Performance Evaluation of Hard Rock TBMs considering ...and rock conditions is still needed to be...

Research ArticlePerformance Evaluation of Hard Rock TBMs consideringOperational and Rock Conditions

Xiaoyang Zou 1 Hui Zheng 12 and YongzhenMi 2

1Shanghai Key Laboratory of Digital Manufacture for Thin-Walled Structures Shanghai Jiao Tong University800 Dongchuan Road Shanghai 200240 China2Institute of Vibration Shock and Noise Shanghai Jiao Tong University 800 Dongchuan Road Shanghai 200240 China

Correspondence should be addressed to Hui Zheng huizhengsjtueducn

Received 7 September 2017 Accepted 10 January 2018 Published 11 March 2018

Academic Editor Miguel Neves

Copyright copy 2018 Xiaoyang Zou et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper focuses on studying the correlations of the performance of hard rock tunnel boring machines (TBMs) with operationaland rock conditions Firstly a rigid-flexible coupled multibody dynamic model of an opening hard rock TBM is established for theanalysis of its vibrationThen four performance indexes including mean vibration energy dissipation rate dynamic specific energy(DSE) disc cutter wear rate and load sharing coefficient are introduced and formulated respectively for evaluating the vibrationlevel excavation energy efficiency cutterrsquos vulnerability to wear and load transmission performance of cutterhead driving system ofthe TBM Finally numerical simulation results of the TBM tunneling performance evaluation are obtained and validated by on-sitevibration measurement and tunneling data collection It is found that operational and rock conditions exert important impact onTBM vibration level excavation energy efficiency and structure damage When the type of rock to be cut changes from soft to hardwith operational parameters held constant TBM performance evaluated by these three indexes deteriorates significantly and boththe decrease of excavation energy efficiency and the increase of cutter wear rate caused by TBM vibration are obvious This studyprovides the foundation for a more comprehensive evaluation of TBM performance in actual tunneling process

1 Introduction

With excellent capacity to cut rock up to 300MPa hardrock tunnel boring machines (TBMs) have been widely usedin todayrsquos tunnel excavation [1] To explore the realisticcutter-rock interaction and its characteristics various in situmeasurements of cutter forces on TBMhave been carried outEarly measurements with strain gauges boned on the cuttershaft indicated that the main energy components of cutterforces lie in the frequency range below 10Hz [2] Some yearslater measurements considering force-coupling revealed thecutter forces of the front cutter are much larger than therespective forces of the gauge cutter [3 4] The tunnelingquality such as the relationship between normal force androck fracture crack length and the energy utilization instatic and dynamic loadings were investigated based on thesemeasurements results [4 5] Recently themeasurements withsensors placed in the cutter saddle show the cutting forcevaries temporally and spatially even for the same cutter in

actual tunneling [6 7] These works are beneficial for theTBM dynamic modeling and performance evaluation Own-ing to complex TBM-rock interactions the rock cutting forceloaded by disc cutter is nonlinear and irregular and oscillatesviolently [2 3 7 8] Undermultipoint impact excitation fromcutters TBM vibrates strongly premature failure of cuttersand serious damage in cutterhead driving system occur fre-quently and excavation energy efficiency declines resultingin the increase of tunneling project expense [8 9] There isno doubt that these sufferings of TBM performance have aclose correlation with TBM-rock interactions For an actualtunneling project one of the major concerns is how the TBMperformance evaluated from the aspects of vibration levelexcavation energy efficiency cutterrsquos vulnerability to wearand load transmission performance of cutterhead drivingsystem changes with operational and rock conditions

On the issue of TBM vibration the dynamic characteris-tics of the cutterhead driving system with a joint cutterheadpanel were investigated based on a multi-degree of freedom

HindawiShock and VibrationVolume 2018 Article ID 8798232 17 pageshttpsdoiorg10115520188798232

2 Shock and Vibration

(MDOF) model [10] Later the vibration investigation wasextended to TBM main system which was modeled usinglumped parameter method [9] Recently this investigationwas pushed forward by establishing a rigid-flexible coupledmultibody dynamic model of an opening hard rock TBM[11] In an investigation performed [11] the bottom shield-rock mass interaction was studied in detail Nevertheless thevibration level of the whole TBM varying with operationaland rock conditions is still needed to be systematicallystudied

Specific energy (SE) defined by energy consumed incutting a unit volume of rock has been widely applied tothe performance evaluation of the rock cutting by disc cutterThe variation of SE was predicted for TBM operation in ahard and brittle crystalline rock of moderate strength withcutting tests [12] The SE of rock cutting was evaluated fordifferent geological and operational parameters by numericalsimulation of which the results were comparable with thoseof cutting tests [13 14] As is indicated in [15] energyefficiency is low in dynamic rock cutting because a largeamount of energy is carried away by reflected stress waveand transmitted stress wave In TBM tunneling processthe energy carried by the reflected wave could be a majorexcitation source of TBMvibration but it is not considered inthe calculation of current SE which results in a less accurateprediction of excavation energy efficiency in the case ofserious vibration of TBM Therefore the energy dissipateddue to TBM vibration should be considered when the changeof the energy efficiency with operational and rock conditionsis to be investigated

The expenditure on disc cutter is at least one-fifth ofthe project cost and the time spent on replacing the cutterconstitutes is about one-third of the total project time whichmeans that cutter failure is one of the major topics in TBMtunneling [16] As is the main cause of cutter failure cutterwear statistically caused 78 of the total consumed cuttersin some TBM tunneling projects [17] Therefore cutter wearhas been predicted in a number of studies for improvingTBM performance in the past years [18] SE was used topredict the average wear extent of all disc cutters [16 18] Amodel of disc cutter wear rate was built [19] Later a modifiedmodel for the evaluation of cutter wear rate considering theinfluence of vibration was developed [20] Based on thismodified model it is possible to further evaluate cutterrsquosvulnerability to wear considering the operational and rockconditions

The load transmission performance of multiple pinions-gear ring meshing was evaluated for TBMrsquos cutterhead driv-ing system by load sharing index considering meshing fre-quency bearing stiffness and mounting locations of pinions[21] In [22] the load transmission was investigated by loadsharing coefficient considering bending-torsional coupling ofpinions Generally the large load sharing coefficient meanspoor load transmission performance and serious unevenloading conditions on pinions which easily cause structuredamage such as tooth fracture and broken shaft of pinionsIn the published works there is a lack of investigationof the correlation of load transmission performance withoperational and rock conditions

(1) (2) (3) (4)(5) (6) (7)

(8)

Figure 1 Schematics of an opening hard rock TBM (1)Cutter head(2) Shield (3)Main beam (4)Thrust cylinder (5) Saddle (6) Shoe(7) Torque cylinder (8) Support cylinderThis paper presents a study of TBM performance evalu-

ation considering operational and rock conditions from theaspects of vibration level energy efficiency cutter wear andload transmission performance of cutterhead driving systemFollowing a statement of the problem to be investigated arigid-flexible coupled multibody dynamic model of an open-ing hard rock TBM is established for the vibration analysisof TBM To deal with the performance evaluation problemfour indexes namely mean vibration energy dissipation ratedynamic specific energy (DSE) disc cutter wear rate andload sharing coefficient are then introduced and formulatedrespectively Finally numerical simulations are performedto obtain the results of the TBM performance varying withoperational and rock conditions The obtained numericalresults are further validated through comparing with thosefrom on-site vibration measurement and collected tunnelingdata

2 Modeling of Hard Rock TBMs

21 Dynamic Model of Opening Hard Rock TBMs An open-ing hard rock TBM consists essentially of a cutterheaddriving system and a hydraulic thrust system as shownin Figure 1 In rock cutting process the cutterhead rotatesand moves ahead simultaneously and consequently rock ontunnel face spalls continuously under cutting forces Theopening hard rock TBM is a multibody system Taking themain components the connection between them and theTBM-rock interactions into consideration a rigid-flexiblecoupled dynamic model of TBM is established and shown inFigure 2

