trans inst mining a methodology for estimating specific rock energy ei

7/28/2019 Trans Inst Mining a Methodology for Estimating Specific Rock Energy EI

1/12

P

ublishedbyManeyPublishing

(c)IOMC

ommunicationsLtd

A methodology developed to estimate with accuracy the

instantaneous specific rock energy using corrected down-

the-hole (DTH) drill monitoring data is presented. A

specific rock energy profile can be generated for every

hole, and thus a drilling site can be mapped for this index.

A special data acquisition system was developed to

measure and register the following operational variables:penetration rate, torque, hole depth, pull-down force, air

pressure, revolutions per minute (rpm) and the hammer

percussion frequency, the latter obtained by sound

recording and signal processing. The measured data are

fed into two simulation models that estimate the power

absorbed by the rock through impact, and then the specific

rock energy index. The first of these models simulates the

thermodynamic cycle of the DTH hammer, rendering the

piston kinetic energy at impact, impact velocity as well as

impact frequency. The second model is used for stress

wave propagation analysis to estimate the effective energy

delivered to the rock. Correlations were found between the

specific rock energy and penetration rate, and between the

specific rock energy and impact frequency, as well as

between the penetration rate and applied torque, and

between the penetration rate and impact frequency.

Luis E. Izquierdo ([email protected]) and Luciano E. Chiang([email protected]) are at the Departamento de Ingeniera

Mecnica, Pontificia Universidad Catolica de Chile, 4860

Vicuna Mackenna Ave, Casilla 306 Correo 22, Santiago, Chile.

2004 Institute of Materials, Minerals and Mining and

Australasian Institute of Mining and Metallurgy. Published

by Maney on behalf of the Institutes. Manuscript received 1

October 2002; accepted in final form 28 May 2004.

Keywords: Down-the-hole hammer, drilling monitoring, hammer

percussion frequency, specific rock energy, percussion drilling, air

drilling

Mining Technology (Trans. Inst. Min. Metall. A) December 2004 Vol. 113 A225DOI 10.1179/037178404225006218

A methodology for estimation of the specific rock energy indexusing corrected down-the-hole drill monitoring data

Luis E. Izquierdo and Luciano E. Chiang

Nomenclature: A, hole area (m2); EImpact

, impact energy (piston contribution) (J); ETorque

, torque energy (J); EThrust

, thrust energy (J); e, pistonimpact restitution coefficient; F, percussion frequency; F

Pull-down, applied pull-down force (weight on bit) (N); F

Thrust, thrust force (N); m

Piston,

piston mass (kg); SRE, specific rock energy (J cm3); PowHammer

, hammer power (W); VImpact

, piston impact velocity (m s1); VPenetration

,penetration rate (m s1); Torque, torque applied to the hammer (N m); W

Rods-hammer, rods and hammer weight (N); , hammer angular velocity

(rad s1); t, time increment; , hammer spin angle increment; x, hammer displacement increment; Vo, rock volume increment

INTRODUCTIONThe operation of rock drilling systems is an importantissue in many industries such as mining, construction,petroleum and water well drilling. Due to its economicimportance, it has motivated many research studies;recently, monitoring systems have been used tounderstand rock drilling better. In such systems, thevariables most commonly measured are: penetration

rate, penetration depth, torque, rotation speed(RPM), pull-down (feed force) and the air pressure.The analysis of these data has provided importantinformation about the drilled rock mass such ashardness, fracturing and weathering.15 It haspermitted the location of rock boundaries, rock-typeboundaries to name the most important, and it hashelped in blast hole array design.15,18,20

One advantage of drill monitoring is the possibilityto extract valuable information without causingdisturbances in the drilling process. Monitoring isconsidered an important necessary step prior to theautomation of the entire drilling process2 because ithelps to understand better how the different parameters

affect rock drilling. Rock-drill monitoring can be usedto detect anomalies in the hammer operation therebyhelping to avoid potentially disastrous situations such asstalling.

THE DATA ACQUISITION SYSTEMFor the purpose of this research, the authors

developed in-house, a computer-based monitoringsystem. This decision was taken for both economicand technical reasons: (i) available special-purposecommercial systems are high-priced; and (ii) generallyfor technical and legal reasons, the vendors do notallow modifications such as those this researchrequired. The data acquisition and processing systemdevelopment took more than a year of design andtesting. The resulting system consists of severaldifferent sensors connected to an industrial computerthat processes and stores the incoming data. Tomeasure torque, pull-down and air pressure, pressuretransducers were connected to the corresponding fluidlines on the drill rig as shown in Figure 1. Penetration


2/12

P


(c)IOMC

ommunicationsLtd rate and depth were measured using an optical

encoder connected to the feed (displacement) chain ofthe drilling rig. A proximity sensor was used tomeasure rotation speed. The position of each hole inspace was recorded using a GPS receiver. Finally, thehammer impact frequency was extracted from thepost-test analysis of sound recordings made during insitu hammer operation sound recordings.

