13 Trends of the rotary-percussive drilling load of the LRCB as functions of the percussion frequency and PPR

the magnescale sensor in a drilling cycle a best-fit functionalrelationship between the fluctuation in the cut depth and thePPR of the coring bit is roughly estimated as follows

Δℎ119875119899 = (532 sdot 1198962PPR minus 34 sdot 119896PPR + 1789) times 10minus4 (33)

Figure 13 shows that once the impact load has been intro-duced the drilling load of the LRCB decreases by differentamounts and decreases further as the percussion frequencyincreases When the percussion frequency increases to 20Hzand the PPR is 004mmr and 02mmr the rotary torque

required to fracture the lunar rock simulant is reduced by086Nm and 056Nm respectively the drilling pressurerequired to fracture the lunar rock simulant is decreasedby 858N and 116N respectively Additionally the variationtrend of the drilling load as a function of the PPR and thepercussion frequency matches the theoretical prediction

For percussion frequency 20Hz and PPR 01mmr thevariation trend of the drilling load of the LRCB is shownin Figure 14 As the rotational velocity increases both theTOB and the WOB increase This is because the increase inthe bitrsquos rotational velocity decreases the number of impact



0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)

Figure 14 Trend of the LRCB load in rotary-percussive drilling with the increased rotational velocity and fixed PPR

loads applied to the lunar rock simulant by the bit in eachrotation cycle of the drilling process that is the decrease inthe blow per revolution decreases the proportion of fracturedue to impact-cutting coupling for the lunar rock simulantTherefore the drill should provide a larger TOB and a higherWOB

5 Conclusions

In this paper the process of penetrating lunar rock simulantvia LRCB rotary-percussive drilling is analyzed The follow-ing conclusions are reached

(1) A load prediction model for lunar rock simulantpenetration via LRCB rotary-percussive drilling iscreated It effectively predicts the characteristics ofthe load on lunar rock simulant during rotary-percussive drilling within known parameter ranges(the rotational velocity is between 30 and 100 rpmthe penetration rate is between 3 and 20mmminthe percussion frequency is between 0 and 20Hzand the single percussion energy is 26 J) for a fixeddrill configuration These parameter ranges coverthe adjustable ranges of the lunar surface samplingmechanism

(2) The effects of the PPR the percussion frequency andthe rotational velocity on the lunar rock simulantrsquosdrilling load are determined The PPR is the primaryparameter influencing the drilling load When thePPR is fixed introducing an impact load effectively

decreases the drilling load on the lunar rock simulantAdditionally the drilling load is inversely propor-tional to the percussion frequency When the per-cussion frequency reaches its upper limit reducingthe rotational velocity increases the blow per revolu-tion improves the bitrsquos efficiency at penetrating andfracturing rock in a cycle and further decreases thedrilling load on the rock

To simplify the model impact load loss induced by thebitrsquos configuration is not considered in this paper A relevantinvestigation will be conducted in subsequent research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was financially supported by the technologyresearch projects of the China lunar exploration (Project noTY3Q20110005) the National Natural Science Foundationof China (Grant nos 51575122 and 51575123) and the Self-Planned Task (no SKLRS201616B) of State Key Laboratory ofRobotics and System (HIT)

References

[1] Y Bar-Cohen and K Zacny ldquoDrilling in Extreme Environ-mentsrdquo in Chapter Extraterrestrial Drilling and Excavation pp347ndash546 VILEY-VCH 2008


[2] B Huang Z Jiang P Lin and D Ling ldquoResearch on impactprocess of lander footpad against simulant lunar soilsrdquo Shockand Vibration vol 2015 Article ID 658386 24 pages 2015

[3] X Shi Z Deng Q Quan D Tang X Hou and S JiangldquoDevelopment of a drilling and coring test-bed for lunarsubsurface exploration and preliminary experimentsrdquo ChineseJournal of Mechanical Engineering (English Edition) vol 27 no4 pp 673ndash682 2014

[4] J Allton Catalog of Apollo Lunar Surface Geological SamplingTools and Containers NASA 1989