In Figure 2 119874119883119884119885 is a global coordinate system where119885 is tunneling direction 119884 is vertical direction and 119883 isdetermined by right-hand rule 119874119894119883119894119884119894119885119894 (119894 = 1 13) arelocal coordinate systems which are established at the centroidof the corresponding substructures and parallel to OXYZ atinitial time The main components in Figure 2 are modeledas rigid-flexible coupled structures M119894 (119894 = 1 13)are the corresponding mass matrix The bending-torsionalcoupling of each pinion is considered with 119898119901119894 and 119868119901119894 (119894 =1 119873) denoting the equivalent mass and inertial moment

Shock and Vibration 3

X

O

Y

XO

Y

M12M10 M11 M13

M9

M8

M7

M7

M7M2M1

M12

M10

M9

M2

M3

M1

M6

M5

M12

M13

M8

M4

M6

M2

M3

M1

M4

M5

Y1

Y1

X1

O1

Z1 X1

O1

Z1O1

kpi cpi

kmi cmi

kmi cmiIpimpi

bpi

kbsn cbsnkbst cbst

kblcbl

klsxclsx

kshi1cshi1

kshi2cshi2

ktlctl

ktsx1ctsx1

ktsx2ctsx2

ktsy2ctsy2

ktrctr

middot middot middot middot middot middot

middot middot middot


middot middotmiddot

middotmiddotmiddot

middot middotmiddot middotmiddot

middot



krsxcrsx

kbrcbr

klgtclgt ksupy1

csupy1

ksupy2csupy2

ksjy2csjy2

c supy1

csupz1

ctht2

c sjy

1

csjz1

krgtcrgt

krgncrgn

ktor2ctor2

ktor3ctor3

kjxcjx

kgx1

cgx1

klgnclgn

kbsxi

kb3i

cbsxi

cb3i

kbsxi cbsxi

ksjx1 csjx1

klsx clsx

kb2i cb2i

kb1i cb1i

krsx crsx

krgz crgz

krg

nc r

gn

ksjy1 csjy1

ksupx1 csupx1 ksjx2 csjx2ksupx2 csupx2

ktsy1c tsy

1

kgy1

kgy2

c gy1

kgy1

c gy1

c gy2

kgx2

cgx2

ZO

Y

Z

O

X

ktsz1 ctsz1

kb1i cb1i ktsy1c

tsy1

kb2i cb2i

cgbzi

cjz

clgzkgbzi

kbszi cbszi

kbsyic b

syi

kgby

ic g

byi

kbs

nc

bsn

kbsz cbsz

ktor2

ktor1

ksu

py1

ksupz1

kjz

klgz

ktht2

ctht2

ktht2cgbxi

cgbzi

kgbxi

kgbzi

ctht1

ktht1

ctht3

ktht3

ksjz1

ksjy1

klgz clgz

klgnc lgn





c tor

2

c tor

1

Figure 2 Dynamic model of an opening hard rock TBM (1) Cutter head (2) Gearbox (3) Bottom shield (4) Top shield (5) Left shield (6)Right shield (7)Main beam assembly (8) Saddle (9) Support cylinder body (10) Left cylinder rod (11) Right cylinder rock (12) Left shoe(13) Right shoe


respectively The dynamic equations of TBM vibration arederived using Newton-Euler method as follows

The generalized displacement (ie the generalizedDOFs)vectors of substructures are written as

120595119894 = (xT119894 120572T119894 120578T119894 )T x119894 = (119909119894 119910119894 119911119894)T 120572119894 = (120572119894 120573119894 120574119894)T 120578119894 = (1205781198941 120578119894119873119894)T

(1)

where 120578119894 is the coefficient vector related to structural elasticmodematrixΦ119894 T denoted the transpose ofmatrix or vectorThe dynamic equations of TBM are derived inmatrix form as

M + C + K120595 = f1 + f2 (2)

with

120595 = ( 119909119901119894 119910119901119894 120579119901119894 120595T1 120595T13)TM = diag ( 119898119901119894 119898119901119894 119868119901119894 M1 M13)M119894 = sum ΓT119894 119898119894Γ119894 = [[[

M11989411 M11989412 M11989413M11989422 M11989423

symmetric M11989433

]]]K = [[[[

d

K119894119895 + 120575119894119895k119887119894symmetric d

]]]]C = [[[[

d

C119894119895 + 120575119894119895c119887119894symmetric d

]]]]K119894119895 = sum ΓT119894 119896119894e119883119894e119883119894Γ119895C119894119895 = sum ΓT119894 119888119894e119883119894e119883119894Γ119895Γ119894 = [I A119903119887119894RT

(u1198870119883119894+120588119887119883119894)A119903119887119894Φ119894]

k119887119894 = diag (01times6 12059621198941 1205962119894119873119894)c119887119894 = diag (01times6 212057711989411205961198941 2120577119894119873119894120596119894119873119894)120575119894119895 =

1 119894 = 1198950 119894 = 119895

f1 = ( 0 0 0 fT11 fT131)Tf2 = ( minus119865119901119894119909 minus119865119901119894119910 minus119877119901119894119865119901119894 fT12 fT132)T

A1199031198871 = [[[cos (120579) minussin (120579) 0sin (120579) cos (120579) 00 0 1

]]]A119903119887119894 = I (119894 = 2 13)

Rk = [[[0 minusk (3) k (2)

k (3) 0 minusk (1)minusk (2) k (1) 0]]]

(3)

where M K and C are mass matrix stiffness matrix anddamping matrix respectively diag denotes diagonal matrix120596119894119895 is natural circular frequency 120577119894119895 is modal damping factorwith the value of 001 used in this simulation u0 is staticdeformation vector in steady motion 120588 is the relative vectorof point119883119894 on substructure I is a third-order unit matrix Rvis a matrix formed from coordinate vector v A119903119887119894 is directioncosine matrix and e is a unit vector denoting the directionof damping spring which connects substructures in systemOXYZ [23] During steady state TBM tunneling cutterheadrotates around 119911-axis at a constant rotational velocity and120579 denotes the rotational angle Other substructures have norotation and their directional cosine matrix are third-orderunit matricesM11989411M11989422 andM11989433 are the mass matrices fortranslational rotational and elastic vibrations respectivelyM11989412 M11989413 and M11989423 are the coupled mass matrices betweentranslational rotational and elastic vibrations respectivelyThe elastic modes natural frequencies and the discretizedmass 119898119894 can be obtained by using commercial finite elementcode It should be noted that the modes of each substructureare obtained under free boundary conditions thus the firstsix modes are rigid body movement modes with naturalfrequency of 0Hz resulting in the fact that the first sixentries in k119887119894 and c119887119894 are zeros Furthermore for a fixed pointon substructure its modes are obtained in local coordinatesystem of the substructure at initial attitude thus its modematrix Γ119894 measured in 119874119883119884119885 will change with attitude ofthe substructure Vector f1 denotes inertial forces arisingdue to MDOF rotation Due to very low rotation velocityof cutterhead in practice the inertial forces are small andthus ignored in this simulation Vector f2 denotes excitingforces including nonlinear time-varying multiple pinions-gear ring meshing forces cutter-rock interaction forces andbottom shield-rock mass contact forces Meshing forces 119865119901119894and the values of structural parameters including equivalentstiffness and damping can be obtained by empirical formulasor finite element analysis as well as those recommended in[11]

22 TBM-Rock Interactions TBM-rock interactions includ-ing disc cutter-rock interaction and bottom shield-rock massnonlinear contact are mainly responsible for the vibrationof TBM These interactions correlate with a number offactors such as geotechnical parameters cutter geometryindentation cutterhead rotation speed and distribution ofcutters on cutterhead [4 8] The asymmetric distribution ofcutter easily results in large side force and further leads tostrong vibration of TBM in the direction perpendicular tothe axis of the tunnel [4] Similar to earth drilling describedin [24] rock cutting by disc cutters makes TBM suffer fromvibration due to regenerative effect that is the dependence ofpenetration on the history of cuttermotion in cutting processFor a TBM because of the quasihelical motion of cutter