The results reported in this work were obtainedduring drill tests carried out at a diorite quarry

located in the commune of Quilicura (Chile). Verticalholes were drilled with an Ingersoll Rand DM-45drilling rig on which the developed monitoring systemwas mounted. Five- and six-inch diameter PumaDTH hammers supplied by Drillco Tools were used.These were equipped with 55- and 65-inch diameterdrill bits, respectively. The system was set to store dataevery 5 cm of hole length. A total of 400 m of drilledholes considered representative of the rock mass wereselected for the present discussion.

FORMULATION OF THE SPECIFIC ROCK

ENERGY INDEX USING DTH DRILLING

DATAThe specific rock index (SRI) quantifies the energynecessary to remove a given volume of rock. In theearly 1960s, it was proposed by Teale21 as a way todetermine the amount of energy required to drill aspecific volume of rock, using roller cone-bits. Rollercone sits are generally used to drill in low-to-mediumhardness rock formations. Hustrulid,7,8 on the other

hand, used an SRE index obtained by laboratory teststo estimate the penetration rate in percussive drilling.Other authors have extensively explored the use of

the specific energy as an index to characterise the easeof rock removal as well. More recently, Thuro22,23

applied a similar index (the destruction work index) todrifter hammers used in underground horizontal rockdrilling. He found a strong correlation of this index,defined as the area under the stressstrain curve of the

rock obtained from unconfined compression tests,and the penetration rate.

In this study, the SRE index is developed usingDTH drilling data. This is not simple because it isnecessary to account for the energy supplied by threeseparate sources impact, rotation and pull-down inorder to determine the energy effectively absorbed bythe rock. Thus, an in-depth knowledge of the DTHhammer drilling operation is required.

If the SRE index can be computed from drill

monitoring data, then it can be used as a localdrillability index to map and characterise the rockmass at the given drilling site.15,18 Measured variationsin the value of the index can be helpful in identifyingthe boundaries between different rock formations. Italso can be indicative of a rock mass with a highdegree of geological alteration, something that oftenoccurs in mineral deposits.18

The SRE index is defined as the amount of energy(J) needed to remove a unit volume of rock. To derivean expression for the SRE, it is considered that the

energy required to fragment the rock (ERock) is entirelyprovided by the drilling system. Hence:

ERock

= EDTH system

The energy absorbed by the rock in a short timeinterval can be written as:

E SRE VRock o:=D D Eq. (1)

where Vo

= A x x is the volume of rock removedwhen generating a hole of cross-sectional area A anddepth x.

Recalling that the energy provided by the drilling

system comes from three separate sources impact,torque and thrust then:

E E E EDTH System Impact Torque Thrust= + + Eq. (2)

Therefore, it is possible to write the followingexpression for the SRE:

SREA x

EA x

E

A x

E

A xERock Impact Torque Thrust

: : : :

= = + +D

DD

DD

DD

D Eq. (3)

A226 Mining Technology (Trans. Inst. Min. Metall. A) December 2004 Vol. 113

Izquierdo and Chiang Methodology for estimation of the specific rock energy index

1 Schematic of the data acquisition system


3/12

P


(c)IOMC

ommunicationsLtd

The EImpact

increment can be approximated as theproduct of the average impact power supplied by thehammer (Pow

Hammer) and the duration of the time

interval (t) over which the volume of rock (Vo) is

removed. The energy increment provided by therotation torque (E

Torque) can be approximated as the

product of the average applied torque and the spinangle increment () during the same time interval.

Finally, the product of the average thrust force (FThrust)and the displacement interval (x) accounts for theenergy supplied by the thrust force (E

Thrust). It is

important to note that the thrust force considers boththe pull-down force supplied by the drilling rig, andthe weights of the rods and the hammer. It is assumedthat the depth interval is selected conveniently so thatthe measurements are representative of such aninterval. Then it is possible to write:

E Pow tHammer Hammer :=D D

E TorqueTorque := iD D Eq. (4)

E F xTh ru st Th ru st :=D D

F F WThrust Pull down Rods Hammer = +- -

Substituting each term in Equation (4) into Equation(3) gives:

SREA x

Pow t A x t

Torque t

AFHammer Thrust

:

:

: :

: :

= + +i

DD

D DD D

Eq. (5)

Introducing the penetration velocity (VPenetration

) andthe angular velocity ():

Vt

xPenetration =

DD

t=s i

DD Eq. (6)

Then, an expression to compute directly the SREindex (in J m3) is:

SREA V

PowA V

Torque

AF

Penetration

Hammer

Penetration

Thrust

: :

:

= + +~

Eq. (7)

In Equation (7) the Torque, FThrust

, and VPenetration

magnitudes can be estimated from sensor readings.