[5] K Zacny J Wilson P Chu and J Craft ldquoPrototype rotarypercussive drill for theMars sample returnmissionrdquo in proceed-ing of the 2011 IEEE Aerospace Conference AERO rsquo11 9 pagesMontana MT USA March 2011

[6] K Klein M Badescu N Haddad L Shiraishi and P Walke-meyer ldquoDevelopment and testing of a rotary percussive SampleAcquisition Toolrdquo in proceeding of the 2012 IEEE AerospaceConference Montana MT USA March 2012

[7] Y Tian Z Deng D Tang S Jiang and X Hou ldquoStructureparameters optimization and simulation experiment of augerin lunar soil drill-sampling devicerdquo Journal of MechanicalEngineering vol 48 no 23 pp 10ndash15 2012

[8] Z Y Ouyang ldquoScientific objectives of chinese lunar explorationproject and development strategyrdquo Advance in Earth Sciencesvol 19 pp 351ndash358 2004

[9] L Barsukov ldquoPreliminary data for the regolith core brought toEarth by the automatic lunar station luna 24rdquo in proceeding ofthe 8th Lunar Planetary Science Conference pp 3303ndash3318 1977

[10] Y TianD Tang ZDeng S Jiang andQQuan ldquoDrilling powerconsumption and soil conveying volume performances of lunarsampling augerrdquo Chinese Journal of Mechanical Engineering(English Edition) vol 28 no 3 pp 451ndash459 2015

[11] S-M E Jalali and M Zare Naghadehi ldquoDevelopment of anew laboratory apparatus for the examination of the rotary-percussive penetration in tunnel boring machinesrdquo Tunnellingand Underground Space Technology vol 33 pp 88ndash97 2013

[12] K Hashiba K Fukui Y Z Liang M Koizumi and T MatsudaldquoForce-penetration curves of a button bit generated duringimpact penetration into rockrdquo International Journal of ImpactEngineering vol 85 pp 45ndash56 2015

[13] T Saksala D Gomon M Hokka and V-T Kuokkala ldquoNumer-ical and experimental study of percussive drilling with a triple-button bit on Kuru graniterdquo International Journal of ImpactEngineering vol 72 pp 56ndash66 2014

[14] T Saksala ldquoNumerical study of the influence of hydrostaticand confining pressure on percussive drilling of hard rockrdquoComputers and Geotechnics vol 76 pp 120ndash128 2016

[15] T Saksala M Hokka V-T Kuokkala and J Makinen ldquoNumer-ical modeling and experimentation of dynamic Brazilian disctest on Kuru graniterdquo International Journal of Rock Mechanicsamp Mining Sciences vol 59 pp 128ndash138 2013

[16] J Tian C Wu L Yang Z Yang G Liu and C Yuan ldquoMath-ematical Modeling and Analysis of Drill String LongitudinalVibration with Lateral Inertia Effectrdquo Shock and Vibration vol2016 Article ID 6281264 8 pages 2016

[17] L J Dong and X B Li ldquoA microseismicacoustic emissionsource location method using arrival times of PS waves forunknown velocity systemrdquo International Journal of DistributedSensor Networks vol 2013 Article ID 307489 8 pages 2013

[18] L Dong X Li and G Xie ldquoNonlinear methodologies foridentifying seismic event and nuclear explosion using random

forest support vector machine and naive Bayes classificationrdquoAbstract and Applied Analysis vol 2014 Article ID 459137 8pages 2014

[19] L-J Dong J Wesseloo Y Potvin and X-B Li ldquoDiscriminantmodels of blasts and seismic events in mine seismologyrdquoInternational Journal of Rock Mechanics amp Mining Sciences vol86 pp 282ndash291 2016

[20] P Li S Jiang D Tang et al ldquoDesign and testing of coring bits ondrilling lunar rock simulantrdquo Advances in Space Research vol59 pp 1057ndash1076 2017

[21] D Zhao D Tang X Hou S Jiang and Z Deng ldquoSoil chipconvey of lunar subsurface auger drillrdquo Advances in SpaceResearch vol 57 no 10 pp 2196ndash2203 2016

[22] D Zhao S Jiang D Tang et al ldquoStructure design of lunar sub-surface sampling drillrdquo Journal of Jilin University (Engineeringand Technology Edition) vol 46 pp 1ndash10 2016