Rotationdirection

Angle of contact area

R

minusF

F

p(t)

v

R

FR

FN

N

Figure 3 Generalized illustration of cutter-rock interaction

the instantaneous cutter penetration is determined by thecurrent position and the position of the cutter at the previousrevolution of cutterhead Disc cutter-rock interaction isillustrated in Figure 3 Cutter forces can be calculated usingthe model of Colorado School of Mines (CSM) which hasbeen successfully applied to TBM design and performanceevaluation [25] Considering the varying cutter penetrationand even the loss of contact between cutter and rock whencutter penetration is not positive or cutter moves away fromrock under vibration conditions disc cutter force in dynamicrock cutting process can be expressed throughmodifying theformula given in [25] as

119865 = 119862119879119877120593 3radic 1205902119888120590119905119878120593radic119877119879119867(119901)119867 (119889)119865119873 = 119865 cos (120573) 119865119877 = 119865 sin (120573)

(4)

with

120593 = cosminus1 (119877 minus 119901119877 ) 120573 = 1205932

119867 (119910) = 1 119910 ge 00 119910 lt 0

119901 = 119911 (119905) minus 119911 (119905 minus 120591) 120591 = 2120587Ω0119889 = V119873 cos (120573) + V119877 sin (120573)

(5)

where 119865119873 is normal force 119865119877 is rolling force C is a constantequal to 212 according to [25]119879 is cutter tip width119877 is cutterradius 120590119888 is uniaxial compressive strength of rock (UCS) 120590119905is Brazilian indirect tensile strength of rock (BTS) 119878 is cutspacing 120593 is angle of the contact area 119901 is cutter penetration119867(sdot) is the Heaviside function 119911 is the position of cutter innormal direction 120591 is time delay and V119873 and V119877 are the veloc-ity of cutter center in normal and that in rolling direction

respectively Due to the regenerative effect in rock cuttingafter integrating (4) into (2) delay differential equations areobtained Because (2) are the differential equations about thegeneralized displacementsmeasuredwithmodal coordinatesthe forces in (4) should be converted into generalized forcesthrough left multiplying the transpose of the mode matrix Γ119894corresponding to the force point on cutterhead and then beadded to vector f2

The bottom shield-rock mass contact is considered in thedynamic modeling of the TBM Shield slides on rock massalong tunneling direction when bottom shield-rock mass isin frictional contact but this state transits to stick whenthe velocity vanishes due to vibration and vice versa Evenin more serious vibration bottom shield-rock mass contactseparates thus introducing discontinuities in TBM dynamicmodel Rock mass serves as a support and can be modeledas a Winkler foundation with damping springs uniformlydistributed in both normal direction and tangential directionof shield circumference [26] In tunneling direction whetherbottom shield is in friction or not should be determined byits motion state

The equivalent normal and tangential distributed stiffnessof Winkler foundation can be obtained by [26]

119896119899 = 119864119903119877119903 (1 + V) 119896119905 = 119896119911 = 1198961198993 (6)

where 119864119903 is Youngrsquos modulus of the ground 119877119903 is tunnelradius V is Poissonrsquos ratio which is 03 in this study Consid-ering the state transition of bottom shield and the separationof bottom shield-rock mass contact the distributed forces inbottom shield-rock mass interaction are obtained as119865119904119899 = minus (119896119899 (119909119899 + 1205750) + 119888119899119899)119867 (119909119899 + 1205750)119865119904119905 = minus (119896119905119909119905 + 119888119905119905)119867 (119909119899 + 1205750)119865119904119911=

minus (119896119911119909119911 + 119888119911119911)119867 (119909119899 + 1205750) minus (119896119911119909119911 + 119888119911119911) lt 120583 (119911) 119865119904119899120583 (119911) 119865119904119899 minus (119896119911119909119911 + 119888119911119911) ge 120583 (119911) 119865119904119899(7)

where 119909119899 119909119905 and 119909119911 are the displacements of contact point innormal tangential and tunneling direction respectively 1205750 is


the initial compression of normal spring due to TBM gravityand 120583 is a velocity related frictional coefficient According to[20]120583 is taken as120583 = 015ndash030 for kinetic coefficient and120583 =025ndash045 for static coefficient To reduce the computationaldifficulty due to discontinuity brought by bottom shieldrsquosstick-slip state a smooth representation of 120583 with velocity-weakening law is adopted and expressed as

120583 (119911)= 2120587 arctan (120576119911) (120583119896 + (120583119904 minus 120583119896) exp (minus120582 10038161003816100381610038161199111003816100381610038161003816)) (8)

where 120583119896 is kinetic coefficient 120583119904 is static coefficient 120576 is asmooth coefficient and 120582 is a characteristic coefficient

3 Performance Evaluation Indexes forHard Rock TBMs

31 Mean Vibration Energy Dissipation Rate Mean vibrationenergy dissipation rate119906 is equivalent to the energy dissipateddue to TBM vibration in a unit time It is calculated by

119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)

where 119882119889 is the energy dissipated due to TBM vibrationin a time period C is the damping matrix in (2) F119891 isa column vector formed by friction forces of all contactpoints on the bottom shield-rock mass interface and v119891 isthe corresponding velocity column vector Mean vibrationenergy dissipation rate 119906 is equivalent to a quadratic form ofvibration velocity and thus is similar to the square of vibrationseverity Vibration severity is the root mean square (RMS)of vibration velocity and used as a traditional assessment ofvibration level Therefore 119906 is suitable for the evaluation ofvibration level of the whole TBM

32 Dynamic Specific Energy Specific energy (SE) is theenergy consumed in cutting a unit volume of rock and hasbeen widely used to evaluate the cutting energy efficiency ofa TBM disc cutter The calculation of the current SE usingmean cutting force eliminates the consideration of influenceof vibration [13 14]Therefore it is less accurate for evaluatingthe realistic excavation energy efficiency of TBM particularlywhen it undergoes serious vibration Taking both the energyconsumed in rock cutting and the energy dissipated by TBMvibration into account a new index called dynamic specificenergy (DSE) is proposed and defined as

DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)

where 1198651198941198730 and 1198651198941198770 are mean normal force and mean rollingforce on the 119894th cutter respectively 119873119888 is the number ofcutters Γ is contact area between shield and rock mass 119877119894is the radius where the cutter mounted on the cutterhead 120579is the rotation angle of cutterhead 119878 is the cut spacing 119901119894 iscutter penetration of the 119894th cutter and119867(sdot) is the Heavisidefunction

33 Disc Cutter Wear Rate Disc cutter wear is the majorone among cutter failure modes which is determined by theamount of cutter wear To estimate cutterrsquos vulnerability towear disc cutter wear rate is used Based on CSM modelshown in (4) disc cutter wear rate can be calculated by [20]

d119876d119905 = 119896119862119879119877120593119867119888 3radic 1205902119888120590119905119878120593radic119877119879 int120593

0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22

V1 = 2Ω0119877119894sin2 (1206012) + (Ω01199012120587 + V119911) sin120601 minus V119905 cos120601V2 = Ω0119877 sin120601 minus V119877

(14)

where 119876 is the amount of cutter wear 120595 is a constant oftypically 02 to minus02 for disc cutter 120601 is the central angle ofthe arc length between a point on cutter-rock contact areaand the point determining the cutter penetration as is shownin Figure 3 119896 is wear coefficient usually of 10minus1 to 10minus6119867119888 is surface hardness of cutter Ω0 is cutterhead rotationspeed and V119911 V119877 and V119905 are the perturbations of the steadyvelocity of cutter center in tunneling direction and radialand tangential direction on tunnel face that is the vibrationvelocity of cutter center respectively [20] When V119911 V119877 andV119905 are equal to zero (13) is identical to the one in [19] whichhas no consideration of the influence of TBM vibration

34 Load Sharing Coefficient The rotation of cutterhead ofTBM is driven by multiple pinions-gear ring meshing Smalldifference between meshing forces 119865119901119894 (119894 = 1 119873) meansgood load transmission performance of cutterhead drivingsystemThe load transmission performance can be evaluatedby load sharing coefficient which directly reflects the loaduneven level in each pinion at a certain time [22] The loadsharing coefficient of the cutterhead driving system in onetooth frequency cycle is calculated as