Therefore, in order to compute the SRE index usingEquation (7), only the effective power Pow

Hammer

transferred to the rock by impact remains to beidentified. This term turns out to be the mostsignificant of all, so that an accurate computation ofPow

Hammeris of paramount importance in obtaining a

trustworthy value of the SRE index. For this purpose,the magnitude ofPow

Hammerwill be computed from the

following expression:

Pow PowHammer Raw Transmission:= h Eq. (8)

where PowRaw is the raw power developed by thepneumatic hammer engine, which is the piston impactenergy times the impact frequency. The magnitude ofPow

Rawdepends on the thermodynamic behaviour of

the hammer, that is to say how efficiently the high-pressure air energy is converted into kinetic energy ofthe piston at impact. The impact between the pistonand drill bit generates a stress wave that propagatestoward the bitrock hammer interface. Depending on

the geometry of the hammer components and themechanical properties of the rock, a percentage of thestress wave energy is actually absorbed by the rock,causing its failure, and the remaining is reflected anddissipated by the hammer itself and the supportingstructure. The magnitude of

transmissiontakes into

account these stress-wave propagation effects.Chiang et al.35 have developed computational

models to compute the magnitude of the terms PowRawand

transmissionin Equation (8). A thermodynamic

model of the hammer permits the computation ofPow

Raw. A second model allows one to compute the

stress-wave transmission efficiency transmission

. For thepurpose of clarity, these models will be brieflydescribed. A discussion of both models can be foundin Appendices A and B.

THERMODYNAMIC MODEL OF A DTH

HAMMERIn order to determine the contribution of impactpower in the drilling performance of a DTH hammer,a thermodynamic model is required to calculateimpact energy per blow, and impact frequency. Theimpact power developed by a DTH hammeroriginates from air supplied at high pressure. Thebalance of pressures in the front and rear chambers ina DTH hammer causes alternate up and down motionof a piston (see Fig. 2). At the end of the forwardstroke, the moving piston impacts a drill bit, initiating

a stress wave that travels towards the rock.To simulate the thermodynamic operation of theDTH hammer, a model developed by Chiang andStamm5 was used. This relates air pressure, pistonimpact velocity, piston rebound velocity and impactfrequency for a given DTH hammer geometry. It isimportant to note that the rock behaviour in thismodel is taken into account by an impact restitutioncoefficient e between the piston and drill bit.

Mining Technology (Trans. Inst. Min. Metall. A) December 2004 Vol. 113 A227


2 DTH hammer schematics


4/12

P


(c)IOMC

ommunicationsLtd

' '

e piston impact factor

piston rebound velocity

=

The term e can be determined by simulation using a stress-wave propagation model developed by Chiang et al.,3,4

described in the following section, or by experimentalmeasurements. Hence, the thermodynamic model and thestress wave propagation model are coupled by parameter e.

This thermodynamic model has been experimentallyvalidated for a number of DTH hammers in anexperimental test bench. For example, Figure 3 showsthe simulated pressure versus displacement diagram forthe front and rear chambers of a DTH hammer. Theactual pressure versus displacement diagrams obtainedexperimentally are included for comparison.

The model as well as laboratory and fieldmeasurements reveal that the predominant variable inthe operation of any DTH hammer is the input airpressure. Figure 4 shows the raw power generatedversus restitution coefficients for different air inputpressure for a given hammer. Note that the predictedraw hammer power does not vary substantially withthe restitution coefficient of the rock (Fig. 4), allowingone to conclude that rock behaviour has little effect on

the raw power developed by the hammer.

The corresponding impact and rebound velocitiesand impact frequencies (percussion frequency) areshown in Figures 57, respectively. With these resultsand considering the fact that the raw power(maximum available power) of a DTH hammer isobtained as the product between the piston kineticenergy difference (impact and the rebound, the lastrepresented by e2) and the percussion frequency, it ispossible to compute the raw power:

Pow m V e F 21

1Raw Piston Impact2 2

: : := -_ i Eq. (9)An increase of the air pressure produces an increase ofthe impact velocity, which is independent of therestitution coefficient, as shown in Figure 5. A lineardependence was observed with the piston reboundvelocity (Fig. 6).