[23] P Li S Jiang D Tang et al ldquoA PFC3119863-based numerical simu-lation of cutting load for lunar rock simulant and experimentalvalidationrdquo Advances in Space Research In press 2017

[24] Q Quan P Li S Jiang et al ldquoDevelopment of a rotary-percussive drilling mechanism (RPDM)rdquo in proceeding of the2012 IEEE International Conference on Robotics and Biomimet-ics ROBIO rsquo12 pp 950ndash955 Guangzhou China December2012

[25] D Jie P Li Q Quan et al ldquoOptimization of percussivemechanism in rotary-percussion drill for lunar explorationrdquo inproceeding of the 2013 IEEE International Conference on Roboticsand Biomimetics ROBIO rsquo13 pp 2130ndash2135 Shenzhen ChinaDecember 2013

[26] I Argatov and M Jokinen ldquoLongitudinal elastic stress impulseinduced by impact through a spring-dashpot system optimiza-tion and inverse problems for the spring stiffnessrdquo InternationalJournal of Solids and Structures vol 50 no 24 pp 3960ndash39662013

[27] D Tang P Li S Jiang Q Quan X Hou and Z DengldquoNumerical simulation of lunar rock simulant cutting loadbased on discrete element modeling and experimental valida-tionrdquo Journal of Mechanical Engineering vol 52 no 15 pp 192ndash203 2016

[28] P Li S JiangQQuanD Tang XHou andZDeng ldquoAdrillingtactic to tackle indeterminable environment in lunar regolithsamplingrdquo in proceeding of the IEEE International Conferenceon Robotics and Biomimetics IEEE-ROBIO rsquo15 pp 2347ndash2352Zhuhai China December 2015

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


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RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


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Navigation and Observation



DistributedSensor Networks



study of excavation and percussion of rock using a disccutter tooth in a tunnel excavating machine The resultshowed that the sample excavation efficiency of the disc cuttertooth improved significantly under the combined effect ofcutting and percussion Additionally the percussion loadeffectively improved the penetration rate of the simulatedtunnel excavating machine [11] Hashiba et al conducted anexperimental study of a single percussion rock penetrationprocess via button bits and modified the obtained load-penetration depth curve using numerical simulation [12]Based on the fracture criteria for viscoplastic rock Saksala etal conducted a simulation analysis and an experimental studyof the percussive drilling of granite via a specially designedtriple-button bit The results showed that the rock fracturedwhen the percussion velocity was ascending Additionallylateral compressive fracture occurred between adjacent but-tons [13ndash15] Furthermore based on theRayleigh-Lovemodeland a one-dimensional viscoelastic model Tian et al derivedan equation for the axial vibration of a drill string during oilexploration and verified it experimentallyThe results showedthat the length of the drill string is inversely proportional tothe damping at the bottom of the bore When the string wasshorter the effect of horizontal inertia on the dynamic rigidityof the drill string was more significant [16]

Besides acoustic emission (AE) techniques have alwaysbeen adopted in identifications of microseismic source (MS)locations Dong and Li have proposed an innovative MSAEsource location method without the need for premeasuredPS wave velocities and this method greatly weakens theinfluence of the big error derived from the change ofthe wave velocities and propagation traces [17] Then heapplies three nonlinear methodologies (such as randomforests support vector machines and naive Bayes classifier)to discriminate between 20 earthquakes and 27 nuclearexplosions And based on the leave-one-out cross-validationROC curve and test accuracy random forests method clearlyshows the best predictive power [18] Recently Dong etal investigate the typical characters of seismic parametersbetween events and blasts using the datasets of three minesin Canada and Australia and 7 parameters are extractedas discriminant indicators to establish discriminant modelsusing the logistic regression method The classified accuracyof training samples test samples and cross-validated resultshave demonstrated that the discriminant models with gooddiscriminant performance are effective and efficient methodsto identify the blasts from events in real-time [19] Thesemethodologies provide an effective way to quantify theprocess of rock fragmentation which are not easy to observein rock impacting or cutting process