119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)


Table 1 Structural parameters in TBM dynamic model

Structural parametersMass of TBM (t) 135Diameter of cutterhead (m) 4Length of main machine (m) 10Number of pinions 8Number of cutters 24Cutter spacing (mm) 84Diameter of cutter (mm) 432Cutter tip width (mm) 92

Table 2 Parameters of three types of rock

Rock type Soft rock Moderately hard rock Hard rockYoungrsquos modulus (GPa) 18 50 80UCS (MPa) 60 100 150BTS (MPa) 4 5 6

And the load sharing coefficient of the cutterhead drivingsystem in one system period is calculated as

119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)

where 119889119901119894 is the load sharing coefficient of cutterhead drivingsystem in one tooth frequency cycle and 119863119901 is the loadsharing coefficient of cutterhead driving system in one systemperiod

4 Results of PerformanceEvaluation and Discussion

41 Parameters in Numerical Simulation The opening hardrock TBM used in an actual water tunnel project wastaken as the application example in the evaluation of TBMperformance Structural parameters of the dynamic modelof the opening hard rock TBM in numerical simulation arepresented in Table 1 Other structural parameters in thissimulation are listed in Appendix For themain substructuresmentioned in Section 2 the elastic modes are obtained bymeans of commercial finite element code ANSYS resultingin a TBM dynamic model with a total of 137 generalizedDOFs Based on the rigid body modes elastic modes naturalfrequencies mass matrices and stiffness matrices extractedfrom ANSYS entire dynamic equations (2) are constructedinMATLABThen the dynamic equations are solved by usingMATLAB R2013a built-in function ldquoode45rdquo with ldquoRelTolrdquovalue of 1 times 10minus6 and other parameters default The rock con-ditions encountered in tunneling are complicated in terms ofrock property For simplicity but not loss of generality threetypes of rock namely soft moderately hard and hard rockrespectively are considered in numerical simulation Theaverage values of the relevant property of the three types ofrock are listed in Table 2The operational parameters in TBMtunneling include cutterhead rotation speed Ω0 and advancerate 1198810 by which the penetration can be determined Withdifferent operational and rock conditions the performance

of TBM is evaluated with the four indexes introduced inSection 3

42 Correlation of TBM Performance and Operational andRock Conditions The correlation of mean vibration energydissipation rate 119906 and operational and rock conditions isshown in Figure 4 where the penetration changes from4 to 12mmr and the advance rate varies in the rangeof 04ndash08mms The values of operational parameters inthis regime are frequently used in practical TBM tunnelingprojects [1 25] and agree with those collected from on-sitemeasurements shown in next subsection It can be seen inFigure 4 that 119906 increases largely from soft rock to hard rocktunneling with its value in the range of 900ndash1400 1100ndash2200and 1700ndash3500 Js respectively which means TBM vibrationbecomes much stronger in hard rock tunneling In soft rockand moderately hard rock tunneling the variations of 119906 withvarying penetration and advance rate are very complicated Inthe case of hard rock tunneling however 119906 increases rapidlywith the increase of the penetration

The correlation of DSE and operational and rock condi-tions is shown in Figure 5 where maximum DSE is used asan indicator of excavation energy efficiency of TBM It can beseen in Figure 5 that DSE increases significantly as the rocktype changes from soft to hard DSE in hard rock tunnelingreaches several times as that in soft rock tunneling For thesame rock to be cut DSE decreases and the decreasing ratebecomes slow with the increase of the penetration whichis similar in trend to those simulation results presented in[14 16] Furthermore the change of DSE originates fromthe fact that the difference of advance rate for the samepenetration is significant For the penetration of 8mmr inboth soft rock and hard rock tunneling the difference of DSEvalues at advance rate of 04 and 08mms is larger than 5However the variation of DSE with different advance rate isvery complicated

The complicated variation of DSE with different advancerate results from the influence of TBM vibration on DSETheresults of DSE in soft rock tunneling for cutterhead rotationspeed of 6 rpm and advance rate of 12mms are shown inFigure 6 where the results of SE are also shown for thecomparison with DSE It can be seen in Figure 6 that atstrong vibration moments DSE increases significantly withthe appearance ofmultiple peaks on the curve ofDSE leadingto the decrease of excavation energy efficiency When TBMvibrates weakly DSE decreases to a value close to SE whichtakes no consideration of the influence of vibrationThe slightvariation of SE with time is due to variation of excavated rockvolume which is influenced by dynamic cutter penetration

The statistical results that is the mean and the standarddeviation of percentage increases of maximum DSE andmean DSE relative to SE are shown in Figure 7 It is seenthat the percentage increase of maximumDSE to SE is nearly8 and that of mean DSE to SE is about 14 In otherwords the ratio of vibration energy dissipation to the energyconsumed in rock breakage is approximately 14 in thewhole TBM tunneling process but can reach as high as 8at the strongest vibration moment The fluctuation of the


800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)

6 8 10 124Penetration (mmr)

Advance rate (mms)040506

0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)

Figure 4 Correlation of mean vibration energy dissipation rate 119906 and operational parameters for (a) soft rock (b) moderately hard rock and(c) hard rock

results in hard rock tunneling is larger than those in soft andmediumhard rock tunneling which results from the strongerimpact of TBM vibration in hard rock tunneling It can beconcluded that severe vibration in TBM largely deterioratesthe excavation energy efficiency In addition the fluctuationof maximum DSE shown is larger than that of mean DSEwhich means maximum DSE is more effective and sensitivein revealing the variation of DSE with operational and rockconditions

The change of mean cutter wear rate with the operationaland rock conditions is shown in Figure 8 where wear rate is

for the cutter mounted on cutterhead panel at a radius of 1mAs shown in the figure for the same rock to be cut cutter wearrate increases with the increase of the penetration which is inaccordance with the results presented in [19] Furthermorethe increase of cutter wear rate with the change of rock typefrom soft to hard indicates that the cutter is more vulnerableto wear and the prematurity of cutter failure caused by wearmore easily occurring in hard rock tunneling than in soft rocktunneling which agrees with project practice [1] With thetype of rock and penetration held constant the cutter wearrate increases with the increase of the advance rate This is



11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)

Figure 5 Correlation of dynamic specific energy (DSE) and operational parameters for (a) soft rock (b) moderately hard rock and (c) hardrock

because higher advance rate results in larger excavated rockvolume in a unit time and consequently increases the amountof cutter wear in a unit time

The time history of wear rate of this cutter is shown inFigure 9 where the mean wear rate and the wear rate withoutconsidering vibration are also shown As is illustrated thecutter wear rate oscillates strongly with time and its peaksare several times of the wear rate without consideringvibration Comparing with the wear rate without consideringvibration the mean wear rate of the cutter at a radius of

1m increases by 75 in this case Therefore affected byvibration cutters are more vulnerable to wear than withoutvibration

The statistical results that is the mean and the stan-dard deviation of percentage increases of mean wear ratecompared with the wear rate without considering vibrationfor this cutter are shown in Figure 10 It is shown thatthe percentage increase of mean wear rate of cutter causedby TBM vibration reaches 8 10 and 18 in soft rockmoderately hard rock and hard rock tunneling respectively


DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

Figure 6 DSE in soft rock tunneling for Ω0 = 6 rpm and 1198810 = 12mms

HardModerately hardSoftRock type

Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()

Figure 7 Percentage increases of maximum DSE and mean of DSE relative to SE

The fluctuation of the results in hard rock tunneling is largerthan those in soft andmoderately hard rock tunneling Also itis revealed that the TBM in high vibration level for hard rocktunneling worsens the working condition of disc cutter andaccelerates cutter wear Therefore excessive vibration shouldbe avoided as far as possible to protect cutters from wear toofast