Despite the fact that the rock behavioursimultaneously affects both the impact energy and theimpact frequency, this occurs in such a way that the rawimpact power delivered by the hammer (as shown inFigs. 57) remains basically constant for a given input

air pressure. In fact, according to computer simulations



3 Actual and predicted front and rear chamber

pressure versus piston displacement diagrams

4 Hammer raw power versus restitution coefficient

5 Piston impact velocity versus restitution coefficient 6 Variation of the piston rebound velocity versus

restitution coefficient


5/12

P


(c)IOMC

ommunicationsLtd and also to field measurements, the impact frequency

will increase (Fig. 7) as the rock becomes harder, that isto say when the penetration rate decreases. Thisfrequency increment is compensated by a decrease in thepiston kinetic energy transferred by impact (by way ofan increase in the magnitude of the restitutioncoefficient e). This means that the overall raw powerdeveloped by the hammer does not change significantlyfor a wide range of values of the restitution coefficient,and hence for a wide range of medium-to-hard rocktypes being drilled.

This can be explained in terms of the piston cycle.If the restitution coefficient is low, then the reflectedvelocity is smaller. If the initial return velocity is less,the return piston cycle will increase with time. Thus, alow value of the restitution coefficient causes adecrease in the impact frequency and vice versa.

STRESS-WAVE PROPAGATION MODELThe drill bit interacts with the rock mass throughtungsten carbide inserts (Fig. 2). When the stress wave

reaches the bitrock interface, energy is transferred tothe rock causing its fragmentation. Then, the cuttingsare removed by the airflow exiting the hammer.

The raw power developed by the hammer is nottransferred completely to the rock because intransferring energy, by means of a stress wave, there isa loss due to reflection and also due to friction at drillbar joints.

An algorithmic model developed by Chiang and Elas4permits the estimation of the efficiency of stress-wavetransmission between the piston and drill bit and betweenthe bit and rock mass. This model is based on the linearimpulsemomentum principle. The geometry andmaterial of the piston and of the bit must be specified, aswell as a reference forcepenetration curve for thebitrock combination used. The latter is obtainedexperimentally. The stress-wave transmission model hasbeen experimentally validated for a number ofpistonbitrock configurations by measuring stresses

at selected sections in a pneumatic gun speciallydesigned to investigate the effect. A similar method toestimate the efficiency of stress-wave transmission hasbeen proposed by Lundberg1012 and by Pang14.Rossmanith et al.17 have proposed a finite differencemethod to solve this problem.

In Figure 8, the results of experimental stressmeasurements in a pneumatic canon are shown. Inthis case, a piston at a velocity of 10 m s1 impacts astationary bit which, at the other end, is in contactwith a rock specimen. Strain gauges are placed atdifferent sections of the bit to record the stress-wavepattern. Both the model and theoretical stress-wavepatterns are included in Figure 8 for comparison.

The efficiency of the energy transmission for agiven pistonbit configuration can be estimated usingthe described model. Hence, a representative value of

transmissioncan be obtained by computer modelling.

Through the use of the thermodynamic and theimpact models previously described, it is possible toestimate with adequate accuracy the energy and power(Pow

Hammer) actually transmitted to the rock by impact

for a given working pressure. By substituting this



7 Percussion frequency in blows per minute (bpm)

versus restitution coefficient

8 Experimental versus theoretical comparison of stress


6/12

P


(c)IOMC

ommunicationsLtd

known value in Equation (7), the correspondingcomplete SRE index can be obtained.

IMPACT FREQUENCY MEASUREMENTThe hammer percussion frequency has also beenmeasured and analysed in order to check the estimated

values of the frequency given by simulation, and to studyits behaviour (i.e. variability) during rock drilling. Theimpact frequency is obtained from the analysis of soundrecordings of the hammer in operation.

Measurements of frequency show that the range ofvariability is small5 (about 160 blows per minute or 10%;Fig. 13). However, through the continuous monitoring ofthe impact frequency one can examine whether thevariability can be correlated to other operational variables,such as torque, rotation speed, thrust force andpenetration rate.