In 2014 the Research Center of Aerospace Mechanismand Control (RCAMC) at Harbin University of Technologysuccessfully designed a lunar regolith coring bit (LRCB)that exhibited excellent drilling performance in tasks suchas continuous chip removal without an auxiliary mediumand rock blockage breakthrough with a limited ability todrill Compared with other geological drill bits and planetarysampling bits it has advantages such as a low load per unitarea for fracturing rocks [20 21] In this paper based onan optimized LRCB configuration and the Mohr-Coulomb

criterion a model of cutting and percussive fracture forlunar rock simulant is created and expanded to the rotary-percussive drilling process to analyze the load characteristicsof rotary-percussive drilling of lunar rock simulant with acoring bit The effect of the impact load on the rockrsquos fractureload for different drilling parameters is determined thisprovides a basis for optimizing the drilling parameters forlunar surface drilling and sampling

The structure of this paper is as follows Section 2 mainlyintroduces the background of previous research that is theLRCB configuration and themodel for the load during rotarydrilling of lunar rock simulant Section 3 describes howthe interaction between the LRCB and lunar rock simulantduring rotary percussion is modeled Section 4 providesexperimental verification of the rotary-percussive drillingload for lunar rock simulant and Section 5 is the conclusion

2 LRCB Configuration andDrilling Load Analysis

21 LRCB Configuration Parameters Based on requirementsof sampling deep lunar soil the LRCB should support the fol-lowing functions (i) ensuring smooth lunar soil chip removalwithout an auxiliary chip removal medium (ii) specifyingthe coring rate of the lunar soil sample and ensuring theability to collect original information and (iii) being able tobreak lunar rock with less than grade-VI drillability withoutexceeding the drilling load limit [22]Therefore the RCAMCteam developed the LRCB shown in Figure 1 which employsinner and outer rows of sharp cutting blades (SCBs) (iedual primary cutting blades) to increase the stability of thedrilling system in the initial stage of lunar rock drillingLaboratorial tests showed that this bit excels at coring lunarsoil and removing chips and has excellent lunar rock drillingload characteristicsThe detailed configuration parameters ofthe LRCB are listed in Table 1

22 Analysis of the Drilling Load of the LRCB The LRCBrsquosconfiguration parameters are abstracted as an analytic geo-metrical model which is shown in Figure 2The relationshipsof the torque on bit (TOB) and the weight on bit (WOB) tothe cutting load of the elemental blade are shown in

119879TOB = 2sum119896=1

2sum119894=1

Δ119865119897119894_119896 sdot radic1199092119887119898119894_119896 + 1199102

119887119898119894_119896

119865WOB = 2sum119896=1

2sum119894=1

Δ119865119899119894_119896(1)

where 119909119887119898119894_119896 is coordinate of the midpoint of the 119894th ele-mental blade at the 119896th row of SCBs on the I axis 119910119887119898119894_119896 iscoordinate of the midpoint of the 119894th elemental blade at the119896th row of SCBs on theK axisΔ119865119897119894_119896 is cutting force of the 119894thelemental blade at the 119896th row of SCBs along the l axis andΔ119865119899119894_119896 is cutting pressure of the 119899th elemental blade at the 119896throw of SCBs along the n axis

In (1) Δ119865119897119894_119896 and Δ119865119899119894_119896 are the cutting loads of elementalblade in the absolute coordinate system The cutting load of



Forward rake angle

Outward rake angle

훾on

휆sn

wb1

wSb

h s kr = wb1wSb

ΔΨb

Δhb


DH

DC

(b) The actual LRCB


휙bg


Rock

ℎH

I

K

J

ℎo Δℎb

ΔΨb

Om2_II

훼H

l2_IIn2_II

휆sn_II훾on_II

Oe2_II

sퟐ_II

bퟐ_II

rퟐ_IIoퟐ_II

v ퟐ_II

ℎpe

n

FRg 훼

훾nΨ휆

휆s

wb Fcut

Fpen

Δℎpn

o

IIII

W Ua

V

s

bFRU

120588b2_II

FRW

e

휆shIIFFR

휙휙bgI

I










Row II 0∘


Row I 25∘

Row II 25∘









(2)








cam


Roller

Auger

Spline joint










HammerHammer

Hammer

Blade BladeBlade

Rock




lpos lforlcra

Cut

nPerPer


0 0

P0 kP

x

wP uP

bP

mP

Fi(t)