The correlation of load sharing coefficient of the cutter-head driving system and operational and rock conditions isshown in Figure 11 It can be seen that the correlation ofload sharing coefficient and operational parameters that ispenetration and advance rate is very complicated Overallthe load sharing coefficient varies between 135 and 165 whenoperational parameters change in the regime of advance rateof 04ndash08mms and penetration of 4ndash12mmr and it alsoslightly decreases with the change of rock type from soft tohard From (4) it can be seen that with other parameters

held constant cutter forces increase when the rock to becut becomes harder which leads to a larger driving torquein cutterhead driving system Therefore the results of theslight decrease of load sharing coefficient with the changeof rock type from soft to hard are in accordance with theconclusion that load sharing seems to get better for highertorque [27] Although load transmission performance slightlychanges with different rock types higher torque in harderrock tunneling increases the absolute difference betweenmeshing forces loaded on pinions and more easily causesstructure damage such as tooth fracture and shaft broken ofpinions

43 Results of Vibration and DSE from On-Site Measurementand Tunneling Data Collection An on-site measurement ofTBM vibration acceleration was performed for the openinghard rock TBM used in an actual water tunnel project The



05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)

Figure 8 Correlation of cutter wear rate and operational parameters for (a) soft rock (b) moderately hard rock and (c) hard rock

vibration measurement system consists of a data acquisitionsystem a laptop several 3-directional accelerometers andconnecting wires The time history of acceleration was thenacquired during TBM tunneling The measuring points inthis on-site measurement were distributed on main beamand grippers Figure 12 shows two measuring points at mainbeam back tip and right gripper respectively A samplefrequency of 1000Hz was adopted in this TBM vibrationmeasurement

The water tunnel project where the on-site measurementis carried out is in Northeast China and is a part of LiaoningNorthwest Water Supply Project The tunneling section at

measurement moment is buried at depth of 200m and islocated in a geological fault zone where themajor constituentof rock mass is granodiorite Rock mass is not very stable inthe developed joint fissures zone with a wide range of rockblocks falling from tunnel arch andwater gushing Accordingto the project office the rock mass encountered in themeasurement section is classified as soft rock or moderatelyhard rock

The results of acceleration response at main beam backtip and right gripper obtained by numerical simulation arecompared with those obtained from on-site accelerationmeasurement For example Figure 13 shows the comparison


dQdtMean dQdtdQdt without vibration

05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)

Figure 9 Cutter wear rate in soft rock tunneling forΩ0 = 6 rpm and 1198810 = 12mms

HardSoft Moderately hardRock type

0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)

Figure 10 Percentage increases of mean cutter wear rate caused by vibration

of acceleration responses at main beam back tip in 119883-direction where the parameters cutterhead rotation speed of6 rpm advance rate of 12mms and soft rock in simulationare close to those in measurement The values of accelerationtime history between simulation andmeasurement results arequite close and the distribution of dominant spectrum peaksin frequency spectrum between simulation and measure-ment results is similar The reasonable agreement betweensimulated acceleration and measured acceleration showsthat the developed dynamic model of TBM is reasonablyfaithful

The correlation of TBM vibration level and operationalparameters obtained from this on-site measurement andtunneling data collection is revealed by Figure 14 wherethe TBM vibration level is simply evaluated by the RMS ofacceleration in 119885-direction measured at main beam back tipThe correlation of DSE and operational parameters obtained

is shown in Figure 15 where the dashed red line denotesthe quadratic fitting line of the scattered data shown inFigure 5(a) Geological conditions of fault zone encounteredin this on-site measurement are very complicated and leadto large margin variations of acceleration RMS and DSEas shown in Figures 14 and 15 respectively Operationalparameters that is the penetration and advance rate alsoexert significant influence on these results In tendency thecorrelation of vibration level and operational parametersobtained from on-site measurement revealed by Figure 14 issimilar to the obtained simulation results in Figure 4(a) andthe correlation of DSE and operational parameters obtainedfrom on-site measurement in Figure 15 is similar to theobtained simulation results The reasonable trend agree-ment between the simulation correlations of vibration leveland DSE with operational parameters and those obtainedfrom on-site measurement in soft rock tunneling validates



14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)

Figure 11 Correlation of load sharing coefficient and operational parameters for (a) soft rock (b) moderately hard rock and (c) hard rock

the performance evaluation of hard rock TBMs presented inthis paper

5 Conclusions

From the investigations of TBM performance consideringoperational and rock conditions three major concludingremarks can be made as follows(1) The values of mean vibration energy dissipation rate119906 DSE and cutter wear rate increase significantly whenthe type of rock to be cut changes from soft to hard

with operational parameters held constant However thevariations of these performance indexes with the changeof operational parameters are with different tendency fromeach other For the cases of soft rock and moderately hardrock tunneling the variation of 119906 is very complex withchanging penetration and advance rate For the case ofhard rock tunneling generally 119906 significantly increases withthe increased penetration DSE decreases with the increaseof penetration and varies significantly with the change ofadvance rate Cutter wear rate increases significantly withboth the increased penetration and advance rate For thecorrelation of load sharing coefficient and operational and


(a) (b)

Figure 12 Measuring point at (a) main beam back tip and (b) right gripper

minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)

Figure 13 Acceleration responses of (a) simulated time history (b) simulated spectrum (c) measured time history and (d) measuredspectrum at main beam back tip in119883-direction


Advance rate (mms)lt0404ndash0505ndash06

06ndash0707ndash08gt08

10 155Penetration (mmr)

05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)

Figure 14 Correlation of acceleration RMS in 119885-direction mea-sured at main beam back tip and operational parameters




10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y

Figure 15 Correlation of DSE and operational parameters obtainedfrom on-site measurement (dashed red line is the fitted curve ofsimulation DSE in soft rock tunneling)

rock conditions the overall trend is that changing oper-ational parameters results in a large margin variation ofload sharing coefficient and the change of rock type fromsoft to hard makes the load sharing coefficient decreaseslightly(2) Due to the TBMrsquos severe vibration DSE and cutterwear rate oscillate strongly with time In the regime ofadvance rate of 04ndash08mms and penetration of 4ndash12mmr

statistically the percentage increase of DSE to specific energy(SE) is nearly 8 at the strongest vibration moment whichmeans vibration significantly deteriorates the excavationenergy efficiency of a TBM The percentage increases ofmean wear rate of cutter caused by TBM vibration reaches8 10 and 18 in soft rock moderately hard rock andhard rock tunneling respectively which means that TBMvibration worsens the working condition of disc cutterand accelerates cutter wear especially in hard rock tunnel-ing(3) The simulation results are basically consistent withthe field measurements These results could provide thefoundation for a more comprehensive evaluation of TBMperformance in actual tunneling process

Appendix

Structural parameters in this simulation are as follows

1198721 = 458 t1198722 = 162 t1198723 = 38 t1198724 = 37 t1198725 = 20 t1198726 = 20 t1198727 = 278 t1198728 = 141 t1198729 = 63 t11987210 = 15 t11987211 = 15 t11987212 = 51 t11987213 = 51 t119898119901119894 = 01 t119868119901119894 = 1 times 106 tmm2119887119901119894 = 002mm119896119901119894 = 1 times 106Nmmminus1119896119898119894 = 1 times 106Nmmminus11198961198871119894 1198961198872119894 1198961198873119894 = 1 times 106Nmmminus1119896119887119904119909119894 119896119887119904119911119894 = 4 times 106Nmmminus1119896119887119904119910119894 = 8 times 106Nmmminus1119896119892119887119909119894 119896119892119887119910119894 = 1 times 106Nmmminus1