The strategy followed in the frequency analysis is toprocess short periods of the signal, in this case windows of152 s. For each window, an average frequency iscalculated. Timefrequency analysis1,6 is used because it

gives better results than alternatives such as signal peakdetection that are affected strongly by signal noise. Inparticular, we used the Short Time Fourier Transform(STFT),16 that involves calculating the Fourier transformof short signal portions using a window that slides overtime along the signal. The results are visualised in the formof a spectrogram, a 3-D representation of the frequency,

amplitude and time variation of a signal. In Figure 9, aspectrogram along a part of a drilled hole is shown.

DISCUSSION

SRE profile and individual source contributions

The specific rock energy profile, computed usingEquation (7) for a selected drilled hole, is shown inFigure 10. In Figure 11, the contributions of eachenergy source (hammer, torque and pull-down) to the

SRE total are shown. The type of behaviour shown wasconsistent throughout the drilling measurements.Regarding the SRE index, it can be noticed that eventhough the impact (hammer) is dominant, sur-prisingly,



9 Spectogram representing the frequency, amplitude and time variation of a signal along a part of a drilled hole

10 SRE profile


7/12

P


(c)IOMC

ommunicationsLtd

in this case the contribution of the rotation torque

amounts to an important fraction of the total SRE,contributing as much is 30%. It is important to note thatsome rocks will not allow such high torque input becauseof the danger of stalling. Also, if the hole is deep, torsionalelasticity may become an issue limiting the amount oftorque that can be applied. In this particular case, themagnitude of the torque contribution may look at firstinordinately high; however, the values measured are of thesame order of magnitude as those obtained by Ming13 in astudy of vibration in DTH rock drilling. Also, it can beseen that the pull-down contribution to the energytransferred to the rock is small in comparison to theimpact and rotation sources.

Correlation between torque and penetration rate

A correlation between the external rotation torqueand the average penetration rate has also been noticedin our measurements. As shown in Figure 12,obtained by discretisations in torque increments of100 Nm, it was found that as the average penetrationrate increases, the rotation torque increases.Schunnesson19,20 observed the same behaviour, and weagree with his explanation that when the rock

becomes less competent the bit buttons (inserts), onthe average, have a tendency to penetrate deeper intothe rock. For this reason, the torque required to rotatethe bit increases.

Correlation involving impact frequency

Another interesting correlation found in this study relatesthe frequency of the hammer and the penetration rate. Asshown in Figure 13, an increment in the penetration rateproduces a decrease in the impact frequency. This can beexplained because when the rock is less competent, theelastic recovery will be lower because more of the energythat initially arrives at the rock is actually absorbed by therock. If there is less reflected energy, the piston will have alower reflected velocity. Therefore, the piston will takelonger to complete its return stroke because it begins thecycle at a lower velocity. The longer duration of the returnstroke will consequently cause a decrease in impactfrequency.

Additionally and for the same reasons explainedabove, a correlation between the frequency and theSRE index was found. The behaviour is such thatwhen the SRE index increases the frequency increasesand vice versa9 as shown in Figure 14.

CONCLUSIONSIn the present study, the SRE index is developed usingDTH drill monitoring data. This is not a simple task

because it is necessary to account for the energysupplied by three separate sources impact, rotationand pull-down and then determine the energyeffectively transmitted to the rock. It is necessary to



11 Individual source contributions to the SRE

12 Correlation between torque and penetration rate


8/12

P


(c)IOMC

ommunicationsLtd

correct the experimental data to make it rock-

dependent only, and in this way meaningful resultscan be obtained. Thus, an in-depth knowledge of theDTH hammer drilling operation is required.

If the SRE index can be computed from drillmonitoring data, then it can be used as a local drillabilityindex to map and characterise the rock at a given drillingsite. Measured variations in the value of the index can behelpful in identifying the boundaries between differentrock formations. It also can be indicative of a rock masswith a high degree of geological alteration, somethingthat often occurs in mineral deposits.

It was found that a correlation exists between theSRE index and the penetration rate, as well as betweenthe SRE index and the impact frequency.

Additionally, this study has shown two interestingcorrelations between DTH hammer operationalvariables. The first is between frequency and penetrationrate, where for an increasing penetration rate thefrequency drops. This is thought to occur because largepenetration rates are normally associated with lesscompetent rock and low elastic recovery. In this case, thereflected speed of the piston after impact is lower so thatthe return stroke takes longer; therefore, the frequency ofoperation is reduced. Thus, the variation of hammer

frequency could give important information on the rock

mass being drilled, at least in terms of the energyabsorption characteristics. A second correlation wasobserved between penetration rate and torque. Thetorque increases when the penetration rate increases.This is thought to happen because in softer rock, theaverage indentation depth of the bit buttons into the rockis larger and, therefore, it requires more torque to rotateat the same speed.