119908119875 (0) = 0119875 (0) = V1198750119906119875 (0) = 0

(5)




(6)

where

1205962119875 = 1612057821198751205962

1198750 minus (12059621198750 minus 4120585119875120578119875)2

16 (120585119875 + 120578119875)2

120572119875 = 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875)

1205731198751 = 81205782119875 minus 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

120573119875 = 12059621198750 minus 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

(7)


Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)


and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)





119865Per = 119870ℎPer (10)





(11)



119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)



(119870lowast minus 120572)2 + 1205962


(13)



120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)





119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Forward rake angle

Outward rake angle

훾on

휆sn

wb1

wSb

h s kr = wb1wSb

ΔΨb

Δhb


DH

DC

(b) The actual LRCB


휙bg


Rock

ℎH

I

K

J

ℎo Δℎb

ΔΨb

Om2_II

훼H

l2_IIn2_II

휆sn_II훾on_II

Oe2_II

sퟐ_II

bퟐ_II

rퟐ_IIoퟐ_II

v ퟐ_II

ℎpe

n

FRg 훼

훾nΨ휆

휆s

wb Fcut

Fpen

Δℎpn

o

IIII

W Ua

V

s

bFRU

120588b2_II

FRW

e

휆shIIFFR

휙휙bgI

I










Row II 0∘


Row I 25∘

Row II 25∘









(2)








cam


Roller

Auger

Spline joint










HammerHammer

Hammer

Blade BladeBlade

Rock




lpos lforlcra

Cut

nPerPer


0 0

P0 kP

x

wP uP

bP

mP

Fi(t)






119908119875 (0) = 0119875 (0) = V1198750119906119875 (0) = 0

(5)




(6)

where

1205962119875 = 1612057821198751205962

1198750 minus (12059621198750 minus 4120585119875120578119875)2

16 (120585119875 + 120578119875)2

120572119875 = 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875)

1205731198751 = 81205782119875 minus 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

120573119875 = 12059621198750 minus 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

(7)


Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)


and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)





119865Per = 119870ℎPer (10)





(11)



119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)



(119870lowast minus 120572)2 + 1205962


(13)



120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)





119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(2)








cam


Roller

Auger

Spline joint










HammerHammer

Hammer

Blade BladeBlade

Rock




lpos lforlcra

Cut

nPerPer


0 0

P0 kP

x

wP uP

bP

mP

Fi(t)






119908119875 (0) = 0119875 (0) = V1198750119906119875 (0) = 0

(5)




(6)

where

1205962119875 = 1612057821198751205962

1198750 minus (12059621198750 minus 4120585119875120578119875)2

16 (120585119875 + 120578119875)2

120572119875 = 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875)

1205731198751 = 81205782119875 minus 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

120573119875 = 12059621198750 minus 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

(7)


Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)


and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)





119865Per = 119870ℎPer (10)





(11)



119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)



(119870lowast minus 120572)2 + 1205962


(13)



120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)





119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










HammerHammer

Hammer

Blade BladeBlade

Rock




lpos lforlcra

Cut

nPerPer


0 0

P0 kP

x

wP uP

bP

mP

Fi(t)






119908119875 (0) = 0119875 (0) = V1198750119906119875 (0) = 0

(5)




(6)

where

1205962119875 = 1612057821198751205962

1198750 minus (12059621198750 minus 4120585119875120578119875)2

16 (120585119875 + 120578119875)2

120572119875 = 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875)

1205731198751 = 81205782119875 minus 12059621198750 + 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

120573119875 = 12059621198750 minus 41205851198751205781198754 (120585119875 + 120578119875) 120596119875

(7)


Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)


and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)





119865Per = 119870ℎPer (10)





(11)



119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)



(119870lowast minus 120572)2 + 1205962


(13)



120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)





119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Per FPer(t)

FPen

Fr(t)

휃p

O

rp 휎휃

휎r

ℎPer(t)