119896119892119887119911119894 = 2 times 106Nmmminus11198961199051199041199091 1198961199051199041199092 1198961199051199041199111 1198961199051199041199112 = 5 times 106Nmmminus11198961199051199041199111 1198961199051199041199112 = 5 times 104Nmmminus1119896119904ℎ1198941 119896119904ℎ1198942 = 5 times 104Nmmminus1119896119897119904119909 119896119903119904119909 = 5 times 106Nmmminus1119896119887119897 119896119887119903 119896119905119897 119896119905119903 = 1 times 107Nmmminus11198961198921199091 1198961198921199092 1198961198921199101 1198961198921199102 = 1 times 107Nmmminus1119896119905ℎ1199051 119896119905ℎ1199052 119896119905ℎ1199053 119896119905ℎ1199054 = 24 times 105Nmmminus11198961199051199001199031 1198961199051199001199032 1198961199051199001199033 1198961199051199001199034 = 55 times 105Nmmminus1119896119895119909 119896119895119911 = 5 times 105Nmmminus11198961199041199061199011199091 1198961199041199061199011199092 = 13 times 106Nmmminus11198961199041199061199011199101 1198961199041199061199011199102 1198961199041199061199011199111 1198961199041199061199011199112 = 1 times 107Nmmminus11198961199041198951199091 1198961199041198951199092 1198961199041198951199101 1198961199041198951199102 1198961199041198951199111 1198961199041198951199112 = 5 times 107Nmmminus1

(A1)

The equivalent damping coefficients can be obtained byusing damping ratios as recommended in [10]

Conflicts of Interest

The authors declare no conflicts of interest including specificfinancial interests and relationships relevant to subject of thispaper

Acknowledgments

This work is financially supported by the Basic ResearchProgram of China (973 Program) (Grant no 2013CB035403)

References

[1] B Maidl L Schmid W Rits and M Herrenknecht HardrockTunnel Boring Machines Ernst and Sohn Berlin Germany2008

[2] A E Samuel and L P Seow ldquoDisc force measurements ona full-face tunneling machinerdquo International Journal of RockMechanics andMining Sciences andGeomechanics Abstracts vol21 no 2 pp 83ndash96 1984

[3] Z X Zhang S Q Kou X C Tan and P-A Lindqvist ldquoIn-situ measurements of cutter forces on boring machine at AspoHard Rock Laboratory Part I Laboratory calibration and in-situ measurementsrdquo Rock Mechanics and Rock Engineering vol36 no 1 pp 39ndash61 2003

[4] Z X Zhang S Q Kou and P-A Lindqvist ldquoIn-situ mea-surements of cutter forces on boring machine at Aspo HardRock Laboratory Part II Characteristics of cutter forces andexamination of cracks generatedrdquo Rock Mechanics and RockEngineering vol 36 no 1 pp 63ndash83 2003

[5] Z X Zhang ldquoEstimate of loading rate for a TBM machinebased on measured cutter forcesrdquo Rock Mechanics and RockEngineering vol 37 no 3 pp 239ndash248 2004

[6] M Entacher G Winter T Bumberger K Decker I Godorand R Galler ldquoCutter force measurement on tunnel boringmachines - System designrdquo Tunnelling and Underground SpaceTechnology vol 31 pp 97ndash106 2012

[7] M Entacher G Winter and R Galler ldquoCutter force measure-ment on tunnel boring machines - Implementation at Koralmtunnelrdquo Tunnelling and Underground Space Technology vol 38pp 487ndash496 2013

[8] M Entacher K Lassnig and R Galler ldquoAnalysis of force pathdiagrams of linear cuttingmachine-tests regarding geotechnicalparametersrdquo in Proceedings of the GeoCongress 2012 State ofthe Art and Practice in Geotechnical Engineering pp 3258ndash3267USA March 2012

[9] J Huo H Wu G Li W Sun and J Chen ldquoThe couplingdynamic analysis and field test of TBM main system undermultipoint impact excitationrdquo Shock and Vibration vol 2015Article ID 313259 14 pages 2015

[10] W Sun J Ling J Huo L Guo X Zhang and L DengldquoDynamic characteristics study with multidegree-of-freedomcoupling in TBM cutterhead system based on complex factorsrdquoMathematical Problems in Engineering vol 2013 Article ID635809 17 pages 2013

[11] X Y Zou H Zheng Y Z Mi and X Xie ldquoA study on vibrationof tunnel boring machine and the induced shield tangentialforcerdquo Journal of Vibrational Engineering and Technologies vol4 no 4 pp 373ndash381 2016

[12] R Gertsch L Gertsch and J Rostami ldquoDisc cutting testsin Colorado Red Granite Implications for TBM performancepredictionrdquo International Journal of RockMechanics andMiningSciences vol 44 no 2 pp 238ndash246 2007

[13] J-W Cho S Jeon S-H Yu and S-H Chang ldquoOptimumspacing of TBM disc cutters A numerical simulation using thethree-dimensional dynamic fracturingmethodrdquoTunnelling andUnderground Space Technology vol 25 no 3 pp 230ndash244 2010

[14] J-W Cho S Jeon H-Y Jeong and S-H Chang ldquoEvaluation ofcutting efficiency during TBM disc cutter excavation within aKorean granitic rock using linear-cutting-machine testing andphotogrammetric measurementrdquo Tunnelling and UndergroundSpace Technology vol 35 pp 37ndash54 2013

[15] Z X Zhang S Q Kou L G Jiang and P-A Lindqvist ldquoEffectsof loading rate on rock fracture fracture characteristics andenergy partitioningrdquo International Journal of Rock Mechanicsand Mining Sciences vol 37 no 5 pp 745ndash762 2000

[16] L Wang Y Kang Z Cai et al ldquoThe energy method to predictdisc cutter wear extent for hard rock TBMsrdquo Tunnelling andUnderground Space Technology vol 28 no 1 pp 183ndash191 2012

[17] H-S Jung J-M Choi B-S Chun J-S Park and Y-J LeeldquoCauses of reduction in shield TBMperformance - A case studyin Seoulrdquo Tunnelling and Underground Space Technology vol26 no 3 pp 453ndash461 2011

[18] L Wang Y Kang X Zhao and Q Zhang ldquoDisc cutter wearprediction for a hard rock TBM cutterhead based on energyanalysisrdquoTunnelling andUnderground Space Technology vol 50pp 324ndash333 2015

[19] Q Tan L Xie Y Xia Z Zhu X Sun and Y Wang ldquoAnalysis ofwear rate of TBMdisc cutterrdquo Journal of Central SouthUniversityScience and Technology vol 46 no 3 pp 843ndash848 2015

[20] X Zou Y Mi H Zheng and J Tao ldquoInfluence of vibration onthe performance of tunnel boring machinesrdquo in Proceedings of


the 12th IEEEASME International Conference on Mechatronicand Embedded Systems and Applications MESA 2016 NewZealand August 2016

[21] H Yu P Eberhard Y Zhao and H Wang ldquoSharing behaviorof load transmission on gear pair systems actuated by parallelarrangements of multiple pinionsrdquo Mechanism and MachineTheory vol 65 pp 58ndash70 2013

[22] J Wei Q Sun W Sun X Ding W Tu and Q Wang ldquoLoad-sharing characteristic of multiple pinions driving in tunnelingboring machinerdquo Chinese Journal of Mechanical Engineeringvol 26 no 3 pp 532ndash540 2013

[23] J Hong Computational Dynamics of Multibody System HigherEducation Press Beijing 1999 in Chinese

[24] C Germay V Denoel and E Detournay ldquoMultiple modeanalysis of the self-excited vibrations of rotary drilling systemsrdquoJournal of Sound and Vibration vol 325 no 1-2 pp 362ndash3812009

[25] J Rostami ldquoHard rock TBM cutterhead modeling for designand performance predictionrdquo Geomechanics and Tunnellingvol 1 no 1 pp 18ndash28 2008

[26] O Arnau and C Molins ldquoThree dimensional structuralresponse of segmental tunnel liningsrdquo Engineering Structuresvol 44 pp 210ndash221 2012

[27] H Ligata A Kahraman and A Singh ldquoAn experimental studyof the influence of manufacturing errors on the planetary gearstresses and planet load sharingrdquo Journal of Mechanical Designvol 130 no 4 Article ID 041701 2008

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(MDOF) model [10] Later the vibration investigation wasextended to TBM main system which was modeled usinglumped parameter method [9] Recently this investigationwas pushed forward by establishing a rigid-flexible coupledmultibody dynamic model of an opening hard rock TBM[11] In an investigation performed [11] the bottom shield-rock mass interaction was studied in detail Nevertheless thevibration level of the whole TBM varying with operationaland rock conditions is still needed to be systematicallystudied