It was also found that correlations do exist betweenthe SRE index and the penetration rate, as well asbetween the SRE index and the impact frequency.

Finally, this work is a contribution towards improvingthe performance of rock drilling impact hammers andreducing operational costs because the informationgenerated can be used in conjunction with simulationmodels such as that developed by the authors in order tooptimise hammer settings from a design or operationalperspective.

ACKNOWLEDGEMENTSThe authors would like to thank Drillco Tools forfunding this research and Dr William Hustrulid forhis valuable comments and suggestions.



13 Correlation between frequency and penetration rate (bpm, blows per minute)

14 Correlation between frequency and the SRE index


9/12

P


(c)IOMC

ommunicationsLtd

REFERENCES1. L. ATLAS, G. BERNARD and S. NARAYANA: Applications

of timefrequency analysis to signals from manufacturingand machine monitoring sensors, Proc. IEEE, 1996, 84,13191329.

2. W. CHANGMING and T. SINKALA: Thrust: a keyparameter in automatic control of percussive drilling,Proceedings of the International Symposium on MineMechanization and Automation, Colorado School ofMines, Vol. 1. Golden, Colorado, USA, 1991, 8(11-20).

3. L. CHIANG and D. ELAS: A study on the thrust effect inthe stress wave propagation in down-the-hole rock drilling,4th World Congress on Computational Mechanics,IACM, Vol. 2, Buenos Aires, Argentina, June, 1998,10631068.

4. L. CHIANG and D. ELAS: Modeling impact in down-the-hole rock drilling. Int. J. Rock Mech. Min. Sci., 2000, 37,599613.

5. L. CHIANG and E. STAMM: Design optimization ofvalveless DTH pneumatic hammers by a weighted pseudo-gradient search method, ASME, J. Mech. Design, 1998,

120, 687694.6. N. DJORDJEVIC: Timefrequency analysis of blast

induced vibration, Min. Technol. (Trans. Inst. Min.Metall. A), 1999, 108, A139A142.

7. W. HUSTRULID: Theoretical and experimental study ofpercussive drilling of rock, Unpublished PhD Thesis,University of Minnesota, 1968.

8. W. HUSTRULID: A theoretical and experimental study ofpercussive drilling of rock, Int. J. Rock Mech. Min. Sci.,1971, 8, 311333.

9. L. IZQIERDO: Monitoring, analysis ,and characterizationof roto-percusive rock drilling systems (in Spanish),

Unpublished MSc thesis, Department of MechanicalEngineering, Pontificia Universidad Catolica de Chile,Chile, 2001.

10. B. LUNDBERG: Microcomputer simulation of stress wavesenergy transfer to rock in percussive drilling, Int. J. RockMech. Min. Sci., 1982, 19, 229239.

11. B. LUNDBERG: Computer modelling and simulation ofpercussive drilling of rock, (ed. J. Hudson),Comprehensive rock engineering, Vol. 4, 1993, 137154.

12. B. LUNDBERG and L. KARLSSON: Influence ofgeometrical design on the efficiency of a simple down-the-hole percussive drill, Int. J. Rock Mech. Min. Sci., 1986,

23, 281287.13. J. MING: Theoretical and experimental studies of ITHpercussive drill vibration, Unpublished MSc thesis,Department of Mining and Metallurgical Engineering,McGill University, Canada, 1994.

14. S. PANG: Investigations of pneumatic percussive processesinvolving rocks, Unpublished PhD thesis, Mechanical

Engineering Department, University of California atBerkeley, 1987.

15. J. PECK: Performance monitoring of rotary blast holedrills, Unpublished PhD thesis, McGill University,Montreal, Canada, 1989.

16. G. PROAKIS and D. MANOLAKIS: Digital signalprocessing: principles, algorithms and applications, 3rdedn, New York, Prentice-Hall, 1995.

17. H. P. ROSSMANITH, L. MISHNAEVSKY JR, R. E.KNASMILLNER and K. UENISHI: Numerical simulationof dynamic fracture and damage of rock during impact,(eds. M. Cerrolaza, C. Gajardo, C. A. Brebbia), Numericalmethods in engineering simulation, 1996, 148154.

18. H. SCHUNNESSON: RQD predictions based on drillperformance parameters, Tunnel. Underground SpaceTechnol., 1996, 11, 345351.

19. H. SCHUNNESSON: Drill process monitoring inpercussive drilling for location of structural features,lithological boundaries and rock properties, and fordrilling productivity evaluation, Unpublished PhD thesis,Lule University of Technology, Sweden, 1997.