Rock

Blade

Fi(t)


and 120585119875 120578119875 and 1205961198750 satisfy

119887119875119898119875

= 2120585119875119864119860119888119898119875

= 2120578119875119896119875119898119875

= 12059621198750

(8)





119865Per = 119870ℎPer (10)





(11)



119889119865Per119889119905 + 119870119885 sdot 119865Per = 2119870119885 119865119894 + 119870119885119865Pen (12)



(119870lowast minus 120572)2 + 1205962


(13)



120590119903 = 2119865Per cos 120579119901120587119903119901119908119887

120590120579 = 0120591119903120579 = 0

(14)





119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119903119901 = 1199031199010119890plusmn120579119901 cot120582119891 (15)



120591119901 = 119865Per sin 21205821198911205871199031199010119908119887


120590119901 = 119865Per (1 minus cos 2120582119891)1205871199031199010119908119887






Rock

BladeCut

F휎F휏

휆sh

q0

휙c

휙b

FR

훼

F휎p

휆c O

A

GF

C

B

E

D

FPer (t)FCut_cra

FPen_cra




(18)






119902 = 1199020 sdot sin 120579 (20)






119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119897119898119894 = int120579119894+1

120579119894

radic(119889119909119889120579)2 minus (119889119910119889120579)2119889120579

= 1199030radic(cot 120582119891)2 + 1cot 120582119891 119890120579 cot120582119891

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(22)


119865119899119894 = 1199020 sdot sin 120579119898119894 sdot 119897119904119894


10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120579119894+1

120579119894

(23)



119865119899119909 = 119899sum119894=1

119865119899119894 sdot cos120593119899119894

119865119899119910 = 119899sum119894=1

119865119899119894 sdot sin120593119899119894(24)




119865119899119909 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


119865119899119910 = 11990201199030radic(cot 120582119891)2 + 1cot 120582119891

sdot 119899sum119894=1


(26)




sdot 119865120590119901(27)

where

119870119865119899119909 = 119899sum119894=1


119870119865119899119910 = 119899sum119894=1


(28)








Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Cutting blade



Magnescale


Mobile plate


(a)



(RPDM)


Rock holder

Load cell

Torque sensor

Magnescale

(b)





119870pre = 1 minus 119870cra(31)










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0


FPe

r(N

)

500

1000

1500

2000

2500

3000

3500

4000

02 03 04 05 06 07 08 0901WP (J)













(32)



0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

400

800

1200

1600


1510231


005 01 015 02 0250time (s)


FPe

n(N

)


(a)

04 08 12 16 20time (ms)

minus500

0

500

1000

1500

2000


FPe

r(N

)

(b)








0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0005

01015

020

510

1520

25

fP (Hz)

FF

Cut

(N)

50

100

150

200

250

h Pen(mm)

(a) Cutting force

0005

01015

020

510

1520

25

FF

Pen

(N)

50

100

150

200

250

300

fP (Hz)

h Pen(mm)


05

1015

20

FP

Cut

(N)

0

50

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

(c) Cutting force

05

1015

20

FP

Pen

(N)

0

50

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)


05

1015

2050

100

150

200

250

fP (Hz)

0005

01015

02

h Pen(mm)

FCu

t(N

)

(e) Cutting force

05

1015

2050

100

150

200

250

300

fP (Hz)

0005

01015

02

h Pen(mm)

FPe

n(N

)





0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

2

371

308

4

6

Rotary drilling

Rotary-percussive

drilling

TTO

B(N

m)



Rotarydrilling

Rotary-percussive

drilling

0

200

3486

4823

600

800

FW

OB

(N)



05

1015

20

1

2

3

4

5

6

7

fP (Hz)

0005

01015

02

TTO

B(N

m)

kPPR (mm)

(a) TOB

05

1015

20

200

300

400

500

600

700

800

fP (Hz)

0005

01015

02

FW

OB

(N)

kPPR (mm)

(b) WOB









0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

05

1

15

2

25

3

35

4

40 60 80 10020nD (rpm)

TTO

B(N

m)

(a)

0

50

100

150

200

250

300

350

400

450

40 60 80 10020nD (rpm)


FW

OB

(N)

(b)



5 Conclusions








Acknowledgments


References































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









analysis and testing of load characteristics for rotary

Documents