Specific energy (SE) defined by energy consumed incutting a unit volume of rock has been widely applied tothe performance evaluation of the rock cutting by disc cutterThe variation of SE was predicted for TBM operation in ahard and brittle crystalline rock of moderate strength withcutting tests [12] The SE of rock cutting was evaluated fordifferent geological and operational parameters by numericalsimulation of which the results were comparable with thoseof cutting tests [13 14] As is indicated in [15] energyefficiency is low in dynamic rock cutting because a largeamount of energy is carried away by reflected stress waveand transmitted stress wave In TBM tunneling processthe energy carried by the reflected wave could be a majorexcitation source of TBMvibration but it is not considered inthe calculation of current SE which results in a less accurateprediction of excavation energy efficiency in the case ofserious vibration of TBM Therefore the energy dissipateddue to TBM vibration should be considered when the changeof the energy efficiency with operational and rock conditionsis to be investigated

The expenditure on disc cutter is at least one-fifth ofthe project cost and the time spent on replacing the cutterconstitutes is about one-third of the total project time whichmeans that cutter failure is one of the major topics in TBMtunneling [16] As is the main cause of cutter failure cutterwear statistically caused 78 of the total consumed cuttersin some TBM tunneling projects [17] Therefore cutter wearhas been predicted in a number of studies for improvingTBM performance in the past years [18] SE was used topredict the average wear extent of all disc cutters [16 18] Amodel of disc cutter wear rate was built [19] Later a modifiedmodel for the evaluation of cutter wear rate considering theinfluence of vibration was developed [20] Based on thismodified model it is possible to further evaluate cutterrsquosvulnerability to wear considering the operational and rockconditions

The load transmission performance of multiple pinions-gear ring meshing was evaluated for TBMrsquos cutterhead driv-ing system by load sharing index considering meshing fre-quency bearing stiffness and mounting locations of pinions[21] In [22] the load transmission was investigated by loadsharing coefficient considering bending-torsional coupling ofpinions Generally the large load sharing coefficient meanspoor load transmission performance and serious unevenloading conditions on pinions which easily cause structuredamage such as tooth fracture and broken shaft of pinionsIn the published works there is a lack of investigationof the correlation of load transmission performance withoperational and rock conditions

(1) (2) (3) (4)(5) (6) (7)

(8)

Figure 1 Schematics of an opening hard rock TBM (1)Cutter head(2) Shield (3)Main beam (4)Thrust cylinder (5) Saddle (6) Shoe(7) Torque cylinder (8) Support cylinderThis paper presents a study of TBM performance evalu-

ation considering operational and rock conditions from theaspects of vibration level energy efficiency cutter wear andload transmission performance of cutterhead driving systemFollowing a statement of the problem to be investigated arigid-flexible coupled multibody dynamic model of an open-ing hard rock TBM is established for the vibration analysisof TBM To deal with the performance evaluation problemfour indexes namely mean vibration energy dissipation ratedynamic specific energy (DSE) disc cutter wear rate andload sharing coefficient are then introduced and formulatedrespectively Finally numerical simulations are performedto obtain the results of the TBM performance varying withoperational and rock conditions The obtained numericalresults are further validated through comparing with thosefrom on-site vibration measurement and collected tunnelingdata

2 Modeling of Hard Rock TBMs

21 Dynamic Model of Opening Hard Rock TBMs An open-ing hard rock TBM consists essentially of a cutterheaddriving system and a hydraulic thrust system as shownin Figure 1 In rock cutting process the cutterhead rotatesand moves ahead simultaneously and consequently rock ontunnel face spalls continuously under cutting forces Theopening hard rock TBM is a multibody system Taking themain components the connection between them and theTBM-rock interactions into consideration a rigid-flexiblecoupled dynamic model of TBM is established and shown inFigure 2

In Figure 2 119874119883119884119885 is a global coordinate system where119885 is tunneling direction 119884 is vertical direction and 119883 isdetermined by right-hand rule 119874119894119883119894119884119894119885119894 (119894 = 1 13) arelocal coordinate systems which are established at the centroidof the corresponding substructures and parallel to OXYZ atinitial time The main components in Figure 2 are modeledas rigid-flexible coupled structures M119894 (119894 = 1 13)are the corresponding mass matrix The bending-torsionalcoupling of each pinion is considered with 119898119901119894 and 119868119901119894 (119894 =1 119873) denoting the equivalent mass and inertial moment


X

O

Y

XO

Y

M12M10 M11 M13

M9

M8

M7

M7

M7M2M1

M12

M10

M9

M2

M3

M1

M6

M5

M12

M13

M8

M4

M6

M2

M3

M1

M4

M5

Y1

Y1

X1

O1

Z1 X1

O1

Z1O1

kpi cpi

kmi cmi

kmi cmiIpimpi

bpi

kbsn cbsnkbst cbst

kblcbl

klsxclsx

kshi1cshi1

kshi2cshi2

ktlctl

ktsx1ctsx1

ktsx2ctsx2

ktsy2ctsy2

ktrctr




middot middotmiddot

middotmiddotmiddot


middot



krsxcrsx

kbrcbr

klgtclgt ksupy1

csupy1

ksupy2csupy2

ksjy2csjy2

c supy1

csupz1

ctht2

c sjy

1

csjz1

krgtcrgt

krgncrgn

ktor2ctor2

ktor3ctor3

kjxcjx

kgx1

cgx1

klgnclgn

kbsxi

kb3i

cbsxi

cb3i

kbsxi cbsxi

ksjx1 csjx1

klsx clsx

kb2i cb2i

kb1i cb1i

krsx crsx

krgz crgz

krg

nc r

gn

ksjy1 csjy1


ktsy1c tsy

1

kgy1

kgy2

c gy1

kgy1

c gy1

c gy2

kgx2

cgx2

ZO

Y

Z

O

X

ktsz1 ctsz1

kb1i cb1i ktsy1c

tsy1

kb2i cb2i

cgbzi

cjz

clgzkgbzi

kbszi cbszi

kbsyic b

syi

kgby

ic g

byi

kbs

nc

bsn

kbsz cbsz

ktor2

ktor1

ksu

py1

ksupz1

kjz

klgz

ktht2

ctht2

ktht2cgbxi

cgbzi

kgbxi

kgbzi

ctht1

ktht1

ctht3

ktht3

ksjz1

ksjy1

klgz clgz

klgnc lgn





c tor

2

c tor

1





120595119894 = (xT119894 120572T119894 120578T119894 )T x119894 = (119909119894 119910119894 119911119894)T 120572119894 = (120572119894 120573119894 120574119894)T 120578119894 = (1205781198941 120578119894119873119894)T

(1)


M + C + K120595 = f1 + f2 (2)

with


M11989411 M11989412 M11989413M11989422 M11989423

symmetric M11989433

]]]K = [[[[

d

K119894119895 + 120575119894119895k119887119894symmetric d

]]]]C = [[[[

d

C119894119895 + 120575119894119895c119887119894symmetric d


(u1198870119883119894+120588119887119883119894)A119903119887119894Φ119894]


1 119894 = 1198950 119894 = 119895



]]]A119903119887119894 = I (119894 = 2 13)

Rk = [[[0 minusk (3) k (2)

k (3) 0 minusk (1)minusk (2) k (1) 0]]]

(3)




Rotationdirection


R

minusF

F

p(t)

v

R

FR

FN

N




(4)

with

120593 = cosminus1 (119877 minus 119901119877 ) 120573 = 1205932

119867 (119910) = 1 119910 ge 00 119910 lt 0


(5)





119896119899 = 119864119903119877119903 (1 + V) 119896119905 = 119896119911 = 1198961198993 (6)










119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)



DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)




0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22


(14)



119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)