20. H. SCHUNNESSON: Rock characterisation usingpercussive drilling, Int. J. Rock Mech. Min. Sci., 1998, 35,711725.

21. R. TEALE: The concept of specific energy in rock drilling,Int. J. Rock Mech. Min. Sci., 1965, 2, 711725.

22. K. THURO: Prediction of drillability in hard rocktunnelling by drilling and blasting, Proceedings of theWorld Tunnel Congress 97, Vol. 1, Vienna, Austria, 1997,103108.

23. K. THURO and G. SPAUN: Introducing the destructionwork as a new rock property of toughness refering todrillability in conventional drill and blast tunnelling, (ed.

G. Barla), Prediction and performance in rock mechanicsand rock engineering. Eurock 96, Vol. 2, Turin, Italy, 1996,707713.

Authors

Luis E. Izquierdo was awarded a Master of EngineeringScience degree from the Catholic University of Chile in2001. He is currently employed as lecturer/researcher in theMechanical Engineering Department of the CatholicUniversity of Chile.

Luciano E. Chiang was awarded a MSc in MechanicalEngineering, a MSc in Electrical Engineering, and a PhD inMechanical Engineering from Stanford University, USA, in1983, 1988 and 1989, respectively. He is an Associate Professorand currently the Chairman of the Mechanical EngineeringDepartment of the Catholic University of Chile.



APPENDIX A: Thermodynamic DTH model

See next page
http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0018-9219(1996)84L.1319[aid=6473544]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(2000)37L.599[aid=6473543]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1971)8L.311[aid=6473542]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1982)19L.229[aid=6473541]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1986)23L.281[aid=6473540]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]http://www.ingentaconnect.com/content/external-references?article=0148-9062(1998)35L.711[aid=6473539]


10/12

P


(c)IOMC

ommunicationsLtd

Dynamic model

The hammer components are basically two chambers the piston and the bit. As the air enters the chambers(Fig. A1), the piston will be moved due to the pressureof each chamber.

Nomenclaturexp, xpo , piston position and velocity with respect to the

impact plane

vp, vpo , piston velocity and acceleration with respect to

the impact plane

Ad1RC

, Ad3RC

, rear chamber input discharge area(d1RC), output discharge area (d3RC)

Ad1FC

, Ad3FC

, front chamber input discharge area(d1FC), output discharge area (d3FC)

AFP

, ARP

, piston front and rear area

CRC, CFC, polytropic expansion constante, restitution coefficient

, miFC iRC o o , air mass flow at point iof the front chamber(FC) and rear chamber (RC)

mb, bit mass

mp, piston mass

n, polytropic expansion coefficient

,p p* *

iFC iRC , critical air pressure at point i of the frontchamber (FC) and rear chamber (RC)

piFC

,piRC

, air pressure at point iof the front chamber

(FC) and rear chamber (RC)p

d1,p

d3, discharge pressure at points 1 and 3

R, air constant for ideal gas law

TiFC

, TiRC

, air temperature at point i of the frontchamber (FC) and rear chamber (RC)

viFC

, viRC

, air specific volume at point i of the frontchamber (FC) and rear chamber (RC)

vb, bit velocity

vpA

, vpB

, piston impact and reflected velocity

Vmfront

, passive volume of the front chamber

Vmrear

, passive volume of the rear chamber.

Set of differential equations

x vp p=o

v m p A p A p A m1

pp

FC FP IC IC RC rRP pg2 2= - - -o _ im m mFC FC RC2 1 3= -o o o

T m m T m T m T 1

FCFC

FC FC FC FC FC FC22

2 2 1 1 3 3= - + -o o o o_ i

m cp A v

FC p

FC FP p

2

2

-

m m mFC RC RC2 1 3= -o o o Eq. (A1)

T m m T m T m T 1

RCRC

RC RC RC RC RC RC22

2 2 1 1 3 3= - + -o o o o_ i

m cp A v

RC p

RC RP p

2

2

-

Front chamber non-linear algebraic equations

V V A xFC mfront FP p2 = + Eq. (A2)

v mV

FCFC

FC2

2

2= Eq. (A3)

If the outlet sections of the front chamber are closed,then:

pvC

FC

FC

nFC

2

2

= Eq. (A4)

TR

P vFC

FC FC2

2 2= Eq. (A5)

else

p vRT

FCFC

FC2

2

2= Eq. (A6)

C pFC FCv2 FCn2= Eq. (A7)