119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



X

O

Y

XO

Y

M12M10 M11 M13

M9

M8

M7

M7

M7M2M1

M12

M10

M9

M2

M3

M1

M6

M5

M12

M13

M8

M4

M6

M2

M3

M1

M4

M5

Y1

Y1

X1

O1

Z1 X1

O1

Z1O1

kpi cpi

kmi cmi

kmi cmiIpimpi

bpi

kbsn cbsnkbst cbst

kblcbl

klsxclsx

kshi1cshi1

kshi2cshi2

ktlctl

ktsx1ctsx1

ktsx2ctsx2

ktsy2ctsy2

ktrctr




middot middotmiddot

middotmiddotmiddot


middot



krsxcrsx

kbrcbr

klgtclgt ksupy1

csupy1

ksupy2csupy2

ksjy2csjy2

c supy1

csupz1

ctht2

c sjy

1

csjz1

krgtcrgt

krgncrgn

ktor2ctor2

ktor3ctor3

kjxcjx

kgx1

cgx1

klgnclgn

kbsxi

kb3i

cbsxi

cb3i

kbsxi cbsxi

ksjx1 csjx1

klsx clsx

kb2i cb2i

kb1i cb1i

krsx crsx

krgz crgz

krg

nc r

gn

ksjy1 csjy1


ktsy1c tsy

1

kgy1

kgy2

c gy1

kgy1

c gy1

c gy2

kgx2

cgx2

ZO

Y

Z

O

X

ktsz1 ctsz1

kb1i cb1i ktsy1c

tsy1

kb2i cb2i

cgbzi

cjz

clgzkgbzi

kbszi cbszi

kbsyic b

syi

kgby

ic g

byi

kbs

nc

bsn

kbsz cbsz

ktor2

ktor1

ksu

py1

ksupz1

kjz

klgz

ktht2

ctht2

ktht2cgbxi

cgbzi

kgbxi

kgbzi

ctht1

ktht1

ctht3

ktht3

ksjz1

ksjy1

klgz clgz

klgnc lgn





c tor

2

c tor

1





120595119894 = (xT119894 120572T119894 120578T119894 )T x119894 = (119909119894 119910119894 119911119894)T 120572119894 = (120572119894 120573119894 120574119894)T 120578119894 = (1205781198941 120578119894119873119894)T

(1)


M + C + K120595 = f1 + f2 (2)

with


M11989411 M11989412 M11989413M11989422 M11989423

symmetric M11989433

]]]K = [[[[

d

K119894119895 + 120575119894119895k119887119894symmetric d

]]]]C = [[[[

d

C119894119895 + 120575119894119895c119887119894symmetric d


(u1198870119883119894+120588119887119883119894)A119903119887119894Φ119894]


1 119894 = 1198950 119894 = 119895



]]]A119903119887119894 = I (119894 = 2 13)

Rk = [[[0 minusk (3) k (2)

k (3) 0 minusk (1)minusk (2) k (1) 0]]]

(3)




Rotationdirection


R

minusF

F

p(t)

v

R

FR

FN

N




(4)

with

120593 = cosminus1 (119877 minus 119901119877 ) 120573 = 1205932

119867 (119910) = 1 119910 ge 00 119910 lt 0


(5)





119896119899 = 119864119903119877119903 (1 + V) 119896119905 = 119896119911 = 1198961198993 (6)










119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)



DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)




0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22


(14)



119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)







119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





120595119894 = (xT119894 120572T119894 120578T119894 )T x119894 = (119909119894 119910119894 119911119894)T 120572119894 = (120572119894 120573119894 120574119894)T 120578119894 = (1205781198941 120578119894119873119894)T

(1)


M + C + K120595 = f1 + f2 (2)

with


M11989411 M11989412 M11989413M11989422 M11989423

symmetric M11989433

]]]K = [[[[

d

K119894119895 + 120575119894119895k119887119894symmetric d

]]]]C = [[[[

d

C119894119895 + 120575119894119895c119887119894symmetric d


(u1198870119883119894+120588119887119883119894)A119903119887119894Φ119894]


1 119894 = 1198950 119894 = 119895



]]]A119903119887119894 = I (119894 = 2 13)

Rk = [[[0 minusk (3) k (2)

k (3) 0 minusk (1)minusk (2) k (1) 0]]]

(3)




Rotationdirection


R

minusF

F

p(t)

v

R

FR

FN

N




(4)

with

120593 = cosminus1 (119877 minus 119901119877 ) 120573 = 1205932

119867 (119910) = 1 119910 ge 00 119910 lt 0


(5)





119896119899 = 119864119903119877119903 (1 + V) 119896119905 = 119896119911 = 1198961198993 (6)










119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)



DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)




0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22


(14)



119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)







119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Rotationdirection


R

minusF

F

p(t)

v

R

FR

FN

N




(4)

with

120593 = cosminus1 (119877 minus 119901119877 ) 120573 = 1205932

119867 (119910) = 1 119910 ge 00 119910 lt 0


(5)





119896119899 = 119864119903119877119903 (1 + V) 119896119905 = 119896119911 = 1198961198993 (6)










119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)



DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)




0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22


(14)



119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)







119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119906 = 1198821198891199052 minus 1199051 (9)

with

119882119889 = int11990521199051

(TC + kT119891F119891) d119905 (10)



DSE = 11986501198710 +119882119889119881119889 (11)

with

11986501198710 = 119873119888sum119894=1

(11986511989411987301198851198730 + 1198651198941198770119877119894120579) +∬Γ11986511990411991101198851198730dΓ

119881119889 = 119873119888sum119894=1

int11990521199051

119877119894120579119878119901119894119867(119901119894) d119905(12)




0(1 minus 120601120593)

120595

Vd120601 (13)

with

V = radicV21 + V22


(14)



119889119901119894 = 119873(119865119901119894)maxsum119873119894=1 (119865119901119894)max

(15)







119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119863119901 = 10038161003816100381610038161003816119889119901119894 minus 110038161003816100381610038161003816max + 1 119894 = 1 119873 (16)










800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



800

1000

1200

1400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(a)

1200

1500

1800

2100

2400

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(b)

1500

2000

2500

3000

3500

Mea

n vi

brat

ion

ener

gy d

issip

atio

n ra

te u

(Js

)



0708

(c)







11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




11

12

13

14

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)


0708

(a)

17

18

19

20

21



0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(b)


22

24

26

28


0708

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)

(c)







DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



DSESE

05 1000Time (s)

104

106

108

110

Dyn

amic

spec

ific e

nerg

yD

SE (－

Ｇ

3)



Max DSEMean DSE

0

2

4

6

8

10

12

Perc

enta

ge in

crea

se(＄

３minus３

)３

()








05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




05

10

15

20Cu

tter w

ear r

ate d

Qd

t(10minus11

Ｇ3s

)


0708

(a)


10

15

20

25

30

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(b)


2

3

4

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)


0708

(c)








05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




05 1000Time (s)

2

4

6

Cutte

r wea

r rat

e dQ

dt

(10minus11

Ｇ3s

)



0

4

8

12

16

20

24

28

Perc

enta

ge in

crea

se o

f mea

n w

ear r

ate (

)







14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




14

15

16

17Lo

ad sh

arin

g co

effici

entD

p


0708

(a)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(b)


13

14

15

16

Load

shar

ing

coeffi

cien

tDp


0708

(c)



5 Conclusions




(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



(a) (b)


minus4

minus2

0

2

4

Acce

lera

tion

in X

(mＭ2

)

05 1000Time (s)

(a)

00

01

02

03

04

05M

agni

tude

in X

(mＭ

2)

100 200 300 4000Frequency (Hz)

(b)

minus6

minus3

0

3

6

Acce

lera

tion

in X

(mＭ

2)

05 1000Time (s)

(c)

00

01

02

03

04

Mag

nitu

de in

X (m

Ｍ2)

100 200 300 4000Frequency (Hz)

(d)






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






05

10

15

20

Acce

lera

tion

RMS

(mＭ

2)





10

20

30

40

DSE

(－Ｇ

3)

Dyn

amic

spec

ific e

nerg

y




Appendix





(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




(A1)




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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