The critical pressure at the inlet section is given by:p p

*

FC FCn

1 0

1

2 n

n

1=+

-` j Eq. (A8)The actual pressure at the inlet throat P

d1is now

computed. If [equation] then [equation], otherwisepd1

=p2FC

. Thus:

m c ARvc p

pp

pp2

FC m FC d FCFC

p FC

FC

dn

FC

d

n

n

1 1 10

0

0

1

2

0

1

1

12

-=

-

o

J

L

KKKKe e

] N

P

OOOO

o ogR

T

SSSSS

V

X

WWWWW

Eq. (A9)

The critical pressure at the outlet section is given by:

p pn 1

2*FC FC

n

n

3 21

=+

-c ]m g Eq. (A10)

The actual pressure at the inlet throat Pd3

is nowcomputed. If [equation] then [equation], otherwisep

d3=

p4FC

. Thus:



APPENDIX A: Thermodynamic DTH model

A1 DTH hammer schematics


11/12

P


(c)IOMC

ommunicationsLtd

m c ARvc p

pp

pp2

FC m FC d FCFC

p FC

FC

dn

FC

d

n

n

3 3 32 2

3

2

2

3

12

-=

-

o

J

L

KKKKe e

] N

P

OOOO

o ogR

T

SSSSS

V

X

WWWWW

Eq. (A11)

Rear chamber non-linear algebraic equations

Rear chamber equations are the same as frontal ones.

Analysis of the piston

Linear conservation of momentum

m v m v m vp pA p pB b bB= + Eq. (A12)

Energy conservation

m v m v m v21

21

21

p pA p pB b bB

2 2 2= + Eq. (A13)

thus

v m mm m

vpBb p

b ppA= +

- Eq. (A14)

and

v m mm

v2

bBb p

ppA= +

Eq. (A15)

The energy absorbed by the rock is the kinetic energytransmitted by the bit by the impact

E m v21

R b bB

2= Eq. (A16)

The energy reflected through the piston is:

E m v21

p p pB

2= Eq. (A17)

Thus, the energy lost by the piston could be estimatedby:

E m v e21

Lp p pA

2 2= -_ i Eq. (A18)



APPENDIX B: Impact simulation

Stress wave computation using nodes

The computation of the stress wave propagation isdivided into time intervals. At the beginning of everytime interval, the principle of linear momentumconservation is applied to each node (Fig. B1). We canobtain an expression for the new node velocity V

Nthat

is computed as a function of the connecting elements,force and velocity, at the previous time interval.

Va A A

a A V A V P P P N

L R

L L R R L R T

=+

+ + - +

t

t

__ ii Eq. (B1)Applying the same linear momentum principle bothto the left part and to the right sides of the node, themagnitude of forces reflected at the node can beevaluated according to Equation (B2), P

NL(force

propagated towards the left) and PNR

(forcepropagated towards the right).

P aA V V P NL L L N L= - +t _ iand

P aA V V P NR R N R R= - +t _ i Eq. (B2)Note that if more than two elements connect to onenode, Equation (B1) should be modified accordingly.

For example, at the interface between the drill bar andthe drill bit shown in Figure B2, if the gap in betweenis null then the equation for the node velocity is:

Va A A

a A V A V A V P P P P N

L R

b b L L R R L b R T

=+

+ + + + - +

t

t

__

ii

Eq. (B3)

In addition, in this case the forces reflected at the nodecan be computed as:

P aA V V P Nb b b N b= - +t _ iand

P aA V V P NR R N R R= - +t _ i Eq. (B4)

Stress-wave computation at elements

On each element, the velocity is calculated at the endof the time interval using the following equation:

V

aA

aA V V P P

2E

E

E NL NR NL NR

=- + -

t

t _ iEq. (B5)

P P A a V V E NL E NL E= + -t _ i orP P A a V V E NR E E NR= + -t _ i Eq. (B6)

B1 Drill bardrill bit interface


12/12

P


(c)IOMC

ommunicationsLtd

Solid body interfaces

A gap element was use to model the interface betweenelastic solid bodies. When two elastic solid bodies arein contact, the gap element transmits the forces from

the end node of one body to the end node of thesecond body and vice versa.

Rock interaction

The rock behaviour during impact is a very complexsubject because of its non-linearity, and because the

contact geometry between tungsten carbide inserts

and the rock is also complex. Essentially, in ourmethod, the rock behaviour is introduced as aboundary condition in the form of aforcepenetration law. This is derived experimentallyfor every different combination of drill bit and rockthat is of interest (Fig. B3).


B2 Linear momentum principle applied to a node

between times t and t+

B3 Experimental force penetration curve

trans inst mining a methodology for estimating specific rock energy ei

Documents